wow, thanks, great explanation
I liked the monk analogy
Discussions of large numbers inevitably lead to Graham’s Number. It’s, well, it’s really quite big - so much so that the observable Universe isn’t large enough to write it out in standard notation, one digit to every Planck volume. We do know that it’s last digit is 7 however.
24 is the highest number.
Last I heard, there was no “end” to the universe. It does not stop nor have any end.
Therefore the answer to this question is that both numbers would be dynamic (constantly growing with the count of atoms), but the larger number would be growing at a faster rate or be at least 1 higher than the atom count number, thus would always be larger.
However many atoms there are in the universe there are six times as many quarks.
First, a nitpick: this number is inaccurate. Each proton and each neutron is formed from three quarks, so the total number of quarks will vary by element (and its isotopes). Standard hydrogen has one proton and therefore three quarks. Uranium 235 will have 705. Since the vast majority of the universe is hydrogen, the average is probably just over three quarks per atom. (Mesons have only two quarks, but they were more predominant in the very early universe. And dark matter may or may not have quarks in its makeup, whatever it is.)
Quarks are bound inside particles, though. They are found independently only under rare and extreme circumstances. You can’t properly think of them as little balls rattling around inside, either. So do they exist? What sense of “existence” do they reside in? They are real matter and a concept simultaneously.
“Common sense” earthling notions of existence don’t play well with the realities of the entire universe.
Can you imagine a deck containing 60 cards? Can you imagine shuffling that deck? That’s something that you can hold in the palm of your hand. And yet, there are almost 10^82 different possible shufflings of those cards. Does that make that number “real”?
Or is it only “real” if you can conceive of that number directly, all at once? If that’s your standard, then no number greater than 9, at best, is “real”, since humans can only think of between 5 and 9 distinct things at once.
Well really it was more that the total of all atoms is 80 characters but the prime number filled up 3 notebooks (printed on both sides of the page).
I have a friend who subscribes to this belief. A “number” has to represent something that can, at least in the abstract ideal, be counted. The number of atoms in the universe. The number of grains of sand on the beach. etc. No one is ever actually going to count these, but the ideal is there.
In contrast, 10^900 does not represent anything physical. There aren’t 10^900 anythings.
So, my friend says, 10^900 is “not a number.”
Now, this destroys many of the properties of numbers that mathematicians admire. The counting numbers would no longer be closed under addition; they cease to be a field; the axiom of succession is thrown out.
“I’m not a Platonist” my friend says, haughtily.
Shrug. As far as that goes, 10^9 is “not a number” because nobody is ever actually going to count that high. Here is a 500 pound bag of rice. How many grains of rice are in it? “That’s not a number.” Nobody is ever going to sit down and count them. How many people are there on earth? “Not a number.”
Ideologically-driven arithmetic is as stupid as any other ideologically-driven dogma.
While that is true, it does have a “size.” Four-dimensional geometry is weird.
Maybe I could of phrased it better my saying a number that fills up 3 notebooks is really hard to comprehend…
But the TREE function is even more hilarious TREE(1) is 1, TREE(2) is 3, then TREE(3) is vastly bigger than even Graham’s number. If you really want to hurt your brain, think about TREE(Graham’s Number).
@Trinopus, do the things have to be physical objects? You can get numbers that make 10^900 completely insignificant if you are counting things like ‘how many different paths can you make using a certain number of vertices’. The absurdly fast growing TREE function is actually counting something clearly defined, and you could set up physical objects in the pattern that it counts.
Ok, let me ask it a different way, is there any way to put: 2 to 74,207,281 − 1, into an analogy/example that is comprehendable to the average person???
One of the largest numbers it mentions is the Graham-Rothschild Number which appeared in a 1971 mathematical paper as the upper bound on a certain Ramsey number N*. The paper proved that
N* < F(F(F(F(F(F(F(12,3),3),3),3),3),3),3)
where F is a function similar to Ackermann’s famous big-number generator. The paper is classic because of its concluding sentence about the known lower bound for N*:
But my response is the same: why does the universe have to be restricted to numbers comprehensible to average primates on a nothing planet?
The distance to the moon isn’t comprehensible to the average person.