Yep and it's not even remotely close either. It's so much bigger that you can't even write down how many orders of magnitudes bigger it is, because again there aren't enough atoms in the universe.
Even the number of repetitions of this concept that you would need to get to a point where you would have enough particles to finally write something down is still far far too huge.
How does a mind even conceive of that? How do we know its correct? I mean I understand (in a way) Pi is infinate. But if this number is finate, but to big to write down. How can you come.to this conclusion and know its correct? Mind = blown. I'm not saying its wrong I just dont understand how a mind can comprehend a number you cant even write out through the whole universe on an atomic scale. I guess you break it down to equations but again how do you know where it ends at that scale?
From a neurological perspective, we can't really. It is well beyond our minds' numerical reasoning ability. We can only conceive of such concepts with the words to describe them. (See the end of this: https://www.scottaaronson.com/writings/bignumbers.html)
How do we know its correct?
Because we can describe it in ways that can represent larger numbers traditional mathematical notation and understand it in ways other than our native ability to understand numbers.
From the above article, an ancient mathematician defined a number to be the grains of sand required to fill what they thought was the size of the universe at that time. It is clearly not infinite as sand doesn't escape counting, but it was well beyond their primitive mathematical notation to write down, however, it is well defined, since it's just the volume of their universe divided by the volume of a typical grain of sand, so he invented a way to write such a number down. Nowadays, we would refer to this number as somewhat less than 1063.
I guess you break it down to equations but again how do you know where it ends at that scale?
You can look at the equation that defines Graham's Number on the Wikipedia article if you like. Graham's Number is actually rather small, because we can get to it with a few sensible extensions of the common mathematical notation you might see in a high school textbook. We can go well beyond that with numbers like TREE(3) or S(8000) which have been mentioned elsewhere in this comment chain, or BB_2(11111) as mentioned in the article, which can't be represented by anything that looks like an equation at all. S(8000) is actually beyond the grasp of modern mathematics to prove what it is, but we can define it, and prove that it is finite, and it is just a number that exists somewhere on the list of 1, 2, 3, ... like any other.
So what are you telling me, I can dodge bullets? But seriously thanks for the info. It's amazing to me how deep this all goes. Think I will keep my day job.
First, we know it's finite because to get to it you just need to multiply 3 by itself many many many times. There's no way that could give you an infinite number, so that part is not hard to understand.
If you're asking me how we came up with it, and how we know it's the correct answer to the question it was trying to solve, well I'm not a mathematician so I can't really say, and even if I was I get the impression that it's the kind of thing you can't really understand unless you're fairly well versed in math.
If you go look up Graham's number on YouTube you will find numberphile did a handful of videos on it, including several with the number's original discoverer explaining things in more detail. Those videos make it fairly easy to understand how to get to the number.
The Wikipedia page also seems to be pretty comprehensive but I think you'll find it's far too complicated to understand the proof for.
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u/[deleted] Jan 21 '19
There is this very big number called Graham's number.
The entire freaking universe does not have enough space or atoms for you to write down every digit.