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 TeasersMartin@GNXP Blogview

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My office mate’s sixth grader brought home the following math homework:

Marbles come in 10 colors. There are always seven marbles in a bag, always of seven different colors.
How many bags would you need to be 100% certain of having 10 marbles of the same color?

I logically arrived at 91 marbles clinching it, so 13 bags. 1. Is that correct? 2. In any event, I have no idea how to produce a general equation governing this situation. What is it?

Any assistance is appreciated. I apologize in advance if I have overlooked something glaringly obvious.

Posted by martin at 06:39 AM

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An interesting article on irrationality, inter alia. “In short, the evolutionary design features of the human brain may well hold the key to our penchant for logic as well as illogic.”

Consider the following problems:

Problem 1:

“Imagine that you are confronted with four cards. Each has a letter of the alphabet on one side and a number on the other. You are also told this rule: If there is a vowel on one side, there must be an even number on the other. Your job is to determine which (if any) of the cards must be turned over in order to determine whether the rule is being followed. However, you must only turn over those cards that require turning over. Let’s say that the four cards are as follows:

T 6 E 9

Which ones should you turn over?

Problem 2:

You are a bartender at a nightclub where the legal drinking age is 21. Your job is to make sure that this rule is followed: People younger than 21 must not be drinking alcohol. Toward that end, you can ask individuals their age, or check what they are drinking, but you are required not to be any more intrusive than is absolutely necessary. You are confronted with four different situations, as shown below. In which case (if any) should you ask a patron his or her age, or find out what beverage is being consumed?

#1 -Drinking Water
#2 -Over 21
#3 -Drinking Beer
#4 -Under 21

Did you find one problem easier than the other? Answers and speculation within.

“Answers:

Problem 1:

Most people realize that they don’t have to inspect the other side of card T. However, a large proportion respond that the 6 should be inspected. They are wrong: The rule says that if one side is a vowel, the other must be an even number, but nothing about whether an even number must be accompanied by a vowel. (The side opposite a 6 could be a vowel or a consonant; either way, the rule is not violated.) Most people also agree that the E must be turned over, since if the other side is not an even number, the rule would be violated. But many people do not realize that the 9 must also be inspected: If its flip side is a vowel, then the rule is violated. So, the correct answer to the above Wason Test is that T and 6 should not be turned over, but E and 9 should be. Fewer than 20 percent of respondents get it right.

Problem 2:

Nearly everyone finds this problem easy. You needn’t check the age of person 1, the water drinker. Similarly, there is no reason to examine the beverage of person 2, who is over 21. But obviously, you had better check the age of person 3, who is drinking beer, just as you need to check the beverage of person 4, who is underage. The point is that this problem set, which is nearly always answered correctly, is logically identical to the earlier set, the one that causes considerable head scratching, not to mention incorrect answers.

Why is the second problem set so easy, and the first so difficult? This question has been intensively studied by the evolutionary psychologist Leda Cosmides. Her answer is that the key isn’t logic itself — after all, the two problems are logically equivalent — but how they are positioned in a world of social and biological reality. Thus, whereas the first is a matter of pure reason, disconnected from reality, the second plays into issues of truth telling and the detection of social cheaters. The human mind, Cosmides points out, is not adapted to solve rarified problems of logic, but is quite refined and powerful when it comes to dealing with matters of cheating and deception. In short, our rationality is bounded by what our brains were constructed — that is, evolved — to do. “

Posted by martin at 10:24 AM

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This book is gaining attention: “Seductress: Women Who Ravished the World and Their Lost Art of Love” by Betsy Prioleau. A study of “50 of the world’s most famous seductresses — from Cleopatra to Catherine the Great to Mae West” it makes the point “that physical beauty was not — and is not — a required attribute in the arts of seduction. Many, if not most, of the women she writes about were not beauties. Far more important are the gifts of wit, brains, empathy and self-sufficiency — the opposite of neediness.”

Dr. Prioleau is completely correct imho. In a recent thread, I was alarmed to see the admiration expressed for the girls (literally) who compose Google’s top 10 image search. Not one truly sexy woman on the list. Note- this is expressly not that cliched call to “see the inner beauty,” but a different concept of what sexiness really is. Sexiness that will take some time to be replicated in a haptically present Real Doll, if ever. The triumph of the visual is the mark of the adolescent.

Posted by martin at 01:17 PM Comments

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This Economist article on the above topic is interesting, especially the graphs showing an inverse relationship between American and European responses as to “Religion plays an important role in my life” and the most important function of government is “to guarantee no one is in need.”

Europe is increasingly effete for a reason. Might American religiosity be a source of national power, rather than an intellectual embarassment?

The decadent left has always attacked religion for obvious reasons-it cuts into the State’s market share. Now a new faction of scientific realists (“brights” is just too ridiculous) attacks it from another angle. Just the other day, a very smart fellow told me the Declaration of Independence failed scientific scrutiny. No doubt he’s right, but the virus-like quality of that idea has the potential to destroy the body politic.

As Parapundit and Razib correctly note infra, many totalitarians claim God on their side. That hardly ends the debate, however. Secular totalitarianism is far from dead. The “sharp and educated” may prove just as much a threat in the end as “massive unskilled immigration.”

(Republished from GNXP.com by permission of author or representative)
 
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The frontiers of science keep expanding. New research indicates that bubbles observed coming out of a herring’s anus produce a high pitched noise that may aid in keeping the shoals together after dark.

(Republished from GNXP.com by permission of author or representative)
 
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Johannes Kepler has a good a claim as anyone to be the father of empiricism. He was the first to formulate scientific “laws” based on rigorous observation (e.g. Planets travel in ellipses- based on Brahe’s meticulous observations of Mars’ orbit).

His first book, the Mysterium Cosmographicum, published at age 25 in 1596, singehandedly makes the transition from ancient metaphysical speculation to modern empirical science.

Kepler first posits the idea that the universe is built around the Platonic solids-which form its invisible skeleton, i.e. the five Platonic solids comprise the five intervals between the then known six planets. Illustrations from the work are here (scroll down).

Kepler noted the exact date this flash of insight came to him (July 9, 1595) and as one biographer states: “it determined the course of life, and remained his main inspiration throughout it.”

But that was the ancient metaphysics-Kepler later goes on to state: “If [the observations] do not confirm the thesis, then all our previous efforts have been in vain.” And modern empirical science is away and running.

Historians of science have noted the falseness of Kepler’s inspiration, which nevertheless paved the way for the formulation of his groundbreaking laws. E.g. Koestler writes in The Sleepwalkers: “For Kepler’s misguided belief in the five perfect bodies was not a passing fancy, but remained with him, in a modified version, to the end of his life, showing all the symptoms of a paranoid delusion.”

How much we have yet to learn from the old masters.

Catching up on the science news of the week, I note that the October 9 issue of Nature features an article entitled: “Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background.”

If you’re sort of out to lunch-a dodecahedron is a…yep… a Platonic solid!

The gist of it is that observations by NASA’s Wilkinson Microwave Anisotropy Probe (WMAP), launched in 2001 to measure temperature ripples in the afterglow radiation from the big bang, have caused Weeks and his colleagues to posit that “space wraps back on itself in a bizarre way… Effectively, the universe [is] like a hall of mirrors, with the wraparound effect producing multiple images of everything inside… According to Weeks, the WMAP results point to a very specific illusion- that our universe seems like an endlessly repeating set of dodecahedrons, football-like shapes with a surface of 12 identical pentagons…If you exit the football through one pentagon, you re-enter the same region through the opposite face and you keep meeting the same galaxies over and over again.”

In other words, one of the galaxies in the Hubble Deep Field may be the Milky Way? weird whacky stuff- anyway, i hope they give a shout out to Johannes.

Could Kepler’s flash of insight in 1596 be confirmed (to an extent-I won’t get carried away) by a 2001 space probe? And what does that portend for what is really the source of scientific knowledge and discovery?

(Republished from GNXP.com by permission of author or representative)
 
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Rush Limbaugh is a junky and has checked into drug rehab. No link necessary-that’s the declarative fact. That’s the most valuable public service he has ever performed. Mark this date as commencing the United States’ treatment of drug addiction as a genetic/medical issue rather than a matter for the criminal justice system.

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“52 percent of Levites of Ashkenazi origin have a particular genetic signature that originated in Central Asia, although it is also found less frequently in the Middle East,” according to a new report. “The ancestor who introduced it into the Ashkenazi Levites could perhaps have been from the Khazars, a Turkic tribe whose king converted to Judaism in the eighth or ninth century.”
I remember Arthur Koestler asserting this in The Thirteenth Tribe. Apparently, the potentate was trying to split the difference between the Christian west and the Moslem east, and made his kingdom jewish by fiat.

See extended entry for the full report.

(Republished from GNXP.com by permission of author or representative)
 
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Excerpt from Tony’s Blair’s speech to the U.S. Congress yesterday:

“The spread of freedom is the best security for the free. It is our last line of defense and our first line of attack. And just as the terrorist seeks to divide humanity in hate, so we have to unify around an idea. And that idea is liberty. (Applause.) We must find the strength to fight for this idea and the compassion to make it universal. Abraham Lincoln said, “Those that deny freedom to others deserve it not for themselves.” And it is this sense of justice that makes moral the love of liberty.”

That’s a lot of idealism for one paragraph. Is Tony Blair really just pushing the same supernatural claptrap as the Pope with a different spin (e.g. just substitute ‘Christ’s love’ for ‘freedom’ and ‘salvation through Christ’ for ‘liberty’ above)? What is “liberty” in a material world?

(Republished from GNXP.com by permission of author or representative)
 
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A dustup over Dusty Baker’s physiological assessment of certain Cubs. Baker stands by his assertion that black and Hispanic players can take the heat better than whites. Great defense: “I’m not playing the race card. I’m telling it like it is,” Baker said.

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The MIT OCW “Course 7.03: Genetics” from MIT Professors Chris Kaiser and David Page features 36 Lecture notes addressing the structure and function of genes, chromosomes, and genomes. Also offered: “The 7.03 Bible,” a set of detailed study guides, problem sets, and exams from 1993 through 2001.

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Imbler State University has onlined the Linus Pauling Papers, including scanning and indexing forty-six research notebooks spanning the years 1922 to 1994 : “The notebooks contain many of Pauling’s laboratory calculations and experimental data, as well as scientific conclusions, ideas for further research and numerous autobiographical musings.” Interesting stuff; see esp. books 1-13 containg his notes re: crystal structure; “[T]his work informed Pauling’s eventual publication of The Nature of the Chemical Bond, one of the seminal texts of modern science.”

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Most mammals are hairy beasts. Short article on what we and naked mole rats are up to; Gene/culture evolution seems an interesting idea.
Also, this NewScientist anthology loosely grouped on human nature, including Dennett on free will.

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Genes are at your mercy, says Matt Ridley in this short essay, which appears to be an extended abstract of his recent book, reviewed infra by Razib.

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Interesting new study:

“Human beings may have made their first journey out of Africa as recently as 70,000 years ago… Writing in the American Journal of Human Genetics, the researchers estimate that the entire population of ancestral humans at the time of the African expansion consisted of only about 2,000 individuals.

-Martin

Posted by martin at 12:31 PM

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