Talk:Graham's number

From Wikipedia, the free encyclopedia
Jump to: navigation, search
WikiProject Mathematics (Rated C-class, Low-priority)
WikiProject Mathematics
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
C Class
Low Priority
 Field: Discrete mathematics
One of the 500 most frequently viewed mathematics articles.

"all sorts of poorly chosen words"[edit]

I have reverted most of this edit which changed "Graham's number is unimaginably larger than other well-known large numbers such as a googol, googolplex, and even larger than Skewes' number and Moser's number" to "Graham's number is much larger than other large numbers such as a googol, googolplex, Skewes' number and Moser's number." While this might seem like just dealing with a case of WP:WTW, in fact it ends up with the sentence saying nothing at all, or even being wrong. "Graham's number is much larger than other large numbers"? Really? Larger than any of them? Even the ones larger than Graham's number? Obviously, that isn't true. It is only larger than large numbers that are commonly discussed. "Unimaginably larger" in most circumstances would be making unwarranted assumptions about our readers imagination, but in this case the epithet is truly appropriate. SpinningSpark 17:01, 3 August 2014 (UTC)

The sentence says exactly what it said before, just without the subjective terms "well-known" and "unimaginably". It did not previously say that Graham's number is larger than numbers that are larger than Graham's number, and it doesn't say that now. And no, "unimaginably" is not appropriate. You could try fine tuning the wording - "vastly" or "enormously" perhaps; simply reverting to restore unverifiable claims is not at all helpful. (talk) 21:16, 3 August 2014 (UTC)
And what the hell would "beyond useless" mean, anyway? That is not the kind of tone an encyclopaedia should be written in. (talk) 21:17, 3 August 2014 (UTC)
I don't agree. What you have written gives no sense at all of how much larger this number is. You might also want to read WP:BRD on the right way to behave in disputes. SpinningSpark 21:55, 3 August 2014 (UTC)
So first of all you said that the sentence implied that Graham's number was larger than itself. Now you say it doesn't give a sense of how much larger it is than other numbers. Which is it? In neither case does my removal of the words "well known" and "unimaginably" make any difference. What do you want the article to say - "mind-bogglingly"? "humungously"? Probably either of these would actually be better than "unimaginably" which makes unwarranted judgements about the limits of the human imagination. I am sure we can converge on a more suitable adverb than either of those though.
WP:BRD is an essay that leads many people to feel entitled to simply undo any edit they don't like without feeling the need to explain themselves. It is not policy and I happen to think it is an immensely damaging idea. Better is to continue with the dialogue we are having right now. (talk) 22:58, 3 August 2014 (UTC)
Well first of all I did explain myself. Then you undid my edit, so where does that leave us? SpinningSpark 23:27, 3 August 2014 (UTC)
I didn't mean to imply that you didn't explain yourself - I appreciate the time you took to do so. I just meant that WP:BRD is widely used by people as an excuse to revert without explanation, and I don't view simply reverting on sight edits that you don't like as "the right way to behave".
So anyway, let's recap. What you said about my edit was that "in fact it ends up with the sentence saying nothing at all, or even being wrong". But the information contained in the sentence was identical to the previous version. Then you said the your problem was actually just that it didn't give the sense of scale that you considered necessary. So I asked what adverb you'd prefer to use. You haven't answered. So where this has left us is that I don't know what your complaint actually is right now. (talk) 00:03, 4 August 2014 (UTC)
I thought I made that clear. I think the original wording of "unimaginably larger" nicely summed it up. And my point about your revert is that you are just as guilty of an "I don't like it edit". Even more so, as you have now twice inserted your favourite version. If I had replied in kind would you have reverted again? SpinningSpark 00:38, 4 August 2014 (UTC)
You didn't make it clear, no - your first revert undid everything I did except the removal of the word "easily". If it's just "unimaginably" you were fighting for, why remove all the other changes?
The word is a poor word. "Vastly" would be fine, "enormously" would be fine, some sort of attempt at actual quantification would be even better. Like saying for example how much bigger than the observable universe a representation of the number would be with each digit taking up a planck volume, and comparing that to the equivalent "size" of other large numbers, if such things have been discussed in reliable sources. "Unimaginably" just sounds like hyperbole. (talk) 01:36, 4 August 2014 (UTC)
The fact that you have suggested making such comparisons shows you have failed to grasp how truly unimaginably large the number actually is. The size of the universe, even divided up into planck volumes, is nowhere near big enough to be able to make a comparison. A number so expressed would be indistinguishable from zero by any measure we have at our disposal. That is why unimaginable is the right word - because it is truly unimaginable, there is no possible comparison that one can imagine. SpinningSpark 01:41, 5 January 2016 (UTC)

────────────────────────────────────────────────────────────────────────────────────────────────────How about "quite literally unimaginable" ? DS (talk) 02:31, 5 January 2016 (UTC)

I would agree with that. The 190.161 IP probably doesn't though. Let's see if they comment. Meanwhile, let me just say that dozens of reliable books say Graham's number is "unimaginably large". SpinningSpark 16:59, 5 January 2016 (UTC)

Planck volume[edit]

@Cookiefonster: "if you could fit a digit into each planck volume in the observable universe there would be enough space to write out a googolplex". I find it hard to see how that could be construed as "an ordinary digital representation". In fact, I cannot think of any way that a digit could be written in a Planck volume. SpinningSpark 01:23, 19 November 2014 (UTC)

that's true, but "if you could fit a digit into each planck volume" is used for argument's sake here and to signify how big the numbers are. -Cookie Fonstertalk sign! 01:28, 19 November 2014 (UTC)


Er... there's an image on this page that appears to be completely blank. What happened to it? — Preceding unsigned comment added by (talk) 20:46, 12 October 2015 (UTC)

Can't figure out what's happened to that so I've raised it at WP:VPT. SpinningSpark 21:38, 12 October 2015 (UTC)

Rightmost digits in the lead[edit]

@Peter Isotalo: why are you so determined to remove the actual digits from the lead? This is an article about a number after all. SpinningSpark 01:34, 5 January 2016 (UTC)

Because the digits are completely irrelevant to the understanding of this number. The amount of digits given is also completely arbitrary.
But seriously. Do not remove my attempts to clarify. Either correct my summary or complement it with the digits. Reflex reverts are not constructive.
Peter Isotalo 08:16, 5 January 2016 (UTC)
Please look again at what I reverted, I was careful only to revert the part I had a problem with. The combined diff of your edits and my revert shows that it was not a rollback of your entire edit. Here is a diff of what I actually reverted. You inserted a claim in the lead that is not discussed in the body of the article, is unreferenced, and is demonstrably untrue, at least in certain counting bases.
As for the relevance of the digits, you could make the same arguemnt for pi, or any other number, but if readers look up a number they are quite likely to want to know what the digits are. In the case of this article it is particularly egregious to remove them as a good third of the article is taken up with their derivation. It is more than reasonable to have one sentence in the lead giving the last few digits. SpinningSpark 10:54, 5 January 2016 (UTC)
The lead of the article about pi specifies a common approximation for a number where the value is extremely relevant. That's a very notable fact. The approximation for pi is also fairly accurate and quite applicable in a vast number of fields. In any explanation of Graham's number, though, the last digits are mostly a byline and seem pretty irrelevant to the number's application in mathematics. Regardless of how detailed a Wikipedia article is about the calculation of the last digits, the derivation has fairly minor general relevance. I don't want to start a huge dispute over whether to include a few digits in the lead, but I think it's accurate to describe the statement as fairly trivial.
You actually reverted[1] my attempt the article content about derivation. Surely you must agree that explaining the nature of derivation and its limitation are far more relevant than the actual outcome of the derivation. I have only a basic understanding of math, but it seems strange to insist that the final digits in base-10 are notable enough to put in the lead, but that a derivation of the first digits in base-3 or base-9 invalidates any claim that the first digits are unobtainable in base-10. Even if you feel that my summary is incorrect, why not supplement the added information instead of just removing it altogether?
Peter Isotalo 12:36, 5 January 2016 (UTC)
I removed it altogether because it is WP:OR. It is for you to provide a source, not for me to replace it with my own OR. In any case, your insertion is based on uninformed guesswork. That does not improve the article in the slightest. SpinningSpark 13:21, 5 January 2016 (UTC)
I don't follow you here. What do you consider original research? And how would you summarize the derivation section?
Peter Isotalo 14:33, 5 January 2016 (UTC)
I define it the same way as the guideline. Either you can name a source for your claim or you can't. If the latter, it's original research. Listen, you've been called out for making half-baked claims on a subject you know nothing about. Stop wasting everybody's time trying to defend the indefensible. SpinningSpark 16:44, 5 January 2016 (UTC)
That's not a constructive response to an open question. You pointed out that you felt that my addition was original research and I'm trying to understand what you mean by that. To me it seems like a reasonable summary of the section in the article relating to derivation of the figures. We appear to disagree, but I don't see any reason to "call me out" on anything.
For clarity, here is the disputed summary:
The first digits of Graham's number are unobtainable due to its magnitude, but many of its last digit can be derived through use of simple algorithms.
Peter Isotalo 16:57, 5 January 2016 (UTC)
What I object to is the claim that the digits are unobtainable. That might well be true, I have no idea, but to in mathematics to say that something is impossible requires a proof. If it is only someone's opinion that it is likely impossible then that requires a cite to a reliable source because no one gives a toss about your (or my) opinion. To base three, the first few digits are 100..., to base nine the the digits are 300..., so there is no prima facie reason to believe that this is an impossible problem. The size certainly makes it difficult, but that alone does not prove it - ten to the power of Graham's number is a number hugely orders of magnitude bigger, but the first digits of that number base ten are trivially found to be 100.... SpinningSpark 22:17, 5 January 2016 (UTC)
Well, we seem to agree on the basic issues here. It's currently possible last numbers, but not the first number in base-10. You're perfectly welcome to add the caveat that it's possible in base-3 or base-9. The two statements don't contradict each other. But the article is clearly focused on the number's rendering in base-10.
Try to keep in mind that the article is supposed to be written for the general public. There's nothing wrong with being overly obvious so don't treat every statement as though it's written for mathematicians. If you're adamant about keeping trivial stuff like a certain number of the last digits of an absurdly large number, it would be prudent of you to make a minimum of effort to accommodate other aspects.
Peter Isotalo 23:55, 5 January 2016 (UTC)

Who is this Graham?[edit]

First he invents some crackers, and then he invents a number? (talk) 00:43, 8 August 2016 (UTC)