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Posts Tagged ‘math’

Math and History United at Last

Posted by Ethan Clow on May 17, 2012

I came across this TED talk by Jean-Baptiste Michel, he’s a Founding Director of Harvard’s Cultural Observatory, where their research team pioneers the use of quantitative methods for the study of human culture, language and history. His talk is quite interesting, he suggests how you can use mathematical formula’s to understand history. This is by itself not a radical idea as its one of the central premises of Steven Pinker’s book, The Better Angels of our Nature.

And we all know there are trends in history that can be tracked mathematically, nevertheless it is an intriguing idea that the development of human civilization could follow a predictable pattern. The implication for this could be huge. Consider our interest in discovering alien civilizations. What if we could add a deeper understanding of how civilizations develop and plot what age that civilization might be in?

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Math the Gateway Drug to Atheism

Posted by Ethan Clow on May 4, 2012

Are you good at math? You might be an atheist. At least in theory. I’m terrible at math and I’m an atheist.

But a new study is making the rounds these days regarding your ability to do math and whether or not your an atheists. Or to put it more accurately, how likely you are to be a non-believer. The study produced out of UBC by Psychologist Will Gervais, the author of the study about trusting atheists which we discussed in a previous episode.

image

This new study which Gervais conducted with fellow psychologist Ara Norenzayan, posed some analytical math questions to subjects. The hypothesis was that people who answered with more analytical answers, opposed to more innate and intuitively which would predict a religious believer.
example:

If a baseball and bat cost $110, and the bat costs $100 more than the ball, how much does the ball cost?

The wrong answer — the one you come up with when you don’t put any thought into it or simply go with your gut, which is what I would do, so don’t feel bad. — would be $10.

The right answer — which requires a bit of analysis — would be $5. (The bat costs $105.)

The study has certainly caught the public’s attention with numerous write up in science blogs and newspapers.

The study, which looked at 179 Canadian undergraduate students, showed that people who tend to solve problems more analytically also tended to be religious disbelievers. This was demonstrated by giving the students a series of questions like the one above and then scoring them on the basis of whether they used intuition or analytic logic to reach the answers. Afterward, the researchers surveyed the students on whether or not they held religious beliefs. The results showed that the intuitive thinkers were much more likely to believe in religion.

Now being good skeptics, what do we have here? Correlation but do we have causation? Turns out we do.

To test for a causal relationship between analytical thinking and religious disbelief, the researchers devised four different ways to promote analytic thinking and then surveyed the students to see if their religious disbelief had increased by the interventions that boosted critical thinking.

Basically they tried to see if they could prime subjects for analytical thinking which would then increase the subjects disbelief. Subjects would be shown various images which previous psychological studies had shown a connection to increasing performance on analytical problems. Sort of like the way listening to classical music or certain kinds of art can prime the viewer to behave a certain way.

Subconscious suggestions about thinking apparently gets the cognitive juices flowing and suppresses intuitive processes. The researchers confirmed this effect but also found that the self-reported religious disbelief also increased compared with subjects shown a different image before being tested that did not suggest critical thinking.

The same result was found after boosting critical reasoning in three other ways known to stimulate logical reasoning and improve performance on reasoning tests. This included having subjects rearrange jumbles of words into a meaningful phrase, for example. When the list of words connoted thought (for example, “think, reason, analyze, ponder, rational,” as opposed to control lists like “hammer, shoes, jump, retrace, brown”), manipulating the thought-provoking words improved performance on a subsequent analytic thinking task and also increased religious disbelief significantly.

So okay, what about all the non-believers like me out there who are saying “hold on, I suck at math” Of course the thing is, math is only one area where one can be analytical. As I’m sure we can all agree, sitting down and thinking rationally about a topic, math, history, science, art… that will stimulate the cognitive juices and this effect of decreasing religious belief would be seen as well, regardless of the field of study.

What’s also interesting about this, especially with all the press its getting, is the reaction from various religious groups and people. I saw one interview where the religious proponent suggested this wasn’t an issue of science vs religion because science can only answer questions of what is, compared to religion which provides a moral compass to civilization. Not surprisingly I rather disagree with that assessment.

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Is math innate to humans?

Posted by Don McLenaghen on February 21, 2011

Innate Knowledge

Tabula Rasa

An interesting controversy in philosophy, linguistics and psychology is whether or not numbers and counting is an innate human ability or something learnt. There is a certain portion of what we think of a consciousness that is strictly speaking instinct…our animal brains…but how much? One of the areas thought to be instinctual was our ability to count…that anyone anywhere at any time in history could count and understand simple numbers; such 1, 30, 523, etc. It seemed obvious, every society on the planet has a numbering system; the earliest evidence of humanity contains counting. The early ‘documents’ archaeologist find tend to be accounting forms of grain, wine or livestock. Everyone I now can count simple numbers and scientist only find exception in those with brain damages.

Previous research into an ‘isolated’ tribe in the Amazon showed this assumption to be wrong. MIT professor in 2008 published findings in the journal Cognition that showed this tribe had 1, 2 and many…anything larger than 2 was many…very large ‘quantities’ would be many many…etc. They also showed it was not that they lacked the language for numbers but the concept. When asked to count up from 1-10 (they were counting piranhas) they went 1,2,many BUT when they asked to count down 10-1, they discovered that the word used for “2” was first said, then eventually “1”…that the tribe did not use the ‘counting words’ to describe numbers but relative quantities. These results were seen as interesting but explained away by saying that these cultures were just too simple to have a more complex language for numbers…that they still had the innate concepts just lacked the words or the need to express it.

 

Math humour

This explanation however recently has been ruled out. In research, by Elizabet Spaepen published in the journal Proceedings of the National Academies of Science, into a group of deaf Nicaraguans who did not learn Spanish or conventional sign language shows that they did not develop an innate counting system in spite of the fact they lived in a ‘modern’ numerate community. The study subjects were unique because of the political situation and other issues, a large number of deaf Nicaraguans did not learn traditional sign language but in isolated communes ‘for the deaf. There were attempts to teach them lip reading but this failed but being intelligent curious and inventive these children invented a sort of pidgin sign language…as it turned out one absent of counting numbers beyond three. Further, they did not develop the concepts of higher simple numbers later when they were reintegrated with the larger numeric society although they did learn the ‘words’.

 

This group had ‘numbers’ in their sign but not the concept associated with them. For example, one of the tests done was hand-bumps. One researcher would ‘bump’ hands a set number of times with the subject to repeat the number of bumps back. They found that numbers beyond three where not repeated back consistently. This correlated with the ‘numbers’ they did use for sign…these numbers were more indicative of relative quantity than actual counting.

Researches of course though maybe it was related to their deafness so they conducted research into the deaf taught traditional sign language. They did not find this deficit…that it was not deafness but the fact that this latter group grew up in a numeric society that seemed to account for their ability to understand simple counting numbers.

The take home message here is that what we thought to be an innate ability of humans seems to yet another thing we can chalk up to cultural learning. It seems our ability to understand the concept of larger counting numbers is learnt at an early age and from our culture.

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