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Point of View

To infinity and beyond

January 25, 2019

What’s a bigger number, the total number of atoms in Dwayne “The Rock” Johnson’s body or the total number of microprocessor clock cycles since the dawn of time?

Think of a big number. A really big number. Grains of sand on a beach. Bigger. On all the beaches. Bigger still. Stars in the universe. The number of atoms in Dwayne Johnson’s body. Microprocessor clock cycles since the dawn of time????

A few things I inherited from my father – other than a prematurely receding hairline and a predilection for dad jokes — were a love of math and an insatiable curiosity for bizarre and random statistics. As a young kid, I became fascinated with the concept of “countable infinities,” an esoteric and weird mathematical concept proposed by Georg Cantor (an esoteric and weird mathematician from the late 1800s). OK, I was a weird young kid —but perhaps not as weird as Georg — who believed his theory of transfinite numbers had been communicated to him directly by God.

I won’t dig into the theory of countable infinities — mainly because this allows me to elegantly sidestep the fact that I don’t really understand it (mentioning it as if I did makes me sound much smarter than I am), but it did get me thinking about really big numbers. In ancient times, the philosophers would ponder huge numbers in terms of physical quantities – how many grains of sand on the beach? How many stars in the sky? Today, we spend too much time glued to our smartphones to bother going to the beach or looking at the sky. Accordingly adapted to our modern time, one more contemporaneously huge number that occurred to me is microprocessor clock cycles.

Just a bit of background on the CPU clock. As a mechanical engineer, my grasp on this is tenuous, and most certainly flawed, but as near as I understand and can explain, the true magic of a computer lies not in its brilliance but rather the ability to subdivide and break the amazing things it does down into gazillions of ridiculously simple tasks. It’s true, the fundamental capabilities of a computer are all distilled down into a set of remarkably mundane logical tasks – all basically comparing a pair of zeros and ones and passing on the results. That’s it. That a computer can do these tasks doesn’t seem all that amazing.

What’s amazing to me is that zillions of these simple tasks can be combined almost instantaneously in an artful way that allows me to type this blog or watch a silly cat gif. But they can. What makes cat gifs possible - is that computers are really, really, really, really fast at doing those simple comparisons. Incomprehensibly fast. Unfathomably fast. Mind-blowing fast. In every computer, there is a “clock” – basically the metronome conducting each one of these basic operations. And that clock FLIES! Tempus fugit. On steroids.

Example – that smartphone in your pocket most likely has a clock speed around two GHz. We sometimes hear those numbers without taking the time to think about them. So, let’s break that down. A Hertz – just means “times per second.” A Giga is a one followed by nine zeros. So, two Giga Hertz means your smartphone is executing one of those basic comparison operations 2,000,000,000 TIMES PER SECOND. Not just this second but every second.

Think about that for a second. No wait — don’t. It probably makes your head hurt. That means in the time it’s taken to read this; your smartphone has quietly gone off and executed about 12,000,000,000 clock cycles. Oh, and it’s not like YOUR phone is so special (although that is a lovely Hello Kitty case). Oops… there goes another 6,000,000,000 ticks of the clock. Where was I? Oh yeah, how fast the clock in your phone is. It is. So is the phone in your neighbor’s pocket. The computer on your desk is likely a bit faster. By the way, the main processor in your phone isn’t the only thing with a ticking clock. The Wi-Fi chip, PMIC, cellular module, Bluetooth module, are all ticking away too. Not to mention multi-core processors… Whew. And it turns out that phones and computers are just the tip of the iceberg when it comes to CPUs and their attendant clocks.

There are literally billions of microprocessors manufactured every year and only a tiny fraction of these end up running cat videos on smartphones and computers. The remainder serve as the brains of far more pedestrian applications – the clock on your microwave, your thermostat, heart lung pumps, traffic signals, airplane navigation, your fitness monitor. Just about every conceivable modern product that runs on electricity has some sort of microprocessor humming away in its guts. Depending on its vintage, your car might have 50 or more — most likely running a bit slower than your smartphone but still buzzing away with their clocks ticking away at fairly scalding speeds.

Every one of these microprocessors is adding up clock cycles at a furious and unfathomable rate. So, still being a somewhat weird adult, I got to wondering – if you were to add up all of the clock cycles on all of the microprocessors built since the dawn of time, how incomprehensibly big would that number be? How does it compare to the other really big numbers of antiquity? Like the stars in the sky or atoms in the Rock’s body?

Are you math-curious?

Doing this requires a bit of math – and making a handful of completely indefensible and certainly incorrect assumptions. If you’re math-curious, you can follow along and feel free to spot mistakes and poke holes in my very questionable reasoning. If you’re not so curious, you can skip to the end* and see what I came up with.

Let’s start with how many microprocessors have been made since the dawn of time. One of the fascinating things about this particular “countable infinity” is that unlike grains of sand in the world or stars in the universe, it has its genesis in my lifetime (so does the number of Atoms in Dwayne “The Rock” Johnson, but more on that later).

It’s generally agreed that the first commercial microprocessor was the Intel 4004 —invented in 1971 — less than 50 years ago. So, one useful data point is the assumption that the total number of microprocessor clock cycles in 1970 was essentially zero. So that’s a start. From there on it gets a bit fuzzier. I found an article referenced by Wikipedia that claims the total number of microprocessors manufactured in 2008 was around 10 billion(!).

There’s no doubt that the number of microprocessors manufactured has been increasing at a staggering rate. But how staggering? To estimate the total number of microprocessors made since the dawn of time I made the heroic assumption that the number of microprocessors manufactured is following a second-order polynomial equation. Please note that this is a mathematical trick. By taking an assumption that I pulled completely out of thin air and giving it a fancy name, I’m tricking you into thinking I know more about what I’m talking about than I actually do. But I don’t. It’s sort of a total guess. Got it? Onward.

Thanks Dad… you just cost me a wasted Sunday morning.

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