# a number that exceeds the total number of atoms in the universe **URL:** \ **Category:** Factual Questions\ **Created:** [February 1, 2016, 9:46pm UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884 "2016-02-01T21:46:12Z")\ **Posts on this page:** 20\ **Page:** 3
**Author:** ![Xema](https://avatars.discourse-cdn.com/v4/letter/x/9de053/32.png) [@Xema](https://boards.straightdope.com/u/Xema)\ **Post date:** [February 2, 2016, 3:20am UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/41 "2016-02-02T03:20:29Z")
> [@Trinopus](#): > > 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. Tell him to be quite careful. He should not, for example, start thinking about the number of different ways you can pick up 5 golf balls. Because that might get him thinking about the different ways you could scrape 200 insects off a windshield. And so on. IOW, accepting the constraint that “a number has to represent something that can, at least in the abstract ideal, be counted” will by no means allow you to cap things at 10[sup]900[/sup]. ---
**Author:** ![Robert163](https://avatars.discourse-cdn.com/v4/letter/r/4af34b/32.png) [@Robert163](https://boards.straightdope.com/u/Robert163)\ **Post date:** [February 2, 2016, 3:24am UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/42 "2016-02-02T03:24:57Z")
> [@Exapno\_Mapcase](#): > > Nope. > > But my response is the same: why does the universe have to be restricted to numbers comprehensible to average primates on a nothing planet? > [@Richard\_Pearse](#): > > The distance to the moon isn’t comprehensible to the average person. Ok, thanks for the replys… ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [February 2, 2016, 3:36am UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/43 "2016-02-02T03:36:49Z")
> [@Robert163](#): > > 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??? Suppose you want to make a list of all the residents of Los Angeles. The number of distinct ways to _order_ that list is greater than the largest known prime number. ---
**Author:** ![Robert163](https://avatars.discourse-cdn.com/v4/letter/r/4af34b/32.png) [@Robert163](https://boards.straightdope.com/u/Robert163)\ **Post date:** [February 2, 2016, 3:38am UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/44 "2016-02-02T03:38:40Z")
> [@septimus](#): > > Suppose you want to make a list of all the residents of Los Angeles. The number of distinct ways to _order_ that list is greater than the largest known prime number. ok thanks 🙂 ---
**Author:** ![Trinopus](https://avatars.discourse-cdn.com/v4/letter/t/2bfe46/32.png) [@Trinopus](https://boards.straightdope.com/u/Trinopus)\ **Post date:** [February 2, 2016, 4:08am UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/45 "2016-02-02T04:08:23Z")
> [@Pantastic](#): > > @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. I actually asked him this, and he rejected it completely. He’s a bit of a doof… (Does one have to be a “Platonist” to accept the conventional Peano axioms regarding numbers?) (What the foobar is a “Platonist” anyway?) ---
**Author:** ![Trinopus](https://avatars.discourse-cdn.com/v4/letter/t/2bfe46/32.png) [@Trinopus](https://boards.straightdope.com/u/Trinopus)\ **Post date:** [February 2, 2016, 4:13am UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/46 "2016-02-02T04:13:57Z")
> [@Xema](#): > > . . . IOW, accepting the constraint that “a number has to represent something that can, at least in the abstract ideal, be counted” will by no means allow you to cap things at 10[sup]900[/sup]. Well, he’s limiting it to physically real things, like atoms, or stars. He rejects things like “the number of subsets of a large set.” He also rejects “real numbers,” but accepts “rational numbers” within certain ranges. Pi, beyond forty digits or so, stops being meaningful, so he truncates it there. In practice, there is some real use for such things as the “calculus of finite differences.” You can do some solid and productive work with this kind of material. Engineering generally stops at four or five decimal places. It just seems strange that this guy would insist on engineering limitations to mathematics. Again, he’s putting ideology first. Is this at all a “movement” in the philosophy of numbers and arithmetic? Are there other “constructivists” out there? ---
**Author:** ![Your\_Great\_Darsh\_Face](https://avatars.discourse-cdn.com/v4/letter/y/ac8455/32.png) [@Your\_Great\_Darsh\_Face](https://boards.straightdope.com/u/Your_Great_Darsh_Face)\ **Post date:** [February 2, 2016, 6:37am UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/47 "2016-02-02T06:37:32Z")
> [@Exapno\_Mapcase](#): > > You’re going down a very bumpy road. Can you show me that a square root “exists”? That -53 “exists”? That the square root of -53 “exists”? That matrixes, or quaternions, or null sets “exist”? That countable or uncountable infinities “exist”? That the stuff in a whole library of math textbooks “exists”? > > Thousands of years of teaching and learning go into mathematics, all of it, every single bit, dedicated to saying that countable things is not mathematics and should not limit our understanding of the world. Every concept in mathematics is just as real and exists just as surely as five does. > > The dark side of the moon existed before we sent a satellite to photograph it, too. “Dark side of the moon”? :dubious: You did that on purpose, didn’t you. ---
**Author:** ![cmyk](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cmyk/32/3353_2.png) [@cmyk](https://boards.straightdope.com/u/cmyk)\ **Post date:** [February 2, 2016, 7:31am UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/48 "2016-02-02T07:31:19Z")
> [@Richard\_Pearse](#): > > The distance to the moon isn’t comprehensible to the average person. I don’t know about that. I remarked to one of my (not-very-science-inclined) friends who put about 120,000 miles on his old Jetta that he “drove half-way to the Moon.” He just sort of paused while digesting that notion with a smile, probably thinking of all the years and trips it took just to put that much milage on his car, and thinking he’d have to drive that much more, again, to “reach the Moon.” ---
**Author:** ![octopus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/octopus/32/3716_2.png) [@octopus](https://boards.straightdope.com/u/octopus)\ **Post date:** [February 2, 2016, 7:40am UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/49 "2016-02-02T07:40:46Z")
> [@Robert163](#): > > I have asked this question before, this type of question but now I have a more detailed way of asking it. If a number that exceeds the total number of atoms in the universe, is that number “real” or is it just made up simply for mathematicians to talk about? > > The general question is math something humans invented or is it distinct and separate from humans? > 2 rocks plus 2 rocks makes 4. You can count that. Rocks exist therefor we didn’t create math. > > Well, the number of atoms in the universe is estimated at to contain between 10^78 and 10^80 atoms (e.g. 10 followed by 80 zeros!). If you type that number out it doesn’t even fill up half a sheet of paper. The newest prime number, however, is so large that it fills up 3 notebooks when you type it out!!! > > As of January 2016 , the [largest](https://www.google.com/search?sourceid=chrome-psyapi2&ion=1&espv=2&ie=UTF-8&q=largest%20prime%20number&oq=largest%20prime&aqs=chrome.0.0j69i57j0l4.5437j0j7) known prime number is 2 to 74,207,281 − 1, a number with 22,338,618 digits. ([three](https://www.youtube.com/watch?v=tlpYjrbujG0) notebooks) > To use the analogy, if a number is larger than all of the known rocks in the whole universe, ie, if it can’t actually be proven to exist via counting, how doe we know that number exists? Most positive numbers are larger than any number you can write. ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [February 2, 2016, 1:42pm UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/50 "2016-02-02T13:42:34Z")
What is a number? That is the real question. I am a platonist, which means that I believe there is some etherial domain in which the infinitude of natural numbers “exists”. Another theory is that a number is a social agreement among all the world’s people. Then, there is Alexander Esenin-Volpin (see: [Alexander Esenin-Volpin - Wikipedia](https://en.wikipedia.org/wiki/Alexander_Esenin-Volpin)) who argued that to exist a number had to be comprehensible and claimed that 1,000,000,000,000 (a trillion) is incomprehensible and doesn’t exist. So you pay your money and you take your choice. Maybe this should be moved to IMHO. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [February 2, 2016, 1:55pm UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/51 "2016-02-02T13:55:48Z")
OK, so this guy rejects things like “the number of possible shuffles of a deck of cards” as not “really existing”. And yet, we can use that number to calculate things like “the number of possible poker hands of five cards”, and “the proportion of those hands that are Full Houses”. And we can further observe that a gambler who recognizes the validity of those calculations will consistently take money from a gambler who doesn’t recognize the validity of those calculations. So your friend’s assertion is that, even though those numbers don’t really “exist”, they can still lead to money that presumably does really “exist”. ---
**Author:** ![Your\_Great\_Darsh\_Face](https://avatars.discourse-cdn.com/v4/letter/y/ac8455/32.png) [@Your\_Great\_Darsh\_Face](https://boards.straightdope.com/u/Your_Great_Darsh_Face)\ **Post date:** [February 2, 2016, 2:03pm UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/52 "2016-02-02T14:03:20Z")
On the subject of the sheer hugeness of Graham’s Number, note that ordinarily huge numbers can be written as a few layers of exponentiation - that is, a Googol is just 1 followed by a hundred zeroes (10[sup]100[/sup]) and even a Googolplex is 1 followed by a Googol of zeroes (so can be written as 10^10^100 since we can’t cope with showing multi-level exponents directly on the screen). And you can easily imagine ridiculously bigger numbers such as 10^10^10^10^10^10 and so on. The sheer awfulness of Graham’s number becomes apparent when you grasp that it can’t even be written down as a “tower of exponents” - that is, if you start trying to write it down like I just wrote down five successive exponentiations, you run out of space before you get the number written. ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [February 2, 2016, 2:03pm UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/53 "2016-02-02T14:03:51Z")
> [@Your\_Great\_Darsh\_Face](#): > > “Dark side of the moon”? :dubious: > > You did that on purpose, didn’t you. There is no dark side of the moon really. Matter of fact it’s all dark. ---
**Author:** ![watchwolf49](https://avatars.discourse-cdn.com/v4/letter/w/e9c0ed/32.png) [@watchwolf49](https://boards.straightdope.com/u/watchwolf49)\ **Post date:** [February 2, 2016, 2:06pm UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/54 "2016-02-02T14:06:44Z")
> [@Chronos](#): > > Can you imagine a deck containing 60 cards? … [snip] Half those cards should be lands … just saying … ---
**Author:** ![Pantastic](https://avatars.discourse-cdn.com/v4/letter/p/3bc359/32.png) [@Pantastic](https://boards.straightdope.com/u/Pantastic)\ **Post date:** [February 2, 2016, 4:02pm UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/55 "2016-02-02T16:02:06Z")
> [@Your\_Great\_Darsh\_Face](#): > > The sheer awfulness of Graham’s number becomes apparent when you grasp that it can’t even be written down as a “tower of exponents” - that is, if you start trying to write it down like I just wrote down five successive exponentiations, you run out of space before you get the number written. You misspelled awesomeness. But seriously, one of the things I find interesting about really large finite numbers is that they feel much larger than infinite numbers. I can easily get my head around the concept of a line being made of an infinite collection of points, that there are as many even as odd numbers, and the like, but really comprehending something like Graham’s number take a big effort and isn’t something I can casually call back up. ---
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [February 2, 2016, 5:08pm UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/56 "2016-02-02T17:08:32Z")
> [@Pantastic](#): > > You misspelled awesomeness. But seriously, one of the things I find interesting about really large finite numbers is that they feel much larger than infinite numbers. I can easily get my head around the concept of a line being made of an infinite collection of points, that there are as many even as odd numbers, and the like, but really comprehending something like Graham’s number take a big effort and isn’t something I can casually call back up. In many ways there’s no such thing as large finite numbers, only very small ones. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [February 2, 2016, 5:37pm UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/57 "2016-02-02T17:37:35Z")
> [@Pantastic](#): > > But seriously, one of the things I find interesting about really large finite numbers is that they feel much larger than infinite numbers. I can easily get my head around the concept of a line being made of an infinite collection of points, that there are as many even as odd numbers, and the like, but really comprehending something like Graham’s number take a big effort and isn’t something I can casually call back up. I see what you mean. I can imagine seeing infinitely many things at once (the points on a line segment) but I can’t imagine seeing Graham’s number (or even a much smaller finite number) of things at once. ---
**Author:** ![whc.03grady](https://avatars.discourse-cdn.com/v4/letter/w/a6a055/32.png) [@whc.03grady](https://boards.straightdope.com/u/whc.03grady)\ **Post date:** [February 2, 2016, 5:37pm UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/58 "2016-02-02T17:37:42Z")
How about a little Reductio? Assume there are 10^86 elementary particles in the universe. Assume, like the OP, that numbers up to that number are okay, but any greater than that number are basically meaningless. Now tell me why (10^86)+1 is such a horror. ---
**Author:** ![74westy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/74westy/32/3950_2.png) [@74westy](https://boards.straightdope.com/u/74westy)\ **Post date:** [February 2, 2016, 6:46pm UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/59 "2016-02-02T18:46:09Z")
It seems to me that I’ve heard the objections in the OP before and that there’s a school of philosophy of math that explores it. A quick wiki-walk suggests its called [Ultrafinitism](https://en.wikipedia.org/wiki/Ultrafinitism) or at least that’s the closest I could find without spending any amount of time on it. ---
**Author:** ![Ornery\_Bob](https://avatars.discourse-cdn.com/v4/letter/o/da6949/32.png) [@Ornery\_Bob](https://boards.straightdope.com/u/Ornery_Bob)\ **Post date:** [February 2, 2016, 8:30pm UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/60 "2016-02-02T20:30:19Z")
_2 rocks plus 2 rocks makes 4. You can count that. Rocks exist therefor we didn’t create math._ Absolutely wrong. Rocks exist. But they don’t count themselves. They only get counted when people are around. Two and four are human inventions. Math only exists inside human brains. [Previous page](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884.md?page=2) [Next page](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884.md?page=4)