I swear mathematicians are witches.
You just get dizzy even thinking about it. The observable universe is just not really that big when talking about this stuff, there are not even 100 orders of magnitude in the universe from smallest to biggest. Anything that you can have a conception of (even stuff like the number of possible lottery tickets or possible books that could ever be written etc) is just indistinguishable from mundane everyday sizes when dealing with googology. You're trying to roar but it comes out as a whisper. You have to explicitly design these. Most of the time if you think "but wouldn't it be comparable if we counted the XYZ) the answer is no.
It's like an adult equivalent of a kid saying "I get that galaxies are big, but are they also bigger than really big houses? How about a house with its own swimming pool? Really really big mansion of a big movie star?"
Edit: Tone is difficult in writing, I don't mean to be condescending, I'm getting dizzy myself when thinking of this and remember my frustration and amazement when first hearing about these.
Why did nobody ever tell me to think of logs like this before!!?
https://math.stackexchange.com/questions/1384917/relation-be...
Or, in other words, blowing a kiss against a nuclear blow? That absolutely hugely more relevant than taking the log of the Graham's number. I can't even say how hugely more relevant it is without an almost equally irrelevant comparison.
(And yes, I am certain you know this. It's a pedantic clarification, I hope it made the point clearer.)
On the other hand there is just maybe a page of explanation needed for a somewhat educated layperson to understand the construction of Graham's number.
So on one hand it's unexplicably big to the point where it's even unexplicable how unexplicably big it is etc, on the other hand it can be compactly described. It's an example of the power of thought and reason and deliberate design, making so much of so little.
Fwiw, I did't read it that way at all. I thought the child's question was a great analogy.
A million seconds is 11.5 days from now. A billion seconds is 31 years, 8 months, and 15 days from now. A trillion seconds is 31,709 years from now.
and it's companion https://waitbutwhy.com/2014/11/from-1-to-1000000.html are pretty cool.
But they grow very rapidly. Ramsey theory has usually the biggest constants found in mathematical papers.[1] There is a famous quote by Erdos:
"Suppose aliens invade the earth and threaten to obliterate it in a year's time unless human beings can find the Ramsey number for red five and blue five. We could marshal the world's best minds and fastest computers, and within a year we could probably calculate the value. If the aliens demanded the Ramsey number for red six and blue six, however, we would have no choice but to launch a preemptive attack."
[1]https://en.m.wikipedia.org/wiki/Graham%27s_number