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On Daniel Tammet's Calculative Methods

Scientific American published online an interview with savant Daniel Tammet and I was much impressed by what he had to say about his calculation methodology.  He says that when he adds or multiplies numbers he envisions textures and colors and so he forms a mental landscape of his answers.  He is also able to lump numbers with certain properties.  I began thinking whether this really couldn't be a method that should be taught at early age.  I don't know what his exact idea is, and this is entirely extrapolated based on the example he gave, but what about teaching multiplication like this. Imagine at first a most generic sphere.  When multiplying numbers, the primes, one, and zero have particular properties, as:

Zero zaps the mental spherical object and makes it explode or disappear (nullify).

One makes the mental sphere object do nothing (nothing).

Two makes the mental sphere object square from the center (squarify).

Three makes the mental sphere object lumpy (lumpify).

Five makes the mental sphere object liquid (liquify).

Seven makes the mental sphere object rough (enroughen).

Eleven makes the mental sphere object slippery (slipperify).

Thirteen makes the mental sphere object metal (metalify).

And so on.  So now we need to associate the operation "multiply" with an effect.  Let's say an initially sphere object acquires the above properties when these numbers are multiplied together.  So then 21, which is 3 times 7, is a rough lumpy sphere.  Then 39, which is 3 times 13, is identified with a lumpy, metal sphere. Perhaps  3^2 \cdot 7 = 63 might be a rough lumpy-by-squares sphere.  In such a way you go about constructing numbers and associating them with textures, and each new prime number you encounter becomes a property of the sphere you initially envisioned.  As Tammet implies (though he never specifically states), it is now super easy to group all "divisible by three" numbers by associating them with roughness.  "Division" is the "taking away" of such an effect.  Since each prime number is like having acquired a new "power" or property that you can use on the "number sphere," it becomes super easy to remember the prime numbers.  It also becomes very fun for kids, I think.

I don't know about associating "properties" to the other ring operation of addition (must one create a parallel system? Can you do away with just the above?) -- I'll have to think about it or perhaps wait for Tammet's book, in case he describes the way he does it.

Categories: Arithmetic, Mathematics
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