A Whole ‘Nother Digit

On October 6, 2018 – in what now seems like a different age – the Machine coughed out its first post, ingeniously titled “Welcome to the Machine”. Today, a little over three years, 99 posts, and a pandemic and a half later, comes post #100. While it’s tempting to make this post all about the Machine and its magnificent journey to self-perceived super-stardom, we here at Parallax Plaza have decided instead to force the Machine to talk about the number 100, which actually has a remarkable history all its own.

While the number 100 has some interesting intrinsic characteristics (which we will get to momentarily), it’s first worth exploring why humans find it so important. Ultimately that traces back to why humans find the number 10 so important. And ultimately that traces back to a complete accident of our evolution on this world: most of us have 10 fingers (unceremoniously lumping the thumbs in with the rest). When it first became useful to start counting stuff, we didn’t have to look very far for a convenient way to do that, since our hands are typically right in front of our eyes helping us do any number of different things. Hence began our general affinity for the decimal system of numbers, also affectionately known as “base ten”. We do math in base ten every day, so much that we don’t even notice it, and are therefore completely unaware that we could have just as easily used any other number as a base – had we only been endowed with a different number of fingers. And in fact, a few isolated cultures have put their own twists on things: for example, using the spaces between the fingers to count, leading to an octal (base eight) system, or using both the fingers and the toes, leading to a base twenty approach.

When you decide on the base for your number system, you also set the number of usable digits in stone. In base ten, that means we have ten digits to choose from (0 to 9). If you count from 0 on up, once you exhaust all ten digits, you move up to the next order of magnitude (10 through 99), and then you exhaust the options for that first digit again, and you move up again (100 through 999). It works just the same in binary (base two), which uses only two digits (0 and 1), octal (which uses 0 through 7), and the infamous hexadecimal (base sixteen, which uses digits 0 through nine and then adds A through F to round things out).

When you move up to a new number of digits in a number, you’ve also gone to a higher power, which sounds religious but isn’t. The number 10 can also be expressed as 10 to the 1st power. 100 is 10 to the 2nd power, 1000 is 10 to the 3rd power, and so on. A million is 10 to the 6th power, a billion is 10 to the 9th, and a trillion is 10 to 12th. If you’re reading this blog post, there’s a good chance you’ve also used Google on a fairly regular basis to search for things. But there’s actually also a number called a googol: 10 to the 100th power, and another number called a googolplex, which is 10 to the googol power, and for which Carl Sagan noted you couldn’t fit a piece of paper with that many zeros written down in the known universe.

But let’s get back to 10 to the 2nd power – the number 100. I think there is possibly one reason more than any other why this number seems so special to us: it’s the power of 10 that most closely matches what we would consider to be the number of years in a nice long life. The average human lifespan falls considerably short of 100, but more and more people do manage to get there. On the flip side, the longest lives have been only a little more than a century, with the oldest having belonged to Jeanne Calment, who passed away in 1997 at the age of 122. So in a sense, the number 100 defines our mortality, and therefore us. That might be one reason why it’s found its way – perhaps subconsciously – into so many other things, like percentages, fractions of currency, the boiling point of water in degrees Celsius, and various religious traditions.

The number 100 has some interesting mathematical properties beyond being a power of 10. It happens to be the sum of the first 9 prime numbers. It is also the sum of the cubes of the first 4 positive integers. I could go on, but then I’d be Wikipedia, and Wikipedia I am not.

In closing, the Machine is deeply humbled to have reached this transcendental milestone. But let’s be honest, the real trick will be reaching 1000.

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