u/Warm-Contact738

So, I get that TREE(3) is too big a number to represent in the universe with physical things, as there are not enough physical things, nor is there enough space to put them. And I get that even by reducing that to just trying to write the number, we are still unable to represent TREE(3), as there are more digits in the number than there are places to put them, even if each digit were only to take a planck volume, as there aren't enough of those to assign to the digits.

But, given all the space in the universe, could we write down the number that represents the number of digits in TREE(3)? Or could we write down the number of digits in that number?

How many layers of reduction before we arrive at a number that we can write down?