A taste of infinity

Graham's number.

Music by Kevin MacLeod ( http://incompetech.com/ )

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[Overlord484]

To the maker of this video:

you list 3(up)(up)3 as being equal to 3(up)3(up)3 as being equal to 3^27, this is untrue. By the order of operations 3(up)3(up)3 is equal to 27^3 where (up) is the up arrow symbol. 3(up)(up)3 is actually equal to 3(up) [3(up)3] where square brackets indicate grouping. Please fix this admittedly minor error.

[ZJemptv]

@Overlord484 Actually, exponentiation is right-associative, meaning it is carried out from right to left.

[Spooneads]

Thumbs up if this is the first thing that told you about what grahams number is!

[skoockum]

@Weendigo172 Are you still impressed with 7 trillion?

One drop of water, one measly little drop of water, has 7 trillion water molecules in it --- 240 million time over.

As you sit there quietly typing away on your keyboard, with just one breath you inhale a number of air molecules that is somewhere in the neighborhood of 2 billion times bigger than 7 trillion.

No, 7 trillion just isn't all that big. When you think about it, it's really kind of puny.

[skoockum]

@Weendigo172 As a matter of fact, 1 is as you put it, "an insanely large number on its own merit" when you compare it to 1/7 trillion. But it's even more insane when you compare it to 1/googol. You're prolly starting to see that "big" and "small" are relative terms (ie Big? Compared to what?)

Your body has roughly 7 trillion human cells and 70 trillion microbial cells. Every time you take a step to the west, you move 77 trillion cells one step to the west. 7 trillion? Big whoop.

[skoockum]

@Weendigo172 Being wowed by the vastness of 7 trillion is comparable to looking up at the Empire State building and being impressed with its size: sure, it's a lot bigger than you are, but it disappears when you step back to the moon and look at the earth. And if you look at size of the known universe, the building is so small as to be insignificant.

As the size of the known universe dwarfs an electron, so googol dwarfs 7 trillion. And Graham's number to googleplex.

[Weendigo172]

@skoockum But keep in mind, this is just a tenth, of a billionth of what a trillion objects is. A trillion dollars is still just one sum of money. If in a hypothetical scenario the trillion of one dollar notes stretched out before you in a row 1000 notes wide, it would still reach to the horizon and back. 15 times.

[Weendigo172]

@skoockum Hell, even imagining 100 single objects is starting to get actually difficult.(Or I don't know, maybe this is just me.) Remember, don't group these objects together. Imagine them all as single objects. Can you do 100? If so, I applaud your mental flexibility.

[Weendigo172]

@skoockum While it's true that a trillion isn't even a drop in the bucket by comparison, it is still an insanely large number on its own merit. Think of it this way - How many singular things can you imagine? The ability of humans to imagine solid objects is great in detail but when you go above a certain number, it becomes hugely difficult. Nine objects in a three by three square is easy, and so is sixteen or perhaps even 25. But when you get to 36 and beyond, things start to go fuzzy.

[skoockum]

@Weendigo172 7 trillion isn't even a drop in the bucket. Just raise it to itself once and you'll see what I mean. And since you can raise that result to the power of itself, well, the second number begins to look insignificant by comparison, and so on with each iteration.

By the only the 3rd iteration 7 trillion is so close to one in scale to the two subsequent values that it is essentially 1.

[skoockum]

My calc 3 teacher once said that the grader was infinitely fast. I nearly spit in his face.

[axion419]

Graham's number is precisely as far away from infinity as is the number one. Interesting video, it just has nothing to do with infinity.