Logarithmic Thinking


Bring up the word “logarithmic” and I am guessing it brings back painful memories of highly complicated rules on how multiply or divide. To make matters worse, logarithms never seemed to get used in real life in an area that any of us cares about. Other than the Richter scale that is used to measure earthquakes, that is.

And yet, counter-intuitively, it turns out that instinctively we humans are programmed to look at numbers logarithmically, not linearly! And how do we know this? The discovery happened when scientists examined how South American Munduruku Indians visualized numbers spread on a line. This seems like a no-brainer at first: after all, which one of us doesn’t think of numbers as being spread evenly across a number line (think of graphs, house numbers etc)? But stop and think a bit and you realize that’s only because of how we were taught at school.

Now these Munduruku Indians, they don’t even have the concept of numbers. So the scientists devised an experiment where they put a single dot at one end of a line and ten dots at the other end. Then each volunteer was shown a random number of dots (between one and ten) and asked where it “fit” on the number line. Surprisingly, the unaware-of-numbers Indians spaced the numbers such that the gap between numbers started being large and then reduced as they went further to the “right” side of the line. In other words, they spaced the number logarithmically!

So is this just a cultural or racial thing? Not so. When the same experiment was conducted on American kindergarten kids with no number teaching yet, they spaced the numbers logarithmically too! In other words, we are born to think of numbers logarithmically.

Ok, but does this mean anything? Scientists discovered the spacing was logarithmic because the Indians and kids think in terms of ratios when it comes to numbers (spacing between 2 and 1 is 2 divided by 1, hence 2; but the spacing between 6 and 5 is 6 divided by 5, which is 1.2, much smaller than the spacing between 2 and 1).

Which then leads us to the next question: why do “uneducated” people and kids think this way? As usual with such questions, it’s an evolutionary thing! Faced with enemies, it is critical to know who has more numbers: your side or their side? Knowing exact numbers is irrelevant when making split second decisions in the wild. Ratios, on the other hand, meant the difference between life and death.

So the next time you curse a logarithmic scale, remember, that’s the form of thinking that comes to us naturally!

Comments

  1. KumarSeptember 17, 2012 at 7:33 PM

    Interesting.

    By the way, the logarithmic way to understand numbers is not limited to the Richter scale that is used to measure earthquakes. The loudness scale is also along the same principle. A jet engine noise (at defined distance) would be 110 decibels for example while whisper sound may be of the order of 20 db or so. Sometimes common man also comes into this, because he/she may have to face industry noise or traffic noise which are all measurable.

    Many engineering charts use the log scale in one direction (x or y axis) often. It is very convenient. In physics, the log being part of a process comes out in charging a capacitor through a resistance from a DC voltage source. Those who can understand electronics can appreciate why it has to be the log way. Though not for most engineers engineer or the common man, log is the way of radioactive decay.

    While it is possible to consider that an approximate estimation of the strength of enemy armies could be behind our mind conceiving numbers in the logarithmic way, I am of the following opinion. The human mind has an inherent ability to invoke an "inner mind model" for what is observed in external nature. Knowledge is indeed arriving at the correspondence in each such situation and the goodness of that knowledge is about how good in the inner to outer correlation. Log scale is thus part of the human mind, while "log" behavior (with no 'knowledge' at all of maths log concept) is the way of external nature. I feel convinced that this is the way of all scientific discoveries actually. I have never stopped feeling amazed at our mind potential!

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