...>

in this context :

<"Most people still don't get the idea that spirituality is not religious dogma. Spirituality is expanding awareness">

"The Mind of the Mnemonist" by the psychiatrist A.R. Luria [ http://www.amazon.com/The-Mind-Mnem... ] describes a patient S. with the inability to forget. Luria gave S. lists to memorize, e.g., and S. would unhesitatingly recite them 20 years later. S. also was unable to abstract, so the concept of "nothing" was a mystery to him.

The book describes a problem about mushroom collecting, similar to the bat and ball, and solvable by simultaneous equations, but which S. solved concretely by visualizing piles of mushrooms. Given my adolescent predilection for rapid calculation, the book taught me that visualization was even more rapid for this type of problem.

In the terminology of <frogbert>'s post, with the problem of the bat and ball, I momentarily went for "system 1" type reasoning, but mistrusted it. Instead of going to "system 2", however, I went to "system 1.5", learned from S.: I visualized $5, then $100, and then the remaining $5, to get the correct answer.

Humans use many different algorithms, depending on their abilities. We are all truly amazing, each in our own way. Here is one of the more interesting examples I know.

Given any date, I can calculate the day of the week by casting out 7s implicitly from the number of days between the date and Jan 1, 1900. (Once, a computer programmer asked me what my "base date" was!) I have known two piano-bar pianists, each with a brilliant musical ear, and each with a superlative memory. One of them (who had significant mathematical abilities as well) learned the calculation from me, but the other was able to perform the calculation before I met him. When I asked the second how he did it, he said that he remembered a day of the week about every two weeks throughout his life, so he just took the nearest date that he knew and counted from it.

Three playing cards are placed face down in front of you, one red and two black suited. You're asked to guess which one is the red one.

You're told that one of the other cards is not the red one, and you can change your pick or stick with your original choice.

Should you change or not?

Kahneman in his book (p. 44) used $1.10 as the cost of the bat and ball, so his numbers are a hundredth those of Gervais and Norenzayan, who used $110. As for mistakes, I don't bother pointing out your laughable attempts at spelling. I can start if you like.

<I'm sorry I don't measure up to your staggering intellectual heights. I mean, you can post links with the best of them.>

As opposed to you, who just makes stuff up or bases it on his looking-in-the-mirror conversations with God.

<Would you be up for a challenge as to our respective intelligence levels?>

Sigh. Mistrust a problem when it seems too simple :)

in his book, Kahneman is dealing with how decisions with risk are evaluated.

frogbert provides a concise summary. in addition, system 2 processing is influenced by system 1. duality is a tightly-coupled relationship!

The bat and ball math/word problem is commonly used to sell courses on how to improve SAT scores and prove instincts are often wrong.

al wazir, i think you're jumping to conclusions here, baffled by how much can be gleaned from the answers to very simple questions. :o)

in fact, <shane frederick> invented a "test" consisting of this baseball & bat question + 2 more questions equally simple, which all 3 taken together can be answered in about 1 minute. he shows that the information that can be drawn from this "cognitive reflection test (crt)" is as good as that from much more time-consuming and "costly" tests in some areas. also, there's a significant correlation to for instance sat tests.

you might be surprised, al wazir!

<This paper introduces a three-item "Cognitive Reflection Test" (CRT) as a simple measure of one type of cognitive ability—the ability or disposition to reflect on a question and resist reporting the first response that comes to mind.>

see http://www.aeaweb.org/articles.php?... for the article, published in Journal of Economic Perspectives in 2005. kahneman lists this article in his notes to 'thinking, fast and slow'.

<also, there's a significant correlation to for instance sat tests.> And hundreds are better still. But what do SATs really measure?

<For decades many critics have accused designers of the verbal SAT of cultural bias toward the white and wealthy. A famous example of this bias in the SAT I was the oarsman–regatta analogy question. The object of the question was to find the pair of terms that have the relationship most similar to the relationship between "runner" and "marathon". The correct answer was "oarsman" and "regatta". The choice of the correct answer presupposed students' familiarity with crew, a sport popular with the wealthy, and so upon their knowledge of its structure and terminology. Fifty-three percent (53%) of white students correctly answered the question, while only 22% of black students also scored correctly. [...] Recent research has linked high family incomes to higher mean scores. Test score data from California has shown that test-takers with family incomes of less than $20,000 a year had a mean score of 1310 while test-takers with family incomes of over $200,000 had a mean score of 1715, a difference of 405 points.> (http://en.wikipedia.org/wiki/SAT#Cr...)

*Anyone* can learn how to solve problems like these, just as anyone can learn a language (if you can read this you must have learned at least one sometime in your life) or how to drive or cook. Anyone. All that's needed is taking it a little bit at a time ("little steps for little people," as one of my professors in grad school used to say), and practice. Proper instruction helps but is not indispensable.

exactly. i have taught such problems to kids as young as 12 years and 10 years old and made them proficient in solving such problems.

now, those 12 year olds have not got something which make them examine the issue of existence of 'god' or 'universal intelligence', 'universal consciousness' intelligently or 'intuitively' .

may be this a necessary but not sufficient skill ? that is , if someone can not solve such simple problems , then can it be concluded s/he is incapable of examining deeper issues of existence?

not really. these days many people like to understand both spirituality and science which is good. however, it is not necessary to know science/maths to examine the questions/issues of existence/'sirituality' . also, learning science and maths properly (from properly i mean solving the kind of questions asked in olympiad etc.) helps develop reasoning but converse is not neccesarily true. if someone is not good in maths, physics etc , one may still have great logical intelligence and reasoning.

also, someone may have very good logical intelligence but poor intuitive intelligence.

"Dogma is the established belief or doctrine held by a religion, or a particular group or organization. It is authoritative and not to be disputed, doubted, or diverged from, by the practitioners or believers.": http://en.wikipedia.org/wiki/Dogma

Believing in something which cannot be proved to exist is faith.

Not believing in something which cannot be proved to exist is not dogma, it's a choice, a logical choice.

Science does not require its practitioners to <believe> anything, only to <practise> evidence-based scientific methodology that could falsify a hypothesis or theory.

Science allows its practitioners to believe anything they like, which they can and do.

the assumption of the researchers is that nearly everyone would indeed be able to answer correctly *if* they would engage their system 2. hence, the real test is, who do engage their system 2?

of course, reasonably clever people will be able to become "experts" on this type of questions with only a little training, possibly allowing them to answer correctly in an instant, maybe even without using system 2. however, i find that rather irrelevant both for the theoretical impact and the practical implication of crt-like tests: the specific crt questions are only examples - numerous others can be created using the same basic "trap", i.e. hiding an intuitive and incorrect answer in there. i assume that the number of people that would a) be aware of and b) bother to prepare for crt-type tests is negligible compared to those who wouldn't.

You got my point, which was not well expressed, that problems are usually susceptible to many, often radically different, solutions.

< however, i find that rather irrelevant both for the theoretical impact >

I agree.

< and the practical implication of crt-like tests: the specific crt questions are only examples - numerous others can be created using the same basic "trap", i.e. hiding an intuitive and incorrect answer in there. >

The point in the economic context is incredibly important, because I have seen examples where you can phrase the same economic payoff in two different ways, and people (using system 1) prefer one over the other, sometimes with a very strong emotional response.

< hence, i still think you're a bit quick to categorically reject this research. >

a logical choice?

ok. may be.

however, let's put the semantics aside (whether it is dogma or not) and examine this : <fsr> and <al wazir> are atheists. that is their belief. nothing wrong with that choice. however, what is that choice based on? you suggest that this choice could be logical. what is that logic?

<colonel mortimer> says he is agnostic and i can understand the logic of that choice.

but atheism? what is the logic/source of this belief/choice?

i would like to understand that.

http://en.wikipedia.org/wiki/Monty_...>

Thanks for the discussion of the monty hall problem. I was surprised to find that when the problem was discussed by Marilyn vos Savant (who rose to fame due to her listing in the Guinness Book of World Records under "Highest IQ")in parade magazine that as many as 1,000 individuals with PhDs wrote in to say they disagreed that the odds of winning increased from 1 in 3 to 2 in 3 by switching (i.e. after the host revealed one of the wrong choices). Intuitively, most people initially think the choice of winning is still 1 in 2, after a losing choice is revealed. However, this is another case where math beats out intuition.

While the wikipedia article does a good job of revealing the math and some explanations as to why switching improves the odds of winning, some might still want to see it put to the test.

A short video with Alan Davies and Oxford Mathematics Professor Marcus Du Sautoy does just that by testing out the Monty Hall problem at http://www.youtube.com/watch?v=o_dj... with an easily understood experiement.