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Infinite number counting machine

ScienceInfinite number counting machine

The counting machine of numbers from 0 to 1 googol, that counts, counts and counts and will never stop

Sam from Look, Mom, No Computer! is dedicated to building electronic gizmos of all kinds, many of which combine music with electronics. In this project called Googol Counter he shows a machine whose sole purpose is to count, from 0 to 1 googol, at every possible speed, in this case at about 30,000 numbers per second.

The googol is, as we learned from Carl Sagan in Cosmos, 10100, that is a 1 second of a hundred zeros or ten thousand sexdecillions. It is a number so incredibly large that it surpasses common human perception, because the exponential effect of “adding another digit” tricks our way of understanding the growth of things. In the machine, which Sam starts by equipping with a few 10-segment displays, more and more digits are added until the hundred is complete.

The electronics of the invention are relatively simple, and durable, because such a machine should have a long life. All that is needed to “count” is 4026 and 555 chips and a clock signal. And the rest is a lot of custom 3D printing. At the beginning of the video, you can see how it starts testing with 1,000 Hz (cycles per second) and gradually increases to about 30,000 Hz, without seeming to have a major problem.

The real problem is the size of the project. If you look at the counter you will see that the first digits go so fast that you can’t even see them change, but a little further on, five or six digits, they slow down to the rate of one change every second. Each digit moves ten times slower than the previous one.

To make a rough calculation: let’s say we start with 100,000 per second (6 digits). A day has 86,400 seconds, so after one day you could see about six more digits change. But a year is only 365 days, so every three years another four digits would move. What about a century? Three more. The age of the universe? Add another 10 or 11, to give us those 13.7 billion years. If the clock had started counting with the Big Bang it still wouldn’t have gone past about 29 or 30 digits… infinitely far from the 100 – the googol – it’s aiming for.

As Sam says, it’s rare to get such a project going, of which you’ll maybe see some of the digits change once or twice in your lifetime (around the 14th digit), which gives you an idea of the immensity of a googol. Leaving aside the number of possible problems of wear and tear, power supply or even the impacts of cosmic rays (or the disintegration of the very electrons, for that matter), it is clear that although the counting machine could theoretically reach 10100, it never will.

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