Exploring the Depths of Thought: Problem Solving Part 3

Let's proceed from where we left off in our previous blog-isode.

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It is possible that processes similar to chunking underlie the cognitive growth that occurs in childhood.

As infants grow into toddlers, and toddlers into children, they gradually acquire many concepts that adults take for granted, so that they eventually comprehend space, time, and causality in much the way their parents do.

It may be that the way in which they achieve this has much in common with the route that beginners take in becoming masters in a particular skill.

We will return to this issue in a later blog-isodes of cognitive development.

Now based on our previous blog-isodes, we know that acquiring the appropriate chunkings is in part a matter of experience,

But in part, it is also a matter of talent, for some people can see chunks where the rest of us cannot.

When the mathematician Karl Friedrich Gauss was a young boy in grammar school, his teacher asked the class to add all the numbers from 1 to 10. Young Gauss got the answer almost immediately.

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Unlike his classmates, he did not chug through all of the tedious steps of the summation.

He recognized that the series 1+ 2+ 3 ... + 100 can be rewritten as a sum of 50 pairs each of which equals 101.

Given this insight, he quickly came up with the correct answer, 5050, no doubt to the considerable amazement of the teacher.

This process of reorganizing bits and pieces so that they form a unified whole is also found in artistic creation.

Wolfgang Amadeus Mozart describes it in one of his letters:

Those ideas that please me I retain in memory, and am accustomed, as I have been told, to hum them to myself. If I continue in this way, it soon occurs to me how I may turn this or that morsel to good account, so as to make a good dish of it, that is to say agreeably to the rules of counterpoint, to the peculiarities of the various instruments, etc. All this fires my soul, and provided that I am not disturbed my subject enlarges itself and becomes methodized and refined, and the whole, though it be long, stands almost complete and finished in my mind, so that I can survey it, like a fine picture or a beautiful statue at a glance. Nor do I hear in my imagination the parts successively, but I hear them, as it were, all at once. What a delight this is, I cannot tell.... What has been thus produced, I do not easily forget, and this is perhaps the best gift I have my divine maker to thank for.

So far, we have primarily dealt with situations in which problem solvers succeed.

How can we explain their all too many failures?

In many cases, the solution is simply out of reach. The problem solver lacks some necessary informational prerequisites or relevant chunkings, as when a ten-year-old is unable to solve a problem in integral calculus.

But failure often occurs even when all the necessary ingredients for solution are known perfectly well, for the would - be problem solver may get stuck in a wrong approach and may not be able to get unstuck.

When finally told the answer, his reaction often shows that he was blind rather than ignorant:

"How stupid of me. I should have seen it all along".

He was victimized by a powerful mental set that was inappropriate for the problem at hand.

In tomorrow's blog-isode, We will look at a well-known study that shows how mental set can make people rigid.

Yeah

They became fixated on one approach to the task, which made it hard for them to think of it in any other way.

The Bus Stops Here for today:

Thank you, friends, for staying with me through these blogisodes. Your thoughts and opinions are always welcome and appreciated. I'd be happy to hear them. We will build on this in tomorrow's blogisode. Until then, stay safe, friends.♥️

References and Links:

https://betterexplained.com/articles/techniques-for-adding-the-numbers-1-to-100/

https://www.britannica.com/biography/Carl-Friedrich-Gauss

https://www.invisionapp.com/inside-design/mozart-creative-success/

https://www.britannica.com/biography/Wolfgang-Amadeus-Mozart

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