Steinhaus-Moser notation is a method of displaying staggeringly large numbers.
SHN works by putting polygons around integers.
It starts with triangles. A number N in a triangle is equal to NN. 1 in a triangle = 1. 2 in a triangle = 4.
You can nest the polygons - you just calculate from the inside out. So N inside two triangles = NN inside one triangle = (NN)NN. 2 in two triangles = 4 in one triangle = 256. And you can add more triangles around the outside to keep going.
Fine. Next up is squares. A number N in a square = N in N nested triangles. So 2 in a square = 2 inside two nested triangles = 4 inside one triangle = 44 = 256. That's pretty manageable! Right? Hope so!
Fine. Pentagons? N inside a pentagon = N inside N nested squares. We're stuck with integers here, and the smallest integer is 2 (1 will just always give you 1 whatever it's surrounded with) so 2 inside a pentagon = 2 inside two squares = (2 inside a square) inside a square = 256 inside a square. Which is 256 inside 256 triangles.
Wait, what?
256 inside 256 triangles = 256256 inside 255 triangles. Which is (256256)256256 inside 254 triangles. I could go on. That's a big, big tower of numbers. These are already ridiculously large numbers. And we're still just 2 inside a pentagon? Imagine putting 3 in there! Imagine going on, logically, to hexagons and heptagons (which keep going in the fashion you'd expect)!
(In general, N inside a triangle represents NN, and N inside a polygon of X sides (where X>3) is equal to N inside N polygons of X-1 sides.)
This allowed the creation of numbers such as the inconceivable 10 inside a pentagon, which is called a Mega, and 2 inside a Mega-gon, which is called a Moser. Both of these numbers are staggeringly gigantic and utterly incomprehensible.
Aaaaand useless.
Graham's Number, however, treads on all of them.