When the daughter was younger and had yet to start going to a classroom atmosphere, the father asked her to lift her right leg. Being the loving grand-daughter, she did. Then he asked her to lift her left leg and she obliged, by stamping the right foot down and lifting the other. Not satisfied with the legs, he started in with the little arms and asked for the left arm. Then the right arm, and both arms together. (Luckily, we have only 2 arms and 2 legs, for this gripping tale would have had us spouting steam otherwise.)

Having seen all this, he asked her to lift both legs together, to which she hardly spent a moment thinking and simply lay down on the floor and lifted both legs looking like a very adorable pup waiting to be tickled by the owner.

Fast forward to a time when formal schooling did start and the same exercise has her thinking about the problem and saying, “But the only way to do that is jump and see if we can fly!”

What makes me remember this you ask. A book I was reading recently: It spoke about how some tribes know not the notion of time or numbers. (They don’t need either concept for their survival.) This book actually has remarkable powers, because it has enabled me to forget the title and clean swiped the power of resurrecting the title from the dark crevices of the brain.

Anyway, according to the author, who spent many happy months among the tribes, Piraha Tribe in Amazon, trying to observe and study their behavioral patterns, he noticed something. When given a series of dots and told to plot them on a number scale between 1 and 10, the tribes with no formal introduction to numbers placed the numbers closer together as they approached 10, and farther and farther apart near 1 and 2. Their natural instincts were to think logarithmically.

A study that coincided with how kindergartners plotted their numbers. Basically, the tribes and the children saw the combination of dots as the pattern. Two dots together doubles the area of one dot, but 9 dots clustered together is only marginally smaller than 10 dots together.

But as these kindergartners approached second grade, they plotted the numbers from 1 to 10 evenly spaced on the number line. We move away from a more complex method of thinking logarithmically naturally to thinking linearly, and then relearn the logarithmic concept later in life.

It is a fact that structured thinking has its benefits, but I often wonder how different we would be if we were allowed to retain our ability to think with out being clouded by what is taught to us.

Edit: Relevant links:

Piraha tribe

Kindergartener Number Study


14 thoughts on “Logarithmic-Linear-Logarithmic”

  1. Which book is this? Sounds very interesting…

    I think, we did invent number system for a reason or for that matter, whatever advances in math/science or whatever there is. The problem is that, people who learn the outcome of an invention care less about the reason. For example, when I learnt microprocessors and knew what each machine code meant, it was interesting. I could then appreciate why assembly language was a ton better and why high level languages were even better and so on. But, when people learn and don’t take time to understand where it all stem from, they are missing the basics… One could argue that there is no need to know the background for one wants to specifically do. I think that’s where the disconnect is…

    1. I agree with your point of people not wanting/caring to learn how something came about to be used in its current state. That is a big woe of the educational system. We are quicker to chase results by rote learning and not spend enough time understanding.

  2. That was a very interesting post. This reminds me of what I heard recently about Stephen Hawking. Supposedly the reason he could come up with his theories is because of his inability to write!!! When most scientists think they write it down in terms of a+b…=c (linear fashion) but all Stephen Hawking can do is observe and think and that helps him think in a much more non-linear fashion.

    P.S: What is the title of the book? Would make an interesting read.

    1. Interesting…..about Stephen Hawking. Gosh – I really forgot the name. I only had with me for a couple of days, that is the reason!

  3. Very interesting.

    Also noted the lateral thinking on the part of your daughter when she was younger. She really didn’t really “analyze” on how to get both legs of the floor – she just focussed on the solution and there it was!

  4. Hi I’m Srikrish’s ex-colleague from Redback. I recall hearing about this tribe on a piece from NPR. I’m not sure, but it could be the Piraha tribe from the Amazon…

  5. Cool..that was very smart of her to do it I think!! I wouldnt have thought of it!
    Human instincts are much more sharper and can solve many a problem in their own way . Otherwise, the evolutionary process from an ape to a sapien wouldnt have been so amzingly sequenced.
    I have also read another nove “Clan of the cave Bear” which shows how only a wise man in the tribe figures out how to count the days by keeping track of the number of times he sees the sun. He draws a line onth wall of his cave each time and then starts counting and evolves a nice process…its a very gripping novel…

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