TREE(Graham's Number) (extra) - Numberphile

You see the number 10^122 and think: "wow, that's tiny, absolutely minuscule".

I love how he calculated the size of the universe in Plank lengths so casually. 10^122 is clearly an unimaginably large number, yet since it can be expressed so concisely it's also unimaginably miniscule compared to these other numbers that cannot even be expressed via recursive arrow notation

Love that he approximates in seconds the size of the universe in Planck lengths but has to ask what 70 + 52 is

Out of all the videos on the entire internet, this is the last one I expected to make a brexit reference.

"Allocate more information to the simulation - Why ? - The Sim I wanted to be a mathematician is back at it with trees and that graham guy"

The universe should just download more energy

“Universe says no.”

I think it's kind of cool that we've compressed numbers so efficiently that we can talk about stuff like TREE(g(64)) which is so unimaginably more massive than anything the universe could ever contain... and yet it takes about 11 bytes to write it down.

"TREE is daddy" - Tony

Love this, this is the pub chat after filming a numberphile video and sinking a few pints

I can see the struggle Tony has while explaining what De Sitter space is After 5:50 he wanted to say De Sitter several times but stopped each time, it's both funny and somewhat frustrating for him

Reminds me when I realise that number of decimal places of Pi needed to measure the diameter of the visible universe in Planck lengths was smaller than than we have already calculated.

That should be 2^(10^122) then, since 10^122 is the number of bits you can store in the universe, and 2^(10^122) is the largest possible number you can store with that many bits.

These rabbit holes of numbers just fill me with awe. He is literally thinking about how you should tinker with the laws of the universe JUST in order to be able to think about bigger numbers. The fact i listened to that, that it got in my mind is beautiful. This is the purest form of curiosity i have encountered - people invented the model maths is, then tried really hard to make an efficient way of describing it(I.e. explored it) and now they are pushing the limits. And yet again they just explore how to most efficiently push them, just so they can see the next boundary and push it. An endless pit of possibilities that can not be even imagined, yet are perfectly described. Just because we are curious what lies beyond in a model we invented. My eyes are watering at the thought of the beauty of human curiosity.

This man has made a gallery for his children in his office.

I think he left out a step in his calculation of the biggest possible number that can exist. 10^122 is simply the SIZE of the biggest number, not the biggest number itself. If each of those Planck units can store one bit of data, then the actual "biggest number" is 2^(10^122), which is quite a bit bigger, but still much smaller than Graham's number.

Is this the reason why WinRar never expire?

String theorists: we think there's 10^{500} possible versions of string theory! That's clearly way too many! TREE(3): You are little baby

Thanks so much for making these videos, and for supporting a great cause. I truly appreciate your work, and the work of the people you talk with.

I love big number videos, thanks for this! I do want to disagree though with the latter half of your video, on the nominal reality of TREE(Graham's) as your argument seems to ignore combinatorics - a simple 3x3x3 Rubik's cube has 43 quintillion possible combinations, for a mere volumetric cost of nine cubes. I feel it would be tough to convince me of the unreality of those combinations, too, as I can use a very simple algorithm to access any one I want in a few seconds. I would love to see a comparison of TREE(g(64)) to the universe's possibility space, especially as Everett's interpretation of QM asserts the reality of that space.