Talk:Dirac large numbers hypothesis

Suggested correction
In the section "Dirac's interpretation of the large number coincidences" the article presents the value 10^40, and then says it is of the same order of magnitude as a formula which gives a value of 10^-40. It's basically the formula is the wrong formula and needs replacing (turning upside down). Andrewthomas10 (talk) 09:38, 12 October 2015 (UTC) I've just made the change. Andrewthomas10 (talk) 09:44, 12 October 2015 (UTC)

Numerology or Mach's principle?
It seems very unfair to chalk this idea up to numerology, especially when it has a theoretical basis in Mach's principle. 15:42, 22 September 2006

What units?
What is meant by "Hence, taking ..., as units"? Does that mean you are assuming that the constant's are 1? Or just that the constants units are the units that are used in G? Also if you do the derivation it seems that $$m_p/m_e$$ should be $$m_p*m_e$$ but I am unwilling to make the change without the paper to back me up. Finally if you do take all of those constants to be 1 then $$G$$≈$$4.4*10^{-40}$$ not $$G=10^{-40}$$ and thus $$G$$α$$1/t$$ --157.182.186.101 20:32, 22 September 2006 (UTC) Adam

The mass of the electron an proton are similar? me=9.109*10-31 and mpr=1.672*10-27 which is 4 orders of magnitude difference. --157.182.186.101 19:43, 22 September 2006 (UTC) Adam


 * The ratio is about 1836. 'Similarity' is a relative concept. Sorry for the five-year delay in responding. David Spector (talk) 20:31, 28 January 2012 (UTC)

Not untested but disproved!
Unfortunately for lovers of funny old theories, this one has been falsified. If G really evolved proportional to time then stars could not form and burn in the early Universe. Observations of light reaching us from the early Universe show that stars were burning in a way consistent with G being unaltered. --Tdent 23:22, 1 December 2006 (UTC)
 * Interesting, Tdent, do you have a reference? I think it would be worthy of including in the article. - LesPaul75 talk 08:50, 1 February 2010 (UTC)


 * If it's a troll claim (one designed to create furor), a reference won't exist. David Spector (talk) 20:33, 28 January 2012 (UTC)

Proof
I edited out this claim (in italics):
 * The Large-Number Coincidence concerning pure numbers of order near $$10^{40}$$, was solved in 2006 by Scott Funkhouser (Funkhouser 2006). He found that the coincidence was, as predicted by Weyl, Eddington and Dirac, the result of implicit physical connections, thus validating the Large Numbers Hypothesis.  Funkhouser's resolution obviates the need for Dirac's suggestion concerning time-variation of $$G$$.  In 2008 Funkhouser introduced and resolved a new large-number coincidence involving pure numbers of order near $$10^{121}$$.  If the two sets of large numbers are related, as expected from the Large Numbers Hypothesis, then the two coincidences would explain the value of the putative cosmological constant (Funkhouser 2008).

I removed it because Funkhouser has not proved that the large numbers have any physical significance. He has extended the range of coincidences and (to my mind at least) he has provided additional circumstantial evidence that the numbers might have physical significance, but few people in the scientific mainstream would believe the numbers are anything more than a coincidence even in spite of Funkhouser's work. In other words, it's too soon to be making any claims on behalf of Funkhouser's work, excellent though it is. Whoever wrote this paragraph should write it again but with a more conservative approach. Lucretius (talk) 05:09, 16 July 2008 (UTC)

Larger article
Dirac's hypothesis was his personal interpretation of the large number coincidences that have intrigued many theorists, including Weyl and Eddington. I think this Dirac article should be replaced by a broader article to allow for these other views. Lucretius (talk) 05:15, 16 July 2008 (UTC) However, I will not be available to work on an enlarged section, nor even on this section, as I'm too busy with STUFF already. Lucretius (talk) 22:40, 17 July 2008 (UTC)

Lucretius should read Funkhousers papers
Lucretius' claims concerning my work are incorrect, and he should abstain from deleting claims that are taken directly from peer-reviewed, published work in leading journals unless other published work supports his edits. Lucretius claimed, "I removed it because Funkhouser has not proved that the large numbers have any physical significance." Apparently he has not bothered to read my publications, whose references I provided. There are a host of very tangible physical meanings associated with the large numbers of order near 1040 and of the numbers of the order 10121. For instance, there are roughly 1040 available bits of information allowed to a nucleon. The maximum number of bits of information allowed to the universe is of the order 10121. I would go on, but my articles in ProcRoySocA speak for themselves. Furthermore, I showed that the numbers of the order 1040 are in fact connected through standard physics. The coincidence is thus resolved. I did the same for the pure numbers of the order 10121. 206.74.147.131 (talk) 15:15, 24 July 2008 (UTC)scottfunkhouser


 * Hi Scott. I'm sorry if I offended you. However, contributors aren't supposed to cite their own work. Also, I'm not sure what you mean by 'resolved'. Dirac and others believed the numbers must signify some new physics, or what today we would call 'quantum gravity'. Unless you've come up with a successful theory of quantum gravity, I don't see how you can claim to have resolved anything. I think your work will persuade more people to take the numbers seriously but not if you go around web sites like this claiming to have resolved such an important issue (you should reserve that claim for your nobel prize speech). I won't undo your edit - I hope you'll undo it yourself (you probably were not aware of the rules here). I also hope somebody will cite your work but in a more cautious manner so that we all know exactly what claims are being made on your behalf. Lucretius (talk) 07:32, 25 July 2008 (UTC)


 * Scott, perhaps we should rename this article 'The Scott Funkhouser Validation of the Dirac Hypothesis'. Of course 'resolved' and 'validated' are very wishy-washy words and I still don't know what you mean by them (do you mean the coincidences could have a basis in physical fact - but what's new about that?). I've added some new links to the works of just a few of the authors who have contributed to our understanding of LNH but who are more unassuming in their estimates of their own work. I think many authors have 'resolved' and 'validated' LNH (i.e. they also have shown that the coincidences could have real physical significance). Like you, however, they haven't yet demonstrated how the electromagnetic/gravity ratio happens to be one of the large numbers. The theorist who enlightens us about that ratio is the only person who can indisputably claim to have resolved or validated LNH - and I'm not sure he/she has even been born yet! Lucretius (talk) 08:21, 26 August 2008 (UTC)


 * I've now started a new edit of the article, putting Scott's work in its historic context, where it can be understood as an example of renewed efforts by the scientific community to understand LNH. Lucretius (talk) 03:12, 27 August 2008 (UTC)


 * Sadly, Scott has now reversed my edit and restored his claims to have 'resolved' the large number coincidences and to have 'introduced' a new large number approx10^121 . I regard this as quite disgraceful. Read Nottale's paper (1993), and Genreith's (1999) listed in the external links, and compare them with Funkhouser's referenced papers (2005 and 2008). The ideas were already out there before Scott came along and it seems to me to be quite wrong for anyone to put his brand on ideas that have been in the public domain for many years. Scott has rephrased the coincidences, that's all - and it's not a significant change in phrasing! I've read both his listed papers and I cannot see anything in them that justifies his claim to fame. I have temporarily shelved plans to rewrite this article as its present form appears to have attained the permanence of holy writ and the stature of the Great Wall of China. Paul Dirac R.I.P. - Your hypothesis is resolved Lucretius (talk) 04:47, 29 August 2008 (UTC)

In private correspondence, I have pointed out to Lucretius that I simply copy-edited recent references to standardise the appearance of existing references. I did not insert these. In addition, I should also like to state that is is unfortunate that Scott has edited this article to the benefit of his own scientific reputation. This is not normally the case on Wikipedia. If Nottale's and Genreith's papers are germane to the ideas expressed, then these external links should be promoted to full references, and the text edited accordingly. I have not read these papers and do not claim to be expert in this scientific area - but I am concerned that the article should faithfully represent the history of this topic. Would the expression: "Funkhouser, building on earlier ideas by Nottale and Genreith, ..." be more appropriate here? Ian Cairns (talk) 09:44, 29 August 2008 (UTC)


 * I took a look at one of Scott Funkhouser's papers (physics/0502049). The physics seems fine (with one exception, see below), but it doesn't explain or even attempt to explain the coincidence described in this WP article. The coincidence in this article is that $$\frac{r_e}{ct_0} \approx \frac{4\pi\epsilon_0 G m_p m_e}{e^2}$$. Everything in there except $$t_0$$ is the same in all cosmological eras, so this seems to say that the present era is special. Dirac's proposal was that G varies with time and some unknown physical principle makes this equation hold in all eras, implying that $$G(t) \propto 1/t$$.


 * Funkhouser's paper says:
 * The age of the universe is T0 ≈ 4.3 × 1017 seconds (about 14 billion years). That's the metric age of the universe, but he repeatedly refers to T0 as the conformal age, which is significantly larger (at least 46 billion years). I don't understand how he made this mistake since he seems to have written a cosmology calculator which gets this right.
 * In a matter-dominated critical-density universe H(T) ~ c/R ~ 1/T, where R is the distance to the particle horizon (i.e. radius of the observable universe) in a given era and T is "the conformal time associated with the comoving particle horizon R". I gather this means T is the conformal age as reckoned by a civilization living in that era, which is trivially equal to R/c, but it's a bit of a strange thing to call "conformal time" since a spacetime diagram plotted with respect to this T won't be conformal. Also, nobody uses this T; when people talk about "the age of the universe" they're talking about the metric age. Fortunately H(t) ~ 1/t also, where t is the metric age, so it doesn't really matter.
 * In a matter-dominated critical-density universe GM/R ~ c², where R is the comoving distance to the particle horizon in a given era and M is the total mass within that radius. That's true, though his justification for it seems to be wrong because of the odd metric/conformal confusion.
 * mp/me ≈ 1/α. That's true (at the level of precision we're using here).
 * These three relations can be used to connect various combinations of physical constants that work out to about 1040. That's true, but these relations are elementary and were known at least as far back as the 1920s. There's no way Dirac was unaware of them in 1937. The coincidence described in this article is not explained by these relations.
 * -- BenRG (talk) 19:06, 1 September 2008 (UTC)

Hi BenRG - thanks for the input here. You're right - Scott's work belongs more properly in a larger article about large number coincidences, not specifically about Dirac's hypothesis. I mentioned that in the previous section. I think he put it here because the larger article has yet to be created. You are right also in your last paragraph that the relations are very old - they are at least implicit in previous work by others and Scott seems merely to be rephrasing some things. The referees of his papers should not have let him use loaded terms like 'resolved' - because what does it mean? Does it mean Scott has found THE physical explanation or merely A physical explanation for the large numbers? If the former, he would deserve the gratitude of mankind; if the latter, what's new? Others have come up with their own physical explanations, including Dirac himself. Above all, Scott doesn't explain the electromagnetic/gravity ratio, so it's hard to understand why he thinks he deserves any special mention. Still, the publication of his papers by a prestigious journal is noteworthy as it could indicate a growing awareness in the scientific establishment that the large numbers could have real significance. For that reason alone, maybe his papers deserve mention, and that's how I tried to edit the article, but unfortunately he reverted to his own more portentous edit. Lucretius (talk) 02:18, 2 September 2008 (UTC)

BenRG's baseless claims
BenRG deleted claims that appear in two separate publications in the Proc Roy Soc A and called them false. If BenRG had a legitimate point, he would have the basis for a significant scientific publication, since the claims he deleted were reported by Nature. But, chances are that BenRG is really just an illustration of why Wiki is not accepted as a reliable reference since it allows hacks with no demonstrated expertise to delete content added by experts with first-hand knowledge.

It brings to mind a quote: "Great Ideas Often Receive Violent Opposition from Mediocre Minds ..."

Of course, "mediocre" is probably a generous characterization of BenRG —Preceding unsigned comment added by Scottfunkhouser (talk • contribs) 01:51, 3 September 2008 (UTC)


 * I moved this thread here from my user talk page.
 * Your paper is fine. But you must see that what you added to the Wikipedia article isn't true, and isn't supported by the paper. The two sentences I said were false are:
 * "The large-number coincidence was solved in 2006 by Scott Funkhouser, who demonstrated that the apparent coincidence concerning pure numbers of order near $$10^{40}$$ is, as predicted by Weyl, Eddington and Dirac, the result of implicit physical connections. The implicit connections obviate the need for Dirac's suggestion concerning time-variation of $$G$$."
 * Your paper lists various relationships, like GM/R ~ c² and mp/me ~ 1/α, which are correct (as a consequence of FLRW cosmology or by direct calculation). You use those to explain why various unitless combinations of physical constants come out to the same value (~1040). I have no problem with that. But the particular equivalence which is the subject of the article, $$\frac{r_e}{ct} \approx 10^{-40} \approx \frac{4\pi\epsilon_0 G m_p m_e}{e^2}$$, is not a consequence of those relations. The easiest way to see this is that the left hand side is a function of time while the right hand side isn't. All of your relationships hold in all cosmological eras, so they can't be used to establish a relationship which doesn't.
 * I'd prefer to hold this discussion here on the article talk page rather than my user talk page. I took the time to read your paper and comment on it above, and I'd appreciate it if you responded to those comments. -- BenRG (talk) 02:55, 3 September 2008 (UTC)


 * Scott has now reverted from the edit by BenRG, once again restoring his own controversial edit. BenRG made some points above that ought to be addressed before Scott's edit should be accepted, and I'll add these other concerns: Scott's 'introduction' of the large number coincidence 10^121 (2008) was anticipated by Nottale - see page 2 of Nottale's paper (1995), where Nottale refers to it as {10^40}^3 - and also by Genreith - see equation 19 of Genreith's paper (1999), where he defines a mass (neutrino) that is in fact 120 orders of magnitude smaller than the mass of the universe (see also section 3.4 and the table). I don't doubt there are several other papers out there that introduce 10^120, or some phenomenon represented by it, in an LNH context, earlier than Scott's 2008 paper. So in what sense can Scott be said to have introduced this number? Also if you look at equation 1 in Nottale's paper, you'll find basically the same relations that Scott (2006) relies on, featuring the Planck mass as central to the 'resolved' coincidences. Moreover, Nottale like Scott (2008) appeals to the work of Zel'dovich for a scaling law that could explain the coincidences. And so on. The difference between Scott and theorists like Nottale and Genreith is this - their papers point towards a new kind of physics that is somewhat further than the scientific establishment is prepared to go at present, whereas Scott reamains within the ambit of conventional physics by absurdly avoiding the central issue, as already noted above, which is this:
 * $$\frac{r_e}{ct} \approx 10^{-40} \approx \frac{4\pi\epsilon_0 G m_p m_e}{e^2}$$.
 * Here are the cited papers (Scott's papers will probably be deleted from the article page before very long):


 * L. Nottale: Mach's Principle, Dirac's Large Numbers and the Cosmological Constant Problem
 * H. Genreith: The Large Numbers Hypothesis: Outline of a self-similar quantum cosmological Model
 * S. Funkhouser: The Large Number Coincidence, The Cosmic Coincidence and the Critical Acceleration 2006
 * S. Funkhouser: A New Large-Number 2008
 * Lucretius (talk) 05:59, 3 September 2008 (UTC)

Ben's incorrect claims
Ben, illustrates well why Wiki is not to be trusted.

1. Ben claims that, since i did not relate the one large-pure number concerning electron, my assertion that I have shown relationships among the large-numbers is wrong. ben really should read my paper since I address that issue. It is simply the result of the fact that the fine structure constant is of the order the ratio of the mass of the electron to the mass of the proton. The pure numbers concerning the electron may be therefore ignored since their connections to the other pure numbers are trivial and non-problematic, as I clearly discuss in my published papers. So, it turns out that Ben does not know more than the reviewers and editors at ProcRoySocA.

2. Nottale and Genreith's did NOT introduce a large-number coincidence, which requires the identification of at least three or four physically significant terms of similar order. They did not do that. I introduced six. That is why I claim correctly that I introduced the LNC concerning numbers near 10^121. So, it turns out that Ben does not know more than the reviewers and editors at ProcRoySocA.

3. I thank Ben, however, for giving me a valuable education in why I or anybody else shouldn't waste time with Wiki. "Open source" really just devolves into "Ignorant source". —Preceding unsigned comment added by Scottfunkhouser (talk • contribs) 15:18, 3 September 2008 (UTC)


 * Scott, I'll answer point 2 since it's in reply to an observation that I made, and I'll leave Ben to answer point 1. Your confusion about who said what pretty well indicates how you are approaching this matter generally. You need to read all contributions carefully and you should distinguish the usernames, otherwise the discussion will die a sordid death. I don't agree that a large number like E120 requires 'three or four physically significant terms of similar order' before it can be considered part of the large number coincidences. The Eddington number E80 has long been fundamental to the large numbers hypothesis without needing corroboration by other terms of similar order. You didn't 'introduce' E120 any more than you 'resolved' the numbers coincidences. Incidentally, the large number you define in equation 1 (2008) is the same one cited by Nottale, and the large number you define in equation 2 is the same one in Genreith, so it is true to say that here we have a collection of different numbers of the order E120 and this is a coincidence - but can we really say that you 'introduced' this coincidence when it emerges anyway from the earlier work of others? Lucretius (talk) 10:52, 4 September 2008 (UTC)


 * I don't know how to respond to this because you don't seem to have addressed my complaints in any meaningful way.


 * I'm having trouble parsing the first sentence in paragraph 1 above, but as far as I can tell what you're saying both here and in your paper is that Dirac's coincidence $$\frac{r_e}{ct} \sim \frac{4\pi\epsilon_0 G m_n m_e}{e^2}$$ follows from $$\left( \frac{M_0}{m_n} \right) ^{1/2} \sim \left( \frac{m_P}{m_n} \right) ^2$$ and standard cosmological assumptions (among which are the electron and nucleon masses and the value of α). I agree. The question is, where does $$\left( \frac{M_0}{m_n} \right) ^{1/2} \sim \left( \frac{m_P}{m_n} \right) ^2$$ come from? In your paper you say it "does not constitute a coincidence problem", and above you say it's "trivial and non-problematic". Can you explain why? Am I to understand that your resolution of Dirac's large number coincidence—your self-described Great Idea—is to assert without proof that it's just a coincidence? That possibility did occur to Dirac.


 * I mentioned in an earlier thread that your 2006 paper repeatedly refers to T0 ≈ 14 billion years as the "conformal time". Here's a direct quote from the paper: "According to the interpretation of data from the recent WMAP observations, the Big Bang occurred around T0 ≈ 4.3 × 1017 seconds ago. (Only two significant figures will be employed in this letter.) The conformal time T0 corresponds to a cosmic particle horizon R0 ≈ 1.3 × 1026 m." But the distance to the particle horizon is not 1.3 × 1026 m, as you must realize; your own cosmology calculator correctly computes 4.4 × 1026 m. The conformal time is the distance to the particle horizon divided by c, or 1.5 × 1018 seconds, not 4.3 × 1017. Assuming this version of the paper matches what was published, this would seem to suggest that the reviewers didn't do a very good job. Do you have any comment on this? You haven't said anything about it yet.


 * I haven't read Nottale or Genreith and I haven't made any claims about them here.


 * I know it's frustrating when your edits get reverted, but Wikipedia is just not the place for this. People frown on self-promotion here even when the information is factually correct, and when other editors raise doubts about whether it's even correct, you need to engage with those editors. That's not just part of participating on Wikipedia, it's part of being a scientist. Your responses so far have been full of appeals to authority, claiming that your ProcRoySocA reviewers must be right and that you must be right because of your academic position. You accuse me of incompetence because I haven't said anything about my education, but if you'd look at what I've actually written here you'd see that I have a basic competence in this subject. That's what I did with you: I looked at the paper you wrote and the cosmology calculator you wrote and concluded that you understood the basics of cosmology. I don't care about your education. It's great that you have a PhD in nuclear engineering from Berkeley, but a PhD in nuclear engineering says nothing about your competence in general relativity or cosmology. There are PhD astrophysicists who don't know the first thing about cosmology. You might be interested to know that I'm a fellow Berkeleyite; I have a BA in physics and an MA in mathematics from UCB. Is that enough to win me some courtesy? -- BenRG (talk) 10:44, 4 September 2008 (UTC)


 * You know, I just realized that I've assumed without thinking in all of my replies that Scottfunkhouser is Scott Funkhouser. Which, on reflection, makes no sense at all. Scott Funkhouser is a professional academic with an excellent educational background and an evident understanding of cosmology. Scottfunkhouser has shown no knowledge of cosmology and can barely string together a coherent English sentence. He's also never actually claimed to be Scott Funkhouser as far as I can remember. Scottfunkhouser seems to have also edited as JerryJKing and anonymously from csc.noaa.gov, and I can't find any evidence that Scott Funkhouser was ever affiliated with NOAA. So now I feel like an idiot. My apologies to the real Scott Funkhouser, if he ever reads this. I wonder if I should email him and mention that a NOAA employee seems to be impersonating him on Wikipedia. -- BenRG (talk) 13:00, 12 September 2008 (UTC)

Why mention Funkhouser's work at all?
Scott, you have not yet responded to the observations and questions made by myself and BenRG in the previous section. Meanwhile here are are some more things you need to respond to:
 * There is no reference to your work by Saibal et al. in their paper "Large Number Hypothesis: A Review" dated May 2007. Their paper is a well-referenced, extensive review of the relevant literature dedicated to LNH. Evidently your first paper, which predates theirs, did not impress the authors as very relevant. The neglect of your work is therefore not something peculiar to Wikipedia editors.
 * Your second paper deals with SIX instances of the large number E121, which you say is a remarkable coincidence. I have observed above that the first two instances are also found in Nottale and Genreith. I must now inform you that the other four instances are merely a re-serving of old and very familiar relations. For example, the fourth instance is said to be the maximum number of operations in the universe. Leaving out small factors like 2 and pi it looks like this:


 * $$\frac{Mc^2 T_0}{\hbar}\approx 10^{121}$$
 * where M is the mass of the universe. If T0 approximates to R/c, where R is the radius of the universe and c is speed of light, and if R is a gravitational length well known for instance to Eddington as GM/c^2, then cancellation and arrangement leads to this:
 * $$\frac{GM^2}{c \hbar} = \frac{M^2} {m_P^2} \approx 10^{121}$$,
 * where mP is the Planck mass.


 * You are merely recycling very familiar relations featuring the Planck mass in a LNH context:
 * $$\frac{e^2}{4\pi\epsilon_0 G m_p m_e} = \frac {\alpha c \hbar}{G m_p m_e} = \frac { \alpha m_P^2}{m_p m_e} \approx 10^{40}= N$$,
 * $$\sqrt {\frac {M^2} {m_p m_e}} = N^2 \approx 10^{80}$$,
 * $$\therefore \frac {M} {m_P} = (\sqrt N)^3 \approx 10^{60}$$
 * where lower case p subscript denotes proton, and upper case P denotes Planck mass. All your remarkable coincidences are similarly mere rephrasings of relations taken from the ordinary LNH context. I have the mental image of a magician pulling a coin out of someone's right ear and then pulling another coin out of the left ear - it looks like a remarkable coincidence! In fact it's the same coin and it never left the magician's hand. Dirac's LNH deserves the attention of the scientific community but not like this. Your second paper deserves no more notice than your first paper and Wiki editors have no need to cite either of them. Lucretius (talk) 06:36, 6 September 2008 (UTC)


 * If you don't want to reply, that's fine. In that case however, you have no right to revert edits to your text. All the LNH coincidences require the radius of the universe to be a gravitational length GM/c^2, otherwise they really are just coincidences - that's why Dirac understood them to signify an inflationary universe whose mass increases as the universe expands. It requires a particular kind of quantum gravity. Your papers simply sidestep this issue, you give no explanation for the coincidences and they seem to occur only in this epoch, when the universe's radius happens to approximate to the gravitational length. Your papers do not represent an important advance in our understanding of LNH. If anything, they represent a further mystification. They are significant however as a publishing phenomenon. There is a renewed interest in LNH as a possible means of explaining anomolies in the standard model of cosmology. But your intransigence, your refusal to consider your work as anything other than a leap of creative genius, makes it impossible to include your work at all. Lucretius (talk) 23:05, 7 September 2008 (UTC)


 * Whether or not Ben's doubts about the real identity of 'scottfunkhouser' are valid, doubts about the value of Scott's two cited papers remain. The papers have now been deleted from the article (links are still preserved here on the Talk Page above). I've now restructured the article to ensure that there is a context that makes it difficult for any contributor to insert exaggerated claims. For example, the claims made in Scott's papers are difficult to reconcile with this paragraph:
 * Various authors have introduced new sets of numbers into the original 'coincidence' considered by Dirac and his contemporaries. Jordan (1947) noted that the mass ratio for a typical star and an electron approximates to 1060, an interesting variation on the 1040 and 1080 that are associated with Dirac and Eddington respectively. V.E. Shemi-Zadah (2002) has arrived at various numbers of the order of 1060 by measuring cosmological entities in Planck units. Several authors have recently identified and pondered the significance of yet another large number, approx 120 orders of magnitude. This is for example the ratio of the theoretical and observational estimates of the energy density of the vacuum, which Nottale (1993) associates in an LNH context with a scaling law for the cosmological constant. Carl Friedrich von Weizsaecker identifed the new large number with the ratio of the universe's volume to the volume of a typical nucleon bounded by its Compton wavelength, and this ratio is in turn identified by him with the sum of elementary events or bits of information in the universe. T. Goenitz (1986), building on Weizsaecker's work, posits an explanation for large number 'coincidences' in the context of Berkenstein-Hawking entropy. Genreith (1999) has sketched out a fractal cosmology in which the smallest mass, which he identifies as a neutrino, is 120 orders of magnitude smaller than the mass of the universe (note: this 'neutrino' is conceptually related to the hypothetical particle mH mentioned above in the context of Weyl's work in 1919)


 * It's hard to understand how Scott can claim to have introduced a new large number coincidence based on 10^120! And I've only just scratched the surface of the material that's out there! Also it is still hard to understand what he means by 'resolved' when he relies on scaling laws that are found elsewhere in the literature, both explicitly or implicitly - anyhow, hopefully this is the end of an unfortunate affair. Lucretius (talk) 08:02, 21 September 2008 (UTC)

Re-instating Funkhouser
I think it's time to include some mention of Funkhouser's work, as follows:
 * "Funkhouser sees a new large numbers coincidence in the fact that a number like 10120 can be represented in a variety of ways and he suggests that mainstream physics might yet find a physical explanation for the LNH coincidences."

I think this puts everything in the right perspective. His work doesn't deserve star-billing in the article but it does deserve some mention since it has been published by The Royal Society and by Nature. Lucretius (talk) 01:35, 4 October 2008 (UTC)

I've also added a link to one of B.G.Sidharth's papers which includes a comprehensive explanation of 10120 in a Planckian LNH setting. I've only just discovered Sidharth's work, even though he has produced many papers on a LNH theme! It's like finding an island in the south Pacific - the island might be big but it's easy to miss in the vasteness of the ocean! Lucretius (talk) 23:44, 11 October 2008 (UTC)

Probability of coincidence
Is there a method of calculating the probability that the documented coincidences would occur by chance without a deeper physical explanation? Currently the article (after the intro) almost seems to assume that there IS some deeper physical explanation, whereas in reality this is a fringe view. Eebster the Great (talk) 03:24, 19 February 2009 (UTC)


 * Actually it isn't really a fringe view - the large number coincidences turn out to be typical of a universe that resembles a Hawking black hole. However, the cosmology associated with that kind of universe would certainly be different to the standard cosmology - for a start, there would be no big bang because there could be no singularity. Dirac's theory about a varying G isn't a necessary aspect of the coincidences. Dirac and Eddington both assumed that the coincidence must have some profound physical significance and the article does point out that their view is a minority view. But don't be surprised if those two giants turn out to have been more right than wrong. The present edit is mostly my own work, I thought it was an objective presentation of the case for and against. I'd be delighted if others took the article seriously enough to edit it further. Unfortunately the numbers are largely dismissed out of hand as a mere coincidence even by Wiki contributors, so nothing is done.Lucretius (talk) 04:35, 19 February 2009 (UTC)

Promotional edits
I deleted an edit by 'Hasmukh Khimjibhai Tank' that recorded the conclusions of a paper by 'Hasmukh Khimjibhai Tank' for the same reason that I previously deleted edits by a 'ScottFunkhouser' that promoted Scott Funkhouser's papers. It's wonderful that there are intelligent people around who take the large numbers seriously but Wikipedia is not an opportunity for promoting the work of any particular individual. Anyhow, if the papers are significant they'll get noticed within the scientific community and there is therefore no need to advertise them here. Lucretius (talk) 22:13, 18 April 2009 (UTC)

Dear Sir,Sole purpuse of sharing information that The recurrence of 'large number' has been explained in the proceedings of Indian National Science academy, part-A, volume63,No:(1997), pp.469-474, in a paper titled:"explanation for the 'Large Number' in astrophysics; and some insight into the nature of fundamental forces" is that: Indian Journals are not widely circulated, so Wikipedia will be helpful for interested scientists to read it. Science is for exiting discoveries; and their sharing, and mutual feedback is equally exiting by themselves.I have also written a letter to the Swedish Academy of Sciences that the huge sum of money of the Nobel Prize has converted colleagues in to compititors, and so you are looking at everythig in terms of promotional attempts. May I know, what are the other alternatives to bring an interesting development to notice of the interested colleagues? Self-praise is the ultimte frankness, only hipocrates get themselves praised through their companions. 14:45, 19 April 2009.Hasmukh Khimjibhai Tank (talk) 09:24, 19 April 2009 (UTC)

Read the Wikipedia guidelines on conflicts of Interest (and Conflict of interest while you are at it).Headbomb {{{sup|ταλκ}}κοντριβς – WP Physics} 09:36, 19 April 2009 (UTC)

Since the above paper is already published in a reputed peer-reviewed journal like Proceedings if INSA-A, and since the paper has drawn certain conclusions useful for further research, other readers can not be deprived of knowing about it by deleting it by someone. —Preceding unsigned comment added by 219.90.99.11 (talk) 09:08, 22 April 2009 (UTC)

There are thousands of published papers relevant to LNH and they can't all be cited here. The papers cited here are seminal papers that are are found in references of other papers. Lucretius (talk) 23:02, 22 April 2009 (UTC)

THE purpuse of Wikipedia's discussion-page is to discuss science, whether a particular CONCEPT in the article is correct, or needs improvent; and what could be the correct approach...etc. Whereas this page is mostly discussing PERSONS. NEW ideas should be first proposed in the discussion-page, every participant's idea should be available for every one to read; opinions on them can be expressed, mostly pointing out the correct part and suggestig corrections on the in-correct parts; that is if I can not suggest a correct alternative then I should not criticise in-correct parts. And every participant should register first, giving his/her name,address..etc.Hasmukh Tank. If there are one thousand papers on a subject, Wikipedia's participants should sort out good points from them within a month. —Preceding unsigned comment added by 219.90.99.60 (talk) 09:29, 24 April 2009 (UTC)
 * Wikipedia is not a forum for discussing personal theories - it's an encyclopaedia. There are science forums on the web where people can discuss their theories. Almost nobody reads this talk page and you are wasting your time putting anything here. Lucretius (talk) 21:44, 24 April 2009 (UTC)

Wrong, i am from brazil and i am reading this, many years after you start to delete peoples contributions, what is a deleterious behaviour, indeed, you are the vain person who want to get merit for a crap of wikipedia article, worse, an article that you keep impoverishing just because you cant stand before someone brighter than you, you are indeed a sinkhole for light. I will keep an eye on you for the rest of time... rdg — Preceding unsigned comment added by 189.27.12.81 (talk) 03:53, 28 February 2013 (UTC)

Orders based on 10 dubious
The current article uses orders based on 10. However, it is extremely unlikely that any actual connections would have a causal or semi-causal (or correlated through an indirect causality) root based on 10. Instead 2 and e would be likely candidates. If we further add in that a reader with an insufficient background in science may have an equally insufficient awareness of the arbitrariness of 10 as the basis for our number system (and thus have "superstitious" associations with it), neat numbers like 40 * 10^20 can be misleading.

For these reasons, I suggest that the article is reformulated to counter this problem. 188.100.201.34 (talk) 16:22, 15 November 2009 (UTC)


 * Dirac's large-number and Eddington's large-number are 'ratio'; not 'numbers'; so, it should not matter whether they are written as based on 10, or 'e'. What is significant is their recurrence; and explanation for their recurrence. —Preceding unsigned comment added by 122.170.20.72 (talk) 16:30, 4 January 2010 (UTC)

Why Wikipedia is not trusted
Although it would be pointless for anybody but a qualified psychotherapist to respond to preceding profligate ravings, the present discourse highlights two salient points: (1) There is a reason why the Proceedings of the Royal of Society published my papers on the large number coincidences: Their qualified editorial board and expert referees judged it to be appropriate. (2) The content of Wikipedia, on the other hand, represents not the approval of world experts, but primarily the whim of the most zealous wikipidiots, who generally reek of jealousy and failure.

Dear Funkhouser, I have read your paper published in 2006; and also the papers by:(i)Sidhartha published in 2005,and(ii)Tank published in 1997. I could not find anything new in your paper which was not contained in those earlier papers and in Milgom's 1982 paper. Please read these papers and then re-think of your use of words jelousy and failure. Your paper can be considered as an re-confirmation of earlier authors' works; if you are sure that it is independent. —Preceding unsigned comment added by 123.201.19.251 (talk) 17:44, 24 August 2010 (UTC) 123.201.19.251 (talk) 17:47, 24 August 2010 (UTC)

Research papers in external links
Hi, there are some arxiv research papers in the external links section which I think don't really belong there. It is my opinion that (with the exception of review articles) if any research papers by current authors are relevant enough in the context of improving understanding of the large numbers hypothesis then they should be cited in the "Later developments and interpretations" section. If they are not relevant enough to be cited in this section then I don't think they should be linked to. Thoughts? Polyamorph (talk) 19:41, 8 March 2011 (UTC)
 * I've done some cleanup, but there are still too much painful listing of individual results in this section. We might get rid of the entire section? Isambard Kingdom (talk) 16:26, 15 May 2016 (UTC)

Include the list of numbers in the introduction
As it is, you pretty much have to read the entire article to find out which these numbers/ratios are (the 40 orders of magnitude link only shows the Eddington–Dirac number, which links back to this page). ComaVN (talk) 12:49, 5 October 2013 (UTC)

Deleted material from lead
The last couple of sentence in the lead were of very low quality, containing a mixture of incorrect, poorly sourced, and speculative material. There was a reference to a paper in the journal Cognition, which is obviously out of place in a physics article. There was also a claim that the LNH had "gained new impetus from failures in standard cosmology to account for anomalies such as the recent discovery that the universe might be expanding at an accelerated rate." This is total nonsense, and was supported by a reference to a preprint that does not appear to have been actually published. I've deleted this material from the lead.--76.169.116.244 (talk) 12:03, 1 July 2015 (UTC)

Section on Mathematical Large Number Hypothesis
I understand virtually nothing in this section, in its present form. Should we keep it? Of course in mathematics there are many "large numbers", but if the coincidences could be derived from mathematics, this would mean that some form of the "Large Number Hypothesis" is actually correct, not wrong! Paolo Lipparini (talk) 14:19, 28 July 2015 (UTC)

This entire section was just vague speculation/musing (written in poor English to boot), so I deleted it. — Preceding unsigned comment added by 24.56.116.202 (talk) 16:41, 2 August 2015 (UTC)

Assessment comment
Substituted at 13:28, 29 April 2016 (UTC)

External links modified
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Title
Should the page be named "large numbers hypothesis", "large numbers coincidences" or "cosmological coincidences"? If I am recalling well, what the entry says is correct: a set of large number 'coincidences' that had intrigued other theorists of his time, so, while Dirac's contributions are actually fundamental, the page deals with a more general subject. Paolo Lipparini (talk) 15:04, 3 July 2019 (UTC)
 * No, it's very much dealing with Dirac's theory, as you say his contributions are fundamental. More to the point, we can only use what reliable sources use, and in general sources refer to it as the Dirac LNH. Polyamorph (talk) 20:36, July 3, 2019‎ (UTC)

Suggested addition to last pharagraph
Valev (2019) [18] found equation connecting cosmological parameters (for example density of the universe) and Plank units (for example Planck density). This ratio of densities, and other ratios (using four fundamental constants - speed of light in vacuum c, Newtonian constant of gravity G, reduced Planck constant ℏ, and Hubble constant H) computes to an exact number, 32.8 x 10120. This provides evidence of the Dirac large numbers hypothesis by connecting the macro-world and the micro-world.

Jim Johnson (talk) 21:25, 21 June 2021 (UTC)

"Dirac`s large numbers hypothesis" listed at Redirects for discussion
An editor has identified a potential problem with the redirect Dirac`s large numbers hypothesis and has thus listed it for discussion. This discussion will occur at Redirects for discussion/Log/2022 October 15 until a consensus is reached, and readers of this page are welcome to contribute to the discussion. 1234qwer1234qwer4 15:37, 15 October 2022 (UTC)