Talk:Golden spiral

Equiangular spiral

There is another name for this spiral (see heading) I think. This is because if you draw 8 lines from the centre of the spiral, the angle at which the spiral intersects them is always the same. Would this be worth mentioning?--CarrotMan 06:07, 19 October 2006 (UTC)

The golden spiral is an equiangular spiral, but not the only one. It's already in the first sentence, if not explicitly. Melchoir 23:13, 23 October 2006 (UTC)

The formula

Why not use the formula from logarithmic spiral? The current scheme with b raised to a power of angle in degrees is, I bet, not in any verifiable source, as it is abhorrent to a mathematician to do such a thing. It would be nice if this article would say what value of b makes the logarithmic spiral a golden spiral, instead of defining a couple of new idiosyncratic b's. Dicklyon 06:49, 22 November 2006 (UTC)

I don't really understand the last comment. The form r=ab^θ is a simple polar exponential equation. There's nothing wrong or abhorrent about it. The equation used in the logarithmic spiral article, r =ae^θt, is simply the same thing, using the natural base, e. The previous comment also states that the article doesn't give the values for b that make a golden spiral, when in fact those values are calculated for both radians and degrees. So either I'm really missing something, or the previous commenter doesn't understand the math.Goldbren 19:41, 8 June 2007 (UTC)

I think I understand and sympathize with the comment. It's really three parts:

• 1. why use a different formula, and a different definition of b, than what logarithmic spiral uses?
• 2. what formula is used in verifiable sources? probably not this one.
• 3. raising a number to a power that is an angle is "abhorrent" because an angle is not non-dimensional, unless maybe if you want to call radians non-dimensional; b in the exponent is a scale factor with units of inverse angle, but b as the base is weird.

Dicklyon 02:31, 9 June 2007 (UTC)

I can see now why I sympathize with the comment: I wrote it! I hadn't noticed that until now. Dicklyon 05:12, 9 June 2007 (UTC)

OK, I fixed it to use b the way the logarithmic spiral does, and put the other way with c as an alternate. Dicklyon 05:58, 9 June 2007 (UTC)

Notation: phi

The letter \phi is used in this article for the golden ratio. A confusing point is the two different forms that the letter \phi takes, one in the opening paragraph, the other in the equation

$e^{b\theta _{\mathrm {right} }}\,=\phi$

It took me a couple of re-reads to figure out that this equation referred to the same constant. I'm not sure how to control the fonts used, but they need to appear in a consistent way. —Preceding unsigned comment added by 129.89.14.188 (talk) 16:00, 3 August 2009 (UTC)

So What is a true Golden Spiral? I am no mathematician, but i can see (With my eyes) that this is not a perfect spiral shown as an example. What is the actual measurement of the sides of this box anyway? KAKU —Preceding unsigned comment added by 75.84.119.31 (talk) 10:04, 14 January 2010 (UTC)

Grimoire for the Apprentice Wizard...???

Uhhmmm.... If this is not vandalism... then at least this should be a more scientific source.... — Preceding unsigned comment added by 67.247.20.215 (talk) 01:22, 24 August 2011 (UTC)

Changed to "citation needed" even if that book is the source of this information it's not really something worth mentioning. Jyar (talk) 11:09, 6 October 2011 (UTC)

Spiral inquiry

Is there a spiral that cuts every radius at an angle of 45 degrees and what would be its formula and name?WFPM (talk) 18:36, 1 March 2012 (UTC)

The image

When the image is this small, the red and the green line form one orange line. It would be useful the scale the image up (to about 400px, maybe more), but when I do, the description disappears. Could somebody who has the knowloedge do that please? Thanks in advance.
Bleistift2 (talk) 13:45, 9 July 2012 (UTC)

Convergent point of graph

I realize that there is a convergent point that the spiral is leading towards. If the origin is the lower left corner of the graph , what is the (x,y) location of the convergent point? Also, I realize that there is angle to the tangent line to the line from the convergent point is it constant? --John W. Nicholson (talk) 17:13, 12 October 2013 (UTC)
If anyone is interested... The convergence occurs at the coordinates ( (3*phi+1)/5 ; (3-phi)/5 ). The slope of that point relative to the origin is 2*phi-3. XWolfRH (talk) 14:43, 22 November 2013 (UTC)

The mouse cornea study is dodgy

I do not want to get into an edit war, so I am not touching it with a ten foot pole, I'm just going to say: the mouse corneas thing is crap. It's very "whoah" to see it said that corneas resemble galaxies and golden spirals. However, the study also brings in a bunch of other spirals. They're just imposing whatever they like on the data. It's pretty clear they were just looking for "cool numbers" - check their source for the "silver spiral". — Preceding unsigned comment added by Hamishtodd1 (talk • contribs) 23:00, 20 July 2016 (UTC)

_______ Here is a sequence of recent events but I won’t forget that the burden is on YOU to state why the study should be taken out. You will offer many alternative reasons to distract (e.g., because it’s “whoah”) but you won’t give a good reason because there isn’t one. The mouse study should stay:

Belief is that upon which one is prepared to act. What I call common belief is stated in the mouse paper, which is “The surprising fact, phi spiral C, is observed..” On the other hand, the following demonstrates your special belief because let us not forget that

1) The mouse study was originally edited out based on the editor’s reason: “ 10:34, 13 July 2018‎ Hamishtodd1 (talk | contribs)‎ . .(9,948 bytes) (-581)‎ . . (Removed mouse study; it is again not an example of a golden spiral, but instead about the golden angle.)

2) But the authors of the paper deny this,

“The mouse cornea shares similarity with plant phyllotaxis.. Yet, the ϕ ratio is expressed differently in the cornea.. Such properties make corneal spiraling incongruous with phyllotactic models in which the optimal process involves successive appearance of elements displaced at golden angles that grow away from the center… In summary, while both systems are marked by the ϕ ratio, the extent of common relational structure is ambiguous.”

Therefore, there was no cause in the first place to take out the mouse study because no claim was made that the phi spiral observed had a clear analogous relation to phyllotaxis. You took the action of removing the study based on a wrong/mistaken/false assumption.

3) Therefore, I put the mouse study back on and asked, “What is your reason for deleting the passage if it is published in a scientific report?:

4) Then this is offered as the reason, “(Reverted to revision 850064707 by Hamishtodd1 (talk): Removed unsourced POV diatribe. (TW))

5) So, the reason given is due to its being UNSOURCED, not that it is about the golden angle/phi spiral relation. This is a distraction and not the reason.

6) So, I sourced it as per “(Reverted to revision 855781075 by Wcherowi(talk): If there is a source for this you must provide a citation. Discuss on talk page if you are unclear about Wikipedia policy.

7) Then, my edits were removed again: 11:43, 21 August 2018‎ Dicklyon (talk | contribs)‎ m . .(10,348 bytes) (-531)‎ . . (Reverted 3 edits by Gahnett (talk): Nothing in that sources supports weird statements about popular, common, and special belief, whatever those are supposed to be.

This time, the distraction is that there is nothing in that source that supports weird statements about popular common and special belief. Belief is that upon which YOU are prepared to act. It is stated in the simple statement, “The surprising fact, phi spiral is NOT observed.."

This is what is at stake. You don't believe the paper is a reference that argues for the case of existence of phi spirals in nature. But this is not for you to decide. The paper is published after a refereed process. The arguments for why the observation is not "whoah" has already been decided by those who actually care for the work and is presented to the public in the form of CP 5.189, which states the conclusion.

But you and whoever else who delete the reference have already forgotten that the reason given for striking out the mouse study was false, it was wrong, and you don’t even look to the paper to check your work.

This will happen again because you’ve already made up your mind that there is no such thing as phi spirals in nature. This is your belief; whether special or common simply depends on whether you believe you belong to the majority or minority and whether you believe your understanding to be right.

To recap, the reasons for striking the mouse study was 1) that the paper claimed the phi spiral observed is based on a mechanism involving the golden angle, which is wrong or at best not yet proved. 2) That the editor does not understand what ‘belief’ means. A belief is that upon which one is prepared to act. Your belief is that there is no phi spirals observed in nature and you are willing to act on that belief. My belief is that there are phi spirals observed in nature and it is there, on mouse corneas.

But again, this is not for us to judge. It is published and if you want to strike the record, then publish your own work disproving the case. Otherwise, leave the page alone.

To be productive, you could instead ask, “if you observe phi spirals on mouse corneas, then what is the mechanism”? If you prove that, you will prove to me that there are indeed phi spirals on mouse corneas."

But that is a question to which its being is esse in futuro. But if icosahedral quasicrystals were true..

Again as a reminder, the burden is on YOU to give a reason for deleting the reference. The reference stays.

~gahnett, 8/21/2018  — Preceding unsigned comment added by Gahnett (talk • contribs) 19:14, 21 August 2018 (UTC) 

Your chronology above suffers from the fact that you are not taking into account that there were several editors involved in this and they were dealing with different issues. My own involvement came after the mouse study citation had been removed. What was left was an unsupported POV that did not make much sense. Putting the source in did not really change my opinion of that statement and I support Dicklyon's revert. First of all, the paper is a primary source and it is based on an observation of three samples. In scientific circles such a study provides evidence, not a conclusion. Your statement is way over the top and not supported by this paper. When the subject of this paper is brought up in a secondary source it might be useful in a Wikipedia article, but as it stands now, it isn't. Note that I am not attacking this paper, only your use of it to support your position. --Bill Cherowitzo (talk) 20:09, 21 August 2018 (UTC)

_________

I will address your argument point by point. My responses are preceded by >>.

1) Your chronology above suffers from the fact that you are not taking into account that there were several editors involved in this and they were dealing with different issues.

>> I addressed each and every issue. To all editors. Which issue or editor did I not address? Again, this is a distraction and confirms my previous statement that you will not offer a good reason to retract the reference because there isn’t one.

2) My own involvement came after the mouse study citation had been removed.

>> (cur | prev) 10:34, 13 July 2018‎ Hamishtodd1 (talk | contribs)‎ . .(9,948 bytes) (-581)‎ . . (Removed mouse study; it is again not an example of a golden spiral, but instead about the golden angle.) (undo | thank)

This record suggests it was Hamishtodd1 who removed the mouse study. How else am I to understand this? Are you not Hamishtodd? If not, there it is. That was the reason for removing the mouse reference and that matters more than the next person who deletes it for the same reason. I referenced the section that clearly stated that the authors knew the difference and relation between phi spirals and golden angles.

3) What was left was an unsupported POV that did not make much sense.

>> It doesn’t make sense to you because you don’t believe it. You believe that phi spiral is not observed. Therefore, to have someone state phi spiral is observed does not make sense. Whether supported or unsupported depends on the criteria. What is your criteria if not that it is published? You say things below, and I address them below but they are more distractions. If you are asking about the evidence, there was a blinded study to demonstrate that the phi spiral is present in sense perception. Not only that but the figures show the process of measurement, including a log-transform of the original images, which predicts specific things that were discussed.

4) Putting the source in did not really change my opinion of that statement and I support Dicklyon's revert.

>> I support you supporting Dicklyon’s revert but this is a matter of what is on record, not the many voices. Even if you have not changed your opinion, the burden is on you to support why you don’t believe it when there is a publication that states otherwise.

5) First of all, the paper is a primary source and it is based on an observation of three samples. In scientific circles such a study provides evidence, not a conclusion.

>> Conclusion is that which follows from premisses. It involves an illation- an illative conjunction is a word like "hence", "ergo" or "therefore".. Three is good enough to serve as reasonable suspicion in this case because how many will it take? How many forms are possible? What is the possibility that you see one when the forms are so many? This is the scientific process of abduction, which is to present reasonable suspicion and to state it in clear hypothetical mode. And in every investigation arguments stated in philosophical form are different from those that are non-philosophical..

6) Your statement is way over the top and not supported by this paper.

>> Again, this is not your role. Even besides, which statement is over the top? That my opinion is contrary to yours, which you claim as "contrary to popular opinion"? This is why I labeled your opinion "special" opinion.

7) When the subject of this paper is brought up in a secondary source it might be useful in a Wikipedia article, but as it stands now, it isn't.

>> The ironic thing is, here is a statement that misrepresents the observation and also makes a mistake in referencing. This carelessness is from a study published in Lab Investigation: “The pattern formed by the sub-basal axons is a Phi spiral, which arises frequently in nature and is seen in rat and, to a limited extent, human corneas.5, 6 The Phi spiral is shown in the unwounded mouse cornea in Figure 1 and will be referred to here as the vortex.” https://www.nature.com/articles/labinvest2015113

But this is not the point. It is, again, a distraction. It is YOUR burden to demonstrate why even ONE scientific publication is not credible to YOU because it doesn’t conform to your belief, such that it warrants deleting the reference and my comments. You’re just not convinced, which is ok, but if you look at my statement, it doesn’t say your opinion is not to be respected. It merely asks how we ought to proceed when we are not agreed on the criteria. This is what I am doing; which is to bring attention to this, to make our ideas clear.

8) Note that I am not attacking this paper, only your use of it to support your position. --Bill Cherowitzo (talk) 20:09, 21 August 2018 (UTC)

>> You are ATTACKING my use of it to support my position? Which position, that “The surprising fact, phi spiral, is observed”? But it is an observation that satisfied scientific reviewers and is embraced by the authors.

But again, this is a distraction because it is not your place to argue whether my position is the author’s position. I stated a common position, the position that is embraced by the authors, who state: “the surprising fact C is observed” and is published in a scientific publication. This is not about whether you have the authority to say that your position is the correct one. Let the readers decide. This is about whether there is a scientific publication that supports the possibility of phi spiral observed in nature. You are actively trying to suppress that information, despite your earnestness and good intentions. I mean, why does it even matter to you that a phi spiral in nature is observed or not? ~gahnett — Preceding unsigned comment added by Gahnett (talk • contribs) 21:22, 21 August 2018 (UTC)

This conversation has ended with my editing out of “Contrary to popular belief, golden spirals have not been found in any natural processes“.

I believe this is an important assertion. I think there is value in this assertion because to say there isn’t something is to say very clearly what it is that there isn’t.

Yet, I want to show that if you apply Johnuniq’s rule fairly, then the voice is suppressed because rule of fairness. If the assertion that there is phi spiral observed is not allowed, then the assertion that phi spiral is not observed is also not allowed. The attention is removed of the subject. So there is no movement from positive to positive. Therefore, this is used as a tactic.

This is known as mysterious sameness. Hence you cannot get close to it, nor can you keep it at arm's length; You cannot bestow benefit on it, nor can you do it harm; You cannot ennoble it, nor can you debase it. Therefore it is valued by the empire. ~Lau, Daodejing Chapter 56

People say: between two opposed opinions the truth lies in the middle. Not at all! Between them lies the problem, what is unseeable, eternally active life, contemplated in repose” ~Goethe

To explain all nature is too difficult a task for any one man or even for any one age. ~Newton — Preceding unsigned comment added by Gahnett (talk • contribs) 23:45, 21 August 2018 (UTC)

Gahnett, you have done the right thing in removing the unsourced unproven negative "Contrary to popular belief, golden spirals have not been found in any natural processes." There's no evidence of such a popular belief even, though such a belief or claim does show up in little things here and there. As far as I can tell, though, beliefs are not very relevant in all this. Dicklyon (talk) 02:25, 22 August 2018 (UTC)