Graham's number is one of the largest numbers ever conceived, having heaps of 'power towers' of exponents, even at the lowest of 64 super-exponential levels. Each level effectively becomes the super-exponent of every aspect of the next level. Even the lowest level is supposedly larger than the number of particles in the universe.
The number is a proposed solution to the mathematical problem of the number of dimensions necessary to prove that a two-dimensional figure actually exists.
In a video, Ronald Graham himself proposes that a much smaller number of dimensions may be adequate, but it is more than 12 dimensions, and past 12 we don't have the current computing power to test the problem.
My own proposition is that in a typological system the answer to a similar problem is 21 dimensions. This is a development of my previous writing How to Build a 21-Dimensional Universe, which proposes that the 21st dimension is where quadruple semantics emerges. Therefore, in terms of quadratics, the 21st dimension appears to be where 3-d or 2-d figures could be defined with certainty, e.g. because quadruple complexity is where points exist in 4-d.
For more information on How to Build a 21-Dimensional Universe, which may ultimately be useful for mathematics, see: https://hypercubics.blogspot.com/2015/06/the-tracery-view-of-dimensionalism.html
See also THIS PAGE for clarification on Graham's Number: https://www.quora.com/Is-there-a-Grahams-number-of-something-in-the-universe
Wikipedia also has a page that Graham recommended in one of the Numberophile videos on Youtube: https://en.wikipedia.org/wiki/Graham%27s_number
The primary Numberophile video on Youtube explaining Graham's Number can be found HERE: https://www.youtube.com/watch?v=GuigptwlVHo
Keywords: "lower bound of graham's problem"
International Society for the Philosophy of Architecture » Ethics and Aesthetics of Architecture and the Environment