BusyBeaver(6) Is Quite Large
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BusyBeaver(6) Is Quite Large
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Re: BusyBeaver(6) Is Quite Large
#2> So I said, imagine you had 10,000,000sub10 grains of sand. Then you could … well, uh … you could fill about 10,000,000sub10 copies of the observable universe with that sand.
I don't get this part. Is it really rounding away the volume of the observable universe divided by the average volume of a grain of sand? That is many more orders of magnitude than the amount of mass in the universe, which is a more usual comparison.
Re: BusyBeaver(6) Is Quite Large
#3I wonder if the visible universe is large enough to write down the exact value of BB(6).
Re: BusyBeaver(6) Is Quite Large
#4It boggles my mind that a number (an uncomputable number, granted) like BB(748) can be "independent of ZFC". It feels like a category error or something.
Re: BusyBeaver(6) Is Quite Large
#5> So I said, imagine you had 10,000,000sub10 grains of sand. Then you could … well, uh … you could fill about 10,000,000sub10 copies of the observable universe with that sand. I don't get this part. Is it really rounding away the volume of the observable universe divided by the average volume of a grain of sand? That is many more orders of magnitude than the amount of mass in the universe, which is a more usual compa…
Yes, that's only some normal number amount of orders of magnitude. Even 10,000,000^10,000,000 is already so large that it doesnt matter, let alone after exponentiating _the exponent_ nine times more.
Re: BusyBeaver(6) Is Quite Large
#6I wonder if the visible universe is large enough to write down the exact value of BB(6).
It's not.
Re: BusyBeaver(6) Is Quite Large
#7> So I said, imagine you had 10,000,000sub10 grains of sand. Then you could … well, uh … you could fill about 10,000,000sub10 copies of the observable universe with that sand. I don't get this part. Is it really rounding away the volume of the observable universe divided by the average volume of a grain of sand? That is many more orders of magnitude than the amount of mass in the universe, which is a more usual compa…
With tetration you're not dealing with orders of magnitude anymore, but orders of magnitude of orders of magnitude.
Re: BusyBeaver(6) Is Quite Large
#8[deleted]
Re: BusyBeaver(6) Is Quite Large
#9> So I said, imagine you had 10,000,000sub10 grains of sand. Then you could … well, uh … you could fill about 10,000,000sub10 copies of the observable universe with that sand. I don't get this part. Is it really rounding away the volume of the observable universe divided by the average volume of a grain of sand? That is many more orders of magnitude than the amount of mass in the universe, which is a more usual compa…
Exactly. This number is so so much bigger than 10^100000 or however many grains of sand would fit, that dividing by that amount doesn’t really change it, certainly not enough to bring it down closer to 9,999,999sub10
Re: BusyBeaver(6) Is Quite Large
#10> So I said, imagine you had 10,000,000sub10 grains of sand. Then you could … well, uh … you could fill about 10,000,000sub10 copies of the observable universe with that sand. I don't get this part. Is it really rounding away the volume of the observable universe divided by the average volume of a grain of sand? That is many more orders of magnitude than the amount of mass in the universe, which is a more usual compa…
Yes, that's right, dividing by that ratio essentially barely affects the number in a sense that 'adjacent' numbers in that notation give a much bigger change.
10↑↑10,000,000 / (sand grains per universe) is vastly larger than, say, 10↑↑9,999,999
So on system we're using to write these numbers, there's really no better way to write (very big)/ (only universally big) than by writing exactly that, and then in the notation for very big, it pretty much rounds to just (very big).