That googol machine. Can someone explain what the machine is trying to illustrate and why the final gear can’t turn. I know it takes more energy than exists in the universe or something but why how what?
In: Physics
It demonstrates exactly how absurdly large a number a googol is (1 with a hundred zeros after it).
The machine has 100 gears and it takes 10 spins of a gear to move the one behind it….so it’d take 10 spins of the first gear to move the 2nd, 100 to reach the 3rd, 1k to reach the 4th, a million to reach turn the 7th gear, and a googol to finally reach the last.
If someone were to turn the crank once a second, it would take 32 years before they reached a billion turns- or the 10th gear….then 10x that to reach the 11th.
A fast motor, like one found in a Dremel (or similar rotary tool), spokning a fast 36,000/ minute, would be able to reach that same 10th gear in about 200 days of constant running. To reach the end at that speed, it would still take (roughly)
52,813,400,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00,000,000,000,000,000 years.
You know how when you pedal a bike in first gear it feels like your legs are moving a lot and not really accomplishing anything? It might take 10 turns of the pedals to only achieve one rotation of the bike’s wheel. What’s happened in this machine is that someone has repeated this process over and over. Maybe 10 rotations of the first wheel turn the second wheel once. And 10 rotations of the second wheel turn the third wheel once. That means that you have to turn the first wheel 100 times in order to turn the third wheel once. Add a fourth wheel and you have to turn the first wheel a thousand times to get one rotation on the fourth wheel. Repeat over and over until you get to the number googol. Make sense?
EDIT: The claim that it would take more energy than is in the universe to turn the last wheel is false. It would just take a really, really, really, really, REALLY long time. More time than the universe is likely to exist
This machine visualizes number googol (a 1 with a 100 zeros, bigger than the atoms in the known universe) & has a gear reduction of 1 to 10 a hundred times. To get last gear to turn once you’ll need to spin first one a googol amount around, which will require more energy than entire universe has.
byu/mtimetraveller inThatsInsane
To say a little bit about the energy: moving something takes energy, specifically something called work. This is defined as the distance over which a force works. For example, if you had to move something twice as heavy, you have to put in twice as much energy (ignoring friction) and if you moved it twice as far, you also have to put in twice as much energy. Now this machine requires a massive amount of distance over which the force is applied, 10^100 turns. Even for small forces, this required so much energy it is unfathomable. Wether it is indeed more energy than there is in the universe I don’t know, don’t have any paper for an estimate, but it would be definitely more than our galaxy puts out, by still several dozens orders of magnitude
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