# 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:** 16\ **Page:** 4
**Author:** ![Steophan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/steophan/32/9595_2.png) [@Steophan](https://boards.straightdope.com/u/Steophan)\ **Post date:** [February 2, 2016, 9:39pm UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/61 "2016-02-02T21:39:03Z")
> [@Ornery\_Bob](#): > > _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\*\*. (Bolding mine) So do rocks. Or atoms. Or galaxies. Without a comprehending observer, they’re just things. ---
**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, 10:14pm UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/62 "2016-02-02T22:14:32Z")
> [@whc.03grady](#): > > 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. That’s one of the drawbacks of “constructivist” arithmetic. The “succession” property of the counting numbers must be assumed to fail at some point. This kills closure under addition, which means the numbers aren’t a “group” any longer. It takes some of the fun away from our favorite toys! ---
**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, 10:23pm UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/63 "2016-02-02T22:23:52Z")
> [@Steophan](#): > > (Bolding mine) > > So do rocks. Or atoms. Or galaxies. Without a comprehending observer, they’re just things. I think that is an interesting statement. I disagree. I am interested in your response. In your POV the observer has the significance and not the object. I think the object is more important “philosophically” than the observer. If things don’t have an intrinsic value, ie, rock vs lava vs water… how can we draw an observation if they are not fundamentally different? ---
**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 3, 2016, 12:17am UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/64 "2016-02-03T00:17:57Z")
> [@Your\_Great\_Darsh\_Face](#): > > 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. Need a larger number base. ---
**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 3, 2016, 4:32am UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/65 "2016-02-03T04:32:12Z")
> [@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. I’ve felt exactly the same way! We think of numbers like 10^10^10^10 as ridiculously big, but Graham’s number g = F(F(F(F(F(F(F(12,3),3),3),3),3),3),3) is preposterously bigger and utterly incomprehensible. And of course it doesn’t end there; what about F(F(F(F(F(F(F(g,g),g),g),g),g),g),g) :eek: By comparison, infinite numbers like ℵ[sub]0[/sub] or P(ℵ[sub]0[/sub]) seem very tame. But infinite cardinals are not without preposterosity either. Can any of the Board’s mathematicians explain, in simple words, Woodin cardinals and why they matter? ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [February 3, 2016, 5:25am UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/66 "2016-02-03T05:25:14Z")
[Here’s an example of a wooden cardinal bird feeder.](http://shop.cardinalcorner.com/Cardinal-Shaped-Wooden-Bird-Feeder-woodcardinalfdr.htm) ---
**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 3, 2016, 11:09am UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/67 "2016-02-03T11:09:34Z")
> [@octopus](#): > > Need a larger number base. And enough different digits to make the number base functional. There’s your problem. ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [February 3, 2016, 12:06pm UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/68 "2016-02-03T12:06:14Z")
> [@Trinopus](#): > > That’s one of the drawbacks of “constructivist” arithmetic. The “succession” property of the counting numbers must be assumed to fail at some point. This kills closure under addition, which means the numbers aren’t a “group” any longer. > > It takes some of the fun away from our favorite toys! Worse, it introduces new arbitrary rules about arithmetic. Somehow we must add into our use of numbers rules that place limits on their use. That there are things we can reason about in certain ways, and others that we cannot. Or at least not reason and talk about in _quite_ the same manner. The true constructivists are perhaps not so bad, but those that insist that only numbers within human grasp are meaningful become quickly tiresome. They insist of an ill defined set of rules about what arithmetic can and cannot be done, and can only do so by adding more and more arbitrary constraints. In the end I very much doubt you could get a coherent definition of “number” out of any of them. Not one that was not subject to redefinition each time you asked a difficult question. ---
**Author:** ![Steophan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/steophan/32/9595_2.png) [@Steophan](https://boards.straightdope.com/u/Steophan)\ **Post date:** [February 3, 2016, 12:17pm UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/69 "2016-02-03T12:17:10Z")
> [@Robert163](#): > > I think that is an interesting statement. I disagree. I am interested in your response. > > In your POV the observer has the significance and not the object. I think the object is more important “philosophically” than the observer. > > If things don’t have an intrinsic value, ie, rock vs lava vs water… how can we draw an observation if they are not fundamentally different? Well, they are all just protons, electrons and neutrons in varying arrangements… Except, they’re not, really. Even those “fundamental particles” are just models that we use to observe and classify things, just like we do rocks, or numbers, or anything else. I would say that existence is ultimately a relationship between observer and observed, or conception and conceiver for things like numbers that can’t be adequately represented, or objects like black holes that by their nature can’t be directly observed. Let’s say we hypothesise that there exists an alternate universe that not only can we not observe, but no-one or nothing ever could or ever will observe it. My opinion is that talking about whether or not that universe exists is actually meaningless, as it is completely impossible to ever determine it. ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [February 3, 2016, 1:39pm UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/70 "2016-02-03T13:39:53Z")
As we see, OP is getting at, _in part_, not so much “countability” as an abstract concept, but, at least in the angle **Mangetout** picks up on, and which **Chronos** restates in admirable reductio, on countability by humans, including OP. I cite these two because I think the are the best explanation previous to explanations of things at a more abstract level. > [@Mangetout](#): > > There is an apple on the table and another apple on the table. The notion that these are a set, numbered one and two, is just an idea in your head. > > > [@Chronos](#): > > > > … > > Or is it only “real” if you can conceive of [possible shuffles in a deck of cards] 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. Having said that, I’d like to complicate **Mangetout** in a simple way, an idea fleshed out often in exquisite literary form by the great Jorge Louis Borges. **Mangetout** mentions countability as individual sets of apples. For the sake of the argument he two "cognizables, each of one real countable-by-human (not up to nine, as noted) real things. (I am not getting into other roads to/roads of metaphysics-via-mathematics, let alone metaphysics qua metaphysics, so I don’t need quote marks around that use of “real.”) [And thanks for allowing me to use the “qua.”] The recurring theme of Borges–in one story, eg, it is cognitive by a human of shuffles in the deck of lived experience by one man (“Funes”); in another, it not one man who who tragically remembers each; in another ("The Chinese Emperor’s Dictionary), it is the unenviable task of scholars to portray these shuffles for a book, in case the Emperor can’t remember. Let me return to **Mangetout** ’s apples (a happy username/post). An apple can be rotten, half rotten, poisonous, all depending on mood of the second of observation, the position of the sun at the instant of observation, that it is any or all of the above, those shuffles of whatever the human mind (again, returning to the point of the posts I cited) which may be devoid of enumeration/countability/mental cognition of sets. Perhaps this is what **Mangetout** is on to. But anyway, I liked it. (Also, to all interested in OP, read Borges. He returns to this idea again and again, with bifurcation paths, the library of Babel, you name it, with exhilarating clarity and beauty, faux scholarly papers written by a poet.) ---
**Author:** ![JKellyMap](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jkellymap/32/15880_2.png) [@JKellyMap](https://boards.straightdope.com/u/JKellyMap)\ **Post date:** [February 3, 2016, 1:42pm UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/71 "2016-02-03T13:42:23Z")
> [@Robert163](#): > > I think that is an interesting statement. I disagree. I am interested in your response. > > In your POV the observer has the significance and not the object. I think the object is more important “philosophically” than the observer. > > If things don’t have an intrinsic value, ie, rock vs lava vs water… how can we draw an observation if they are not fundamentally different? Humans impose these values/generalizations/categories, because our brains have evolved to do so (lest we get eaten by lions or whatever). Read the Borges short story “Funes the Memorious” to get a feeling for what it’s like if we DIDN’T do this…but also to better understand that there’s no INTRINSIC reality to these values/generalizations/categories. ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [February 3, 2016, 1:54pm UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/72 "2016-02-03T13:54:15Z")
Addendum re Borges cite above: The book for the Chinese Emperor I mention is in his essay-“fiction” “The Analytical Language of John Wilkins,” another exploration of the themes I mentioned above, in which a language is proposed for one word for everything (the difficulties of which are particularly great for the lexicographer given the scope as suggested); the proposed book discussed as an example is called “The Celestial Emporium of Benevolent Knowledge.” That the book is cited with the context of how such a book presents its own (insurmountable?) difficulties within a discussion of a language in which it could conceivable be written is a virtuoso demonstration of (fractals? Cantor ideas?) the very point. The “analytical language,” as a proposal, is real: _An Essay towards a Real Character and a Philosophical Language_, published in 1668 ([An Essay Towards a Real Character, and a Philosophical Language - Wikipedia](https://en.m.wikipedia.org/wiki/An_Essay_towards_a_Real_Character_and_a_Philosophical_Language)). ETA: or what **JKellyMap** said. ---
**Author:** ![Pantastic](https://avatars.discourse-cdn.com/v4/letter/p/3bc359/32.png) [@Pantastic](https://boards.straightdope.com/u/Pantastic)\ **Post date:** [February 3, 2016, 2:18pm UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/73 "2016-02-03T14:18:34Z")
> [@Francis\_Vaughan](#): > > Worse, it introduces new arbitrary rules about arithmetic. Somehow we must add into our use of numbers rules that place limits on their use. That there are things we can reason about in certain ways, and others that we cannot. Or at least not reason and talk about in _quite_ the same manner. The true constructivists are perhaps not so bad, but those that insist that only numbers within human grasp are meaningful become quickly tiresome. And, like came up earlier in the thread, which human’s grasp? A trained mathematician can easily understand large and complicated numbers, while an average person might not be able to grasp ‘how many bricks are there in the courtyard of the school’ without effort, and someone low functioning may not be able to get beyond finger counting. ---
**Author:** ![AWB](https://avatars.discourse-cdn.com/v4/letter/a/bb73d2/32.png) [@AWB](https://boards.straightdope.com/u/AWB)\ **Post date:** [February 3, 2016, 10:01pm UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/74 "2016-02-03T22:01:38Z")
“God made integers, all else is the work of man.” – Leopold Kronecker ---
**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 5, 2016, 2:49am UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/75 "2016-02-05T02:49:55Z")
I think one could make a case that the integers are actually the _most_ artificial of numbers. If I have one apple, and then I get another, what’s the ratio of the new amount of apple to the old amount? It almost certainly isn’t exactly 2.000000 , since apples vary in size. As do sheep, as do rocks, as does nearly everything. ---
**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 6, 2016, 5:39am UTC](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884/76 "2016-02-06T05:39:27Z")
> [@Chronos](#): > > I think one could make a case that the integers are actually the _most_ artificial of numbers. If I have one apple, and then I get another, what’s the ratio of the new amount of apple to the old amount? It almost certainly isn’t exactly 2.000000 , since apples vary in size. As do sheep, as do rocks, as does nearly everything. Seems like the concept of a property of a set is as artificial as a label for an object. [Previous page](https://boards.straightdope.com/t/a-number-that-exceeds-the-total-number-of-atoms-in-the-universe/744884.md?page=3)