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Here’s a good oped in the *L.A. Times* from Steven “Freakonomics” Levitt and a co-author:

Opinion: Modern high school math should be about data science — not Algebra 2

By JO BOALER , STEVEN D. LEVITT

OCT. 23, 2019 3 AMThanks to the information revolution, a stunning 90% of the data created by humanity has been generated in just the past two years.

Is this true?

That sounds like it very much depends upon your definition of “data”

So if, say, a copy of every phone call is now being saved in the federal government’s Intelligence Community Comprehensive National Cybersecurity Initiative Data Center (a.k.a., Utah Data Center), which was finished last May at a cost of $1.5 billion, then it’s data, where as before phone calls weren’t data because they weren’t being saved except in the memories of the participants?

This is a rather epistemological debate, but my guess is that the amount of data *created* increases about as fast as the global population, while the amount of data *saved* is growing rapidly.

Yet the math taught in U.S. schools hasn’t materially changed since Sputnik was sent into orbit in the late 1950s. Our high school students are taught algebra, geometry, a second year of algebra, and calculus (for the most advanced students) because Eisenhower-era policymakers believed this curriculum would produce the best rocket scientists to work on projects during the Cold War.

My dad used calculus at his first airplane engineering job after graduating from Pasadena City College, but he didn’t use it in his subsequent 40 year career at Lockheed. He remembered it fine 38 years after last studying it, helping me with my calculus homework in 1975.

On the other hand, some guys at Lockheed used calculus, such as Denys Overholser, one of the Lockheed employees who used Soviet mathematician Petr Ufimtsev highly theoretical work to design the Stealth Fighter, which helped terrify the Soviets into making Gorbachev their leader. But at my dad’s less lofty level, engineers didn’t use calculus.

… We surveyed 900 “Freakonomics” podcast listeners — a pretty nerdy group, we must admit — and discovered that less than 12% used any algebra, trigonometry or calculus in their daily lives. Only 2% use integrals or derivatives, the foundational building blocks of calculus. In contrast, a whopping 66% work with basic analytical software like Microsoft Excel on a daily basis.

When was the last time you divided a polynomial? If you were asked to do so today, would you remember how? For the most part, students are no longer taught to write cursive, how to use a slide rule, or any number of things that were once useful in everyday life. Let’s put working out polynomial division using pencil and paper on the same ash heap as sock darning and shorthand.

Well, maybe. On the other hand, it’s really important to find the small percentage of people, such as Denys Overholser and his math wizard Bill Schroeder, who can do this kind of math well. Our current system of obsessing over continuous math probably does a pretty good job of finding those who can do continuous math well.

Discrete math is, in my view, easier. I needed my dad’s help with calculus homework, but I was good at statistics.

What we propose is as obvious as it is radical: to put data and its analysis at the center of high school mathematics. Every high school student should graduate with an understanding of data, spreadsheets, and the difference between correlation and causality. Moreover, teaching students to make data-based arguments will endow them with many of the same critical-thinking skills they are learning today through algebraic proofs, but also give them more practical skills for navigating our newly data-rich world.

I’ve got some critical-thinking skills, as Dr. Levitt discovered in 1999 (here’s our debate in *Slate* over his theory that legalizing abortion cut crime; interestingly, *Slate* has since stripped our names from their debate and only attributes it to “By Authors”: but anyway, here is Levitt’s opening, my opening, his response, my response). Personally, I haven’t noticed that society really wants to encourage critical-thinking.

But I do it anyway. It’s fun.

Data-based math courses allow students to grapple with real-life problems. They might analyze issues about the environment, space travel or nutrition. Students can examine the threat of wildfires or the ways social media is tracking their data, learning how to apply math to real-world issues.

For this revolution to be carried out across the country, decision makers will need to hear from parents and other interested parties who recognize that our children deserve math instruction that is relevant to their lives.

I quite agree, but I recall reading an article in the L.A. Times around 1981 arguing for the same thing, so I don’t expect rapid change.

Levitt theorized that abortion preemptively eliminates criminals. In contrast, Sailer showed that 18 years after abortion became accessible, crime dropped among 20-year-old’s. In other words, younger siblings cause crime.

An unexpected child is a big income shock to poor, single mothers. Extra kids reduce investment in older siblings. Abortion allows parents to plan smaller families and supervise older children. How can we test this with data?

Replies:@Achmed E. Newman@KLMaybe for those who eschew welfare and haven't used the long arm of the law to put the Dad in servitude, it is For most in the Socialist system, it is a some kind of shock indeed, with cash-bearing electrons flowing in the form of extra benefits all around.@KL"An unexpected child is a big income shock to poor, single mothers."

A big shock, is it? Because they don't know the consequences of spreading their legs? Besides, poor single mothers on welfare get a raise with every additional child.

To me, debating abortion as a means to reduce criminality points to the much larger social and demographic problem the US currently faces.

Replies: @nurdle, @Lot@KLAlgebra 2 including matrices is essential to understanding how to dissect and address data sets. Data analysis without an understanding of the base maths would be like modern medicine without a grasp of chemistry.

Replies: @Jim bob Lassiter@KLBirth control.Replies: @Reg Cæsar@KLCan't speak for others but I agree personally with Levvitt on this 1, though it really is a Stalinist type solution. Stalin was said to have said "no man, no problem...."

Abortion of potential criminals is a crude but effective way of getting rid of criminals.....

Replies: @Redneck farmerAt the risk of going off on a tangent, that exchange between you and Levitt is fascinating. What do you think now, 20 years on? Crime did continue a slow gradual decline, with a spike for “the Ferguson Effect.”

The illegal drug landscape has changed a lot. Opioids are the new crack, but there doesn’t seem to have been a big spike in violent crime associated with the so-called “opioid crisis.”

Replies:@JMcG@CloudbusterIllegal drug sales are much less territorial now. Transactions are arranged by cell phone and the individual sales aren’t usually worth shooting someone over. Locally, Mexicans seem to control the heroin trade quietly and with almost no retail level violence.

I have no idea who is using cocaine any more, no one in my social orbit anyway.

@CloudbusterPeople have pointed out that opioids are depressants, not stimulants. Addicts of the former don’t often rob liquor stores nearly as often as the latter. (Or at least not after ingesting depressants.) Law enforcement and lawmakers realized that Low IQ/High Crime individuals are a lot more stupid on stimulants. Thus the ready public outcry against crack cocaine. The opioid crisis came about like a silent warm blanket, slowly singing a lullaby until it was too late. It became a massive problem for whites, not your typical PITA (Pain In The Ass) demographic.

*Also, here’s Fallout 4. This game allows the player to utilize a drug called “psycho.” Something similar to Meth.

https://youtu.be/fE-imzSYcQw

The proposal sounds much less radical when you replace data science with statistics.

Replies:@Bumpkin@AristippusYou took the words out of my mouth. When I finally took an advanced engineering probability and statistics course in my freshman year of an engineering BS at one of the top-ranked schools a couple decades ago, I was shocked that such an obviously fundamental and useful subject had not been taught in all the AP math classes I'd taken in high school before, same when I finally took Linear Algebra.

As Levitt says, the math that is taught today is completely worthless in our age of cheap computation. However, as you, @anon[231], and others point out, his favored replacement of "data science" is a current fad, so we risk jumping from an outdated bandwagon to one that will soon be. The current predilection is to torture bad data till a "result" can be extracted from it, which is no more useful than the practically unused calculus that Steve and his dad were forced to learn, never to use again. Critical thinking, as Steve espouses, is the real need, but I'm not sure that can be taught, or even inculcated much.

Education is off the rails and not just the SJW studies highlighted here: the internet is going to destroy it just like it did the taxi cartels and travel agents.

What do you mean, didn’t use it? If he did engineering (as I’d thought from you mentions of him) rather than being a program manager or some such thing, then any of the analytical calculations he did were based on Calculus (bending, torsion, stress, strain, heat transfer, all of it). It’s not like he would have sat there and done integration by parts, but the Calculus must be understood in order to learn engineering well. It’s fun-da-mental.

(If you do poorly in it, and naturally then hate it, you make call it “Calcuseless”.)

Replies:@Steve Sailer@Achmed E. NewmanI asked in 1975, "If you wanted to know the area under a curve, how did you figure it out without calculus?"

He replied, "We plotted the curve on graph paper, then counted the squares under the curve. If necessary, we cut out the strips with scissors and measured them."

Replies: @anon, @El Dato, @Achmed E. Newman, @dehusker, @Realist, @Jus' Sayin'..., @Anonymous, @Not Raul, @The Alarmist, @Buzz Mohawk, @ThreeCranesMy take on this is a bit contradictory. Yes, we have innumerate people and elites, who cannot think in numbers and, therefore, cannot really understand the world when they only experience it through data (like population growth in Africa).

On the other hand, math is important. And so are many other things. The more you keep people from working because they need to study, the lower their work experience and earnings. An educational premium may be worth it (or may have been worth it), but if it takes more years to get that premium, then it is a loss, on the whole, compared to a more rapid educational process. In addition to pre-med, pre-law etc, you will end up needing pre-engineering or pre-physics.

One of the things that the former Communist camp did was cram the schools full of stuff, so that kids do not require an intermediate institution of training before picking a University track. College is what we call the fancier high schools around here or non-bachelor degree institutions affiliated with universities for continuing education for professionals (shorter courses and the like, but not bachelor, masters or PhD). Less choice and more content translated into frustrated parents, but kids who got a feel earlier on for what they were good at or what they wanted. It was perfectly possible for someone in my high school class, where you had absolutely no choice in what you studied, to go directly to Law School or Medical School or a Polytechnic, with some extra work in the required subjects. But all of the entry level knowledge was guaranteed to be taught so you would not need (collectively) remedial education. Sure, some people were slower in Math or in grammar/literature and got by on tutoring (the Baccalaureate is mostly the same whether you are going to Law School or the Polytechnic – you still get tested on math, grammar/literature, a foreign language, plus some elective exams which you select to line up with what you have been studying because your University examinations require it, like Economics, a second language, geography, history, code writing for basic problem solving).

I think that the movement against math, rigor and so on which is also taking place in my country is down to two things. Firstly, helicopter parents are catching on that their kids are overworked by school AND all of the extracurriculars that they are enrolling their kids in “because [they] never had the same opportunities as kids”, plus the cram-school lite that is the norm here because there is too much curriculum to go through and not enough hours of school to make sure that all the kids grasp it properly (we don’t do study hall, because most schools are too small to have the extra space – one shift of kids leaves as the other comes in for the day)

Secondly, it’s a move by middle class parents to reduce the competition to their overworked kids from poorer kids without the wherewithal to learn a musical instrument or play a sport intensively, but who are smart enough to be beneficiaries of the more demanding schools. If you drop the level of what is expected from everybody, then their kids can still get straight As and be less stressed while maintaining the advantage that comes from being able to send them to coding camp, extra language lessons, performance sports, theater etc. Organized sports have really become the separator between the lower class and the middle class strivers. Any kid can play football in the street, but it takes money to be in a professional club, let alone try something else. Tennis is really popular, because of the current mania for Simona Halep, Bianca Andreescu and others.

We don’t do holistic admissions procedures, but it is a foregone conclusion that who you know and the group you run with and how you present are just as important for success in life as academic success, if not more so. Therefore, the kids get to do all sorts of stuff if the parents can afford it, whether they want to or not. I have a young cousin who was a junior champ in fencing and she eventually gave it up, to the shock of her parents.

Replies:@YetAnotherAnon@Romanian

If the MPs were arguing that attending school had an incapacitance effect, that if they were in class they couldn't be mugging anyone except their classmates, I'd have more respect for them."we have innumerate people and elites, who cannot think in numbers and, therefore, cannot really understand the world when they only experience it through data (like population growth in Africa)"That's how we get "

crime is falling, yet the prison population has never been so high" Guardian pieces.Here's a slightly OT example. Kids (in London at any rate) who are excluded from school (and you have to try hard for that to happen) tend to end up joining gangs and carrying knives.

Therefore, say MPs, don't exclude them from school!

https://www.theguardian.com/uk-news/2019/oct/25/reform-school-exclusions-to-tackle-knife-mps-urge

Replies: @AnonAn unexpected child is a big income shock to poor, single mothers. Extra kids reduce investment in older siblings. Abortion allows parents to plan smaller families and supervise older children. How can we test this with data?

Replies: @Achmed E. Newman, @MikeatMikedotMike, @Yak-15, @Realist, @NeoconnedMaybe for those who eschew welfare and haven’t used the long arm of the law to put the Dad in servitude, it is For most in the Socialist system, it is a some kind of shock indeed, with cash-bearing electrons flowing in the form of extra benefits all around.

(If you do poorly in it, and naturally then hate it, you make call it "Calcuseless".)

Replies: @Steve SailerI asked in 1975, “If you wanted to know the area under a curve, how did you figure it out without calculus?”

He replied, “We plotted the curve on graph paper, then counted the squares under the curve. If necessary, we cut out the strips with scissors and measured them.”

Replies:@anon@Steve SailerDidn't they use Simpson's rule back in the day? Or the Trapezoidal rule?

@Steve SailerWell, this is called "numerical integration" (as opposed to "symbolic integration") today and is of course of high usefulness as there may not be a good symbolic description of the integral at all.

It's basically what computers did back in ENIAC times all the time.

Also, we read:

Out! Now!Anyone who uses Excel for "analytics" (or anything else, actually) is in a state of sin. Similar to someone putting on a beanie hat and hoping he can fly.

Use R! and RStudio.

It's friendly, manageable, traceable, debuggable, shareable and generates publishable results directly with the knitr package.

Yeah, but this means basically having a course in probability and statistics, statistical inference (basics of) and thinking in causality (Judea Pearl & al.). Seriously it would be agood thing, but t would not be in competition in calculus. It's something else entirely. One could maybe get people back to school on Saturdays and have a go at it, hmmm??Replies: @Steve Sailer, @Bill, @Desiderius, @Jokah Macpherson, @Jokah Macpherson, @Mj@Steve SailerSure, Steve, that'd have been the case for any function that wasn't known in simple closed-form, say results from some testing. Even what he was doing requires the

understandingof calculus though, as in "what does the area under that curve mean?"This was before computers were ubiquitous enough to where the engineer could easily program himself the numerical integration, or use a program straight out of his

Numerical Methodsclass, plugging in the curve point-by-point (at a small enough scale to be accurate). By the mid 1980s or so, there'd be a spreadsheet program to do it for you.If you have a curve of a closed-form polynomial, or close approximation, then cutting out skinny rectangles is a waste of time. BTW, that's not how I'd do it - just makes some 1/8" wide spacing for your data, then take your steel scale (with the cork on the bottom) and measure up to each point. Sum them up, and then multiply by whatever that 1/8" on the paper represents. KEEP IN YOUR UNITS! NUMBER WITHOUT UNITS ARE DEAD TO ME.

Replies: @Jus' Sayin'...@Steve SailerBack when an HP integrator cost > 2K (early 80s), we would cut the peaks out of a paper chromatograph and weigh them on a balance to get relative peak areas.

@Steve SailerIf your father knew calculus...why go to all the trouble?Replies: @anon, @astrolabe@Steve SailerThis reminds me of the experiences of a friend who earned a Ph.D. in physics at a university with a respected physics department. The centerpiece of his thesis was the calculation of an integral. There was no closed form solution so he used numerical analysis to compute the required result. Unfortunately, a year or two after he received his degree another graduate student discovered that there were discontinuities in the domain of his analysis. My friend's calculations were essentially worthless. He did get to keep his Ph.D. his later career was outside of physics. In fact, and apropos this discussion, he became a rather prominent statistician.

@Steve SailerApparently, Galileo was unable to calculate the area under a cycloid - that had to wait until Newton. Galileo's solution was to cut out the curve and weigh it.

@Steve SailerSchools serving populations where the teachers have some leverage over the students tend to be very good at crushing this sort of creativity.

@Steve SailerFunny, when I learned calculus in the '70s, that is how we empirically confirmed our integration.@Steve SailerThere is an old story about Thomas Edison welcoming a new, young scientist to the famous R&D laboratory:

Mr. Edison handed the new researcher an empty light bulb and told him to find the volume inside.

The y0ung man, probably a fresh science graduate from a great university, proceeded to measure every part of the bulb and then perform calculations. The top approximated a sphere, so he found that volume; the bottom part was similar to a cylinder, so he did that; in between was a curve that perhaps calculus could be applied to... etc...

While the lad was busy with his pencil and paper, Edison picked up the glass bulb, filled it with water, then poured the water into a graduated cylinder and measured the amount of water and thus the volume inside the bulb.

He was teaching the young man a lesson, and not just one about measuring volume.

Replies: @Joe Stalin@Steve SailerOr you could use a planimeter. Draftsmen had been using them for decades.

I stumbled upon a very interesting book in a used bookstore once. It was called "Graphical Solutions to Civil Engineering Problems", published sometime back in the early 1900's. In it, loads, center of effort, moments of inertia etc. were computed by projecting vectors and then calculating the areas of the resulting triangles.

It looks as though these techniques are experiencing a renaissance.

https://www.amazon.com/Structures-Geometric-Approach-Graphical-Analysis/dp/3319987453

Teaching people how to use statistical concepts is fine. If they really want to understand it, though, they still need a foundation in geometry, algebra, and calculus.

Do these people who use Excel every day really claim not to use algebra? If so, what the hell are they doing?

Replies:@Bugg@AnonymousYou need a base of knowledge of algebra and geometry to understand "data science". And sadly most schools would teach that as badly they do the current math programs. Don't disagree with Leavitt in the Big Picture sense.But the current attack on math has less to do with teaching more relevant concepts in math than dumbing things down altogether.

@AnonymousOur "betters" like Steve Levitt are always lecturing us that

Of course, what is relevant is always debatable. Much like the debate about the purpose of college today--is it a trade school to lean job skills, or is it higher education, i.e. a higher knowledge acquired through subject matter mastery.Similarly, some describe math education as worthless: Who uses geometry, trigonometry or calculus in their workaday world? Students should be taught relevant skills to the job market!! Like "correlation is not causation"!! (BTW, it seems to be math-phobic and innumerate journalists always implying causes from correlations...)

Alternatively, how would students learn analysis, logical argument, deduction, etc. In other words, how do students learn to work their way through a problem to an answer where they can self-check and self-test the solution as sound because they have a firm grasp of the mathematics involved.

Spreadsheets are just as often the product of garbage in/garbage out manipulation, as they are a profound problem-solving solution.

As part of my pre-med schooling in the mid-70s, I took calculus, physics, chemistry including organic and analytic, biochemistry and genetics. In my career as a primary care doctor I used little to none of those disciplines. However it was understood that aceing the classes separated the sheep from the goats. Nowadays the big push for diversity is erasing any reason to care about that.

Replies:@Realist@Dan SmithSadly true.@Dan SmithYes. I thought you needed calculus to take physics, and physics to take anything else scientific.

Algebra 2 plus simulation is enough to solve most real life problems.

Data science? maybe, but you need real data. Good data always turns out to be hard. But you know that

By the way, no one is good at classical statistics. NHST is nonsense.

Replies:@El Dato@anonSays anon on the Internet.(It's the only thing we have. Deal with it!)

Well, actually there is this now:

Causal inference in statistics: An overview -- Judea Pearl

https://ftp.cs.ucla.edu/pub/stat_ser/r350.pdf

Still gotta read...

An unexpected child is a big income shock to poor, single mothers. Extra kids reduce investment in older siblings. Abortion allows parents to plan smaller families and supervise older children. How can we test this with data?

Replies: @Achmed E. Newman, @MikeatMikedotMike, @Yak-15, @Realist, @Neoconned“An unexpected child is a big income shock to poor, single mothers.”

A big shock, is it? Because they don’t know the consequences of spreading their legs? Besides, poor single mothers on welfare get a raise with every additional child.

To me, debating abortion as a means to reduce criminality points to the much larger social and demographic problem the US currently faces.

Replies:@nurdle@MikeatMikedotMikeYes, exactly, they do know the consequence, which is that other people will pay for the childs basic material needs. We are not in a nomadic society where kids that come too soon after their older siblings get abandoned.

@MikeatMikedotMike“Shock” means a sudden change in economic variable, not a surprise, in this context.

Replies: @MikeatMikedotMike@Achmed E. NewmanI asked in 1975, "If you wanted to know the area under a curve, how did you figure it out without calculus?"

He replied, "We plotted the curve on graph paper, then counted the squares under the curve. If necessary, we cut out the strips with scissors and measured them."

Replies: @anon, @El Dato, @Achmed E. Newman, @dehusker, @Realist, @Jus' Sayin'..., @Anonymous, @Not Raul, @The Alarmist, @Buzz Mohawk, @ThreeCranesDidn’t they use Simpson’s rule back in the day? Or the Trapezoidal rule?

@Achmed E. NewmanI asked in 1975, "If you wanted to know the area under a curve, how did you figure it out without calculus?"

He replied, "We plotted the curve on graph paper, then counted the squares under the curve. If necessary, we cut out the strips with scissors and measured them."

Replies: @anon, @El Dato, @Achmed E. Newman, @dehusker, @Realist, @Jus' Sayin'..., @Anonymous, @Not Raul, @The Alarmist, @Buzz Mohawk, @ThreeCranesWell, this is called “numerical integration” (as opposed to “symbolic integration”) today and is of course of high usefulness as there may not be a good symbolic description of the integral at all.

It’s basically what computers did back in ENIAC times all the time.

Also, we read:

Out! Now!

Anyone who uses Excel for “analytics” (or anything else, actually) is in a state of sin. Similar to someone putting on a beanie hat and hoping he can fly.

Use R! and RStudio.

It’s friendly, manageable, traceable, debuggable, shareable and generates publishable results directly with the knitr package.

Yeah, but this means basically having a course in probability and statistics, statistical inference (basics of) and thinking in causality (Judea Pearl & al.). Seriously it would be agood thing, but t would not be in competition in calculus. It’s something else entirely. One could maybe get people back to school on Saturdays and have a go at it, hmmm??

Replies:@Steve Sailer@El DatoExcel is actually pretty terrible for business purposes, where it is most often used.

Replies: @Wency, @Not Raul, @JVenter@El DatoR is "friendly?" I use R every day; I love it; and it's obviously superior to excel, but the syntax its a bit, um, unapproachable. The R online support community is friendly, though, for sure.

Take the average horsepower of blue cars, written using the basic R you would learn in a day of learning it, looks like:

mean(my.cars[my.cars[,"color"]=="blue","hwp"])

It's like a perl one-liner. It invites you to give up before starting to read it. Is it even right? I cut and pasted it into RStudio to make sure. You never feel confident that the parentheses balance or that you haven't put a comma too far outside or inside a nested set of square brackets.

contrast basic stata syntax for the same op:

mean hwp if color=="blue"

And it gets worse the more complicated a thing you want to do. Doing even slightly difficult manipulations requires you to learn the plyr package which is weirdly more difficult than it ought to be. Again, stata's egen syntax is just much more readable and easy to learn. Same for reshaping data. R can do everything stata can do, but the syntax is annoying---"melt" and "cast:" give me a break---though this has been getting better.

The rest I agree with.

@El DatoMy first assignment with my brand new ISyE degree was untangling a 14,000 x 8,000 Excel file used to manage the production schedule by an Assistant Plant Manager who had recently and unexpectedly passed away.

It was the work of years. We had days. Good times.

Replies: @Bill@El DatoNah, R is too expensive.

Replies: @Steve2@El DatoI teach classes on ACL (now rebranded as Highbond Analytics for god knows what reason, in flagrant violation of the trend towards branding simplicity) and in response to the inevitable student question of ‘Why ACL when we have Excel?’ I tell them that Excel is a good

general purpose tool; if you need to document some basic data, formulas, and narrative discussion together in an attractive presentation, it works great, but since it is general purpose, anything heavier in any of those categories can be done easier with a different tool.@El DatoExcel gets a lot of flak mainly because the putrid masses use it. I rely on SPSS or EViews but Excel still gets the job done. Plus, Excel is more sensible for self-study in statistics and financial modeling.

Prof Levitt’s wrong here. I’d argue that the switch from math (algebra, calc, and so on) to data science is dangerous. Data science is hard (in some ways harder than pure math) and its results can be counterintuitive (not to mention politically incorrect). Keep data science in the hands of those who have already taken a lot of math (say, through linear algebra & ODE) or else you will dumb down the field and everyone will come out of the courses with pseudo-intellectual pretensions about their ability to work with data. Better to have a man untrained with data than with a trivial understanding. Otherwise you’ll have even worse decisions in business and public life.

Anyway, last time I checked my alma-mater went from offering three calculus courses (honors, calc for engineering, general) to this

Honors calculus (geared for math majors)

Calculus for engineers

General calculus

Survey of calculus

Brief survey of calculus (!)

Business calculus (huh?)

The above is exactly what will happen to data analysis courses which will result in students that are confident incompetents. It’s like the old saying that a little learning is a dangerous thing.

@Achmed E. NewmanSure, Steve, that’d have been the case for any function that wasn’t known in simple closed-form, say results from some testing. Even what he was doing requires the

understandingof calculus though, as in “what does the area under that curve mean?”This was before computers were ubiquitous enough to where the engineer could easily program himself the numerical integration, or use a program straight out of his

Numerical Methodsclass, plugging in the curve point-by-point (at a small enough scale to be accurate). By the mid 1980s or so, there’d be a spreadsheet program to do it for you.If you have a curve of a closed-form polynomial, or close approximation, then cutting out skinny rectangles is a waste of time. BTW, that’s not how I’d do it – just makes some 1/8″ wide spacing for your data, then take your steel scale (with the cork on the bottom) and measure up to each point. Sum them up, and then multiply by whatever that 1/8″ on the paper represents. KEEP IN YOUR UNITS! NUMBER WITHOUT UNITS ARE DEAD TO ME.

Replies:@Jus' Sayin'...@Achmed E. NewmanAn easier way is cutting out a tracing of your curve on a substrate with a known and reasonably large areal density, weighing the result on an accurate scale, and dividing the weight by the density.

Replies: @Achmed E. NewmanReplies: @Achmed E. Newman, @MikeatMikedotMike, @Yak-15, @Realist, @NeoconnedAlgebra 2 including matrices is essential to understanding how to dissect and address data sets. Data analysis without an understanding of the base maths would be like modern medicine without a grasp of chemistry.

Agree:BubbaReplies:@Jim bob Lassiter@Yak-15Do you think all those doctors from St. Georges Univ. Medical Skoo in Grenada have a grasp of chemistry?

https://degrees.sgu.edu/us/md?&utm_source=google&utm_medium=cpc&utm_term=%2Bst+%2Bgeorges+%2Bmed+%2Bschool+%2Bgrenada&utm_content=St+George+GeoModified_BMM&utm_campaign=Brand_Longtail_BMM&gclid=EAIaIQobChMIgqLr7_255QIViZWzCh33wAoKEAAYASAAEgLHsPD_BwE&gclsrc=aw.ds

BREAKING NEWS! Cursive might be making a comeback! Yesterday we had a parent-teacher conference with our child’s 2nd grade teacher, who told us that some recent studies suggest that writing in cursive helps children think in words, rather than letters, because in cursive the pencil doesn’t lift off the paper until the word is finished.

Personally, I think cursive helps teach children fine motor skills and self-control, although I hated writing in cursive as a kid.

Agree:Jus' Sayin'...Replies:@nymom@RobJI taught my granddaughter cursive writing one summer and then when she used it in class, she got in trouble with the teacher.

Now she's in school in New Jersey where I believe they allow it, so I am hoping she remembers enough of what she learned to pick it right up again...

@RobJWriting and doing arithmetic by hand develops a level of intuition that it is not possible to reach using computers and calculators.I feel my own intuitive grasp of higher-level math was damaged by the ready availability and use of graphing calculators in the mid-90s.

Cursive is relevant because it is far and away the easiest, most efficient, and swiftest means of hand writing. It is not humanly possible to print or block letter nearly as fast as one can write in cursive.

@RobJMy son could not seem to learn to print. I had heard that cursive is easier, and I was frustrated with his bad handwriting, so I taught him cursive. He learned it pretty easily and used it exclusively. When he was in seventh grade, he was embarrassed that he could not print and taught himself. His printing wasn't great, but it was okay. He still writes pretty much everything in cursive because printing is still difficult for him. Nowadays everyone just types everything, so it isn't a big deal for most people. Personally, I think teaching cursive is a lot more worthwhile than much of the crap they have added to the curriculum and waste children's time going on about.

@Steve SailerWell, this is called "numerical integration" (as opposed to "symbolic integration") today and is of course of high usefulness as there may not be a good symbolic description of the integral at all.

It's basically what computers did back in ENIAC times all the time.

Also, we read:

Out! Now!Anyone who uses Excel for "analytics" (or anything else, actually) is in a state of sin. Similar to someone putting on a beanie hat and hoping he can fly.

Use R! and RStudio.

It's friendly, manageable, traceable, debuggable, shareable and generates publishable results directly with the knitr package.

Yeah, but this means basically having a course in probability and statistics, statistical inference (basics of) and thinking in causality (Judea Pearl & al.). Seriously it would be agood thing, but t would not be in competition in calculus. It's something else entirely. One could maybe get people back to school on Saturdays and have a go at it, hmmm??Replies: @Steve Sailer, @Bill, @Desiderius, @Jokah Macpherson, @Jokah Macpherson, @MjExcel is actually pretty terrible for business purposes, where it is most often used.

Replies:@Wency@Steve SailerDepends on your business purpose. Excel is not good for statistics. It is pretty good for financial modeling, manipulating data (or at least the sort of raw data I see), and creating tables. Or at least if there's something better I haven't heard about it. The only alternative I ever hear discussed is Google Spreadsheets, which is good enough for a list of wedding guests or a household budget but not much else.

@Steve SailerTrue; but how many Harvard MBAs have the patience to learn SAS or R?

The good thing about Excel is that even a child can learn how to do a few simple things, so lots of Dunning-Kruger cases consider themselves to be “experts” at Excel, so they trust it.

Of course the peasants who have to deal with workbooks with millions of cells, millions of links, and millions of equations are horrified that one wrong keystroke in one cell could throw everything off, one might not even know that there’s a problem, and if there is, it might be very difficult to find.

@Steve SailerWhat's better in your opinion?

Thanks in advance.

Replies: @Achmed E. Newman, @MikeatMikedotMike, @Yak-15, @Realist, @NeoconnedBirth control.

Replies:@Reg Cæsar@RealistOnly works for those with the intelligence, discipline, and patience to use it correctly. A bug, not a feature.Dysgenesis in action.

Replies: @Realist@Achmed E. NewmanBack when an HP integrator cost > 2K (early 80s), we would cut the peaks out of a paper chromatograph and weigh them on a balance to get relative peak areas.

@Achmed E. NewmanIf your father knew calculus…why go to all the trouble?

Replies:@anon@RealistMaybe experimental data and you don't have a function?

Replies: @Realist@RealistSufficiently complicated functions are difficult or impossible to integrate to closed form.

Replies: @The Wild Geese Howard, @War for Blair MountainReplies: @Realist, @CarolSadly true.

When I went to grad school there was a lot of theory mixed in with the practical side of doing the math…they actually didn’t do a great job of teaching us the most efficient way of doing the type of math I do on the job. I actually did a bunch of learning outside of the curriculum that mostly forms the basis of how I do things at work. I guess I personally believe most people need to be taught practical things rather than understanding why those things work, if that makes sense.

Replies:@JMcG@bigdicknickA fellow I work with needed to know how many yards of stone to order for a walkway he was building. I worked it out for him with a pencil in a minute or so. I felt like David Copperfield making an airliner disappear when I looked up and saw the stunned faces of my coworkers.

Whatever math we’re teaching isn’t getting through very well.

Steve Leavitt was going to make a Freakonimics book on golf and I was part of the experimental group. I got 3 free rounds of golf (Kemper Lake and Dubsdred) plus two months of short game lessons.

The experiment failed I guess since the book was never published. I did find out he only hire female grad assistants.

Replies:@Kibernetika@HodagWhat year was that? There was an MBA student around here who was looking at the potential correlation between golf scores and corporate success. She was stealing data from behind a paywall, essentially. Had to raise an eyebrow like Mr. Spock on that one, heh.

The illegal drug landscape has changed a lot. Opioids are the new crack, but there doesn't seem to have been a big spike in violent crime associated with the so-called "opioid crisis."

Replies: @JMcG, @KronosIllegal drug sales are much less territorial now. Transactions are arranged by cell phone and the individual sales aren’t usually worth shooting someone over. Locally, Mexicans seem to control the heroin trade quietly and with almost no retail level violence.

I have no idea who is using cocaine any more, no one in my social orbit anyway.

A very American approach to the problem; thinking that a thing that’s useful can be taught (and deployed) without the hassle of learning the conceptual framework that is required to prevent GIGO.

This is why Machine Learning (a sexy name for badly-conducted OLS) is so popular with Yanks, Chinks and dot-heads; they have never even heard of the Gauss-Markov conditions, so they have no fucking idea if their grid-search satisfies them or not (usually: not).

Freakonomics is the epitome of shitty data-trawling. They give quant a bad name, which I take personally because I spent a decade learning how to do it properly.

Replies:@Kibernetika@KratoklastesPerhaps :) But now all US universities are scrambling to create new certificate- or degree-track programs related to "Data Science." It's more about appearances and semantics than science.

Most data is junk data. What doesn't often get mentioned is that

much of our research data is simply wrong!Replies: @KratoklastesDiscrete math is, in my view, easier.As a math and physics guy, I found it to be the opposite….

I needed my dad’s help with calculus homework, but I was good at statistics.…but now I wish I’d learned more statistics and less curved-space-time fun ‘n’ games, which might be fun to (try to) think about, but doesn’t make you any money.

And isn’t “data science” really statistics?

I haven’t used a spreadsheet since 1987. I used to use calculus all the time.

Looking at the school syllabus in my day (antediluvian) it would probably have been a good idea to replace some of the excessive geometry by some probability/statistics. We did much more plane geometry than was required to get us to grasp the logic and then proceeded to conic sections and spherical trig. Those latter two would better have been delayed to university or even

sine die.Spreadsheets, I must say, are quite wonderful for people who are lousy at arithmetic and maths but who must nevertheless use numbers. It makes people employable who would otherwise be incapable of some demanding jobs.

Replies: @JMcGA fellow I work with needed to know how many yards of stone to order for a walkway he was building. I worked it out for him with a pencil in a minute or so. I felt like David Copperfield making an airliner disappear when I looked up and saw the stunned faces of my coworkers.

Whatever math we’re teaching isn’t getting through very well.

LOL:jim jones“. . . the Stealth Fighter, which helped terrify the Soviets into making Gorbachev their leader.”

How so?

I read a SciFi short story in the 60’s about a time when no one could do arithmetic let alone higher math. Everybody had a personal calculator so no need. Then we were invaded from outer space. Our computer driven weapons were overwhelmed because the alien computer countermeasures anticipated and neutralized their effectiveness.

Someone had an idea to train our weapons’ operators how to do calculations with pencil and paper. This created a situation where the enemy computers could not anticipate results. We won the war. Why it worked may have been explained. I do not remember. Likely the occasional human error created a factor the alien machines could not anticipate.

We might want to keep the ability in case the Klingons show up. Domestic or foreign.

Replies:@Redneck farmer@John HenryIsaac Asimov, "The Accountant". A war between Earth and Mars, both sides using missiles. BMD has caused a stalemate. An accountant has rediscovered doing math by hand, so his boss invites the military to take a look.

"I predict one day Earth will deploy the manned bomber!"

Replies: @John Henry@John Henry...or EMP fries everything electronic. Advanced math makes one better at basic math and a more numerate country/planet might give some sanity to multi trillion $ deficits with fiat currency. Casual observation of what occurs in US high schools leads me to conclude that the students aren’t doing anything more important with their time.

@El DatoExcel is actually pretty terrible for business purposes, where it is most often used.

Replies: @Wency, @Not Raul, @JVenterDepends on your business purpose. Excel is not good for statistics. It is pretty good for financial modeling, manipulating data (or at least the sort of raw data I see), and creating tables. Or at least if there’s something better I haven’t heard about it. The only alternative I ever hear discussed is Google Spreadsheets, which is good enough for a list of wedding guests or a household budget but not much else.

I think Aristotelian logic should be offered in high school, at least for the more able students. That might make political debate more rational.

@Steve SailerWell, this is called "numerical integration" (as opposed to "symbolic integration") today and is of course of high usefulness as there may not be a good symbolic description of the integral at all.

It's basically what computers did back in ENIAC times all the time.

Also, we read:

Out! Now!Anyone who uses Excel for "analytics" (or anything else, actually) is in a state of sin. Similar to someone putting on a beanie hat and hoping he can fly.

Use R! and RStudio.

It's friendly, manageable, traceable, debuggable, shareable and generates publishable results directly with the knitr package.

Yeah, but this means basically having a course in probability and statistics, statistical inference (basics of) and thinking in causality (Judea Pearl & al.). Seriously it would be agood thing, but t would not be in competition in calculus. It's something else entirely. One could maybe get people back to school on Saturdays and have a go at it, hmmm??Replies: @Steve Sailer, @Bill, @Desiderius, @Jokah Macpherson, @Jokah Macpherson, @MjR is “friendly?” I use R every day; I love it; and it’s obviously superior to excel, but the syntax its a bit, um, unapproachable. The R online support community is friendly, though, for sure.

Take the average horsepower of blue cars, written using the basic R you would learn in a day of learning it, looks like:

mean(my.cars[my.cars[,”color”]==”blue”,”hwp”])

It’s like a perl one-liner. It invites you to give up before starting to read it. Is it even right? I cut and pasted it into RStudio to make sure. You never feel confident that the parentheses balance or that you haven’t put a comma too far outside or inside a nested set of square brackets.

contrast basic stata syntax for the same op:

mean hwp if color==”blue”

And it gets worse the more complicated a thing you want to do. Doing even slightly difficult manipulations requires you to learn the plyr package which is weirdly more difficult than it ought to be. Again, stata’s egen syntax is just much more readable and easy to learn. Same for reshaping data. R can do everything stata can do, but the syntax is annoying—“melt” and “cast:” give me a break—though this has been getting better.

The rest I agree with.

> the amount of data created increases about as fast as the global population,

> while the amount of data saved is growing rapidly.

I think this is a wrong statement for two reasons:

1. Data is, by definition of the word, saved. So for example the sound waves of a conversation are information that only becomes data if it is recorded and saved.

2. The rise of computers creates information that is not directly related to population. The various machines that support our way of life produce massive amounts of information that was not produced 100 years ago. And a lot of this information is at least temporarily saved, so it’s new data.

Data Scientist here. I use multivariate calculus and linear algebra extensively. Pretty much every aspect of this field, aside from basic data analysis, assume an in-depth understanding of each. Granted, the focus is more on translating mathematical concepts into working code, than simplifying an equation by-hand.

Secondary and post-secondary education are obviously out-of-date, but I’m pessimistic on proposals to bring them into the 21th century. If you change the vehicle of education to computers (with a focus on coding), then the superstars in the class would be white males. Women would struggle. NAM’s would have no chance. It would basically recreate the gender dynamic of Silicon Valley in the 10th grade.

Hahaha I’m going to start calling you “Authors.”

In real life, I assure you, there is no such thing as algebra.—Fran LebowitzI believe it was in Morris Kline’s

Why Johnny Can’t Addwhere Kline said it makes no sense for all schoolchildren to suffer through years of primary and secondary math including algebra and trigonometry when only a small percentage of these students will go on to a college major requiring it. (NB: I’m guessing the percentage going into STEM has changed since he wrote the book in 1973 but still the vast majority of secondary students will never use it again after high school).When you then ask educators why all schoolchildren need to study years of math they will will respond with things like the need to balance a checkbook, etc. But does it really take years of math classes to learn the basic math of everyday life? They will also respond with the outdated idea from Plato and the ancient Greeks that it develops deductive thinking skills. But real life is about 99.9% inductive reasoning.

Replies:@Anon@AnonymousIt's possible to teach logical thinking without Plato or Aristotle, and still make it fun enough to motivate kids.

@AnonymousYeah, what the fuck did the Greeks know?

Do you want to learn how to use math as a tool or do you want to understand math? If all you care about is the former, then you probably don’t need to understand the proofs. But, like Sailer said, you do want to find the small percentage of kids that really can understand math deeply. And to do this you need to cast a wide net.

Also, doesn’t data science (aka statistics?) require calculus? I mean how do you know what’s going on in a normal distribution (or any continuous distribution or, even, any discrete distribution with infinite outcomes) without a background in calculus?

Knowing WHY the normal distribution is ubiquitous is also important even if it’s used as a tool. It would be nice to know enough math to understand the

*statement*of the Central Limit Theorem, if not the proof. People wouldn’t be using it where it doesn’t apply so much.Now that I’m typing this I realize that we should teach math pretty much as is. Do we really want a STEM workforce having such a shallow understanding of the mathematical tools that they misuse them?

Agree:BillDoes Levitt ever say anything true? You can’t understand statistics without calculus, both differential and integral. You can’t understand statistics without some notion of formal proofs (which one usually gets first in geometry and then linear algebra, the way math curricula generally work) and limits (which one typically gets in a systematic way in calculus but also in algebra 2 to some extent).

Without these things, the only way to teach statistics is by using Monte Carlo simulation all the time. How do we know sample mean is unbiased for population mean? Here’s a huge Monte Carlo study I did which shows it is unbiased for a bunch of different distributions and parameter values . . .

David Card did an interview, I don’t know, 15 years ago now in which he whined about the fact that young economists don’t know price theory any more (which is true) and thus that they are constantly making bone-headed reasoning mistakes (also true). Of course, it’s his fault they don’t know price theory (or really any economics) any more.

These guys are vandals.

Counterpoint: Modern high schools should offer huge briefcases of cash and virgin brides to boys who bring back the severed heads of the MS Excel development team

Microsoft Excel and its consequences have been a disaster for the human race

Replies:@Kronos@Not My EconomyLet me guess, your a fan of R programming?

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&ved=2ahUKEwjkqtumq7jlAhX4HzQIHT3RB9UQjRx6BAgBEAQ&url=https%3A%2F%2Fenholm.net%2F2014%2F03%2F24%2Fconvert-sas-datetime-to-r-datetime%2F&psig=AOvVaw3EwDkJW8X-UmMC-cDgXgG6&ust=1572124753850862

Algebra is pretty fundamental, but I thought smartish kids knocked out algebra in middle school. I would guess the top 40-50% of kids in my UMC flyover public middle school took Alg 2 in 8th grade.

I would think if you’re not smart enough to learn algebra by 8th or 9th grade, then as an adult you likely won’t be using or retaining any math besides arithmetic anyway so it’s a moot point what they teach you. That still leaves smart people 3-4 years of HS to learn other things.

Stats is probably more important than geometry, trig, and calculus for non-STEM people. I retained basically nothing from trig or geometry except the formula for area of a circle, which I use to compare the value of different deals when ordering pizza (yeah, I’m that guy). I’ve never heard a cosine used out in the real world.

Terms like “second derivative” do come up sometimes when growth is discussed, but I imagine a smartish person could grok the idea of “rate of change of rate of change” in 15 seconds without needing to learn calc.

The vast majority of people, even intelligent people, don’t really perform statistical analysis but they at least need to know how to interpret and question stats that someone else put together.

Replies:@Anon@WencyTo compare prices, you don't need to know the area of a circle, just that it's proportional to the square of the diameter, radius, or circumference.

Replies: @Wency@WencyThough it's like the argument there's no need to learn facts when you can just look stuff up on Wikipedia. Yes, but your understanding will be shallow and slow. That seems like it's a far way off. My experience is even STEM practitioners aren't all that hot with statistics, let alone experimental design and all that. (I'm not either.) Any insightfulquestioningof stats without having even done the subject yourself seems even further off.Replies: @WencyIt would be nice if third-graders still learned to read and write in cursive. Of course, some still do, so they have an advantage. Third-graders are ideal foreign-language learners. Some get to do that, too.

As it is, people graduate from college without understanding compound interest. They think having six figures of debt is perfectly normal for 20-somethings.

Sometimes it seems as if the education system is not what we are supposed to think it is.

Replies:@Reg Cæsar@GrumpyOh, theywill...https://m.youtube.com/watch?v=Ioyvorq_3Sg

The single mathematical ability that is woefully lacking among the people I meet is to understand generalizations. Many people seem to think that one “counterexample” disproves a generalization. The whole notion that an attribute might be distributed throughout one population in a different way than throughout another is very hard to get into people’s heads.

Replies:@Anon@Tono BungayWell, then they should stop being taught that All x is y is refuted by There is at least one x which is not y. Stupid logic.

No one says you can’t have two tracks. As kids we all knew the kids who were good in math and the kids who weren’t. So you could put the kids who were good in math on the Algebra 2 track, and the kids who aren’t on the Practical Math track.

Agree:Desiderius, PiltdownManReplies:@Desiderius@ScarletNumberMoms of the non-algebra kids decided that we really shouldn’t all know which kids are which.

@ScarletNumberAnd the practical math track is important. Just because you aren't cut out for (and probably don't want to learn anyway) partial differential equations doesn't mean you are incapable of not being innumerate.

Mass innumeracy in the United States is a major problem: so often, I get the sense that people don't truly grasp what "a million people" means...

Replies: @Spangel, @Redneck farmer, @Achmed E. Newman, @obwandiyag@ScarletNumberBut that would be racist.Replies: @ScarletNumber@Steve SailerIt's basically what computers did back in ENIAC times all the time.

Also, we read:

Out! Now!Use R! and RStudio.

Replies: @Steve Sailer, @Bill, @Desiderius, @Jokah Macpherson, @Jokah Macpherson, @MjMy first assignment with my brand new ISyE degree was untangling a 14,000 x 8,000 Excel file used to manage the production schedule by an Assistant Plant Manager who had recently and unexpectedly passed away.

It was the work of years. We had days. Good times.

Replies:@Bill@DesideriusHis detailed documentation no doubt saved you. :-)

Replies: @DesideriusReplies: @Desiderius, @nebulafox, @PericlesMoms of the non-algebra kids decided that we really shouldn’t all know which kids are which.

Agree:CloudbusterThe thick-skulled guys who design the shape of planes and the type of materials to be used on planes are no more sophisticated than cave man brutes scratching a picture of a horse onto the wall of a cave using charcoal.

ELECTRONICS SIR!

Electronics is where the intelligence of man is most profitably utilized.

Disagree:Achmed E. NewmanReplies:@Anonymous@Charles PewittIn 1952, eighty percent of working electronics was cookbookery, with the development of integrated circuits it’s higher now. The amount of truly original design from first principles is surprisingly low.

The main problem with Dr. Levitt’s argument is that he doesn’t seem to understand what data science is, at least not in an academic sense. Any decent data science or analytics program is going to require the following math courses: Calc I, Calc II, Linear Algebra, Mathematical Stats & Probability and, perhaps, Calc III as math pre-requisites. If you specialize in a particular area, you may need to delve into Econometrics, Biostatistics, etc. Once you understand this, I struggle to understand what the point of the article is. Is it that data science should focus on just using Excel and statistical software packages without understanding the underlying theory and math (there are those who subscribe to this theory, but I posit that other things being equal, the better you understand the math and algorithms, the more competent a data scientist you will be)? Or, does he think that you can suss out the math and stats you need for data science without teaching all of the requisite math? If he can do the latter, he ought to put together a curriculum and sell it. I hate to be cynical, but most of this just reads as uninformed, non-actionable blather.

Replies:@Spangel@NoWeltschmerzI can’t imagine you’ve looked into the requirements for this field recently, because this isn’t at all true.

Data science people are in such high demand these days that there are dozens upon dozens of programs that have no such pre reqs and can still confer good jobs to those who complete their courses.

Probably only phd track programs require such pre reqs while the vast majority of students in those programs simply want well paying stable employment.

Replies: @Anon, @The Practical Conservative, @Bill, @NoWeltschmerz@NoWeltschmerzYeah, an academic economist like Levitt should know what data science means (even if it is a fairly new term). And maybe he does know, but writing for a general audience he tried to use what he thought was general-audience language.

With his colleagues, he'd call the skills he wishes were taught instead of Algebra 2, "basic data analysis".

I passed my HS AP Calculus exam and placed out of 2 semesters of freshman math as an engineering major in college, where I graduated in 1994.

I don’t even remember where to begin to solve a differential equation now. I’m an engineer but I’ve never used it at all.

I should have taken more chemistry.

Replies:@Alan Mercer@ClemsnmanI'm well tired of engineers bragging of their incompetence.

Hard Rock collapse

FIU bridge collapse

On the other hand, math is important. And so are many other things. The more you keep people from working because they need to study, the lower their work experience and earnings. An educational premium may be worth it (or may have been worth it), but if it takes more years to get that premium, then it is a loss, on the whole, compared to a more rapid educational process. In addition to pre-med, pre-law etc, you will end up needing pre-engineering or pre-physics.

One of the things that the former Communist camp did was cram the schools full of stuff, so that kids do not require an intermediate institution of training before picking a University track. College is what we call the fancier high schools around here or non-bachelor degree institutions affiliated with universities for continuing education for professionals (shorter courses and the like, but not bachelor, masters or PhD). Less choice and more content translated into frustrated parents, but kids who got a feel earlier on for what they were good at or what they wanted. It was perfectly possible for someone in my high school class, where you had absolutely no choice in what you studied, to go directly to Law School or Medical School or a Polytechnic, with some extra work in the required subjects. But all of the entry level knowledge was guaranteed to be taught so you would not need (collectively) remedial education. Sure, some people were slower in Math or in grammar/literature and got by on tutoring (the Baccalaureate is mostly the same whether you are going to Law School or the Polytechnic - you still get tested on math, grammar/literature, a foreign language, plus some elective exams which you select to line up with what you have been studying because your University examinations require it, like Economics, a second language, geography, history, code writing for basic problem solving).

I think that the movement against math, rigor and so on which is also taking place in my country is down to two things. Firstly, helicopter parents are catching on that their kids are overworked by school AND all of the extracurriculars that they are enrolling their kids in "because [they] never had the same opportunities as kids", plus the cram-school lite that is the norm here because there is too much curriculum to go through and not enough hours of school to make sure that all the kids grasp it properly (we don't do study hall, because most schools are too small to have the extra space - one shift of kids leaves as the other comes in for the day)

Secondly, it's a move by middle class parents to reduce the competition to their overworked kids from poorer kids without the wherewithal to learn a musical instrument or play a sport intensively, but who are smart enough to be beneficiaries of the more demanding schools. If you drop the level of what is expected from everybody, then their kids can still get straight As and be less stressed while maintaining the advantage that comes from being able to send them to coding camp, extra language lessons, performance sports, theater etc. Organized sports have really become the separator between the lower class and the middle class strivers. Any kid can play football in the street, but it takes money to be in a professional club, let alone try something else. Tennis is really popular, because of the current mania for Simona Halep, Bianca Andreescu and others.

We don't do holistic admissions procedures, but it is a foregone conclusion that who you know and the group you run with and how you present are just as important for success in life as academic success, if not more so. Therefore, the kids get to do all sorts of stuff if the parents can afford it, whether they want to or not. I have a young cousin who was a junior champ in fencing and she eventually gave it up, to the shock of her parents.

Replies: @YetAnotherAnon“we have innumerate people and elites, who cannot think in numbers and, therefore, cannot really understand the world when they only experience it through data (like population growth in Africa)”That’s how we get “

crime is falling, yet the prison population has never been so high” Guardian pieces.Here’s a slightly OT example. Kids (in London at any rate) who are excluded from school (and you have to try hard for that to happen) tend to end up joining gangs and carrying knives.

Therefore, say MPs, don’t exclude them from school!

https://www.theguardian.com/uk-news/2019/oct/25/reform-school-exclusions-to-tackle-knife-mps-urge

If the MPs were arguing that attending school had an incapacitance effect, that if they were in class they couldn’t be mugging anyone except their classmates, I’d have more respect for them.

Agree:HailReplies:@Anon@YetAnotherAnonThere used to be a simple way to deal with students not in school. They didn't get to eat. No dole. They had to get a job to put a meal in their stomach, and that mean showing up and doing the work or getting fired. It worked reasonably well. Hunger is a good motivator and dealer of discipline. If they were really sociopathic and decided to steal instead, they just got hung to death by the courts.

Almost everything that’s taught in school isn’t used in real life jobs. Teaching calculus or algebra is just a good way to separate people who should be engineers and doctors from those who shouldn’t.

I suspect data science is the same sort of thing. How often do you think Nate Silver actually does some difficult data science? Most of the time he’ll be doing the equivalent of counting squares under a curve (except he’s using a spreadsheet).

It’s a mug’s game to try and work out what subjects pupils will find useful over the next 40 years. They should figure out which subjects are the best at discriminating between the numerate and not so gifted. In that regard, I’d rate Calculus as being better than Statistics. It just seems to lend itself to being able to ask a greater variety of test questions for the amount of learning required.

@KL"An unexpected child is a big income shock to poor, single mothers."

A big shock, is it? Because they don't know the consequences of spreading their legs? Besides, poor single mothers on welfare get a raise with every additional child.

To me, debating abortion as a means to reduce criminality points to the much larger social and demographic problem the US currently faces.

Replies: @nurdle, @LotYes, exactly, they do know the consequence, which is that other people will pay for the childs basic material needs. We are not in a nomadic society where kids that come too soon after their older siblings get abandoned.

Replies: @Achmed E. Newman, @MikeatMikedotMike, @Yak-15, @Realist, @NeoconnedCan’t speak for others but I agree personally with Levvitt on this 1, though it really is a Stalinist type solution. Stalin was said to have said “no man, no problem….”

Abortion of potential criminals is a crude but effective way of getting rid of criminals…..

Replies:@Redneck farmer@NeoconnedBut then we get into HBD, and you know what happens THEN.....

This was the reason I got so excited about those Avalon Hill games in my youth. Now I had a chance to use math in a meaningful way. I had to calculate rations and determine how I was to attack.

Do these people who use Excel every day really claim not to use algebra? If so, what the hell are they doing?

Replies: @Bugg, @ForbesYou need a base of knowledge of algebra and geometry to understand “data science”. And sadly most schools would teach that as badly they do the current math programs. Don’t disagree with Leavitt in the Big Picture sense.But the current attack on math has less to do with teaching more relevant concepts in math than dumbing things down altogether.

Agree:ForbesPeople really do not understand statistical math. I think it freaks people out. If his idea actually happened I think the only outcome would be a vast number of idiots running around yelling “correlation is not causation” and thinking they were saying something profound.

Replies: @Realist, @CarolYes. I thought you needed calculus to take physics, and physics to take anything else scientific.

The math curriculum reflects what’s easy to teach and easy to grade.

NB Steve: this is true of finance too. Discounted present value is still the cornerstone of finance education, even though the real interest rate has been near zero for a generation.

What was the math people used in everyday life back then, compared to now?

A guess: could this mean that most of the podcast listeners use mathematics just enough to be more easily replaceable working goons?

Another guess: the authors resent having had to learn those, and have not written in cursive or shorthand (or anything using pen/pencil and paper) lately. They also throw away their busted socks, and buy new ones instead of darning them. An extra

ad hominem: I bet they both have terrible handwriting and have not fixed anything in a while. (Wasn’t it Levitt who joked about having trouble opening a pickle jar?)Calculus and algebra interact with statistics, of course. Yet another guess: someone who knows algebra and/or calculus will do much better at statistics than someone who knows neither.

By coincidence, this week I was searching around for examples of parents who couldn’t help their children with their math homework. Most of the examples didn’t mention anything other than arithmetics, which I take to mean people, in general, have difficulty with it. They also all put the blame on being taught badly in school, and assured that the thoughts about one just not being a ”math person” must be wrong. Okay.

Replies:@obwandiyag@adreadlineThe Freakonomics guys are neoliberal shills who already know the conclusion and then scrabble around for "evidence" to back it up. Funny how the conclusion always turns out to be "free market is best." Every time.

On the other hand, they could serve very well as examples of "Lying with Statistics 101."

Maybe the math taught has not materially changed since the Eisenhower era, but the demographics of the students have. The issue is not what we are teaching. It is to whom are we teaching. We are replacing (I mean have replaced) our student population from the historical American core to something completely unrelated.

I imagine if we still had the same demographics that we had during Ike’s tenure, this op-ed would not have been necessary.

Agree:AldenReplies:@danand@istevefanI like Ike, he knew how to put math to good use:

https://youtu.be/wnrqUHF5bH8

Replies: @Reg Cæsar, @obwandiyagAn engineering definition of data; “the quantities, characters, or symbols on which operations are performed by a computer, being stored and transmitted in the form of electrical signals and recorded on magnetic, optical, or mechanical recording media.”

Cat videos, selfies and tweets would therefore be data so I suppose the 90% could be valid under that definition.

“. . . the Stealth Fighter, which helped terrify the Soviets into making Gorbachev their leader.”

Gorbachev got the job after his immediate predecessors kept dying. He said he never would have gotten the job if what he planned was known. Regarding weapons, there is no need to fear the Stealth Fighter when you have nuclear-armed submarines as a deterrent to an attack.

Replies:@Kolya Krassotkin@PaulThe Soviet leadership prior to Gorbachev - Brezhnev, Andropov, Chernenko - were a doddering, senile, out-of-touch gerentocracy, much like the current crop of American political leaders. Gorbachev had only to be at the right place at the right time.

That “by Authors” thing is ominous. Are there any other publications that do that? OR do they just erase the story completely from their website?

Steven Levitt is a goddam fool……Even though Data Science is over sold…..His recommendation is to do Data Science in a monumental state of mathematical ignorance…..What could possibly go wrong?…A lot….Statistics….which is what Data Science is……without deep mathematical understanding is a blueprint for the misuse of Statistics…..Statistics is grounded in Mathematical Analysis…You just can’t have a deep understanding of Statistics without having a solid foundation in Mathematical Analysis…..You need to know about limits…converge…….Borel Sets…Sigma Algebras……..Measures….Measurable Functions…..You don’t know this stuff…you have a superficial understanding of Probability Distributions…..Correlations……Big Data as mindless number crunchers….

Replies:@War for Blair Mountain@War for Blair MountainTo follow up....

So basically Big Data with limited deep math understanding=Vast Constellations of spurious correlations....a direct consequence of Ramsey’s Theorem......Essentially Bible Code Shit.......

This is simulacrum mathematics. It is taking the result of a prior combination and using it as an element in new combinations. It is not knowledge, it is the catechesis of cargo cults.

It’s like when International Delight markets a line of Almond Joy flavored coffee creamer. Almond Joy is not a naturally occurring flavor, but a combination of almonds, coconuts, heavily processed and alkalized cacao, and sugar. When this flavored is introduced as a thing-in-itself that is free to enter into new combinations, it amounts to a sort of counterfeit nature. It is now not even difficult to imagine the ultimate absurdity of a “Cafe Almond Joy” flavored candy bar.

The modern world is now perched atop a teetering tower of such recombinations a thousand stories high. Hardly anybody has the will or desire to stare back down through the layers to find out what reality is like at the base, and nobody can predict how the whole thing is gong to fly apart when it collapses.

Replies: @BumpkinYou took the words out of my mouth. When I finally took an advanced engineering probability and statistics course in my freshman year of an engineering BS at one of the top-ranked schools a couple decades ago, I was shocked that such an obviously fundamental and useful subject had not been taught in all the AP math classes I’d taken in high school before, same when I finally took Linear Algebra.

As Levitt says, the math that is taught today is completely worthless in our age of cheap computation. However, as you, [231], and others point out, his favored replacement of “data science” is a current fad, so we risk jumping from an outdated bandwagon to one that will soon be. The current predilection is to torture bad data till a “result” can be extracted from it, which is no more useful than the practically unused calculus that Steve and his dad were forced to learn, never to use again. Critical thinking, as Steve espouses, is the real need, but I’m not sure that can be taught, or even inculcated much.

Education is off the rails and not just the SJW studies highlighted here: the internet is going to destroy it just like it did the taxi cartels and travel agents.

Codenamed Bumblehive. Perfect for the Beehive State. Can they call our ancestors in the Mormon mountain in nearby SLC?

I still darn socks by hand. A handy skill to have. Relaxing, too. Didn’t they use to teach it to soldiers?

Better yet, the center of

grade-school mathematics. They’re still too young for most scientific concepts, but just the right age for soaking up and memorizing formulas. At least that’s what the classical educators tell us. And they have thousands of years of experience to draw on.Now,

there’sa stat to work with…Back before computers, TV stations world wide were broadcasting an immense amount of information — as field intensities, not as bits. It’s easy to generate information that isn’t worth keeping.

Counterinsurgency

Replies: @War for Blair MountainTo follow up….

So basically Big Data with limited deep math understanding=Vast Constellations of spurious correlations….a direct consequence of Ramsey’s Theorem……Essentially Bible Code Shit…….

Math education – what a great topic! No end of opinion there. Here is my opinion.

I believe that applied math, including computer programming, is the cornerstone of most useful activity. Only a small proportion of people will use it with vigor. Those persons need a full math education prior to college. This will include learning in algebra, matrix manipulation, stats, and data representation and analysis. There is no excuse for omission. Tying it together is the hard part.

Data analysis can form a method to drive the math learning. PCness will block any unvarnished look at data, when data fails to support the Narrative. Honest data analysis is subversive.

Normies really should know an appropriate level of math, with an emphasis on quick approximations to check what they are told to believe. Actually, this is a skill that all citizens should have.

R can be a wonderful tool to analyze data for those who are willing to learn it. If this isn’t apparent to you, there is online documentation available, as well as books. R is suitable for other activities, such as studying functions via graphs. R is multi platform and free, which matters a lot. (I prefer Matlab, but it is outside my budget.) An integrated math/programming education using R would have broad utility to society.

Good luck getting the little monsters to do their homework. It’s worthless if they don’t.

The calculus curriculum plus a physics course shows the student that it is possible to understand much of the student’s immediate surroundings: the part described by Classical Physics. That is an important lesson. The computer path shows the student that without a computer and without data given to the student, no understanding is possible. For that matter, it shows the student that _with_ a computer and data [1] the computer does the understanding, not the student.

But, yes, this is just another attempt to teach nothing while appearing to teach much. The ultimate goal is uniform test scores (around zero, maybe, but uniform) for all students. Politicians control the schools, coalitions determine which politicians are elected, and important coalition members demand that their kids not be discernible from White kids in grades, college entrance examinations, discipline records, or any other way. Boaler and Levitt get a career boost for finding one more way to satisfy the important coalition members.

Counterinsurgency

1] Word origin: “data” means “that which is given”.

Replies:@dearieme@Counterinsurgency“data” means “that which is given”Surely it's a plural? So '“those which are given” - the singular is "datum".

Replies: @CounterinsurgencyI use very simple algebra maybe once a month, but not for my job.

As for statistics, a little statistics is dangerous. Have you read any social science research papers lately? I think you need a deep dive or nothing. Statistics for social science, i.e. for dummies, just gives idiots more jargon to throw around.

As for data science, the more critical thing is making sure accurate data exists. So much politically incorrect data is being obfuscated or uncollected these days. How is school discipline going? We don’t really know since you cannot record the truth.

Soon the Seattle public school system will have to create a new math curriculum about the racist origins/applications of data science. Wait until they discover 13/50!

Yeah, that sounds about right to me. He has a point.

This is also true. But I think there are far easier ways to find the people who are good at this than trying to teach everyone. You can probably come up with a 15 minute test to screen those aptitudes almost as well rather than have everyone in school for years worth of instruction in things they’ll never use.

Wait, shouldn’t HIGH SCHOOL math be all about getting girls naked?

Seriously though, this is the issue that will not go away. Mathematics is subject zero for separating ability from wishful thinking, and the entire life of the Woke is wishful thinking.

@Steve SailerIt's basically what computers did back in ENIAC times all the time.

Also, we read:

Out! Now!Use R! and RStudio.

Replies: @Steve Sailer, @Bill, @Desiderius, @Jokah Macpherson, @Jokah Macpherson, @MjNah, R is too expensive.

Replies:@Steve2@Jokah MacphersonHi. I’ve always gotten it for free. Web search will find it for you. Enjoy!

Free as in cost really is a lever for practical people.

R also has an interesting functional approach; use it to brainwash new thinkers. Really enjoy.

Use it for your purposes!

Without algebra & maybe a big of ordinary diff, you will be limited to rule by authority when it comes to things like the CAGW scam.

Understanding exponential growth helps when figuring out what you have to save for retirement, how a mortgage works etc.

You might never actually calculate things, but this understanding the math does color your view of reality in later life, about what is possible and what isn’t.

@Steve SailerIt's basically what computers did back in ENIAC times all the time.

Also, we read:

Out! Now!Use R! and RStudio.

Replies: @Steve Sailer, @Bill, @Desiderius, @Jokah Macpherson, @Jokah Macpherson, @MjI teach classes on ACL (now rebranded as Highbond Analytics for god knows what reason, in flagrant violation of the trend towards branding simplicity) and in response to the inevitable student question of ‘Why ACL when we have Excel?’ I tell them that Excel is a good

general purpose tool; if you need to document some basic data, formulas, and narrative discussion together in an attractive presentation, it works great, but since it is general purpose, anything heavier in any of those categories can be done easier with a different tool.I agree with Levitt. Part of the problem is that statistics is seriously misused for political and social purposes for propaganda. Your average citizen needs to be better armed against this type of lying about real life. Your average citizen, if they were in the habit of examining and understanding methodology, would be more wary of believing what leftists claim. It’s impossible to lie with algebra, but people do it all the time with statistics.

If we made all students take 2 years of statistics in high school, they’d finally believe IQ scores that indicate that blacks really are dumber than whites, and commit more crimes per citizen than whites, and they’d stop voting for impossible nonsense and wasting taxpayer money on the multitude of leftist schemes that don’t work.

Quick test: Would Steven Levitt want these changes for his own children? Drastically cut back traditional math, don’t teach them calculus or trig or Algebra 2, instead, focus on mundane office skills like Microsoft Excel? No. I’m confident that Levitt did not want that for his kids, which tells me this is a terrible idea. I suspect Levitt probably did the complete opposite and invested heavily in advanced traditional math for his own kids.

Elon Musk designed a small private school “Ad Astra”, that he and a few other tech industry elite send their children to. I’d trust that because the most privileged people on the planet are sending their own precious kids there. I bet that school does nothing like Levitt’s proposals.

I personally think there’s no reason we cannot teach college-bound children calculus and (even more importantly) a computational version of linear algebra at 15, assuming previous levels of education are fixed to give them the background they’d need: i.e, they’d get algebra and geometry and trigonometry out of the way before high school. At turn of the century Germany, more than 100 years ago, students being tracked for university learned calculus at 15. It’s deeply pathetic that we can’t beat that, all these years later.

I would guess you’d need a moderately above average IQ level to truly grasp the underlying material (maybe about 110? Above average, but not much more), but beyond that, it would be all about having the right preparation and interest in the subject. The cult of the genius in the United States, which implies that you need to be one in order to master advanced mathematics, is deeply counterproductive. You don’t see that BS in Asia: it is understood that while 99.9% of kids are not going to be Carl Friedrich Gauss no matter how hard they work, once you have the basic mental capacity and preparation, it is about the effort you put in. I do not have experience with Russia or Israel, but I’d be deeply surprised if it wasn’t a similar story there.

Math education in the United States is truly, profoundly terrible if you aren’t lucky enough to live in a great school district, or have parents who both have the means and the awareness to plop you in a private school or send you to a community college or something to escape the math hell of your local public school. Elementary school kids do not need 3 years to learn basic mathematical operations. No wonder they get so bored with math and associate it with tedious calculations. It does not help that most mathematics educators have degrees in education, rather than math or a math-intensive subject.

Replies:@Lot@nebulafox“ I would guess you’d need a moderately above average IQ level to truly grasp the underlying material (maybe about 110?”

“Moderately above average” and 110?

2019 America isn’t Japan or Finland.

Figuring out what we stop teaching in HS is the right idea going forward in Third World USA, but we’ll have to drop two things if we are going to add stats.

Replies: @nebulafox, @JMcG@nebulafoxNebulafox, I agree. Better to receive an education from the “best” with local supervision. Why must we remain stuck with all the inferior instructor replication? After reviewing untold math video instructors I consider this man to among, if not the, best/engaging for youngsters:

https://youtu.be/PXwStduNw14

https://youtu.be/r0_mi8ngNnM

@nebulafoxYour observations posess a lot of merit, but you're forgetting that here in the States, when Fuquan, Shanaynay, Lupita and Ramón are found underrepresented in calculus or AP classes, the cry of "Racism!" will soon go up.

@Achmed E. NewmanThis reminds me of the experiences of a friend who earned a Ph.D. in physics at a university with a respected physics department. The centerpiece of his thesis was the calculation of an integral. There was no closed form solution so he used numerical analysis to compute the required result. Unfortunately, a year or two after he received his degree another graduate student discovered that there were discontinuities in the domain of his analysis. My friend’s calculations were essentially worthless. He did get to keep his Ph.D. his later career was outside of physics. In fact, and apropos this discussion, he became a rather prominent statistician.

I imagine if we still had the same demographics that we had during Ike's tenure, this op-ed would not have been necessary.

Replies: @danandI like Ike, he knew how to put math to good use:

Replies:@Reg Cæsar@danand" ...and especially for the long list of sponsors in the opening credits."Kids, can you say

corporate welfare?Boondoggle? Utilitarianism?Military-industrial complex?https://cdn.groovyhistory.com/content/70011/ee660828c4ce601f803ea148831e3230.jpg

The biddies made some good points. Either way, Eisenhower's best math project was this Operation:

https://adamsigoodman.files.wordpress.com/2015/11/chicagovoluntaryreturns.jpg?w=584&h=522

https://1950immigration.files.wordpress.com/2012/02/wb1.jpg

https://miro.medium.com/max/6144/1*MLVHvv6Sa6kvuQDKDiJw0A.jpeg

https://tshaonline.org/sites/default/files/images/handbook/OO/operation-wetback.jpg

@danandGod. The Interstates. BLGGGGGGGGGGGSHHTFGDFSKJSDLFH.

Is there anything more awful? If that's calculus, then to hell with calculus.

Replies: @Desiderius, @nebulafox, @PericlesAnd the practical math track is important. Just because you aren’t cut out for (and probably don’t want to learn anyway) partial differential equations doesn’t mean you are incapable of not being innumerate.

Mass innumeracy in the United States is a major problem: so often, I get the sense that people don’t truly grasp what “a million people” means…

Replies:@Spangel@nebulafoxWe have created a huge problem by overvaluing ap classes and advanced track classes because those classes teach non essential knowledge. But more and more students feel pressured to take those classes since they are more attractive to college admissions boards.

We should bring back basic track math and require everyone to test out of that track if they want to take anything more advanced. Basic track should include consumer finance and basic statistics and a lab class on commonly used quant applications such as excel.

The advanced track should be more flexible and should include options to study advanced data science and calculus. Calculus should not be seen as a routine track for advanced students any longer because it’s not useful for many. Those who claim one needs to understand calculus to understand statistics are simply mistaken about how statistics is taught these days. Whatever small portion of calculus is needed to understand basic statistics, it can be taught as part of that course.

We need to go back to making sure everyone who graduates high school understands the basics for getting through life- consumer finance, nutrition, computer literacy (this is the kind of course they offer to college interns at major corporations). We have a problem of Americans making poor financial decisions such as not understanding they owe student loan interest and not understanding how to save for retirement. We have a crisis of obesity. We don’t have a crisis of Americans not understanding vector calculus. Before you learn calculus, you ought to test out of the basics to demonstrate that you understand that much.

Replies: @nebulafox@nebulafoxLess than 1/3 of a percent of the total population of the United States.

@nebulafoxAhh, you've got a math test embedded in your comment. Let's see, quadruple negative. (-1)(-1)(-1)(-1) = 1. Uh, means you might be numerate? Math is hard ...@nebulafoxYeah. Like on here, where they think "welfare" is a big big big big "problem" because it costs millions-- yes, millions--of dollars! And that we would all be rich if they just abolished welfare and refunded the tax money formerly earmarked thereunto.

And they'll argue like crazy, adding, subtracting, multiplying, even dividing, giving out those good ol' "proofs" like a house afire, that these lunatic mythical fairy tales they are so attached to are god's honest truth.

@Steve SailerSure, Steve, that'd have been the case for any function that wasn't known in simple closed-form, say results from some testing. Even what he was doing requires the

understandingof calculus though, as in "what does the area under that curve mean?"This was before computers were ubiquitous enough to where the engineer could easily program himself the numerical integration, or use a program straight out of his

Numerical Methodsclass, plugging in the curve point-by-point (at a small enough scale to be accurate). By the mid 1980s or so, there'd be a spreadsheet program to do it for you.If you have a curve of a closed-form polynomial, or close approximation, then cutting out skinny rectangles is a waste of time. BTW, that's not how I'd do it - just makes some 1/8" wide spacing for your data, then take your steel scale (with the cork on the bottom) and measure up to each point. Sum them up, and then multiply by whatever that 1/8" on the paper represents. KEEP IN YOUR UNITS! NUMBER WITHOUT UNITS ARE DEAD TO ME.

Replies: @Jus' Sayin'...An easier way is cutting out a tracing of your curve on a substrate with a known and reasonably large areal density, weighing the result on an accurate scale, and dividing the weight by the density.

Replies:@Achmed E. Newman@Jus' Sayin'...Cool method, of course, but I don't know how even, in density, the paper is. If you want to go near that direction, you can buy an old planimeter (probably "sold out" on ebay due to nobody knows what the hell one is). It has 2 joints and one traces any closed 2-D shape and reads out a number on the scale that's on the fixed portion.

The derivation of how the planimeter works is one thing, but inventing in was another. I will repeat that, before electronics, engineers had to be MUCH more clever. Just sayin'...

@KL"An unexpected child is a big income shock to poor, single mothers."

To me, debating abortion as a means to reduce criminality points to the much larger social and demographic problem the US currently faces.

A big shock, is it? Because they don't know the consequences of spreading their legs? Besides, poor single mothers on welfare get a raise with every additional child.

Replies: @nurdle, @Lot“Shock” means a sudden change in economic variable, not a surprise, in this context.

Replies:@MikeatMikedotMike@LotEven so, 9 months isn't sudden, and poor single mothers are incentivized by increases in income to continue having children out of wedlock. The entire premise is false.

@ScarletNumberAnd the practical math track is important. Just because you aren't cut out for (and probably don't want to learn anyway) partial differential equations doesn't mean you are incapable of not being innumerate.

Mass innumeracy in the United States is a major problem: so often, I get the sense that people don't truly grasp what "a million people" means...

Replies: @Spangel, @Redneck farmer, @Achmed E. Newman, @obwandiyagWe have created a huge problem by overvaluing ap classes and advanced track classes because those classes teach non essential knowledge. But more and more students feel pressured to take those classes since they are more attractive to college admissions boards.

We should bring back basic track math and require everyone to test out of that track if they want to take anything more advanced. Basic track should include consumer finance and basic statistics and a lab class on commonly used quant applications such as excel.

The advanced track should be more flexible and should include options to study advanced data science and calculus. Calculus should not be seen as a routine track for advanced students any longer because it’s not useful for many. Those who claim one needs to understand calculus to understand statistics are simply mistaken about how statistics is taught these days. Whatever small portion of calculus is needed to understand basic statistics, it can be taught as part of that course.

We need to go back to making sure everyone who graduates high school understands the basics for getting through life- consumer finance, nutrition, computer literacy (this is the kind of course they offer to college interns at major corporations). We have a problem of Americans making poor financial decisions such as not understanding they owe student loan interest and not understanding how to save for retirement. We have a crisis of obesity. We don’t have a crisis of Americans not understanding vector calculus. Before you learn calculus, you ought to test out of the basics to demonstrate that you understand that much.

Replies:@nebulafox@Spangel>Those who claim one needs to understand calculus to understand statistics are simply mistaken about how statistics is taught these days.

I think we'd be better off as a society if more people knew and genuinely mastered calculus, simply because calculus is cool and is worth knowing. Why do we still appreciate Beethoven or Virgil? It is no less beautiful. It enrichens your mind to understand how the world works: if you are religious, you can think of it as understanding God's programming.

(And yeah: having a wider pool of potential scientists and engineers is always good. Beats having more lawyers, that's for sure.)

But I'm also aware that most people are not going to practically apply calculus in their daily lives. So, no, it shouldn't be forced on everybody, and we certainly shouldn't make calculus a prerequisite for things like statistics that really do need to be mastered by the overwhelming majority of the populace.

>(*this is the kind of course they offer to college interns at major corporations).

Heh. Dirty little secret: most of those internships can be done by high school students. Hell, most entry-level jobs on Wall Street can be done by good high school graduates after maybe a few months of training.

Start digging deep as to why employers demand college degrees at all, and you uncover a rather dark reality behind the student debt crisis.

Replies: @Spangel, @The Germ Theory of DiseaseNot really.

The ‘data analysis’ being advocated by Levitt, is really in essence ‘hack work’ that is glorified arithmetic rather than mathematics, something that the ancient Greeks left behind millennia ago, and something a computer program can do in its sleep.

The idea of cultivating mathematical thinking in the youthful mind – think of those elegant theorems of Archimedes, Pythagoras, the wonderful world of Euclid etc, not to mention the great 16th century algebraicists, the people who published the solution of the cubic etc, is not only that it gives the student an appreciation of the deep austere beauty of mathematics – and the way nature’s hidden secrets were teased out by men of great talent and ability, but also it is of great utility in developing the logical and analytical faculties of the mind. The fact that in math there is one way and one way only to get the result – even if it takes you through the densest thicket of working – and skilful use of subterfuge! – concentrates the mind wonderfully. It also breeds a certain contempt for the liars, budgets and manipulators of politically motivated ‘social sciences’.

I would guess you'd need a moderately above average IQ level to truly grasp the underlying material (maybe about 110? Above average, but not much more), but beyond that, it would be all about having the right preparation and interest in the subject. The cult of the genius in the United States, which implies that you need to be one in order to master advanced mathematics, is deeply counterproductive. You don't see that BS in Asia: it is understood that while 99.9% of kids are not going to be Carl Friedrich Gauss no matter how hard they work, once you have the basic mental capacity and preparation, it is about the effort you put in. I do not have experience with Russia or Israel, but I'd be deeply surprised if it wasn't a similar story there.

Math education in the United States is truly, profoundly terrible if you aren't lucky enough to live in a great school district, or have parents who both have the means and the awareness to plop you in a private school or send you to a community college or something to escape the math hell of your local public school. Elementary school kids do not need 3 years to learn basic mathematical operations. No wonder they get so bored with math and associate it with tedious calculations. It does not help that most mathematics educators have degrees in education, rather than math or a math-intensive subject.

Replies: @Lot, @danand, @Kolya Krassotkin“ I would guess you’d need a moderately above average IQ level to truly grasp the underlying material (maybe about 110?”

“Moderately above average” and 110?

2019 America isn’t Japan or Finland.

Figuring out what we stop teaching in HS is the right idea going forward in Third World USA, but we’ll have to drop two things if we are going to add stats.

Replies:@nebulafox@LotI'm talking about what should be the college-bound population, not what the whole is the increasingly dysgenic, dual tracked United States. And just because the majority of the population isn't going to be targeted for this doesn't mean it is unimportant: not unless we want all of the scientific innovation in the world to be in China from now on, with our younger generation of aspiring scientists relocating there for a chance to actually do science.

People might think that's far-fetched, but during the late Qianlong period, the Chinese thought similarly, and they've only recently recovered from the result of being arrogant enough to think that they could rest on their laurels.

Anywhom, let me enjoy my idealism when it comes to science and math, man. It's all I've got left. It doesn't care who you are, the contour integral or the electromagnetic field remains the same...

Replies: @Lot@LotI think it’s time we start considering giving up our nuclear arsenal as well. South Africa did the world a great service.

Replies: @J.RossAlgebra is just the table stakes to do anything mathematical. Saying we should replace algebra with data science is like saying we should replace learning the alphabet with the study of Shakespeare. This is just a nonsense statement.

Also, data science is pretty clearly a subset/extension of statistics. Again, before you study data science you need to study statistics. Table stakes.

Whenever soft headed people like Levitt propose stuff like this what ends up happening is you have a generation of people who don’t understand algebra and don’t understand data science, but think they do, because they took a course in it. But they never understood the foundation and thus it is a house built on sand that is easily washed away by next semester’s jell-o shots.

Now, where I do agree with him is that perhaps statistics should replace calculus as the default higher math course in many professions. Or at least supplement it. Physicians and engineers both need to understand statistics but currently study calculus as part of their requirements. (Engineers should do both, physicians could get away with just stats.)

Also no one should ever, ever, say ‘I learned x in college but didn’t use it’ where x is a course that is foundational to the discipline. This is a surefire way to out yourself as a moron. Some obscure seminar your senior year, sure, maybe you don’t use that. Intro stats? C’mon man.

Agree:danandReplies:@Jokah Macpherson@SimpleSongThis is a good comment. I was definitely thinking that 'data science' (intermediate to advanced statistics basically, as far as I can tell) would make much less sense to me without the Algebra and Calculus foundation that I have, but I wasn't sure if others thought differently.

I would guess you'd need a moderately above average IQ level to truly grasp the underlying material (maybe about 110? Above average, but not much more), but beyond that, it would be all about having the right preparation and interest in the subject. The cult of the genius in the United States, which implies that you need to be one in order to master advanced mathematics, is deeply counterproductive. You don't see that BS in Asia: it is understood that while 99.9% of kids are not going to be Carl Friedrich Gauss no matter how hard they work, once you have the basic mental capacity and preparation, it is about the effort you put in. I do not have experience with Russia or Israel, but I'd be deeply surprised if it wasn't a similar story there.

Math education in the United States is truly, profoundly terrible if you aren't lucky enough to live in a great school district, or have parents who both have the means and the awareness to plop you in a private school or send you to a community college or something to escape the math hell of your local public school. Elementary school kids do not need 3 years to learn basic mathematical operations. No wonder they get so bored with math and associate it with tedious calculations. It does not help that most mathematics educators have degrees in education, rather than math or a math-intensive subject.

Replies: @Lot, @danand, @Kolya KrassotkinNebulafox, I agree. Better to receive an education from the “best” with local supervision. Why must we remain stuck with all the inferior instructor replication? After reviewing untold math video instructors I consider this man to among, if not the, best/engaging for youngsters:

@nebulafox“ I would guess you’d need a moderately above average IQ level to truly grasp the underlying material (maybe about 110?”

“Moderately above average” and 110?

2019 America isn’t Japan or Finland.

Figuring out what we stop teaching in HS is the right idea going forward in Third World USA, but we’ll have to drop two things if we are going to add stats.

Replies: @nebulafox, @JMcGI’m talking about what should be the college-bound population, not what the whole is the increasingly dysgenic, dual tracked United States. And just because the majority of the population isn’t going to be targeted for this doesn’t mean it is unimportant: not unless we want all of the scientific innovation in the world to be in China from now on, with our younger generation of aspiring scientists relocating there for a chance to actually do science.

People might think that’s far-fetched, but during the late Qianlong period, the Chinese thought similarly, and they’ve only recently recovered from the result of being arrogant enough to think that they could rest on their laurels.

Anywhom, let me enjoy my idealism when it comes to science and math, man. It’s all I’ve got left. It doesn’t care who you are, the contour integral or the electromagnetic field remains the same…

Replies:@Lot@nebulafox“ I’m talking about what should be the college-bound population”

Should?

60% of the US Pop is in the “some college” or more group.

Just keeping you precise here. By college bound you seem to really mean “selective college bound whites and asians.”

@Achmed E. NewmanApparently, Galileo was unable to calculate the area under a cycloid – that had to wait until Newton. Galileo’s solution was to cut out the curve and weigh it.

@nebulafox“ I would guess you’d need a moderately above average IQ level to truly grasp the underlying material (maybe about 110?”

Figuring out what we stop teaching in HS is the right idea going forward in Third World USA, but we’ll have to drop two things if we are going to add stats.

“Moderately above average” and 110?

2019 America isn’t Japan or Finland.

Replies: @nebulafox, @JMcGI think it’s time we start considering giving up our nuclear arsenal as well. South Africa did the world a great service.

Replies:@J.Ross@JMcGThat "great service" would never have been necessary had they believed in themselves and anyway is soundly refuted by Ice T: we should only give up ours after everybody else gives up theirs.

Replies: @JMcGThe last thing we need is millions of additional Dunning-Kruger cases who think that they know statistics, and remember just enough to feed a bunch of data into a point-and-click statistics package, possibly after cherry-picking the data with Excel first, push a button, and have a computer run a million regressions, fiddling around with parameters until it can spit out a few convenient regressions with low p values.

Agree:utuReplies:@Jokah Macpherson@Not RaulI agree it's not ideal, but it beats arguing based on feelings. I honestly wish a few idiots would at least make a good faith effort to do a little research.

The study of mathematics teaches high level abstraction, working with and critically reviewing definitions, proving propositions within a tightly structured,

verifiable conceptual framework, etc.This is why the Narrative/Ed School crowd want to replace it with something more “relevant.”

Relevantis and always has been a code word meaning “what serfs should be taught.” The unspoken subtext is always:don’t give them ideas.Agree:sayless@El DatoExcel is actually pretty terrible for business purposes, where it is most often used.

Replies: @Wency, @Not Raul, @JVenterTrue; but how many Harvard MBAs have the patience to learn SAS or R?

The good thing about Excel is that even a child can learn how to do a few simple things, so lots of Dunning-Kruger cases consider themselves to be “experts” at Excel, so they trust it.

Of course the peasants who have to deal with workbooks with millions of cells, millions of links, and millions of equations are horrified that one wrong keystroke in one cell could throw everything off, one might not even know that there’s a problem, and if there is, it might be very difficult to find.

Agree:Andy@Achmed E. NewmanSchools serving populations where the teachers have some leverage over the students tend to be very good at crushing this sort of creativity.

@KLCan't speak for others but I agree personally with Levvitt on this 1, though it really is a Stalinist type solution. Stalin was said to have said "no man, no problem...."

Abortion of potential criminals is a crude but effective way of getting rid of criminals.....

Replies: @Redneck farmerBut then we get into HBD, and you know what happens THEN…..

Do these people who use Excel every day really claim not to use algebra? If so, what the hell are they doing?

Replies: @Bugg, @ForbesOur “betters” like Steve Levitt are always lecturing us that

Of course, what is relevant is always debatable. Much like the debate about the purpose of college today–is it a trade school to lean job skills, or is it higher education, i.e. a higher knowledge acquired through subject matter mastery.

Similarly, some describe math education as worthless: Who uses geometry, trigonometry or calculus in their workaday world? Students should be taught relevant skills to the job market!! Like “correlation is not causation”!! (BTW, it seems to be math-phobic and innumerate journalists always implying causes from correlations…)

Alternatively, how would students learn analysis, logical argument, deduction, etc. In other words, how do students learn to work their way through a problem to an answer where they can self-check and self-test the solution as sound because they have a firm grasp of the mathematics involved.

Spreadsheets are just as often the product of garbage in/garbage out manipulation, as they are a profound problem-solving solution.

@nebulafoxWe have created a huge problem by overvaluing ap classes and advanced track classes because those classes teach non essential knowledge. But more and more students feel pressured to take those classes since they are more attractive to college admissions boards.

We should bring back basic track math and require everyone to test out of that track if they want to take anything more advanced. Basic track should include consumer finance and basic statistics and a lab class on commonly used quant applications such as excel.

The advanced track should be more flexible and should include options to study advanced data science and calculus. Calculus should not be seen as a routine track for advanced students any longer because it’s not useful for many. Those who claim one needs to understand calculus to understand statistics are simply mistaken about how statistics is taught these days. Whatever small portion of calculus is needed to understand basic statistics, it can be taught as part of that course.

We need to go back to making sure everyone who graduates high school understands the basics for getting through life- consumer finance, nutrition, computer literacy (this is the kind of course they offer to college interns at major corporations). We have a problem of Americans making poor financial decisions such as not understanding they owe student loan interest and not understanding how to save for retirement. We have a crisis of obesity. We don’t have a crisis of Americans not understanding vector calculus. Before you learn calculus, you ought to test out of the basics to demonstrate that you understand that much.

Replies: @nebulafox>Those who claim one needs to understand calculus to understand statistics are simply mistaken about how statistics is taught these days.

I think we’d be better off as a society if more people knew and genuinely mastered calculus, simply because calculus is cool and is worth knowing. Why do we still appreciate Beethoven or Virgil? It is no less beautiful. It enrichens your mind to understand how the world works: if you are religious, you can think of it as understanding God’s programming.

(And yeah: having a wider pool of potential scientists and engineers is always good. Beats having more lawyers, that’s for sure.)

But I’m also aware that most people are not going to practically apply calculus in their daily lives. So, no, it shouldn’t be forced on everybody, and we certainly shouldn’t make calculus a prerequisite for things like statistics that really do need to be mastered by the overwhelming majority of the populace.

>(*this is the kind of course they offer to college interns at major corporations).

Heh. Dirty little secret: most of those internships can be done by high school students. Hell, most entry-level jobs on Wall Street can be done by good high school graduates after maybe a few months of training.

Start digging deep as to why employers demand college degrees at all, and you uncover a rather dark reality behind the student debt crisis.

Replies:@Spangel@nebulafoxI’m sure college internship work could be done by high school students since ive delt with plenty of interns that are only 2 years out of high school. There is a maturity difference but probably no important difference in ability to learn.

I certainly think physics and cosmology are intrinsically interesting, but years worth of algebra 2 and calculus are a bit much. Rarely do I see anyone who liked calculus, this thread being a notable exception.

Even among math phds, I generally hear that calculus is not interesting enough for them. Less able students tend to find it tedious.

@nebulafox"Why do we still appreciate Beethoven or Virgil? It is no less beautiful."

Ahem.

While I'm sure your points about calculus stand, we do have to clarify here.

Mozart is beautiful. Schumann is beautiful. Wagner is beautiful. Beethoven is merely... interesting.

Similarly, Virgil is not beautiful, he is merely sturdy (which in itself is still a very valuable thing). Homer is beautiful. Catullus is beautiful, in a weird sort of way (just not the zany long stuff).

Throwing a mat of firecrackers into a room full of nerds is not, in itself, beautiful... but it might have beautiful results.

Replies: @Ian M.Replies: @Spangel, @International JewI can’t imagine you’ve looked into the requirements for this field recently, because this isn’t at all true.

Data science people are in such high demand these days that there are dozens upon dozens of programs that have no such pre reqs and can still confer good jobs to those who complete their courses.

Probably only phd track programs require such pre reqs while the vast majority of students in those programs simply want well paying stable employment.

Replies:@Anon@Spangel... churning out nonsense code or nonsense studies? At some point the bottom is going to fall out of every mere fad and it will be better for these people if they have learned something real in the meantime ("data science" is actually statistics, no? Educated statisticians are worth having).Replies: @Spangel@SpangelThis isn't true at all. People say this, but any program that doesn't have those prereqs expects people to come in with them, rather than teaching them. You still need the math.

@SpangelWhat do people trained that way do? They just apply out-of-the-box techniques learned more or less by rote in school?

@SpangelYou must lack imagination. In general, excellent job of missing my point. Well done. Perhaps you are a graduate of one of these not-so rigorous programs and therefore exemplify the point I was making.

Data science is "sexy" and in demand so yes there are hastily produced programs that attempt to confer credentials on people looking to be data scientists. So what? Since you say "dozens and dozens" of programs would you care to list 24? I would love to see them and evaluate the programs (I won't hold my breath waiting for your response). I actually hire data scientists and machine learning engineers (MLEs), do you? I can tell you that my screen involves math and stats question and failure to answer them means you don't get hired. I don't work for a research institution or a think tank, but we know through actual research that people who can use Excel, SAS, SPSS, Python or R, but have no grounding in stats are of limited value as data scientists. I have somewhat less rigorous standards for MLEs, but I do expect them to know statistics to a reasonable degree.

There are lots of companies who still don't understand what data science is and are willing to call report writers or data analysts data scientists, but those who know better only hire people with a good grounding in those subjects I mentioned in my previous post. The reason for this, as I implied earlier, is not because data scientists are solving equations by hand on a daily basis, but instead because lots of decisions when building and evaluating models require a through grounding in math and mathematical statistics. Data science is applied statistics with some additional specialized knowledge thrown in.

If you are ones of those benefiting from the demand for data science and the ignorance of many on what constitutes data science, I would suggest you either bite the bullet and learn your math and stats before you get found out or move into a position where your lack of analytical rigor won't matter.

Replies: @Spangel@Spangel>Those who claim one needs to understand calculus to understand statistics are simply mistaken about how statistics is taught these days.

I think we'd be better off as a society if more people knew and genuinely mastered calculus, simply because calculus is cool and is worth knowing. Why do we still appreciate Beethoven or Virgil? It is no less beautiful. It enrichens your mind to understand how the world works: if you are religious, you can think of it as understanding God's programming.

(And yeah: having a wider pool of potential scientists and engineers is always good. Beats having more lawyers, that's for sure.)

But I'm also aware that most people are not going to practically apply calculus in their daily lives. So, no, it shouldn't be forced on everybody, and we certainly shouldn't make calculus a prerequisite for things like statistics that really do need to be mastered by the overwhelming majority of the populace.

>(*this is the kind of course they offer to college interns at major corporations).

Heh. Dirty little secret: most of those internships can be done by high school students. Hell, most entry-level jobs on Wall Street can be done by good high school graduates after maybe a few months of training.

Start digging deep as to why employers demand college degrees at all, and you uncover a rather dark reality behind the student debt crisis.

Replies: @Spangel, @The Germ Theory of DiseaseI’m sure college internship work could be done by high school students since ive delt with plenty of interns that are only 2 years out of high school. There is a maturity difference but probably no important difference in ability to learn.

I certainly think physics and cosmology are intrinsically interesting, but years worth of algebra 2 and calculus are a bit much. Rarely do I see anyone who liked calculus, this thread being a notable exception.

Even among math phds, I generally hear that calculus is not interesting enough for them. Less able students tend to find it tedious.

Replies: @Spangel, @International JewYeah, an academic economist like Levitt should know what data science means (even if it is a fairly new term). And maybe he does know, but writing for a general audience he tried to use what he thought was general-audience language.

With his colleagues, he’d call the skills he wishes were taught instead of Algebra 2, “basic data analysis”.

New Geico Commercial:

Metrosexual Music in the background…..”Even a Caveman can write a Python script to find a correlation between eating juicy fruits and shoe size…..”

LOL:theMannIn a sense, true. But from a practical point of view I think there is an important difference between data existing in theory and in practice (I think the crux of the definition of “created” here). Consider a weather station. Knowing that there was a temperature at every instant over the last year (say there was a bulb thermometer) is very different from actually having that data recorded at five second intervals. I think only the latter truly merits being called “data created.”

The proliferation of sensors (including audio and video recording) is a huge multiplier effect on turning what is observable into data.

I think increasing emphasis on practical statistics (which IMHO is what Levitt is arguing for here) is a worthy goal. But I am much less sure the appropriate response is to replace Algebra 2 with that. How much of the content in Algebra 2 (and for that matter, basic calculus) is necessary for meaningfully engaging with statistics? (my question is sincere, the same concern comes up with physics/calculus in HS, but there does seem to be some use in teaching basic physics without calculus)

I would ask Levitt to consider how well this recommendation of math background for intro statistics maps to Algebra 2:

https://dcmathpathways.org/sites/default/files/resources/2019-08/Mathematics_Foundations_for_Success_in_Introductory_Statistics_20190809.pdf

Or consider the recommendations for AP Statistics prereqs in this Quora answer: https://www.quora.com/What-is-the-prerequisite-knowledge-for-AP-Statistics/answer/Michael-Thramann

That

isinteresting. What makes it even more interesting is the Internet Archive only has 2019 versions of those files. Were the links you used the original locations of the pages? Or have they reorganized their website?Here is a PDF of your discussion with Levitt: http://pricetheory.uchicago.edu/levitt/Papers/DoesAbortionPreventCrime.pdf

and from looking at the page footers in that, an archive link to part of it which does have author attributions:

https://web.archive.org/web/20030310185735/http://slate.msn.com/id/33569/

Worth mentioning this background from an earlier post of yours: https://www.unz.com/isteve/does-abortion-prevent-crime-steve_26/

And this:

BTW, Steve, is there any chance Ron could write some code which would go through your old posts and any time there is a link to the now dead isteve.com (it looks like isteve.blogspot.com is still alive though?) site either convert the link to the unz.com version or perhaps better, add the Unz version as a note in the original text?

Replies: @Jokah MacphersonI agree it’s not ideal, but it beats arguing based on feelings. I honestly wish a few idiots would at least make a good faith effort to do a little research.

Also, data science is pretty clearly a subset/extension of statistics. Again, before you study data science you need to study statistics. Table stakes.

Whenever soft headed people like Levitt propose stuff like this what ends up happening is you have a generation of people who don't understand algebra and don't understand data science, but think they do, because they took a course in it. But they never understood the foundation and thus it is a house built on sand that is easily washed away by next semester's jell-o shots.

Now, where I do agree with him is that perhaps statistics should replace calculus as the default higher math course in many professions. Or at least supplement it. Physicians and engineers both need to understand statistics but currently study calculus as part of their requirements. (Engineers should do both, physicians could get away with just stats.)

Also no one should ever, ever, say 'I learned x in college but didn't use it' where x is a course that is foundational to the discipline. This is a surefire way to out yourself as a moron. Some obscure seminar your senior year, sure, maybe you don't use that. Intro stats? C'mon man.

Replies: @Jokah MacphersonThis is a good comment. I was definitely thinking that ‘data science’ (intermediate to advanced statistics basically, as far as I can tell) would make much less sense to me without the Algebra and Calculus foundation that I have, but I wasn’t sure if others thought differently.

As it is, people graduate from college without understanding compound interest. They think having six figures of debt is perfectly normal for 20-somethings.

Sometimes it seems as if the education system is not what we are supposed to think it is.

Replies: @Reg CæsarOh, they

will…Gorbachev got the job after his immediate predecessors kept dying. He said he never would have gotten the job if what he planned was known. Regarding weapons, there is no need to fear the Stealth Fighter when you have nuclear-armed submarines as a deterrent to an attack.

Replies: @Kolya KrassotkinThe Soviet leadership prior to Gorbachev – Brezhnev, Andropov, Chernenko – were a doddering, senile, out-of-touch gerentocracy, much like the current crop of American political leaders. Gorbachev had only to be at the right place at the right time.

@El DatoExcel is actually pretty terrible for business purposes, where it is most often used.

Replies: @Wency, @Not Raul, @JVenterWhat’s better in your opinion?

Thanks in advance.

@El DatoNah, R is too expensive.

Replies: @Steve2Hi. I’ve always gotten it for free. Web search will find it for you. Enjoy!

Free as in cost really is a lever for practical people.

R also has an interesting functional approach; use it to brainwash new thinkers. Really enjoy.

Use it for your purposes!

Steve, do you consider yourself a Frequentist or Bayesian statistician?

Replies:@El Dato@KronosWhy not use both depending on what you do.

https://plato.stanford.edu/entries/probability-interpret/

The fun is that the same numbers and the same formulas are used for describing objective facts and describing subjective beliefs, sometimes in the same line. Maybe there should be mandatory color coding.

Anyway, "frequentism" is a self-defeating circular idea (it wants to define the frequency only for processes that actually exist, but then needs to assume that said process run infinitely long to make sense of the frequency, but infinitely-long processes don't exist ... head explodes!!). Break out of the brainlock, assume Kolomogorov's axioms as prior, then be done with it. We assume Causality also as prior, it's just the way it works.

Replies: @KronosWhat is the value of high school in general? Doesn’t the majority of graduates forget all of the education within a couple years? Objectively, it’s all just one of many massive government jobs programs that our society seems to provide so a bunch of mediocrities can be “middle class”

Calculus no longer needs to be understood, since we no longer have much interest in understanding the natural world on a fundamental basis. Modern humans have a tendency to define our surroundings and events with parameters on convenient linear scales for communication (e.g., percent, currency/prices, game scores, distances, etc).

However, the natural world has nonlinear tendencies and events, as do human interactions such as financial markets, traffic flow, and contests, all of which are then tracked with linear metrics. Unfortunately, most people don’t understand functionality and metrics that are complex and relate to changes in variables, which is the core of calculus.

Society often sees a complex relationship in a ‘zero-sum’ linear format:

A + B = 100%…when in the natural world, a nonlinear format often defines functionality:

A x B = 1.@istevefanI like Ike, he knew how to put math to good use:

https://youtu.be/wnrqUHF5bH8

Replies: @Reg Cæsar, @obwandiyag” …and especially for the long list of sponsors in the opening credits.”

Kids, can you say

corporate welfare?Boondoggle? Utilitarianism?Military-industrial complex?The biddies made some good points. Either way, Eisenhower’s best math project was this Operation:

I would guess you'd need a moderately above average IQ level to truly grasp the underlying material (maybe about 110? Above average, but not much more), but beyond that, it would be all about having the right preparation and interest in the subject. The cult of the genius in the United States, which implies that you need to be one in order to master advanced mathematics, is deeply counterproductive. You don't see that BS in Asia: it is understood that while 99.9% of kids are not going to be Carl Friedrich Gauss no matter how hard they work, once you have the basic mental capacity and preparation, it is about the effort you put in. I do not have experience with Russia or Israel, but I'd be deeply surprised if it wasn't a similar story there.

Math education in the United States is truly, profoundly terrible if you aren't lucky enough to live in a great school district, or have parents who both have the means and the awareness to plop you in a private school or send you to a community college or something to escape the math hell of your local public school. Elementary school kids do not need 3 years to learn basic mathematical operations. No wonder they get so bored with math and associate it with tedious calculations. It does not help that most mathematics educators have degrees in education, rather than math or a math-intensive subject.

Replies: @Lot, @danand, @Kolya KrassotkinYour observations posess a lot of merit, but you’re forgetting that here in the States, when Fuquan, Shanaynay, Lupita and Ramón are found underrepresented in calculus or AP classes, the cry of “Racism!” will soon go up.

An important task in data science is classification, for which logistic regression is the simplest model. A logistic function involves the exponential function. Exponentials and logarithms are a topic in Algebra II.

People who can’t learn Algebra II won’t get very far in statistics either.

Data science is a fancy new name for statistics – of course you have to teach statistics in high school. You still need to teach algebra and at least basic calculus in high school too. These fields are still needed in physics and math, and yes, most of engineering. You will not be able to get good mathematicians, physicists and engineers out of higher education if they didn’t learn any of the math basics at high school

I would think if you're not smart enough to learn algebra by 8th or 9th grade, then as an adult you likely won't be using or retaining any math besides arithmetic anyway so it's a moot point what they teach you. That still leaves smart people 3-4 years of HS to learn other things.

Stats is probably more important than geometry, trig, and calculus for non-STEM people. I retained basically nothing from trig or geometry except the formula for area of a circle, which I use to compare the value of different deals when ordering pizza (yeah, I'm that guy). I've never heard a cosine used out in the real world.

Terms like "second derivative" do come up sometimes when growth is discussed, but I imagine a smartish person could grok the idea of "rate of change of rate of change" in 15 seconds without needing to learn calc.

The vast majority of people, even intelligent people, don't really perform statistical analysis but they at least need to know how to interpret and question stats that someone else put together.

Replies: @Anon, @PericlesTo compare prices, you don’t need to know the area of a circle, just that it’s proportional to the square of the diameter, radius, or circumference.

Replies:@Wency@AnonThis is true, unless you're comparing square and circular pizzas. Some places offer both.

Replies: @Anon@NoWeltschmerzI can’t imagine you’ve looked into the requirements for this field recently, because this isn’t at all true.

Data science people are in such high demand these days that there are dozens upon dozens of programs that have no such pre reqs and can still confer good jobs to those who complete their courses.

Probably only phd track programs require such pre reqs while the vast majority of students in those programs simply want well paying stable employment.

Replies: @Anon, @The Practical Conservative, @Bill, @NoWeltschmerz… churning out nonsense code or nonsense studies? At some point the bottom is going to fall out of every mere fad and it will be better for these people if they have learned something real in the meantime (“data science” is actually statistics, no? Educated statisticians are worth having).

Replies:@Spangel@AnonData science is not statistics, which is conceptual at its core. In practice, data science refers to programming skills around being able to implement statistical reasoning concepts.

Understanding statistics at a conceptual level does not actually require learning calculus or matrix algebra as a separate course beforehand even though this is what most people do in practice because calculus is such a ubiquitous course for high schoolers that are even slightly above average.

If we all didn't have calculus beforehand, we could just learn the foundational concepts of calculus and matrix algebra needed for really understanding statistics properly as part of statistics courses. When people learn to visualize statistical concepts, the more abstract mathematical foundations of these concepts should become intuitively inferred even for those not strongly familiar with them beforehand.

Remember that high school calculus is actually weeks and weeks of calculating the area under parabolas, u substitution, days and days and weeks and weeks of repetitive integral and derivative problems. Only a small portion of people will intuitively grasp how this relates to math concepts they more commonly encounter like statistical claims or financial investments over time.

@ScarletNumberAnd the practical math track is important. Just because you aren't cut out for (and probably don't want to learn anyway) partial differential equations doesn't mean you are incapable of not being innumerate.

Mass innumeracy in the United States is a major problem: so often, I get the sense that people don't truly grasp what "a million people" means...

Replies: @Spangel, @Redneck farmer, @Achmed E. Newman, @obwandiyagLess than 1/3 of a percent of the total population of the United States.

@Steve SailerIt's basically what computers did back in ENIAC times all the time.

Also, we read:

Out! Now!Use R! and RStudio.

Replies: @Steve Sailer, @Bill, @Desiderius, @Jokah Macpherson, @Jokah Macpherson, @MjExcel gets a lot of flak mainly because the putrid masses use it. I rely on SPSS or EViews but Excel still gets the job done. Plus, Excel is more sensible for self-study in statistics and financial modeling.

Prof Levitt’s wrong here. I’d argue that the switch from math (algebra, calc, and so on) to data science is dangerous. Data science is hard (in some ways harder than pure math) and its results can be counterintuitive (not to mention politically incorrect). Keep data science in the hands of those who have already taken a lot of math (say, through linear algebra & ODE) or else you will dumb down the field and everyone will come out of the courses with pseudo-intellectual pretensions about their ability to work with data. Better to have a man untrained with data than with a trivial understanding. Otherwise you’ll have even worse decisions in business and public life.

Anyway, last time I checked my alma-mater went from offering three calculus courses (honors, calc for engineering, general) to this

Honors calculus (geared for math majors)

Calculus for engineers

General calculus

Survey of calculus

Brief survey of calculus (!)

Business calculus (huh?)

The above is exactly what will happen to data analysis courses which will result in students that are confident incompetents. It’s like the old saying that a little learning is a dangerous thing.

@Romanian

If the MPs were arguing that attending school had an incapacitance effect, that if they were in class they couldn't be mugging anyone except their classmates, I'd have more respect for them."we have innumerate people and elites, who cannot think in numbers and, therefore, cannot really understand the world when they only experience it through data (like population growth in Africa)"That's how we get "

crime is falling, yet the prison population has never been so high" Guardian pieces.Here's a slightly OT example. Kids (in London at any rate) who are excluded from school (and you have to try hard for that to happen) tend to end up joining gangs and carrying knives.

Therefore, say MPs, don't exclude them from school!

https://www.theguardian.com/uk-news/2019/oct/25/reform-school-exclusions-to-tackle-knife-mps-urge

Replies: @AnonThere used to be a simple way to deal with students not in school. They didn’t get to eat. No dole. They had to get a job to put a meal in their stomach, and that mean showing up and doing the work or getting fired. It worked reasonably well. Hunger is a good motivator and dealer of discipline. If they were really sociopathic and decided to steal instead, they just got hung to death by the courts.

Obviously developing synapses is not in order for US education, so, apart from not having physics as a normal subject (that is where all those derivatives and integrals are needed), I guess it is a good idea to dumb American children down even more. After all, who needs those polynomials.

But, yes, this is just another attempt to teach nothing while appearing to teach much. The ultimate goal is uniform test scores (around zero, maybe, but uniform) for all students. Politicians control the schools, coalitions determine which politicians are elected, and important coalition members demand that their kids not be discernible from White kids in grades, college entrance examinations, discipline records, or any other way. Boaler and Levitt get a career boost for finding one more way to satisfy the important coalition members.

Counterinsurgency

1] Word origin: "data" means "that which is given".

Replies: @dearieme“data” means “that which is given”Surely it’s a plural? So ‘“those which are given” – the singular is “datum”.

Replies:@Counterinsurgency@deariemeYou can use it that way. You have a set of data, an element of which is a datum. It's more precise.You can also us it as "I have a set of data" which becomes in common usage "I have data". "That" then refers to the set, the collection you are given, not to the individual "data" in the set.

English is (of course) becoming a trade language, losing its own grammatical forms and adopting new borrowed grammatical forms. The subjunctive ("if only it were true" vs. "if only it was true") is no longer used, "whom" as an object ("to whom" vs. "to who") was lost back in the 1930s, and "how", as in "I like how" is used much like spanish "como". "Me gusta como . . .".

The data/datum seems to be gradually fading away. Too bad, it is easier to say "We'll take the third datum in our data" than "We'll take the third element in our set of data". OTH, few people say either.

Counterinsurgency

Replies: @PiltdownMan@NoWeltschmerzI can’t imagine you’ve looked into the requirements for this field recently, because this isn’t at all true.

Data science people are in such high demand these days that there are dozens upon dozens of programs that have no such pre reqs and can still confer good jobs to those who complete their courses.

Probably only phd track programs require such pre reqs while the vast majority of students in those programs simply want well paying stable employment.

Replies: @Anon, @The Practical Conservative, @Bill, @NoWeltschmerzThis isn’t true at all. People say this, but any program that doesn’t have those prereqs expects people to come in with them, rather than teaching them. You still need the math.

@El DatoMy first assignment with my brand new ISyE degree was untangling a 14,000 x 8,000 Excel file used to manage the production schedule by an Assistant Plant Manager who had recently and unexpectedly passed away.

It was the work of years. We had days. Good times.

Replies: @BillHis detailed documentation no doubt saved you. 🙂

Replies:@Desiderius@BillGood one. He was popular with the line workers he grew up with, so they were pretty much running shit anyway. We muddled through.

@Spangel... churning out nonsense code or nonsense studies? At some point the bottom is going to fall out of every mere fad and it will be better for these people if they have learned something real in the meantime ("data science" is actually statistics, no? Educated statisticians are worth having).Replies: @SpangelData science is not statistics, which is conceptual at its core. In practice, data science refers to programming skills around being able to implement statistical reasoning concepts.

Understanding statistics at a conceptual level does not actually require learning calculus or matrix algebra as a separate course beforehand even though this is what most people do in practice because calculus is such a ubiquitous course for high schoolers that are even slightly above average.

If we all didn’t have calculus beforehand, we could just learn the foundational concepts of calculus and matrix algebra needed for really understanding statistics properly as part of statistics courses. When people learn to visualize statistical concepts, the more abstract mathematical foundations of these concepts should become intuitively inferred even for those not strongly familiar with them beforehand.

Remember that high school calculus is actually weeks and weeks of calculating the area under parabolas, u substitution, days and days and weeks and weeks of repetitive integral and derivative problems. Only a small portion of people will intuitively grasp how this relates to math concepts they more commonly encounter like statistical claims or financial investments over time.

In real life, I assure you, there is no such thing as algebra.—Fran LebowitzI believe it was in Morris Kline’s

Why Johnny Can't Addwhere Kline said it makes no sense for all schoolchildren to suffer through years of primary and secondary math including algebra and trigonometry when only a small percentage of these students will go on to a college major requiring it. (NB: I’m guessing the percentage going into STEM has changed since he wrote the book in 1973 but still the vast majority of secondary students will never use it again after high school).When you then ask educators why all schoolchildren need to study years of math they will will respond with things like the need to balance a checkbook, etc. But does it really take years of math classes to learn the basic math of everyday life? They will also respond with the outdated idea from Plato and the ancient Greeks that it develops deductive thinking skills. But real life is about 99.9% inductive reasoning.

Replies: @Anon, @AnonIt’s possible to teach logical thinking without Plato or Aristotle, and still make it fun enough to motivate kids.

@NoWeltschmerzReplies: @Anon, @The Practical Conservative, @Bill, @NoWeltschmerzWhat do people trained that way do? They just apply out-of-the-box techniques learned more or less by rote in school?

@Steve SailerIf your father knew calculus...why go to all the trouble?Replies: @anon, @astrolabeMaybe experimental data and you don’t have a function?

Replies:@Realist@anonDevelop one.Replies: @AnonMicrosoft Excel and its consequences have been a disaster for the human race

Replies: @KronosLet me guess, your a fan of R programming?

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&ved=2ahUKEwjkqtumq7jlAhX4HzQIHT3RB9UQjRx6BAgBEAQ&url=https%3A%2F%2Fenholm.net%2F2014%2F03%2F24%2Fconvert-sas-datetime-to-r-datetime%2F&psig=AOvVaw3EwDkJW8X-UmMC-cDgXgG6&ust=1572124753850862

I can ill imagine the American educational establishment wanting to give high school students the mathematical tools to see right through establishmentarian narrative peddling. I mean, Michael Bloomberg and Joel Klein wouldn’t have gotten away with their educational fraud for as long as they did if most people grokked this thing called the standard deviation.

@Achmed E. NewmanAn easier way is cutting out a tracing of your curve on a substrate with a known and reasonably large areal density, weighing the result on an accurate scale, and dividing the weight by the density.

Replies: @Achmed E. NewmanCool method, of course, but I don’t know how even, in density, the paper is. If you want to go near that direction, you can buy an old planimeter (probably “sold out” on ebay due to nobody knows what the hell one is). It has 2 joints and one traces any closed 2-D shape and reads out a number on the scale that’s on the fixed portion.

The derivation of how the planimeter works is one thing, but inventing in was another. I will repeat that, before electronics, engineers had to be MUCH more clever. Just sayin’…

What the guy is proposing sounds reasonable, but it reminds me of what I’ve run into at the college level. Everyone wants to know just the final formulas or “rubrics” to solve problems in engineering, without having to show understanding of the fundamentals (yes, lots of calculus) behind it all on the tests.

If you teach like this, then these students will have NO understanding of all the assumptions made during the derivation phase of getting to the problem solutions. They will never remember the limitations on these “final formulas”, but worse yet, if they come to a problem that looks the same but is actually different in some fundamental way (oh, it’s not laminar flow, or, hmmm, mass is not constant this time) they will use their handy formulas (as is what a technician should be doing, not an engineer) and produce garbage numbers.

I wonder if it would be the same thing, if, to cut down on all the time spent in algebra, students are just given a rubric to solve algebraic equations and never see a graph of different functions. Maybe they don’t need any of that either, but a country full of half-assed statisticians is gonna really prove out the old saw “there are lies, damn lies, and statistics”

ELECTRONICS SIR!

Electronics is where the intelligence of man is most profitably utilized.

Replies: @AnonymousIn 1952, eighty percent of working electronics was cookbookery, with the development of integrated circuits it’s higher now. The amount of truly original design from first principles is surprisingly low.

Seriously, it is inconcievable to me how anyone can do serious Data Analysis without understanding the concept of higher dimensional data….”The curse of dimensionality”….sparse vectors….sparse matrices……conceptually understanding what a matrix is…..What a linear operator is….what a linear mapping is….what is Real Space……Eigenvectors…..Eigenvalues……basis….orthononormal bases- vectors….inner products….matrix norms……onto Random Matrices…onto really cool shit like Reeb Graphs…..Wanna see some really cool shit?…..Go to google images…type in Reeb Graphs…..

The unreasonable effectiveness of Linear Algebra….

Richard Haier, the author of a recent book on the neuroscience of intelligence, wrote this in Quillette:

@ScarletNumberReplies: @Spangel, @Redneck farmer, @Achmed E. Newman, @obwandiyagAhh, you’ve got a math test embedded in your comment. Let’s see, quadruple negative. (-1)(-1)(-1)(-1) = 1. Uh, means you might be numerate? Math is hard …

@LotI'm talking about what should be the college-bound population, not what the whole is the increasingly dysgenic, dual tracked United States. And just because the majority of the population isn't going to be targeted for this doesn't mean it is unimportant: not unless we want all of the scientific innovation in the world to be in China from now on, with our younger generation of aspiring scientists relocating there for a chance to actually do science.

People might think that's far-fetched, but during the late Qianlong period, the Chinese thought similarly, and they've only recently recovered from the result of being arrogant enough to think that they could rest on their laurels.

Anywhom, let me enjoy my idealism when it comes to science and math, man. It's all I've got left. It doesn't care who you are, the contour integral or the electromagnetic field remains the same...

Replies: @Lot“ I’m talking about what should be the college-bound population”

Should?

60% of the US Pop is in the “some college” or more group.

Just keeping you precise here. By college bound you seem to really mean “selective college bound whites and asians.”

The problem with all “we need to reform math because students aren’t going to use their knowledge” is that they aren’t going to use the replacement knowledge either.

They may say that data literacy is central to the framework, but what do the questions actually ask? A lot of education is motivated by the group status aspect. It’s why you’ll read op-eds saying “this kind of education is useless – replace it with a different kind of education” and never “this branch of education is useless – reduce schooling years/hours.” An uneducated group, state, or nation lowers its status even if it could create more widgets if it sends more of its teenagers into the labor force.

This reminds me of a funny anecdote from work. Apparently there are many managers who use excel spreadsheets for data analysis. Someone had the bright idea of teaching them how to write SQL queries. It went nowhere, as they refused to learn even the most basic “SELECT X From Y where conditions…”, saying it was “code” and they weren’t trained to “code,” Instead, they’d download the whole database into excel and then sort excel rows, often tens of thousands, to do in five minutes what could be done in thirty seconds with a SQL query.

Replies:@ScarletNumber@Alexander TurokAn additional 270 seconds doesn't seem excessive.

@LotI think it’s time we start considering giving up our nuclear arsenal as well. South Africa did the world a great service.

Replies: @J.RossThat “great service” would never have been necessary had they believed in themselves and anyway is soundly refuted by Ice T: we should only give up ours after everybody else gives up theirs.

Replies:@JMcG@J.RossI don’t disagree. But thank God the South Africans don’t have nukes. Imagine what 20 years of democratic administrations and legislatures with all the concomitant effect on the military will do.

The protocol for teaching mathematics to young people evolved from many minds over many years to its current steady state. Leavitt might possibly have a better method.

I would estimate the probability of that at around one in a million.

Most kids pick up basic probability-statistics now from studying the sports analytics pages. Then there’s cards. Probability theory was refined very early to a sophisticated level by men who wanted to succeed at gambling. You do not need to force feed this to young people, unlike stuff like cos (A + B).

No part of this works except that excellent aeronautical engineers were produced by Soviet math education and later helped us.

I’m unable to sort these tea leaves either, but I think what’s being channeled here is the idea that a wunderwaffenkaffeeklatsch at Larry Niven’s house enabled the Reagan administration to call the Red Team bluff about Soviet strength, but that happened after Gorby was in, and it was probably good (not the apocalypse promised by lefties), but not as much of a push to stop pretending to be a superpower and deal with domestic collapse as, say, exploding nuclear reactors.

What is important for us now regarding this episode is that we are now the ones who should stop pretending to be a superpower and who should deal with domestic collapse, before we have an exploding nuclear reactor.

Agree:JMcG@KLBirth control.Replies: @Reg CæsarOnly works for those with the intelligence, discipline, and patience to use it correctly. A bug, not a feature.

Dysgenesis in action.

Replies:@Realist@Reg CæsarThat's the kind of person we need spawning.@RealistMaybe experimental data and you don't have a function?

Replies: @RealistDevelop one.

Replies:@Anon@RealistYou mean interpolate? What would the point of that in a general situation be, if you only care (for whatever reason) about the area under the curve?

@RealistOnly works for those with the intelligence, discipline, and patience to use it correctly. A bug, not a feature.Dysgenesis in action.

Replies: @RealistThat’s the kind of person we need spawning.

As an aside, one will have a very hard time reading the research on machine learning in the absence of a pretty heavy math background. You need tensors, calculus on manifolds, probability theory, measure theory, matrix algebra and a host of other things. The more math the better, in fact.

Even statistics at its higher levels tends to get into measure theory, etc.

Replies:@Bumpkin@jbwilson24It is the opposite: all that math is why machine learning is so useless, as all that mathematical dross simply obscures the unsoundness of ML's fundamental workings.

Personally, I think cursive helps teach children fine motor skills and self-control, although I hated writing in cursive as a kid.

Replies: @nymom, @The Wild Geese Howard, @Joe SchmoeI taught my granddaughter cursive writing one summer and then when she used it in class, she got in trouble with the teacher.

Now she’s in school in New Jersey where I believe they allow it, so I am hoping she remembers enough of what she learned to pick it right up again…

I’ll reraise. Since I can’t remember the last time I used a molecule, chem is out. Also we don’t speak English, certainly not the sort found in any book published before 1964, so let’s replace that with a four year sequence of Ebonics, Spanish, Hindi, and Mandarin. People also like to be disgusting sloths, so we’ll make PE relevant to children’s lives by swapping out sports for competitive eating. Etc, etc.

In real life, I assure you, there is no such thing as algebra.—Fran LebowitzI believe it was in Morris Kline’s

Why Johnny Can't Addwhere Kline said it makes no sense for all schoolchildren to suffer through years of primary and secondary math including algebra and trigonometry when only a small percentage of these students will go on to a college major requiring it. (NB: I’m guessing the percentage going into STEM has changed since he wrote the book in 1973 but still the vast majority of secondary students will never use it again after high school).When you then ask educators why all schoolchildren need to study years of math they will will respond with things like the need to balance a checkbook, etc. But does it really take years of math classes to learn the basic math of everyday life? They will also respond with the outdated idea from Plato and the ancient Greeks that it develops deductive thinking skills. But real life is about 99.9% inductive reasoning.

Replies: @Anon, @AnonYeah, what the fuck did the Greeks know?

Replies: @AnonWell, then they should stop being taught that All x is y is refuted by There is at least one x which is not y. Stupid logic.

Good luck doing any kind of data analysis without knowing algebra. You can’t do Excel formulas on your fingers.

@anonDevelop one.Replies: @AnonYou mean interpolate? What would the point of that in a general situation be, if you only care (for whatever reason) about the area under the curve?

The experiment failed I guess since the book was never published. I did find out he only hire female grad assistants.

Replies: @KibernetikaWhat year was that? There was an MBA student around here who was looking at the potential correlation between golf scores and corporate success. She was stealing data from behind a paywall, essentially. Had to raise an eyebrow like Mr. Spock on that one, heh.

This is why Machine Learning (a sexy name for badly-conducted OLS) is so popular with Yanks, Chinks and dot-heads; they have never even heard of the Gauss-Markov conditions, so they have no fucking idea if their grid-search satisfies them or not (usually: not).

Freakonomics is the epitome of shitty data-trawling. They give quant a bad name, which I take personally because I spent a decade learning how to do it properly.

Replies: @KibernetikaPerhaps 🙂 But now all US universities are scrambling to create new certificate- or degree-track programs related to “Data Science.” It’s more about appearances and semantics than science.

Most data is junk data. What doesn’t often get mentioned is that

much of our research data is simply wrong!Replies:@Kratoklastes@KibernetikaThat's true for a lot of data collected 'in the wild' (especially from surveys), but the primary driver of the Replication Crisis isn't the data so much - it's an ~80/20 mix of corruption and incompetence.Starting with shitty data makes bad outcomes almost a foregone conclusion (to a point) - but if everything started with

perfectdata, that 80/20 blend would generate results that do not withstand statistical scrutiny.Between

publication bias;

post-hoc endpoint selection;

p-hacking;

'genr' of data

Replies: @Kibernetika@DesideriusHis detailed documentation no doubt saved you. :-)

Replies: @DesideriusGood one. He was popular with the line workers he grew up with, so they were pretty much running shit anyway. We muddled through.

Mr. Levitt doesn’t know what he’s talking about. The modern science of big data is highly mathematical. It makes use of functional analysis, harmonic analysis, algebraic topology and algebraic geometry. Many aspects of these techniques are still under development, and are not yet highly modularized and reduced to standard commercial algorithms. But even when they are, one has to have an adequate understanding of how the advanced algorithms based on these areas of mathematics actually work, at least qualitatively, in order to know which ones are appropriate for which datasets. Also, the very idea of teaching data science without either assuming a knowledge of linear algebra, or trying to teach it as part of the basic courses,is inconceivable to me.

Replies:@ScarletNumber@Jim GivenThis is why flowcharts were invented.ad hominem: I bet they both have terrible handwriting and have not fixed anything in a while. (Wasn't it Levitt who joked about having trouble opening a pickle jar?)Calculus and algebra interact with statistics, of course. Yet another guess: someone who knows algebra and/or calculus will do much better at statistics than someone who knows neither.

By coincidence, this week I was searching around for examples of parents who couldn't help their children with their math homework. Most of the examples didn't mention anything other than arithmetics, which I take to mean people, in general, have difficulty with it. They also all put the blame on being taught badly in school, and assured that the thoughts about one just not being a ''math person'' must be wrong. Okay.

Replies: @obwandiyagThe Freakonomics guys are neoliberal shills who already know the conclusion and then scrabble around for “evidence” to back it up. Funny how the conclusion always turns out to be “free market is best.” Every time.

On the other hand, they could serve very well as examples of “Lying with Statistics 101.”

@istevefanI like Ike, he knew how to put math to good use:

https://youtu.be/wnrqUHF5bH8

Replies: @Reg Cæsar, @obwandiyagGod. The Interstates. BLGGGGGGGGGGGSHHTFGDFSKJSDLFH.

Is there anything more awful? If that’s calculus, then to hell with calculus.

@ScarletNumberReplies: @Spangel, @Redneck farmer, @Achmed E. Newman, @obwandiyagYeah. Like on here, where they think “welfare” is a big big big big “problem” because it costs millions– yes, millions–of dollars! And that we would all be rich if they just abolished welfare and refunded the tax money formerly earmarked thereunto.

And they’ll argue like crazy, adding, subtracting, multiplying, even dividing, giving out those good ol’ “proofs” like a house afire, that these lunatic mythical fairy tales they are so attached to are god’s honest truth.

Until a system crash wipes (some / large parts / all) of that data out.

Which is to say that much of the “saved data” today is, not just of questionable value, but extremely fragile.

One can find discussions and just-for-fun calculations of what it would take to completely take down the mighty “Internet.” These are easy to find (ironically?) online.

Say a Tex Kaczynski-esque Bond villain-type emerges, and gets the idea to wipe out the Internet. Say he has a few good teams of globe-trotting, Luddite commandos with which to do it. The idea is it could be done surprisingly easily. In 2012, someone calculated the entire Internet could be ‘housed’ within a single international tanker ship, and of course there are numerous server farms and other chokepoints that would be obvious targets of the Luddite commando teams.

Replies:@Hail@HailOn which, by the way, see a discussion this week on getting Steve Sailer's online writing into print (paper) form (the replies to a comment by Redneck Farmer) --

Which is to say that much of the "saved data" today is, not just of questionable value, but extremely fragile.

One can find discussions and just-for-fun calculations of what it would take to completely take down the mighty "Internet." These are easy to find (ironically?) online.

Say a Tex Kaczynski-esque Bond villain-type emerges, and gets the idea to wipe out the Internet. Say he has a few good teams of globe-trotting, Luddite commandos with which to do it. The idea is it could be done surprisingly easily. In 2012, someone calculated the entire Internet could be 'housed' within a single international tanker ship, and of course there are numerous server farms and other chokepoints that would be obvious targets of the Luddite commando teams.

Replies: @HailOn which, by the way, see a discussion this week on getting Steve Sailer’s online writing into print (paper) form (the replies to a comment by Redneck Farmer) —

@MikeatMikedotMike“Shock” means a sudden change in economic variable, not a surprise, in this context.

Replies: @MikeatMikedotMikeEven so, 9 months isn’t sudden, and poor single mothers are incentivized by increases in income to continue having children out of wedlock. The entire premise is false.

The illegal drug landscape has changed a lot. Opioids are the new crack, but there doesn't seem to have been a big spike in violent crime associated with the so-called "opioid crisis."

Replies: @JMcG, @KronosPeople have pointed out that opioids are depressants, not stimulants. Addicts of the former don’t often rob liquor stores nearly as often as the latter. (Or at least not after ingesting depressants.) Law enforcement and lawmakers realized that Low IQ/High Crime individuals are a lot more stupid on stimulants. Thus the ready public outcry against crack cocaine. The opioid crisis came about like a silent warm blanket, slowly singing a lullaby until it was too late. It became a massive problem for whites, not your typical PITA (Pain In The Ass) demographic.

*Also, here’s Fallout 4. This game allows the player to utilize a drug called “psycho.” Something similar to Meth.

@Counterinsurgency“data” means “that which is given”Surely it's a plural? So '“those which are given” - the singular is "datum".

Replies: @CounterinsurgencyYou can use it that way. You have a set of data, an element of which is a datum. It’s more precise.

You can also us it as “I have a set of data” which becomes in common usage “I have data”. “That” then refers to the set, the collection you are given, not to the individual “data” in the set.

English is (of course) becoming a trade language, losing its own grammatical forms and adopting new borrowed grammatical forms. The subjunctive (“if only it were true” vs. “if only it was true”) is no longer used, “whom” as an object (“to whom” vs. “to who”) was lost back in the 1930s, and “how”, as in “I like how” is used much like spanish “como”. “Me gusta como . . .”.

The data/datum seems to be gradually fading away. Too bad, it is easier to say “We’ll take the third datum in our data” than “We’ll take the third element in our set of data”. OTH, few people say either.

Counterinsurgency

Replies:@PiltdownMan@CounterinsurgencyI notice that, in the last couple of decades, "data point" is the term that people use when they mean "datum." Works fine, imho.

Replies: @CounterinsurgencyDiscrete math is about a lot more than statistics. I breezed through high school calculus. College calculus quickly became considerably more challenging, but I could charge into it with a confidence I never felt in discrete math. The topics we covered in discrete math seemed simple enough, but I remember it being a rather frustrating experience, not least because of all the strange new notation. The only topic I remember enjoying (or at least finding easy) was counting methods (permutations, combinations) and maybe recurrence relations too. I wish I’d paid closer attention to it, because when I’ve flipped through discrete math textbooks more recently, the subject has actually seemed rather interesting to me, but trying to properly learn any of it now would have me pretty much starting from scratch.

Replies:@War for Blair Mountain@silviosilverCombinatorics is no longer a collection of tricks thanks to the late great Gian Carlo Rota....

Inrestingly, a Catholic Nun played a major role in the unification of combinatorics.....Sister Celine......There is a well known book written by an Israelie Discrete Mathematician....the book A=B....devoted to Sister Celines’ theory.....Sister Celine’s work in combinatorics is revolutionary.....So revolutionary that the Israelie’s flew her out of a Catholic Nun Nursing Home in the US to Israel to be honored at a conference of Israelie Mathematicians...The C0nference was devoted to Sister Celine’s Algorithm.....

Replies: @War for Blair MountainGood luck to anyone looking for correlations in “Big Data” who does not know advanced statistics, algebra and some calculus.

@deariemeYou can use it that way. You have a set of data, an element of which is a datum. It's more precise.You can also us it as "I have a set of data" which becomes in common usage "I have data". "That" then refers to the set, the collection you are given, not to the individual "data" in the set.

English is (of course) becoming a trade language, losing its own grammatical forms and adopting new borrowed grammatical forms. The subjunctive ("if only it were true" vs. "if only it was true") is no longer used, "whom" as an object ("to whom" vs. "to who") was lost back in the 1930s, and "how", as in "I like how" is used much like spanish "como". "Me gusta como . . .".

The data/datum seems to be gradually fading away. Too bad, it is easier to say "We'll take the third datum in our data" than "We'll take the third element in our set of data". OTH, few people say either.

Counterinsurgency

Replies: @PiltdownManI notice that, in the last couple of decades, “data point” is the term that people use when they mean “datum.” Works fine, imho.

Replies:@Counterinsurgency@PiltdownMan"Data point" is a pretty clear metaphor for a point on a 2D plot, or (generalized) for a particular element in an set of n dimensional points. A bit redundant, but a good usage because it's clear, an extension of: "A point in the plot of a 2D or 3D data set."Thanks!

Counterinsurgency

@Achmed E. NewmanFunny, when I learned calculus in the ’70s, that is how we empirically confirmed our integration.

@SpangelI think we'd be better off as a society if more people knew and genuinely mastered calculus, simply because calculus is cool and is worth knowing. Why do we still appreciate Beethoven or Virgil? It is no less beautiful. It enrichens your mind to understand how the world works: if you are religious, you can think of it as understanding God's programming.

(And yeah: having a wider pool of potential scientists and engineers is always good. Beats having more lawyers, that's for sure.)

But I'm also aware that most people are not going to practically apply calculus in their daily lives. So, no, it shouldn't be forced on everybody, and we certainly shouldn't make calculus a prerequisite for things like statistics that really do need to be mastered by the overwhelming majority of the populace.

>(*this is the kind of course they offer to college interns at major corporations).

Replies: @Spangel, @The Germ Theory of Disease“Why do we still appreciate Beethoven or Virgil? It is no less beautiful.”

Ahem.

While I’m sure your points about calculus stand, we do have to clarify here.

Mozart is beautiful. Schumann is beautiful. Wagner is beautiful. Beethoven is merely… interesting.

Similarly, Virgil is not beautiful, he is merely sturdy (which in itself is still a very valuable thing). Homer is beautiful. Catullus is beautiful, in a weird sort of way (just not the zany long stuff).

Throwing a mat of firecrackers into a room full of nerds is not, in itself, beautiful… but it might have beautiful results.

Replies:@Ian M.@The Germ Theory of DiseaseTo quote our host: "Okaaaay …"Replies: @The Germ Theory of DiseaseEven statistics at its higher levels tends to get into measure theory, etc.

Replies: @BumpkinIt is the opposite: all that math is why machine learning is so useless, as all that mathematical dross simply obscures the unsoundness of ML’s fundamental workings.

@Steve SailerIf your father knew calculus...why go to all the trouble?Replies: @anon, @astrolabeSufficiently complicated functions are difficult or impossible to integrate to closed form.

Replies:@The Wild Geese Howard@astrolabeCorrect.Sometimes it is possible to treat a complex function in a piecewise way that closely approximates the original function with a set of simpler subfunctions that

arepossible to integrate.Replies: @Anon@astrolabeRisch Algorithm....Liouville Principle......

@Achmed E. NewmanThere is an old story about Thomas Edison welcoming a new, young scientist to the famous R&D laboratory:

Mr. Edison handed the new researcher an empty light bulb and told him to find the volume inside.

The y0ung man, probably a fresh science graduate from a great university, proceeded to measure every part of the bulb and then perform calculations. The top approximated a sphere, so he found that volume; the bottom part was similar to a cylinder, so he did that; in between was a curve that perhaps calculus could be applied to… etc…

While the lad was busy with his pencil and paper, Edison picked up the glass bulb, filled it with water, then poured the water into a graduated cylinder and measured the amount of water and thus the volume inside the bulb.

He was teaching the young man a lesson, and not just one about measuring volume.

Replies:@Joe Stalin@Buzz MohawkPretty cool 1940s GE film on how Americans considered research and manufacture of the apparently lowly light bulb was actually pretty neat and useful.

https://www.youtube.com/watch?v=hRxcJH7tKck

Levitt is the second credited author of this op piece. Who is Jo Boaler, the lead? She has a PhD in mathematics education (not to be confused with a PhD in mathematics), gotten after a career as a high school math teacher in the UK.

Her main thing is math equity, not quite to the Seattle Public Schools level of craziness, but not too far from it. She seems to think that girls should be doing better in math than boys.

Never criticize girls doing math!

She’s into “growth mindset,” which seems like the converse of stereotype threat: girls just need to be more psyched into thinking they’re good at math.

She promotes group math, where no individual is held responsible for anything. This is a common theme in equity education reforms into the university level. It’s an easy way to narrow the gap and obfuscate abtilities when assigning grades, since group members all get the group grade. As long as the teach makes sure to put an Asian or Jewish or white guy in the group, everything is hunky dory.

The idea that some kids are better at math than others, and the kids who aren’t cut out for it tend to know it, just infuriates her.

Replies:@Achmed E. Newman@AnonI can't believe WTF goes on in school now, as I just (5 minutes ago) ran into a computer-based reading comprehension program that was going political in a hurry. This is for 2nd to 4th graders. I think we will terminate this program with prejudice and make more trips to the library. Then, there's:

Seriously? I don't think even John Derbyshire talks like this, does he? He's British too and an actual mathematician.I would think if you're not smart enough to learn algebra by 8th or 9th grade, then as an adult you likely won't be using or retaining any math besides arithmetic anyway so it's a moot point what they teach you. That still leaves smart people 3-4 years of HS to learn other things.

Stats is probably more important than geometry, trig, and calculus for non-STEM people. I retained basically nothing from trig or geometry except the formula for area of a circle, which I use to compare the value of different deals when ordering pizza (yeah, I'm that guy). I've never heard a cosine used out in the real world.

Terms like "second derivative" do come up sometimes when growth is discussed, but I imagine a smartish person could grok the idea of "rate of change of rate of change" in 15 seconds without needing to learn calc.

The vast majority of people, even intelligent people, don't really perform statistical analysis but they at least need to know how to interpret and question stats that someone else put together.

Replies: @Anon, @PericlesThough it’s like the argument there’s no need to learn facts when you can just look stuff up on Wikipedia. Yes, but your understanding will be shallow and slow.

That seems like it’s a far way off. My experience is even STEM practitioners aren’t all that hot with statistics, let alone experimental design and all that. (I’m not either.) Any insightful

questioningof stats without having even done the subject yourself seems even further off.Replies:@Wency@PericlesThe way I'm describing it, you don't need an especially deep understanding (not that I believe getting an A in a HS calc class gives you a deep understanding). You just need to know the term "second derivative" so you can follow a conversation and not be embarrassed.

As for stats, a decent stats class (and my HS stats class did this) will teach you to look for sources of bias. To think about things like GIGO. To understand skew, outliers, and when mean and median are more or less meaningful. Yeah, I know academic papers might go a lot deeper on stats, but very people are exposed to academic papers. They're just looking at surveys or other basic summaries of business data.

Replies: @Desiderius, @nebulafox, @PericlesBut that would be racist.

Replies:@ScarletNumber@PericlesI have no issues with being called racist.

I’ll spend my last comment of the hour on this: Tools like Mathematica and Wolfram Alpha can already automatically do basically all the formula manipulation you need to do in high school or even college (and can also provide a lot of nifty stats and data in the process).

Have a look here for instance: https://www.wolframalpha.com/

The question is, if we switch to using programs instead of doing mathematics by hand, will students still attain sufficient mathematical sophistication? Or is it enough that they learn how to wrestle the program until it ‘solves the problem’ for them?

Oh boy. He obviously has not thought through the ramifications this would have for racial grievances and the voodoo shenanigans of “disparate impacts” in employment, incarceration, etc.

If, for example, everyone were able to understand just because a lot of Negroes are in jail for murder, it does not mean they were jailed because they are Negroes (but that, rather, it is because they are – wait for it… – murderers), well, that’ll spoil the racket for everyone.

And maybe, just maybe, Negroes are not often engineers, scientists, and mathematicians not because of a vast conspiracy to crush their dreams and discredit their innumerable contributions to such work account of they are Negroes. Maybe instead it’s account of they are seldom any good at maths.

Black Twitter, do your thang.

There is no simple answer to these questions. Personally, I’ve found many areas of discrete mathematics to be much, much more difficult than calculus. No need to go into further details.

As for data science, it is sexed-up statistics. An acquaintance of mine switched to data science when she was working as post doc in physics (gravity) in the Netherlands. It offered a more dynamic & interesting life (market, travels, communication with people, money ..) in comparison with what academic life could offer.

But, I don’t think that any sci field has much to do with critical thinking, which is something rare, very rare.

Didn’t Bill Gate spend several million dollars lobbying the State of California to make Algebra II mandatory for high school graduation? Didn’t that have the effect of watering down the course requirements so that “math challenged” populations could graduate from high school?

Replies:@ScarletNumber@FPD72Yes and yes. If teachers held the same standards for Algebra II before and after it was a graduation requirement, then the failure rate would have skyrocketed. As any teacher can tell you, if too much students fail, it is not considered the students' fault, it is considered the teacher's fault. So the poor teacher has two choices:

1) Perform a miracle and get all of the new students up to the old standard

2) Lower the standard

Replies: @El DatoWhy not use both depending on what you do.

https://plato.stanford.edu/entries/probability-interpret/

The fun is that the same numbers and the same formulas are used for describing objective facts and describing subjective beliefs, sometimes in the same line. Maybe there should be mandatory color coding.

Anyway, “frequentism” is a self-defeating circular idea (it wants to define the frequency only for processes that actually exist, but then needs to assume that said process run infinitely long to make sense of the frequency, but infinitely-long processes don’t exist … head explodes!!). Break out of the brainlock, assume Kolomogorov’s axioms as prior, then be done with it. We assume Causality also as prior, it’s just the way it works.

Replies:@Kronos@El DatoI’ve been a fan of this book.

https://www.amazon.com/Uncertainty-Soul-Modeling-Probability-Statistics/dp/3319397559/

It makes a superb case for Objective Bayesianism. Also, paints the Bayes Factor as rubbish akin to various Frequentist techniques.

Data science? maybe, but you need real data. Good data always turns out to be hard. But you know that

By the way, no one is good at classical statistics. NHST is nonsense.

Replies: @El DatoSays anon on the Internet.

(It’s the only thing we have. Deal with it!)

Well, actually there is this now:

Causal inference in statistics: An overview — Judea Pearl

https://ftp.cs.ucla.edu/pub/stat_ser/r350.pdf

Still gotta read…

@KLAlgebra 2 including matrices is essential to understanding how to dissect and address data sets. Data analysis without an understanding of the base maths would be like modern medicine without a grasp of chemistry.

Replies: @Jim bob LassiterDo you think all those doctors from St. Georges Univ. Medical Skoo in Grenada have a grasp of chemistry?

https://degrees.sgu.edu/us/md?&utm_source=google&utm_medium=cpc&utm_term=%2Bst+%2Bgeorges+%2Bmed+%2Bschool+%2Bgrenada&utm_content=St+George+GeoModified_BMM&utm_campaign=Brand_Longtail_BMM&gclid=EAIaIQobChMIgqLr7_255QIViZWzCh33wAoKEAAYASAAEgLHsPD_BwE&gclsrc=aw.ds

Replies: @War for Blair MountainCombinatorics is no longer a collection of tricks thanks to the late great Gian Carlo Rota….

Inrestingly, a Catholic Nun played a major role in the unification of combinatorics…..Sister Celine……There is a well known book written by an Israelie Discrete Mathematician….the book A=B….devoted to Sister Celines’ theory…..Sister Celine’s work in combinatorics is revolutionary…..So revolutionary that the Israelie’s flew her out of a Catholic Nun Nursing Home in the US to Israel to be honored at a conference of Israelie Mathematicians…The C0nference was devoted to Sister Celine’s Algorithm…..

Replies:@War for Blair Mountain@War for Blair MountainTo make a long story short:Hopf Algebras are the fundamental unifying structure of combinatorics....And Hopf Algebras have their origin topology.....But you won’t learn about this in a Computer Science Discrete Math course...even though Hopf Algebras are just below the surface....

I just made this post with TRAIN IN VAIN in the background......I have no idea if there is any Cosmic Significance to this...But I wait in vain for the Humpback Whales to show up......I’d even settle for a Pygmy Sperm Whale......

Maybe “Freakonomics” podcast listeners aren’t as mathematically sophisticated as Levitt assumes.

@Achmed E. NewmanOr you could use a planimeter. Draftsmen had been using them for decades.

I stumbled upon a very interesting book in a used bookstore once. It was called “Graphical Solutions to Civil Engineering Problems”, published sometime back in the early 1900’s. In it, loads, center of effort, moments of inertia etc. were computed by projecting vectors and then calculating the areas of the resulting triangles.

It looks as though these techniques are experiencing a renaissance.

@CounterinsurgencyI notice that, in the last couple of decades, "data point" is the term that people use when they mean "datum." Works fine, imho.

Replies: @Counterinsurgency“Data point” is a pretty clear metaphor for a point on a 2D plot, or (generalized) for a particular element in an set of n dimensional points. A bit redundant, but a good usage because it’s clear, an extension of: “A point in the plot of a 2D or 3D data set.”

Thanks!

Counterinsurgency

Replies: @ScarletNumberAn additional 270 seconds doesn’t seem excessive.

Replies: @ScarletNumberThis is why flowcharts were invented.

For some reason, math people are extremely bothered by the fact that most people consider what they do to be irrelevant to their daily lives. Please believe me when I tell you, most people are living completely happy and productive lives without knowing anything they were ever taught in Algebra II or Trigonometry. If for some reason they need one particular fact or skill from those courses in their careers, it can be taught on an ad hoc basis.

A short comment on statistical versus mathematical modelling

https://www.nature.com/articles/s41467-019-11865-8

@silviosilverCombinatorics is no longer a collection of tricks thanks to the late great Gian Carlo Rota....

Inrestingly, a Catholic Nun played a major role in the unification of combinatorics.....Sister Celine......There is a well known book written by an Israelie Discrete Mathematician....the book A=B....devoted to Sister Celines’ theory.....Sister Celine’s work in combinatorics is revolutionary.....So revolutionary that the Israelie’s flew her out of a Catholic Nun Nursing Home in the US to Israel to be honored at a conference of Israelie Mathematicians...The C0nference was devoted to Sister Celine’s Algorithm.....

Replies: @War for Blair MountainTo make a long story short:Hopf Algebras are the fundamental unifying structure of combinatorics….And Hopf Algebras have their origin topology…..But you won’t learn about this in a Computer Science Discrete Math course…even though Hopf Algebras are just below the surface….

I just made this post with TRAIN IN VAIN in the background……I have no idea if there is any Cosmic Significance to this…But I wait in vain for the Humpback Whales to show up……I’d even settle for a Pygmy Sperm Whale……

Someone had an idea to train our weapons' operators how to do calculations with pencil and paper. This created a situation where the enemy computers could not anticipate results. We won the war. Why it worked may have been explained. I do not remember. Likely the occasional human error created a factor the alien machines could not anticipate.

We might want to keep the ability in case the Klingons show up. Domestic or foreign.

Replies: @Redneck farmer, @Seneca44Isaac Asimov, “The Accountant”. A war between Earth and Mars, both sides using missiles. BMD has caused a stalemate. An accountant has rediscovered doing math by hand, so his boss invites the military to take a look.

“I predict one day Earth will deploy the manned bomber!”

Replies:@John Henry@Redneck farmerSuper! Thank you.

Her main thing is math equity, not quite to the Seattle Public Schools level of craziness, but not too far from it. She seems to think that girls should be doing better in math than boys.

Never criticize girls doing math! She’s into “growth mindset,” which seems like the converse of stereotype threat: girls just need to be more psyched into thinking they’re good at math.

She promotes group math, where no individual is held responsible for anything. This is a common theme in equity education reforms into the university level. It’s an easy way to narrow the gap and obfuscate abtilities when assigning grades, since group members all get the group grade. As long as the teach makes sure to put an Asian or Jewish or white guy in the group, everything is hunky dory.

The idea that some kids are better at math than others, and the kids who aren’t cut out for it tend to know it, just infuriates her.

Replies: @Achmed E. NewmanI can’t believe WTF goes on in school now, as I just (5 minutes ago) ran into a computer-based reading comprehension program that was going political in a hurry. This is for 2nd to 4th graders. I think we will terminate this program with prejudice and make more trips to the library. Then, there’s:

Seriously? I don’t think even John Derbyshire talks like this, does he? He’s British too and an actual mathematician.

Replies: @ScarletNumberYes and yes. If teachers held the same standards for Algebra II before and after it was a graduation requirement, then the failure rate would have skyrocketed. As any teacher can tell you, if too much students fail, it is not considered the students’ fault, it is considered the teacher’s fault. So the poor teacher has two choices:

1) Perform a miracle and get all of the new students up to the old standard

2) Lower the standard

@ScarletNumberBut that would be racist.Replies: @ScarletNumberI have no issues with being called racist.

@JMcGThat "great service" would never have been necessary had they believed in themselves and anyway is soundly refuted by Ice T: we should only give up ours after everybody else gives up theirs.

Replies: @JMcGI don’t disagree. But thank God the South Africans don’t have nukes. Imagine what 20 years of democratic administrations and legislatures with all the concomitant effect on the military will do.

Personally, I think cursive helps teach children fine motor skills and self-control, although I hated writing in cursive as a kid.

Replies: @nymom, @The Wild Geese Howard, @Joe SchmoeWriting and doing arithmetic by hand develops a level of intuition that it is not possible to reach using computers and calculators.

I feel my own intuitive grasp of higher-level math was damaged by the ready availability and use of graphing calculators in the mid-90s.

Cursive is relevant because it is far and away the easiest, most efficient, and swiftest means of hand writing. It is not humanly possible to print or block letter nearly as fast as one can write in cursive.

@KratoklastesPerhaps :) But now all US universities are scrambling to create new certificate- or degree-track programs related to "Data Science." It's more about appearances and semantics than science.

Most data is junk data. What doesn't often get mentioned is that

much of our research data is simply wrong!Replies: @KratoklastesThat’s true for a lot of data collected ‘in the wild’ (especially from surveys), but the primary driver of the Replication Crisis isn’t the data so much – it’s an ~80/20 mix of corruption and incompetence.

Starting with shitty data makes bad outcomes almost a foregone conclusion (to a point) – but if everything started with

perfectdata, that 80/20 blend would generate results that do not withstand statistical scrutiny.Between

publication bias;

post-hoc endpoint selection;

p-hacking;

‘genr’ of data

Replies:@Kibernetika@KratoklastesThat’s true for a lot of data collected ‘in the wild’ (especially from surveys), but the primary driver of the Replication Crisis isn’t the data so much – it’s an ~80/20 mix of corruption and incompetence.It's shocking to learn about the incompetence of some labs. Ultimately the errors are found, but what a waste of effort and churn simply because a lab tech or postdoc mis-labelled something or contaminated a sample. And that's just the lab work. Finding distinctive human female microbiome stuff with a fish or tree genome is weird.

Next comes the software drama ;) So many models, so many results.

@RealistSufficiently complicated functions are difficult or impossible to integrate to closed form.

Replies: @The Wild Geese Howard, @War for Blair MountainCorrect.

Sometimes it is possible to treat a complex function in a piecewise way that closely approximates the original function with a set of simpler subfunctions that

arepossible to integrate.Replies:@Anon@The Wild Geese HowardIf the complex (I'm going to assume this means complicated, I'm rusty on complex analysis) function is theoretically integrable at all (I mean that the limit exists, not that a closed form for it exists), isn't this always possible?

Replies: @The Wild Geese Howard@NoWeltschmerzReplies: @Anon, @The Practical Conservative, @Bill, @NoWeltschmerzYou must lack imagination. In general, excellent job of missing my point. Well done. Perhaps you are a graduate of one of these not-so rigorous programs and therefore exemplify the point I was making.

Data science is “sexy” and in demand so yes there are hastily produced programs that attempt to confer credentials on people looking to be data scientists. So what? Since you say “dozens and dozens” of programs would you care to list 24? I would love to see them and evaluate the programs (I won’t hold my breath waiting for your response). I actually hire data scientists and machine learning engineers (MLEs), do you? I can tell you that my screen involves math and stats question and failure to answer them means you don’t get hired. I don’t work for a research institution or a think tank, but we know through actual research that people who can use Excel, SAS, SPSS, Python or R, but have no grounding in stats are of limited value as data scientists. I have somewhat less rigorous standards for MLEs, but I do expect them to know statistics to a reasonable degree.

There are lots of companies who still don’t understand what data science is and are willing to call report writers or data analysts data scientists, but those who know better only hire people with a good grounding in those subjects I mentioned in my previous post. The reason for this, as I implied earlier, is not because data scientists are solving equations by hand on a daily basis, but instead because lots of decisions when building and evaluating models require a through grounding in math and mathematical statistics. Data science is applied statistics with some additional specialized knowledge thrown in.

If you are ones of those benefiting from the demand for data science and the ignorance of many on what constitutes data science, I would suggest you either bite the bullet and learn your math and stats before you get found out or move into a position where your lack of analytical rigor won’t matter.

Replies:@Spangel@NoWeltschmerz"There are lots of companies who still don’t understand what data science is and are willing to call report writers or data analysts data scientists, but those who know better "

And there lies the crux of the matter. Even among people who are being hired and credentialed as "data scientsits", not all- seriously not even most of them- have a strong background in mathematics. And this is actual professional data scientists. Tells you how few people actually really need the strong foundation in calculus to do their jobs.

Lets go back to the matter at hand. For college bound kids, there are three AP math classes offered- AP stats, AP calc AB and AP calc BC. Of those classes, AP calc AB appears to be the most common. It is also the most useless. Useless to the point where it probably should not even exist. calc AB is not a pre req for calc BC though plenty take both classes.

calc AB is basically calculus for people who are not particularly good at math. Everyone who has a strong interest in a quant career should take and must be able to pass calc BC in order to be any good. Plenty of students who pass AB would not pass BC (pass means getting a 3 or higher on the AP test). If you cannot get a 3 or higher on calc BC, you will never be a person who is capable of using calculus in your work, whether as a data scientist or engineer or anything.

What happens right now in high school is that students take geo/trig, algebra 2 and then calc AB if they want to be a lawyer, doctor or consultant or liberal arts major at a selective school etc. They take calc BC if they want to become an engineer or computer scientist etc.

But essentially everyone taking calc AB shouldn't need calculus at all. Instead what they should understand is basic stats. AP stats also does not depend on knowing calculus. It just introduces basic concepts such as the bell curve, skew, outlier, lurking variable, correlation, p value, power, variance, standard deviation etc. As it stands, most high schoolers graduate without exposure to any of those concepts because they take calculus or the path to get to calculus. So you have millions of americans who daily encounter information about studies saying this or that or achievement gaps etc, and they have no background in even the definition of the terms they are reading.

Someone had an idea to train our weapons' operators how to do calculations with pencil and paper. This created a situation where the enemy computers could not anticipate results. We won the war. Why it worked may have been explained. I do not remember. Likely the occasional human error created a factor the alien machines could not anticipate.

We might want to keep the ability in case the Klingons show up. Domestic or foreign.

Replies: @Redneck farmer, @Seneca44…or EMP fries everything electronic. Advanced math makes one better at basic math and a more numerate country/planet might give some sanity to multi trillion $ deficits with fiat currency. Casual observation of what occurs in US high schools leads me to conclude that the students aren’t doing anything more important with their time.

Replies: @nymom, @The Wild Geese Howard, @Joe SchmoeMy son could not seem to learn to print. I had heard that cursive is easier, and I was frustrated with his bad handwriting, so I taught him cursive. He learned it pretty easily and used it exclusively. When he was in seventh grade, he was embarrassed that he could not print and taught himself. His printing wasn’t great, but it was okay. He still writes pretty much everything in cursive because printing is still difficult for him. Nowadays everyone just types everything, so it isn’t a big deal for most people. Personally, I think teaching cursive is a lot more worthwhile than much of the crap they have added to the curriculum and waste children’s time going on about.

Excel is not ‘analytical software’ (basic or otherwise): it’s a toy whose only valid use is to store data (and it does

thatinefficiently). Using it for calculations (beyond summation) is the province of retards.It doesn’t even do Bessel Correction consistently in its default settings for

stdev() andcovar() – despite knowing the number of observations on hand.If you have to check your output against a proper piece of analytical software – and with Excel, you

dohave to – then it’s not even clear what part of workflow is being filled by Excel.It also still has this ‘feature’ whereby it thinks you’re a fuckwit, and so

itshould select the datatype of incoming numerical data (unless you go through the laborious process of defining every new data import). Even MATLAB doesn’t do that, and MATLAB’s pretty awful.Excel’s profound flaws fucked up over decade of work in bioinformatics (see, e.g., Zeeberg et al (2004); Ziemann et al., (2016)).

And as is made clear in the Zeeberg paper, the problem went unnoticed for several years; worse, it is mathematically irreversible – you cannot generally recover the correct gene identifer from the Excel value.

And even

more worser: it contaminated major public data repositories, and it’s unknown how much of the literature was affected.And it’s not like this was not foreseeable. As long ago as the late 1990s (when Excel as we know it supplanted Lotus 1-2-3, and WYSIWYG became a thing), econometrics students at my

alma materwere specifically prohibited from using Excel for data analysis of any type (even exploratory analysis). We had to useTSPorSHAZAM– both of which were non-GUI at the time; for grad subjects SAS, Stata, or R (which was relatively new). Things were less formal in the workplace, but Excel was not trusted (we were the place that developed GEMPACK – also non-GUI).No professional should use Excel for

anything. If it’s part of anyone’s daily workflow, then their enterprise has malinvested in general-purpose analytical tools.There is no excuse – if your data is tabular, store it in a fucking .Rda or .pickle, or in SQL.

.

.

It’s no surprise that Freakonomics listeners will be Excel users, or that Freaksonomics thought that identifying Excel users was a useful thing to do. That’s a handy basic indicator of

low-level numeracy (and statistical incompetence)..

.

This is a fresh scar for me: I’m just finishing up migrating a mutual-fund analysis and testing framework, from a set of interconnected Excel sheets (for data) and MATLAB (for processing), to a Python/R/SQLite framework.

Seriously – fuck Excel.

Ziemann M, Yotam Eren & Assam El-Osta (2016) “

Gene name errors are widespread in the scientific literature“,Genome Biologyvolume 17, Article number: 177Zeeberg BR, Riss J, Kane DW, Bussey KJ, Uchio E, Linehan WM, Barrett JC, Weinstein JN. (2004) , “

Mistaken Identifiers: Gene name errors can be introduced inadvertently when using Excel in bioinformatics“,BMC Bioinformaticsvolume 5, Article number: 80@RealistSufficiently complicated functions are difficult or impossible to integrate to closed form.

Replies: @The Wild Geese Howard, @War for Blair MountainRisch Algorithm….Liouville Principle……

Algebra is fundamental to all areas of math. Of course you should learn it. Knowing how to manipulate symbols per rules has broad applicability.

@astrolabeCorrect.Sometimes it is possible to treat a complex function in a piecewise way that closely approximates the original function with a set of simpler subfunctions that

arepossible to integrate.Replies: @AnonIf the complex (I’m going to assume this means complicated, I’m rusty on complex analysis) function is theoretically integrable at all (I mean that the limit exists, not that a closed form for it exists), isn’t this always possible?

Replies:@The Wild Geese Howard@AnonYes, your point is correct.

Whether or not one would break such an integrable complex function into simpler subfunctions becomes a question of time and effort - i.e. is it simpler to do the breakdown or just work the original function?

A lot of people who call themselves data scientists are not scientists. Rather, they’re people who know how to write SQL queries to get data out of a database. That’s good and all, but it’s not science. Given that this is what data science is, Math beyond algebra 1 is not necessary.

@KronosWhy not use both depending on what you do.

https://plato.stanford.edu/entries/probability-interpret/

The fun is that the same numbers and the same formulas are used for describing objective facts and describing subjective beliefs, sometimes in the same line. Maybe there should be mandatory color coding.

Anyway, "frequentism" is a self-defeating circular idea (it wants to define the frequency only for processes that actually exist, but then needs to assume that said process run infinitely long to make sense of the frequency, but infinitely-long processes don't exist ... head explodes!!). Break out of the brainlock, assume Kolomogorov's axioms as prior, then be done with it. We assume Causality also as prior, it's just the way it works.

Replies: @KronosI’ve been a fan of this book.

It makes a superb case for Objective Bayesianism. Also, paints the Bayes Factor as rubbish akin to various Frequentist techniques.

@nebulafox"Why do we still appreciate Beethoven or Virgil? It is no less beautiful."

Ahem.

While I'm sure your points about calculus stand, we do have to clarify here.

Mozart is beautiful. Schumann is beautiful. Wagner is beautiful. Beethoven is merely... interesting.

Similarly, Virgil is not beautiful, he is merely sturdy (which in itself is still a very valuable thing). Homer is beautiful. Catullus is beautiful, in a weird sort of way (just not the zany long stuff).

Throwing a mat of firecrackers into a room full of nerds is not, in itself, beautiful... but it might have beautiful results.

Replies: @Ian M.To quote our host: “Okaaaay …”

Replies:@The Germ Theory of Disease@Ian M.Well, I suppose I can sympathize. Unfortunately, it isn't a proper bar-room brawl, if only one other nerd shows up to do the brawling. What are the two of us nerds going to do, throw dishes of cornichons at each other?

Guess we'll just have to wait for something that sparks up more nerdish blood... say, maybe, Shirley Jackson versus HP Lovecraft?

First round's on me.

I think Levitt’s idea is silly, but how about this for another ‘radical’ change in math education: teach geometry before algebra.

https://thomism.wordpress.com/2018/03/07/no-algebra-till-junior-year/

Levitt takes the typical soulless, androgynous, technocratic, utilitarian approach to education: that it has to be

practicalfor it to be worth doing.But that was never the reason for learning calculus in high school. The point is that some things are worth knowing for their own sake. Mathematics reveals to us an aspect of truth, and the truth is always worth knowing.

Most of the things we learn in high school are not ‘useful’. Who uses chemistry, or Shakespeare, or his knowledge of the Civil War in his daily life? The very question underscores how silly it is to regard formal secondary education as primarily practical. That’s not the point.

Of course, that’s not to say that every last teenager should learn these things. High school subjects such as these should be reserved for those who have an aptitude for learning, for those who desire to learn higher truths. The majority of children should be done with formal education by around fifth grade, enough to learn the basics of reading, writing, arithmetic, and some basic U.S. and Western history (and ideally, the true religion). After that, it should be training in some sort of trade for most.

The Bostonians, Henry James@The Germ Theory of DiseaseTo quote our host: "Okaaaay …"Replies: @The Germ Theory of DiseaseWell, I suppose I can sympathize. Unfortunately, it isn’t a proper bar-room brawl, if only one other nerd shows up to do the brawling. What are the two of us nerds going to do, throw dishes of cornichons at each other?

Guess we’ll just have to wait for something that sparks up more nerdish blood… say, maybe, Shirley Jackson versus HP Lovecraft?

First round’s on me.

LOL:Ian M.I don't even remember where to begin to solve a differential equation now. I'm an engineer but I've never used it at all.

I should have taken more chemistry.

Replies: @Alan MercerI’m well tired of engineers bragging of their incompetence.

Hard Rock collapse

FIU bridge collapse

@The Wild Geese HowardIf the complex (I'm going to assume this means complicated, I'm rusty on complex analysis) function is theoretically integrable at all (I mean that the limit exists, not that a closed form for it exists), isn't this always possible?

Replies: @The Wild Geese HowardYes, your point is correct.

Whether or not one would break such an integrable complex function into simpler subfunctions becomes a question of time and effort – i.e. is it simpler to do the breakdown or just work the original function?

@SpangelYou must lack imagination. In general, excellent job of missing my point. Well done. Perhaps you are a graduate of one of these not-so rigorous programs and therefore exemplify the point I was making.

Data science is "sexy" and in demand so yes there are hastily produced programs that attempt to confer credentials on people looking to be data scientists. So what? Since you say "dozens and dozens" of programs would you care to list 24? I would love to see them and evaluate the programs (I won't hold my breath waiting for your response). I actually hire data scientists and machine learning engineers (MLEs), do you? I can tell you that my screen involves math and stats question and failure to answer them means you don't get hired. I don't work for a research institution or a think tank, but we know through actual research that people who can use Excel, SAS, SPSS, Python or R, but have no grounding in stats are of limited value as data scientists. I have somewhat less rigorous standards for MLEs, but I do expect them to know statistics to a reasonable degree.

There are lots of companies who still don't understand what data science is and are willing to call report writers or data analysts data scientists, but those who know better only hire people with a good grounding in those subjects I mentioned in my previous post. The reason for this, as I implied earlier, is not because data scientists are solving equations by hand on a daily basis, but instead because lots of decisions when building and evaluating models require a through grounding in math and mathematical statistics. Data science is applied statistics with some additional specialized knowledge thrown in.

If you are ones of those benefiting from the demand for data science and the ignorance of many on what constitutes data science, I would suggest you either bite the bullet and learn your math and stats before you get found out or move into a position where your lack of analytical rigor won't matter.

Replies: @Spangel“There are lots of companies who still don’t understand what data science is and are willing to call report writers or data analysts data scientists, but those who know better ”

And there lies the crux of the matter. Even among people who are being hired and credentialed as “data scientsits”, not all- seriously not even most of them- have a strong background in mathematics. And this is actual professional data scientists. Tells you how few people actually really need the strong foundation in calculus to do their jobs.

Lets go back to the matter at hand. For college bound kids, there are three AP math classes offered- AP stats, AP calc AB and AP calc BC. Of those classes, AP calc AB appears to be the most common. It is also the most useless. Useless to the point where it probably should not even exist. calc AB is not a pre req for calc BC though plenty take both classes.

calc AB is basically calculus for people who are not particularly good at math. Everyone who has a strong interest in a quant career should take and must be able to pass calc BC in order to be any good. Plenty of students who pass AB would not pass BC (pass means getting a 3 or higher on the AP test). If you cannot get a 3 or higher on calc BC, you will never be a person who is capable of using calculus in your work, whether as a data scientist or engineer or anything.

What happens right now in high school is that students take geo/trig, algebra 2 and then calc AB if they want to be a lawyer, doctor or consultant or liberal arts major at a selective school etc. They take calc BC if they want to become an engineer or computer scientist etc.

But essentially everyone taking calc AB shouldn’t need calculus at all. Instead what they should understand is basic stats. AP stats also does not depend on knowing calculus. It just introduces basic concepts such as the bell curve, skew, outlier, lurking variable, correlation, p value, power, variance, standard deviation etc. As it stands, most high schoolers graduate without exposure to any of those concepts because they take calculus or the path to get to calculus. So you have millions of americans who daily encounter information about studies saying this or that or achievement gaps etc, and they have no background in even the definition of the terms they are reading.

@WencyTo compare prices, you don't need to know the area of a circle, just that it's proportional to the square of the diameter, radius, or circumference.

Replies: @WencyThis is true, unless you’re comparing square and circular pizzas. Some places offer both.

Replies:@Anon@WencySquare "Sicilian" pies are usually deeper, though, so you have to compute the volume. On the other hand, the dough/tomato-sauce ratio may be different for a Sicilian or a round "Neapolitan" pie, in which case you have an optimization decision to make.

@WencyThough it's like the argument there's no need to learn facts when you can just look stuff up on Wikipedia. Yes, but your understanding will be shallow and slow. That seems like it's a far way off. My experience is even STEM practitioners aren't all that hot with statistics, let alone experimental design and all that. (I'm not either.) Any insightfulquestioningof stats without having even done the subject yourself seems even further off.Replies: @WencyThe way I’m describing it, you don’t need an especially deep understanding (not that I believe getting an A in a HS calc class gives you a deep understanding). You just need to know the term “second derivative” so you can follow a conversation and not be embarrassed.

As for stats, a decent stats class (and my HS stats class did this) will teach you to look for sources of bias. To think about things like GIGO. To understand skew, outliers, and when mean and median are more or less meaningful. Yeah, I know academic papers might go a lot deeper on stats, but very people are exposed to academic papers. They’re just looking at surveys or other basic summaries of business data.

@John HenryIsaac Asimov, "The Accountant". A war between Earth and Mars, both sides using missiles. BMD has caused a stalemate. An accountant has rediscovered doing math by hand, so his boss invites the military to take a look.

"I predict one day Earth will deploy the manned bomber!"

Replies: @John HenrySuper! Thank you.

@Steve SailerThere is an old story about Thomas Edison welcoming a new, young scientist to the famous R&D laboratory:

Mr. Edison handed the new researcher an empty light bulb and told him to find the volume inside.

The y0ung man, probably a fresh science graduate from a great university, proceeded to measure every part of the bulb and then perform calculations. The top approximated a sphere, so he found that volume; the bottom part was similar to a cylinder, so he did that; in between was a curve that perhaps calculus could be applied to... etc...

While the lad was busy with his pencil and paper, Edison picked up the glass bulb, filled it with water, then poured the water into a graduated cylinder and measured the amount of water and thus the volume inside the bulb.

He was teaching the young man a lesson, and not just one about measuring volume.

Replies: @Joe StalinPretty cool 1940s GE film on how Americans considered research and manufacture of the apparently lowly light bulb was actually pretty neat and useful.

@KibernetikaThat's true for a lot of data collected 'in the wild' (especially from surveys), but the primary driver of the Replication Crisis isn't the data so much - it's an ~80/20 mix of corruption and incompetence.Starting with shitty data makes bad outcomes almost a foregone conclusion (to a point) - but if everything started with

perfectdata, that 80/20 blend would generate results that do not withstand statistical scrutiny.Between

publication bias;

post-hoc endpoint selection;

p-hacking;

'genr' of data

Replies: @KibernetikaThat’s true for a lot of data collected ‘in the wild’ (especially from surveys), but the primary driver of the Replication Crisis isn’t the data so much – it’s an ~80/20 mix of corruption and incompetence.It’s shocking to learn about the incompetence of some labs. Ultimately the errors are found, but what a waste of effort and churn simply because a lab tech or postdoc mis-labelled something or contaminated a sample. And that’s just the lab work. Finding distinctive human female microbiome stuff with a fish or tree genome is weird.

Next comes the software drama 😉 So many models, so many results.

@AnonThis is true, unless you're comparing square and circular pizzas. Some places offer both.

Replies: @AnonSquare “Sicilian” pies are usually deeper, though, so you have to compute the volume. On the other hand, the dough/tomato-sauce ratio may be different for a Sicilian or a round “Neapolitan” pie, in which case you have an optimization decision to make.