Talk:Golden ratio

The value of φ

The value of φ with 2000 digits

Dürer

@Deacon Vorbis: The source clearly states that the vanishing point divides the diameter of the rainbow in the golden proportion, and that could also not be more apparent from the actual measurement. Since the illustration in question is quite literally full of riddles/mathematical puzzles, it would seem highly unlikely that the vanishing point underlying the entire composition would be placed at this location by accident. The article is chock-full of other reliable information, so at least with attribution, it would be appropriate to include. And as far as I'm aware Dürer didn't leave notebooks of his intentions lying around (as Da Vinci did). UpdateNerd (talk) 13:43, 2 May 2019 (UTC)

(edit conflict) The source says "divine proption", not "golden proportion" or even "golden ratio". While I realize that this term is sometimes used instead, the author never did so anywhere else in the source, despite using "golden ratio" five times explicitly. In any case, I'm very hesitant to put in a single "this one person says this one painter did something in the golden ratio this one time" kind of thing, even if the source is otherwise more or less reliable. It starts to get kind of WP:CRUFTy for one thing. But also, if you're specifically looking for φ, and you make enough measurements, you're going to find it all over the place – a point which is made elsewhere in the article even. Without some kind of corroboration or quote from the artist or something providing some context, we can't just WP:INDISCRIMINATEly include these. –Deacon Vorbis (carbon • videos) 14:15, 2 May 2019 (UTC)

Considering there was an edit conflict, did you see the image I mocked up? Also, "divine proportion" explicitly refers to the golden ratio in pretty much all contexts, expecially during the Renaissance when Pacioli (whom the article is primarily about) advocated for calling it that. Yes, it is a single source making an extraordinary claim, so if we include it we should attribute it to "one source" or something like that. There isn't likely to be a bunch of articles repeating such esoterica on the interweb, but if there was, that would make the guideline-stringest case for including this much stronger... but likely without adding any insight. But I don't see how your cruft/indiscriminate arguments apply. This is particularly discriminate on what to include (a rare strong-case use of the golden ratio during the Renaissance, of which there are only 1 or 2 other highly significant examples—currently missing from the article). I agree it would help to find corroboration, but making the point so obvious might not have been the artist's intent. :) UpdateNerd (talk) 14:42, 2 May 2019 (UTC)

Granted about the terminology, but that was the lesser of my concerns really. As for the image, using lines so close together is going to introduce extra uncertainty in determining the vanishing point. Even in the author's diagram, where he used a couple more, one of them didn't intersect the others, yet there was no indication of how much uncertainty there was in his measurements, just a blanket "omgz golden ratio!". Even in your diagram, I see that you've used the outside of the rainbow, rather than the inside. Why? Why not the center? Using one of those will doubtless give a better match than the others. How much other subtle little fudging is made in these sorts of measurements?

Could the artist have done this intentionally? Of course. Did he? Who knows; the author certainly doesn't make any sort of case that he did. And if it was unintentional, then it shouldn't be included. We need to stick to cases where there's some sort of corroboration about intentional use, or at the very least some sort of robust discussion about it, rather than including any questionable case of finding something that was specifically being sought, too obscure to have attracted any other attention. –Deacon Vorbis (carbon • videos) 15:17, 2 May 2019 (UTC)

Ahmes papyrus

While I agree that a letter to editor is not the most reliable source per se, it replicates the quoted portion of the papyrus included in Alger's Mathematics for Science and Engineering, which doesn't make any other outlandish claims related to the golden ratio. It mentions in the same section that the golden ratio was not known until Euclid, which could be added as a quote in the reference (I'll post it when I have time tomorrow). Including the information in the article gives insight as to the more scholarly views that have existed about the golden ratio and the pyramids, without saying that they're true. UpdateNerd (talk) 04:01, 6 June 2019 (UTC)

Please refrain from using bad sources. This article has been infested with woo too much already, you don't need to make it worse. Seked is apparently just a word for the slope of a pyramid; different pyramids had different slopes, and the imputation that the slope is the golden ratio is modern. As the more respectable sources already say. Including this information does not give more insight; it merely makes it look like Wikipedia editors are credulous and unscholarly. —David Eppstein (talk) 05:10, 6 June 2019 (UTC)

I didn't realize they were referring to seked. I figured the translation could have been a weasly one (although slopes derived from two side measurements aren't totally unrelated from ratios). There is nothing wrong with pointing out different views—perhaps mentioning that that's the word transliterated seqt—but I don't see a need for that now. UpdateNerd (talk) 05:59, 6 June 2019 (UTC)

Rotating black holes

Regarding this removal: this isn't one of those cases where there is an unresolved difference of legitimate opinion in the field (like when Physicist A uses a particular approximation that Physicist B thinks is inapplicable). Davies just screwed up. XOR'easter (talk) 13:08, 26 July 2019 (UTC)

The link you included above is a better mathematical source than any of the three I included. It mentions the more nuanced detail that the commenter Greg Egan worked out that the golden ratio does show in black holes in a more subtle way, while "angular momentum is held constant". I personally think it would be worth including in the "Disputed claims" (not as an undisputed fact) with this nuance added for clarity. See the Azimuth Project website for attribution to John C. Baez. UpdateNerd (talk) 19:39, 26 July 2019 (UTC)

I removed this again anyway; sorry I didn't say anything sooner, but I didn't realize you were going to try to re-add. This isn't a purported observation of φ; it's just a random popping out of it during a theoretical physics calculation. And considering the story around this, there doesn't actually seem to be any sort of dispute; there was just a mix-up in exactly what was being calculated. So this isn't appropriate to add, regardless of sourcing. –Deacon Vorbis (carbon • videos) 20:20, 26 July 2019 (UTC)

Fair enough (though I actually disagree; it's an observation even if it's done through equations instead of geometry). If better secondary sources explained the nuances of this, it would be completely appropriate to add. UpdateNerd (talk) 20:24, 26 July 2019 (UTC)

Well, it would be an observation if someone actually measured this on a real black hole, rather than some sort of derivation from an idealized one. And in this case, unlike the real iffy things (like nautilus shells), there would be a theoretical basis for it, too. Moreover, it still wouldn't be interesting enough to include unless there was also some sort of explanation linking a defining property of φ to the result, rather than just something akin to the Strong Law of Small Numbers rearing its head. –Deacon Vorbis (carbon • videos) 20:33, 26 July 2019 (UTC)

Good point about detecting it on a real black hole, or further connecting the data to them somehow. UpdateNerd (talk) 20:36, 26 July 2019 (UTC)

Yeah, it's just a number falling out of an equation (a wrong equation, as it happens). And once the calculation is corrected, the only way to get $\phi$ to pop out is to compute something that's physically irrelevant. Davies' original paper didn't make a big deal out of a threshold working out to be $({\sqrt {5}}-1)/2$; I'd call it a curiosity, except that it turns out to be not very curious. XOR'easter (talk) 23:18, 26 July 2019 (UTC)

Oh, and The Golden Ratio: The Divine Beauty of Mathematics is not a reliable source. XOR'easter (talk) 23:28, 26 July 2019 (UTC)

One other thing: the source in The Fountain is just a typical regurgitation of golden-ratio fannishness. It repeats as fact an explanation for phyllotaxis which is highly dubious (and can't apply to all plants). And it garbles the claim about black holes (I don't even know what it's trying to mean by spinning parameter). It's not reliable either. XOR'easter (talk) 00:07, 27 July 2019 (UTC)

Thanks, I'll disregard those as sources, although I was mostly using them for general details not found in the Livio article—not the accuracy of the claims or mathematics. UpdateNerd (talk) 00:48, 27 July 2019 (UTC)

For posterity: except to point out where Davies went wrong (as on the rotating black hole article), the Azimuth source isn't much good either. It claims that the golden ratio surfaces when the gravitational constant and speed of light equal one, but how can these two velocities be equal? I wish I'd noticed this irregularity before, but I'm also not an astrophysicist. It appears that Egan only found what he was looking for, which shouldn't be too surprising. UpdateNerd (talk) 18:49, 27 July 2019 (UTC)

Setting $G=c=1$ is commonplace. See Planck units. XOR'easter (talk) 19:13, 27 July 2019 (UTC)

I see both G = 1 and c = 1 depending on the context, but nothing about setting them both to 1 in the same equation. UpdateNerd (talk) 20:14, 27 July 2019 (UTC)

The table in §List of physical equations does so, for starters. It is literally a thing that physicists do all the time. It is completely unremarkable. The first reference that springs to mind is Chapter 1 of Gravitation, which explains how to set $G$ and $c$ simultaneously to unity, along with Boltzmann's constant $k$, but any decent set of lecture notes on general relativity will cover the technique. The hoary old joke is that standard practice is to set $G=c=k=\hbar =1$, and if you're really an intense theorist, you set $\pi =1$ as well. XOR'easter (talk) 20:42, 27 July 2019 (UTC)

Do you have a page number for Gravitation? UpdateNerd (talk) 21:11, 27 July 2019 (UTC)

Whoops, I must have missed this notification in my watchlist. There's a box in Gravitation dedicated to the topic on page 36. But pretty much any field theory textbook will discuss the subject at least a little in the course of establishing its notational conventions. Tony Zee's Quantum Field Theory in a Nutshell does so in the preface (p. xxv), for example. XOR'easter (talk) 21:03, 8 August 2019 (UTC)

Thanks for the helpful page references (and I also see that we have an article on the geometrized unit system), but I'm still agnostic on this issue. As far as I can tell, c=1 and G=1 can both be utilized, but I don't see c=G=1 in the same expression. They're fundamentally different values, and therefore seemingly can't be equal. UpdateNerd (talk) 21:27, 8 August 2019 (UTC)

If you choose your units of mass, time and length carefully, then both the speed of light and the gravitational constant are numerically equal to 1. Nothing too hard about it. XOR'easter (talk) 21:32, 8 August 2019 (UTC)

As I said, still remaining agnostic, as that explanation is too vague for me. Thanks for your responses though, as it provides some food for thought. UpdateNerd (talk) 21:35, 8 August 2019 (UTC)

Expressing φ in terms of a and b

I find the mathworld explanation much clearer and more intuitive. My mental picture is of a piece of paper from which you keep cutting squares from the longest size, and the ratio of the sides is always φ.

As it is, it takes several steps to get from the a+b relationship to the one just for φ whereas if you directly make the sides 1 and φ then this relationship "can immediately be seen".— Preceding unsigned comment added by 2A01:CB15:8010:2F00:ECF5:C24C:4992:6347 (talk) 07:56, 7 February 2020 (UTC)

No reference for phi in financial markets

The Reference 9, while covering the first clause of the sentence does not mention financial markets, thus a separate reference for this clause is necessary. Also, I am interested if indeed phi does show up in financial markets.