Our Obsession with 10^x's

Our Obsession with 10^x's

7th March. 1987. A little man nudged a ball delivered by an Ejaz Faikh with a cricket bat, and set off. He ran faster than he ever had before. And with more jubilation than ever before. The little man, Sunil Gavaskar, had crossed a barrier never thwarted before by international cricketers - the landmark of 10,000 career runs. Gavaskar’s celebrations could have been compared to many things - winning the World Cup, getting a winning ticket at the lottery, writing a final exam or defeating Wario at last. This was a mammoth achievement, but it leaves one wondering, why are humans so obsessed with 10^x’s?

Continuing on the cricketing parallel, followers of the game will be well aware of Virat Kohli’s century drought - while still maintaining stellar numbers (at least in comparison to the rest of the team). Batters are known to play a lot slower as they reach the dreaded 3-figure margin. But on close analysis, going from 99 to a 100, is the same impact on a game as going from 98 to 99, 41 to 42, or in general, an increase. Gavaskar himself has known to be extremely critical of young players “squandering” opportunities to reach the glorious mark.

So far, this “obsession” seems to be just a matter of personal pride. However, this has had some pretty bad consequences - in cricket, for starters. Batters slowing down as they reach the landmark is pretty self explanatory - scoring 10 runs in 15 balls because of nerves and the will to reach the century could be a costly brake in the scoring rate. But, another interesting situation is seen in test cricket, where declarations play a part in the game - teams will rarely halt their innings after reaching say, 370, rather, they would prefer to continue to the nearest 100 (or 50) and go on till 400. In a slow moving game, those 30 runs could account for about 30 minutes, leading to rain delays, weather changes or ‘Stop The Oil’ protestors making your stadium unusable.

Here, the results are more visible - waiting for round numbers to tick up can be costly. But they don’t need to be. Reaching a round number has no real significance on its own, rather it has to do with the relative change. And once again, the relative change needn’t be a round number.

The reason humans use base 10 for all modern numeric systems is simple - we have 10 fingers, so 10 fingers to count with. But if we were in the Simpsons’ world (where everyone had 4 fingers), the “special number” would be equivalent to 64 (in base 10) - one would start using the 3rd place right after hitting 64. Your special 100s would instead be 144s - a very ugly number, in all fairness. Cricket has somehow adjusted itself to a stage where the round numbers - the 100s, the 50s and so on, are decent indicators of the effort required. But is this the case everywhere?

A place where we as students would be most familiar with 100s is in examinations - writing papers out of 100 marks, or assignments for 10, hoping to cross 70 or 80 percent in an exam (or aiming for 99 percentile in the JEE examination). Or, as we’re getting older, prices of goods - which always end in 99, making sure that the next digit doesn’t spin over. None of these numbers would have any value had we used a different numbering system. What is somehow more important is the “absolute” number involved - a number which gives you a sense of scale, without being tied down to the rounding off, or crossing certain numeric landmarks.

So how do we gauge this absolute number? Well, we can’t. Humans are hardwired to make comparisons to understand things. Comparing things isn’t a necessarily selfish or narrow-minded act we do, it just helps us gauge things better. We aren’t born with a built in absolute gauge, so we compare things, heights, colours, weights and so on. And when it comes to things that are denoted through numbers, we use the numbers themselves - or more specifically, the things within the numbers that change - the digits in different places, the number of digits involved and so on.

Unfortunately, the absolute number cannot be gauged, but it can be compared to as well. Yes, the absolute number which we should not compare against round numbers, must be compared with yet some more to understand it properly. Take the example of runs - cricketers, through sheer experience know run rates and how much time will be required to score a certain number of them. As such, using this time to figure out how long to bat for is a good strategy. Figuring out prices makes more sense when you compare it against a more common and frequently encountered commodity. Marks in an exam can be compared with previous performances (not peer performances please), expected performances and so on.

The relative nature of numbers does cause some problems to a layman, because well, rounding off is pleasant - but taking a second comparison can make all the difference and can provide better insights into what the numbers truly stand for.

True inspiration is impossible to fake