The use of constants without any actual representation is a bit sneaky. You might apply a ceiling assuming constants are limited to, say, 16x16 pixels, with ea

The use of constants without any actual representation is a bit sneaky. You might apply a ceiling assuming constants are limited to, say, 16x16 pixels, with each pixel marked or unmarked. That gives you 2^256 constants to play with (minus those that are already taken), probably many more than the human mind can effectively remember or distinguish without confusion. I could be bargained into more pixels per symbol, but let's consider this case to start... H(2^256, 10^100) would still be quite large. Considerably less so than G(10^100), but I think it might be more fair (for some arbitrary definition of fair). Of course, pixels per character can vary wildly, based on display size, and even on simple displays often contain more than 256 pixels. A more reasonable assumption for very simple displays might be 32x48. At that large, you're over 10^100, because your options with that much of a canvas have already shot over 400 digits. You can get many more pixels if you assume your constants are a word, but I think Rayo's constraints would start counting subscripts and word-like constants as multiple "symbols". Then again, we usually don't just flip a single pixel to switch symbols either, so I'm being too generous there. I'm not sure anyone's done a study on how many potential single-width characters might be reasonably distinguishable... Studies on human perception seem like a much needed prerequisite for further classification of large numbers!