Some cognitive scientists have done an experiment on some people in Papua New Guinea to test the hypothesis that the number line is based on an in-built intuition that all humans share. They concluded that it isn’t, and that you can use cardinal numbers without placing them mentally on a line.
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- $60\%$ of students who study Chinese are artistic and love poetry.
- $20\%$ of students who study Business are artistic and love poetry, and
- Only about $1\%$ of students study Chinese, whereas about $15\%$ of students study Business.
Trace Heavens by James Nizam
Puzzlebomb – May 2012
Puzzlebomb is a monthly puzzle compendium. Issue 5 of Puzzlebomb, for May 2012, can be found here:
Puzzlebomb – Issue 5 – May 2012
The solutions to Issue 5 can be found here:
Puzzlebomb – Issue 5 – May 2012 – Solutions
Previous issues of Puzzlebomb, and their solutions, can be found here.
The Cryptographer by Raw Color
“Futurama theorem” slightly improved
The “Futurama theorem”, also known as Keeler’s Theorem after its creator, was a bit of maths invented for the Futurama episode The Prisoner of Benda, to solve a problem where the characters get their heads mixed up and need to swap them back without any one pair swapping heads twice. It was enthusiastically reported by the geeky press, and rightly so, because it’s a fun bit of real maths with a wonderful application. Dana Ernst has written some very good slides about the theorem, working from “what is a permutation?” up to the algorithm itself.
Anyway, some students from the University of California, San Diego have extended the result, giving a better algorithm for finding the minimum number of switches to put everyone’s head back in the right places, give optimal solutions for two particular situations, and give necessary and sufficient conditions for it being possible to represent the identity permutation as $m$ distinct transpositions in $S_n$.
Paper: http://arxiv.org/abs/1204.6086
via James Grime
Grow Your Own Food
I recently heard about Herman, the German Friendship Cake (bear with me), a cake which is divided and spread among friends, and it got me thinking about some other foodstuffs I’ve heard of which are made in such a way that the amount you have will grow exponentially. A Herman cake is a special type of sourdough cake which is made with yeast. It’s explained fully here, but the idea is that you start with a solution of yeast, which lives in a little milk, sugar and flour. This small amount of goo can live happily at room temperature on a shelf, and if you stir it every day and give it a little more flour and sugar to eat every few days, after ten days it’s ready to make into a cake.
A student is artistic and loves poetry. Is it more likely she’s studying Chinese or Business?
Let’s suppose that:
Thus, out of every $1000$ students, there are $10$ studying Chinese, of whom $6$ are artistic and love poetry, and also there are $150$ studying Business, of whom $30$ are artistic and love poetry.
So if a student is artistic and loves poetry, it’s $5$ times more likely she’s studying Business than Chinese.
So much for preconceptions (and “correlation”).