User blog comment:Superman37891/PEPTO BISMOL/@comment-30754445-20170427172623/@comment-30754445-20170428113126

Well, I don't see how an imaginary universe with imaginary rules is any more (or less) "real" then the original mathematical ideas we used to construct it.

Imagine an infinite computer that expands the gongulus one step at time. To be more precise: We have a computer that is programmed to follow the rules of BEAF and given the input "{10,10 (100) 2}". It's a reasonably short program that runs on a reasonable short input, yet it will take about a gongulus steps to complete and about a gongulus bits of memory.

This is a very concrete idea. We can't build the thing, of-course. But we can imagine it existing in some imaginary infinite universe and running the program. Why would this be any less "real" than a full-fledged imaginary universe with arbitrary rules? To a platonist, both would be real. To a physicialist, both would be figments of the human imaginations. And both camps would agree, I think, that such imaginary/platonistic universes have very little to do with actual physics.

The important distinction here, I think, should not between "real world" and "abstract". It should be between "exploring the world of large numbers" and merely rushing headlong to create bigger and bigger numbers just for the sake of creating them.

I find the latter approach to be a bit silly. I mean, it's a race we can't win anyway, so what's the point? Only when we put the googological tools to some practical use (and I include expanding our mental horizons under "practical") does it become meaningful.