I did my undergrad in math over 20 years ago and find these discussions interesting but every time I go back to the TREE(3) explanation I glaze over when you jump from 3^3^3 (which isn't too hard to visualize in terms of the big quantity) to Grahams number which makes me return error mentally when I start to try and picture it.
3^3^3 is 3^27 which is straightforward enough. Where it gets hard is when you have to imagine 3^3^3.... 7.6 trillion times, i.e., the power tower stretching from your screen basically to the sun. And how big that number would be.
And then taking it to another level entirely and having that actual number be the height of the tower and that number be the height of the next tower... as many times as the height of the initial tower.
Exactly. Going from numbers that you can write out to numbers that are more conceptual. It stops being something I can sorta picture and turns into abstract concepts. IE- Blob A, say Grahams number {that is this unimaginably huge thing} is a smaller set than Blob B, say TREE(3) {that makes blob A look like a speck of sand}.
yeah, especially TREE(3) is hard to wrap your mind around, but GN (while impossible to really grasp its magnitude) is possible to understand the process by which it's built. Like you know how crazy it is getting from counting to say tetration (two arrows) or pentation (three), and that's just five steps. G2 is G1 *steps*. No way even to wrap your head around it except to understand the process.
In the links, there's one crazy video comparing GN to T3, and it really shows how much larger it is, the way GN is so much larger than any number the average person could name.
Listening to these people try to describe it to us is pretty funny too. They quickly run out of adjectives to relay how much bigger one is from another. We kinda just don't have the words for it in non mathematical language, anyway.
it's only possible to (sort of) understand the rate of rate of growth. The actual numbers can't be understood, and TREE(3)'s rate of growth also can't really be understood except in contrast to other really fast growing functions like GN which is so far down the hierarchy compared to it.
I did my undergrad in math over 20 years ago and find these discussions interesting but every time I go back to the TREE(3) explanation I glaze over when you jump from 3^3^3 (which isn't too hard to visualize in terms of the big quantity) to Grahams number which makes me return error mentally when I start to try and picture it.
3^3^3 is 3^27 which is straightforward enough. Where it gets hard is when you have to imagine 3^3^3.... 7.6 trillion times, i.e., the power tower stretching from your screen basically to the sun. And how big that number would be.
And then taking it to another level entirely and having that actual number be the height of the tower and that number be the height of the next tower... as many times as the height of the initial tower.
Exactly. Going from numbers that you can write out to numbers that are more conceptual. It stops being something I can sorta picture and turns into abstract concepts. IE- Blob A, say Grahams number {that is this unimaginably huge thing} is a smaller set than Blob B, say TREE(3) {that makes blob A look like a speck of sand}.
yeah, especially TREE(3) is hard to wrap your mind around, but GN (while impossible to really grasp its magnitude) is possible to understand the process by which it's built. Like you know how crazy it is getting from counting to say tetration (two arrows) or pentation (three), and that's just five steps. G2 is G1 *steps*. No way even to wrap your head around it except to understand the process.
In the links, there's one crazy video comparing GN to T3, and it really shows how much larger it is, the way GN is so much larger than any number the average person could name.
Listening to these people try to describe it to us is pretty funny too. They quickly run out of adjectives to relay how much bigger one is from another. We kinda just don't have the words for it in non mathematical language, anyway.
it's only possible to (sort of) understand the rate of rate of growth. The actual numbers can't be understood, and TREE(3)'s rate of growth also can't really be understood except in contrast to other really fast growing functions like GN which is so far down the hierarchy compared to it.