25 Aug 2015

On the human information retrieval process

When I was a kiddo I thought solving algebraic equations on paper was lame. I much prefer working things out mentally and putting down the value for \(x\) in the second step.

\[\begin{align} \frac{\frac{(x^5 + 20x)^2}{log_2(x)} - (\sqrt{\frac{x}{4}}+13x)}{159773} &= (3124x- 23901)(x^2-190) \\ x &= 16 \end{align}\]

It is elegant and was a good ego-booster back then. Gradually I developed the inclination to do things mentally. There is something magical about the moment when you arrive at the final answer, the moment when you can let your mind be free as you no longer bear the responsibility to cache the data in your Random-Access Memory, except that we are humans and don’t actually have Random-Access Memory. So when things get really complicated, we would have to resort to writing the working down: there is no way I can solve the equation above without pen and paper. It is too complex.

(Interestingly, even Wolfram Alpha can’t quite solve it, likely a consequence of Abel–Ruffini theorem: the best it can do is to use some approximation algorithm. Perhaps the most efficient approach to obtain a solution for \(x\) is through trial and error - checking integers that are some powers of 2 and for which \(\sqrt{\frac{x}{4}}\) returns a whole number - but that requires one to have access to the information that \(x\) has an integer solution.)

As humans we can retrieve stored information more efficiently by receiving sensory inputs (often in the form of EM radiation or air vibration) that we have associated the information with previously. Suppose a person is given the task to compute the product of two random 4-digit numbers (say \(1241 \times 6539\)). Let’s say the person is not well trained in the art of multiplication, it would be a lot more difficult for him/her to do it mentally than doing it on a piece of scrap paper. Even having the two 4-digit numbers displayed right in front as he/she works on the problem would ease things out slightly, comparing to hearing the numbers for once in the beginning and relying on memories.

We have already been accustomed to interpreting those Arabic symbols as numbers, a concept in which morphisms can happen. So when we do the morphism in our mind, it is much easier to recall the information that would be necessary at the next phase by looking at the symbols we have written, as compared to assigning some part of the brain to keep track of the information. It is not that the later cannot be efficiently done when the amount of information reaches a substantial volume: Kim Peek (who inspired the Oscar-winning film Rain Man) had clearly demonstrated that such feat is doable. The human brain is a powerful computational device. It’d be more logical to conjecture that in general it tends not to retain too much information so as a trade-off to achieve better performance in other areas due to its limited capacity. That is why I believe in learning (which requires a lot of abstract-thinking and deconstructing) the ability to forget plays a much more fundamental role than the ability to memorise.

There are clearly evolutionary advantages in relying on sensory stimuli to retrieve stored information rather than employing other mechanism to retrieve them on a whim. Perhaps this is how the notion of semantics arises at a higher abstraction layer.

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