Numbers, when you have nothing to do
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Some days ago, I found myself with nothing to do for a while. So I spent several minutes watching an ant scurry along the floor of the room. Yes: As is evident, I really had nothing to do.
Still, it wasn’t a total waste of time, for I actually learnt something from the ant. This: For its size, it scurries along nearly four times faster than Usain Bolt at his fastest.
If that makes you splutter in your coffee, note that I’m not suggesting that if we put the ant and Bolt on respective starting blocks and fire the starting gun, the ant will pound a path to the 100m finish line four times faster than Bolt will. But what I am saying is, if you give the ant a distance to cover that is, relative to its size, the same as 100m is to Bolt—well, the ant will indeed win that race. Hands down.
How can I make such a claim? Well, consider that Bolt is about 2m tall. His signature race, the 100m, is about 50 times as long as his body is. His world record at that distance is 9.58 seconds, which means he runs just over 5 body lengths every second. Nobody on the planet runs faster.
I should say, no human on the planet runs faster. But ants, now…. The little lady I watched (I like to think it was a lady) was about a millimetre long.
She ran erratically—back and forth, side to side, but making forward progress all the time—along the edges of the tiles on the floor. I timed her as she scurried right across one such tile. Erratic, yes, but she still made it to the other side, taking just about 15 seconds for the crossing.
Now these were 1x1ft—30x30cm—tiles. That crossing is, therefore, about 300 times as long as the ant is. So if she covered 300 body lengths in 15 seconds, we know she was zipping along at a pace of 20 body lengths every second.
Allow that to sink in: four times as fast as Usain Bolt.
Naturally there are caveats to any such comparison. The ant has six legs at her disposal whereas Bolt has just two. Bolt’s body structure and weight distribution are totally different from an ant’s. If you simply scaled up an ant to Bolt’s size, she would collapse because the increase in her weight would be far greater than in the length and thickness of her legs, and those legs could never support that weight.
But even with caveats, it’s an eye-opening comparison to make. There are more, too.
An earlier column on ants, for example, showed that the load a small group of ants carry for a certain distance is equivalent to you and a small group of your friends carrying 17 cars from Churchgate to Bombay Central. And when that lady ant contemplated crossing that 1x1ft tile, it was like me looking at swimming 25 laps of the nearby pool.
Maybe you can tell I like ants.
You can do similar exercises with other animals and the feats they attempt so casually.
Our late and much loved cat Cleo, for example, would routinely leap down to and back up from the parapet outside our window. That’s a good 1.5m or so, perhaps four times her body length.
If you ever jump up four times your height, you might want to contact athletics authorities somewhere. For you will have nearly trebled the long-standing high jump world record (Javier Sotomayor in 1993, 2.45m).
Not that cats are the world champions in jumping, far from it. That title goes to fleas, the little parasitic insects found on cats and dogs.
We know them for the itchy bites they can give us. But they also have powerful lever-like legs that, when they want to jump, transmit force all the way to their toes. That explosive push can propel them as far as 33cm, or 200 times their own length.
That’s like Sotomayor leaping over New York’s Empire State Building; a long jump of that magnitude would send an athlete soaring over the stands and out of any Olympic stadium in the world to land two stadiums away.
Comparisons like these are a good way to find awe and mystery in the animal world, besides giving humans some perspective on ourselves.
But I like them for another reason: They are a good way to play with numbers and see what turns up. To end this column, I’m going to toss some at you and leave you to do the figuring.
l An average human being weighs about as much as a million average ants. This is the basis of a contested claim that all the ants in the world weigh as much as all 7.2 billion humans. Contested, because it’s hard to estimate how many ants there are in the world.
l Speaking of 7.2 billion humans: If every one of them decided to settle in India, every one of them could be allotted land equal to about 10 ordinary Mumbai flats. Which may suggest that our world is less crowded than we imagine it is.
l Speaking of Mumbai: Are there two human beings in this vast city with exactly the same number of hairs on their bodies? The answer is an unequivocal “yes”. But how do I know that?
l Speaking of hair: Imagine an effort to lay hairs side by side (not lengthwise) along the Equator, encircling our planet. If every human is asked to donate equally to this project, how many hairs will you have to pull off your head, or if you’re bald, elsewhere? 30. All for a good cause, of course.
The stuff that happens when you have nothing to do, of course.
Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. A Matter Of Numbers explores the joy of mathematics, with occasional forays into other sciences.
Comments are welcome at firstname.lastname@example.org. Read Dilip’s Mint columns at www.livemint.com/dilipdsouza