Memory, mathematics and synesthesia.

02Jun12

Sometime ago I saw a TedTalk done by Mr. Daniel Wolpert, which now (once I’ve watched it again) made an even deeper impression on me; The bayesian predictions and the feedback loops are surely something worth thinking about, but the first time I’ve watched it I’ve became instantly occupied with one of the very first sentences he said, paraphrasing: “The brain exists in the first place to produce motions.” (1) 

This thought surely stirred a lot of thinking in me and at first I wasn’t in perfect agreement with it either, but gradually over time I’ve become accustomed to this thought and now I can point a lot of other clues that happen to fit well with it.

Let me give you one example – Recently on TED I saw another TedTalk (which I can’t get a direct link to) in which Mr. Joshua Foer talks about his research on developing amazing memory. He postulates convincingly that our memory capabilities can be extended using our imagination. He even goes on to present some evidence, in which they’ve put both; normal people and the memory savants into an fMRI machine while in the process of remembering and it turns out that the only difference between them was that the memory savants tended to use their spatial memory and navigation areas of the brain… Ehm, sorry, what did you say again? Correct, spatial and navigational areas of the brain. It turns out that we have an exceptional spatial memory. Mr. Foer goes on bringing up ancient orators using the spatial technique and old linguistic analogies to places. The question he asked himself was whether he could perform the same after some training – the answer turned out to be ‘yes’. We can train our minds to pay attention and remember, by recalling the ancient strategies that seem to be forgotten in the era of quick internet access, remainders and flash memory drives.

You may ask what are those strategies precisely doing – are they creating abstract worlds in which we can perform our imaginary walks? It seems so, and in the context of (1) it seems that our brains are just building upon what’s already there, borrowing the method. In other words we’re just looking at the work of the good old patchy-evolution, which tends to translate facts into something the navigating brain can understand and move between – space of events.

Now I’d like to tell you about something that lately occurred to me. This hypothesis may not turn out entirely new ( or true : ) ), but a discussion in the comments would be very welcome.

What if our effectiveness at Mathematics depends on similar strategies, which tend to make our ways of thinking a little more synesthetic?

Mathematics is a universe. Mathematicians are the pioniers, the explorers of new and unknown before. Then, eventually, the paths become so common that they become widely known by many.

One may now think: Wouldn’t it be wonderful if we could come up with a mathematical proof, simply by thinking about a way of getting to a specific point in space? An analogy of saying ‘go straight, then turn right, climb the stairs’…

In the first part of this article we’ve been talking about remembering things that didn’t necessarily have any predefined relation to each other. Mr. Foer taught us how to remember things by using made up connections to create a palace over which we could walk through the eyes of our imagination and amuse ourselves.

Mathematics doesn’t give us that much freedom, it constrains us, in similar fashion that the reality does. While the memory palaces created on Memory Contests are goofy and arbitrary, the palaces of Mathematics need to be ones of fine structure, not connected in arbitrary fashion. Therefore Mathematics is about discovering bridges between islands and describing their properties (is it a one way bridge? does the bridge lead to a parent island or to child island) instead of creating them. Sometimes you even have to stop and decide whether you’ve landed on the same island or a new one.

Of course making up a connection is easier than actually finding out what the connection is, but hey – that’s Math, an activity for real man. How could we get better at it? This was a question I’ve asked myself and I came up with a few proposals:

  • Think about the types of possible connections between structures and compare them with the ones defined already in math (injection, surjection, morphisms etc.)
  • Try to get a good mental picture of each of them, try to associate a color/smell/feeling with each one. Perhaps the relations relate somehow to each other – try to take that into account too.
  • Train logic interference – that is, the speed and accuracy of the evaluation of logic statements (I’m planning to create an app for this during the weekend, but in meantime you can  take a look on this cambridge test which provides one test similar to what I’m about to implement)
  • Translate mathematical objects into space events and use the relations to connect them together building a Math Palace, then take a hike around the place.

In case of memory, Mr. Foer showed us that we can build highways in places where fragile country roads had been. I don’t know how far we can stretch that intuition, but nevertheless I found it worthwhile to think about.

Here’s a bonus thought: Doing Physics requires somehow an inverse process.

It’s process of finding the right structures from the mathematical universe and trying to fit them to the structures of the real world.

Feel free to argue with me in the comments below.

[Edit: 6 May 2012 16:32]

While planning the inner workings of the new app I’ve started researching the topic on pubmed and found some research that seem to back up my hypothesis:

Results suggest that spatial abilities and language comprehension, but not basic numerical processing, may play an important role in advanced mathematics.

“…results of the present study imply that the neural substrate, which is potentially necessary to enhance specific skills dramatically by positively motivated excessive mental training, might be present in every healthy individual.”

[Edit: 9 May 2012 13:48]

I’ve just finished reading Joshua Foer’s book ‘Moonwalking with Einstein’ and I must say that while I had moments of feeling towards discarding this book as completely invaluable, it would be unreasonable to do so.

However, I should warn everyone that saw his TedTalk that he doesn’t in fact use the memory techniques that he so much promoted on the TedTalk, instead in his book he just promotes mindfulness.

His book doesn’t contain any kind of special recipe for improving everyday memory, instead it leaves open questions, describes the history of memory improvement, savants, the process of mastering a skill (worth reading) and his own experience at the memory contest.

That story leaves yet another doubt to how much we can improve ourselves and to the validity of my hypothesis.

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3 Responses to “Memory, mathematics and synesthesia.”

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