Talk:Vesica piscis

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[edit] Use

When and by whom was this symbol used historically? --FOo 06:07, 18 Jul 2004 (UTC)

Pythagoreans and early Christians, and, according to the originator of the article, 'Pagans' (though this is an increadibly vague term). CheeseDreams 18:39, 31 Oct 2004 (UTC)

[edit] Shape

Please note that the Vesica Piscis is the fish shape NOT the overlapping circles. Vesica Piscis is latin for fish face.CheeseDreams 18:40, 31 Oct 2004 (UTC)

Please see the new diagram for explanation. CheeseDreams 21:30, 3 Nov 2004 (UTC)

I'm not sure. I've seen vesica piscis used to refer to the almond-shaped (or, if you're Pagan, vulva-shaped) region formed by the overlapping circles, without the "fish tails" found on the ichthus. See, e.g.: [1] [2] [3]—FOo 23:37, 3 Nov 2004 (UTC)
There is an easy way to settle this issue. If someone could measure the width of the whole shape (including fish tails) and the height, and also measure the width of the shorter tailless shape. And then inform what the height-width ratio is of each of the two shapes. It is quite late in UTC land, so I, myself, will not check it till later.CheeseDreams 00:24, 4 Nov 2004 (UTC)

Here is a detailed link. It is briefly mentioned on this website, and at the bottom of the page on this website. CheeseDreams 19:45, 4 Nov 2004 (UTC)

It looks like a vagina, vaginas give birth, therefore it is symbol of Creation. -Mephisto Shyhawk

[edit] Merge to Fish shaped religious symbol thing

I would like to propose merging this article with that of Ichthys. The object in question is the same, and they are really just uses of the same thing by different peoples. I think there should be a section on "Christian use of THAT SHAPE" and "Pre-Christian use of THAT SHAPE" in the surviving article, and then any other bits that are in each article as well. However, I do not know what the resulting article ought to be called, maybe Fish shaped religious symbol thing CheeseDreams 20:25, 2 Nov 2004 (UTC)

I'd say they're more like twins, raised apart. They have different identities, different religions, and despite a family resemblance they don't look quite the same any more (one being geometric, the other freehand). Even the lack of a common name underscores how forced and difficult it would be to put them together. Leave them with their own pages, each with a link to his "brother". Tverbeek 02:06, 15 Dec 2004 (UTC)

[edit] Formula wanted

Any mathematicians out there that can conjure up a formula for: (a) Area of overlap when both circles are equal size? (b) Area of overlap when the circles are unequal size? 172.152.244.122 02:04, 10 February 2006 (UTC)

See Mrs. Miniver's problem for a little discussion... AnonMoos 15:57, 24 February 2006 (UTC)
(b) does not make sense if each circle goes through the centre of the other. For (a), off the top of my head without checking:
2\pi r^2 - 2 {2 \over 3}\pi r^2 - 2 {\sqrt{3} r^2 \over 4} = \left({2\pi \over 3}-{\sqrt{3} \over 2}\right) r^2
which is about 1.228...r^2, about 0.391... times the area of a circle or about 0.226... times the area of the triple shape. --Henrygb 21:48, 12 March 2007 (UTC)

[edit] "Pythagorean theorem"

Dear "Noe", the Pythagorean theorem has a somewhat tangential relationship to explaining the fact under discussion (since one must FIRST do a fair amount of geometry before being able to apply the Pythagorean theorem) -- but the equilateral triangles can be DIRECTLY SEEN in the construction of the Vesica Piscis (as shown in the diagram). The sqare root of three comes in from the well-known property that if the side of an equilateral triangle is 1, then the height of the triangle -- from center of base to vertex -- is half the square root of three. You could indeed derive this property by means of the Pythagorean theorem, but only if you constructed the triangles first. AnonMoos 02:34, 8 May 2006 (UTC)

I teach an international group of children in an IB school, and though it may depend on different math teaching traditions in different countries, I find that the Pythagorean theorem is known to nearly everyone, but the height of an equilateral triangle is not.--Niels Ø 10:15, 10 May 2006 (UTC)
That's nice -- you can't apply the Pythagorean theorem unless you hjave FIRST constructed the triangles, can you now? AnonMoos 11:29, 10 May 2006 (UTC)
I don't know what the point of that was meant to be, but here is my point (again): I think the explanation I shortened down is too long for the present purposes, and it does not reach the desired conclusion, unless one consideres finding the height of an equilateral triangle to be trivial. So, either the explanation should be finished, making it even longer, or it should be replaced by something shorter and less complicated, that doesn't pretend to be a complete proof. I tried to do the latter, and I still think that is the best choice. The pair of facts that (i) the Pythagorean theorem is involved, while (ii) the Pythagoreans believed in a different result, seems mildly amusing to me, which is why I mentioned the Pythagorean theorem here, but it may really be irrelevant here.--Niels Ø 15:48, 10 May 2006 (UTC)
I really don't understand how your Triangophobia is relevant to the article, but I do know that the fact that the centers of the two circles and the two circle intersection points are at the vertices of two back-to-back equilateral triangles (as shown in red in the construction diagram) is a hightly relevant fact about the geometry of the Vesica Piscis -- and that your edit suppresses all mention of this relevant geometric fact, and replaces it with a vague hand-waving invocation of the Pythagorean theorem (which is utterly useless to explain anything unless you construct the triangles first). AnonMoos 04:36, 11 May 2006 (UTC)

Things that I fail to understand are happening in the section ==Mystical and religious significance==. What does lengthy geometrical arguments and lists of rational approximants have to do with that section? Please explain!--Niels Ø 18:19, 15 May 2006 (UTC)

At least he's not deleting relevant information, the way you have always done... AnonMoos 03:42, 16 May 2006 (UTC)
Now, please be civil and get your facts right. I deleted it from a section where it was irrelevant, and when it was pointed out - correctly - that it was relevant, I added it to the section where it was relevant. Is that a problem? Your using the word "always" suggests you have checked my contributions list, but your accusation tell me you haven't. Your using the word "he" disguises the fact it's yourself you are talking about.--Niels Ø 07:21, 16 May 2006 (UTC)
I'm sorry, but in every single one of your edits, as of 03:42, 16 May 2006, you deleted relevant information FROM THE ARTICLE AS A WHOLE. AnonMoos 16:41, 16 May 2006 (UTC)

What useful information did I remove in the edit [4]? Listing other rational approximations to \sqrt{3} is hardly relevant here. Anyway, I'm glad the two of us are no longer alone in this field, and I warmly welcome user:The Anomes action (see following section in this discussion).--Niels Ø 20:22, 16 May 2006 (UTC)

I'm the one who added the list of rational approximations, replacing this sentence:
The fraction 265:153 is a ratio of whole numbers under 1000 which approximates the square root of 3 (though 362:209 and 989:571 are actually closer approximations).
— which made the choice of approximations seem arbitrary. On the contrary, for any irrational number there is a well-defined sequence of best rational approximations, and you can always do better with big enough integers. I could have expressed that better. The symbolic significance of 153 is interesting and (though I'm not religious) I think it ought to be restored somehow. I wonder whether Dr.I.J.Matrix is aware of it. —Tamfang 05:03, 18 May 2006 (UTC)
I actually agree a little with Noe on this one -- some editor(s) seemed to claim that 265:153 was a remarkably close approximation to the square root of 3, so other editor(s) added the cautionary note that 362:209 and 989:571 were even better, but there's no real reason to go into a whole discussion of fractional rational approximations here... AnonMoos 15:51, 21 May 2006 (UTC)
And (not surprisingly) I agree with AnonMoos here... I'm very interested in rational approximants; in fact, I have written a (so far unpublished) article about them, continued fractions, and related topics. It's just not relevant here. Anyway, 265:153 is a so-called best approximant, as all fractions with smaller denominator (or with smaller numerator) are poorer approximations. Comparing it to other approximants involving numbers less than 1000 is only relevant in the context of a decimal system, where limiting numbers to 3 decimal digits imposes that limit.--Niels Ø 16:41, 21 May 2006 (UTC)

[edit] The "measure of the fish"

I have moved the section below out of the article because of concerns about verifiability.

From the article:

Mystical and religious significance
It has been the subject of mystical speculation at several periods of history, perhaps first among the Pythagoreans, who considered it a holy figure. The mathematical ratio of its width (measured to the endpoints of the "body", not including the "tail") to its height was reportedly believed by them to be 265:153. This ratio, equal to 1.73203, was thought of as a holy number, called the measure of the fish. The geometric ratio of these dimensions is actually the square root of 3, or 1.73205... (since if you draw straight lines connecting the centers of the two circles with each other, and with the two points where the circles intersect, then you get two equilateral triangles joined along an edge, as shown in light red in the diagram).
Rational approximations to the square root of 3, improving as larger integers are used, include:
1:2, 3:5, 4:7, 11:19, 15:26, 41:71, 56:97, 153:265, 209:362, 571:989 . . .
The number 153 appears in the Gospel of John as the exact number of fish Jesus caused to be caught in a miraculous catch of fish, which is thought by some to be a coded reference to Pythagorean beliefs.

This section contains a number of unsourced speculations:

  • "...subject of mystical speculation at several periods of history..." -- which periods of history? Cite please?
  • "...perhaps first among the Pythagoreans, who considered it a holy figure." -- cite please?
  • "...was reportedly believed by them to be 265:153." -- "reportedly"? Reported where?
  • "...a holy number, called the measure of the fish" -- cite please?
  • "...is thought by some to be a coded reference to Pythagorean beliefs." -- thought by whom? Cite please?

Can someone please provide verifiable cites from mainstream sources for these assertions before restoring this material? And, before you ask, please can you give something other than a website that does not appear to me to provide cites for any of these assertions:

-- The Anome 07:20, 16 May 2006 (UTC)

You could read "Musings on the Vesica Piscis" - an article in "Nexus Network Journal" (ISSN: 1590-5869) Volume 6, Number 2 (a maths + architecture journal). If you want an earlier reference, you could read Porphyry and Plato which touch briefly upon it (e.g. in Timaeus), Porphyry recounting that Pythagoras caught 153 fish in a single catch of the net from the side of a boat. "On the Measurement of the Cycle" (Archimedes) also mentions "the measure of the fish" in this 153/vesica piscis context. The significantly more modern "City of Revelation" by Mitchell covers this topic, and goes into detail on the gematria and isopsephia aspects. Clinkophonist 17:15, 20 May 2006 (UTC)

...So I suppose I should add the section back. Clinkophonist 17:18, 20 May 2006 (UTC)

Thanks -- I read the Mitchell book a long time ago (but I don't have it now), and I knew that many of these claims date back at least to late 19th-century / early 20th century books (and certainly weren't invented on some website), but I didn't really have specific references. AnonMoos 15:47, 21 May 2006 (UTC)

Please provide the references as requested, not just a list of books, preferrably with quotations. The religious connections is not a bunch of trivia and must be thoroughly sourced. As for the reference "musings, they are musings to be ignored, unless they quote something serious sources. Mukadderat 19:27, 21 May 2007 (UTC)

Oh, so because the author titled it "Musings on the Vesica Piscis" the paper is to be ignored, no matter the extensive list of references provided in the paper nor the fact of having been published in a peer-reviewed journal devoted to architecture and mathematics. Did you care to have even a cursory look at it? Uaxuctum 19:13, 26 May 2007 (UTC)

[edit] Vulva shape and symbolism

The association of the Vesica Piscis with the Yoni is important and its mention on this page and on the Aureola page should not be deleted by vandals who like to determine for other people what is relevant and what is not.

Just a few references:

  • "The sheela-na-gig is a naked woman...displaying her vulva, which is shown as a vesica piscis." Barbara Walker - The Woman's Encyclopedia of Myths and Secrets (Harper San Francisco, 1983)
  • "The vesica, or central area of the interlocked circles, was treated not only with reverence but as a sacred entity. It was an area from which so much else, geometrically, could be created. With their knowledge of the macro-cosmos, it was not lost on our ancestors that the shape was not dissimilar to that of the female vulva, the origins of intelligent form -the origins of all of us. It thus represented the geometry of life." Kevin L. Gest - The Secrets of Solomon's Temple (ISBN 0853182566)
  • "The Vesica Piscis. Two interlocking circles form the Yoni or Vulva of the Goddess." Kathy Jones - The Goddess in Glastonbury (1990)
  • "As the joining together of two circles of equal radii, creating a third intersecting area that is symbolic of the vulva and the womb, the vesica piscis is one of the fundamental symbols of sacred geometry, and the origin, as well, of the Tree of Life of the Kabbala." Margaret Starbird - Magdalene's Lost Legacy, Symbolic Numbers & Sacred Union
  • "The middle section of the Vesica Piscis is called a mandorla, an almond shape that was seen to be the place of birth, the sacred yoni or vulva. This vulva shape is an ancient motif pointing to the Mother Goddess." Constance S. Rodriguez PhD, LCSW - Sacred Portals, Pathways to the Self (ISBN 9781403375926)

Tchoutoye 01:54, 24 May 2007 (UTC)

Please be careful with strong words, such as "vandalism" etc. Please look up wikipedia:Vandalism. I have nothing againct inclusion of anything provided you provide correct historical context and references. `'mikka 02:07, 24 May 2007 (UTC)

Please keep in mind when providing references to books, a distinction must be made between scholars in mythology and self-proclaimed experts in modern misticysm. Today everyone may print a book with any fantastic theory. `'mikka 02:09, 24 May 2007 (UTC)

Yes, but this guy User:Mukadderat keeps deleting not only material (dealing with the connection between this shape and religious iconography and symbolism) which might be labelled "controversial", but even the very diagram showing the geometric construction of this shape, which is a) well known, b) not disputed in the least, c) the origin of the very name "vesica piscis". First he tried to justify the deletion claiming the diagram "unnecessary" (which is not, since the other picture doesn't make it clear how to construct the shape nor what the proportions are), and now in his last deletion round he has even called it "unsourced", which shows he hasn't even cared to look at a single reference, nor to learn basic geometry for that matter (maybe he would like to check this: http://mathworld.wolfram.com/Lens.html ), and proves he's not in the least interested in improving the article but merely in trolling around deleting content he doesn't want to be there for whatever capricious reason of his. I'm starting to find this behaviour very annoying and I wouldn't doubt calling it "vandalism" if it continues. Uaxuctum 19:13, 26 May 2007 (UTC)

"I have nothing againct inclusion of anything provided you provide correct historical context and references." In that case you should mark the content with "citation needed", not simply delete it.

There is no obligation to use the citation needed tag. Additionally, it doesn't make sense to use the tag to mark a "see also" link. --C S (Talk) 02:52, 24 May 2007 (UTC)

"Please keep in mind when providing references to books, a distinction must be made between scholars in mythology and self-proclaimed experts in modern misticysm. Today everyone may print a book with any fantastic theory." In this case the issue is not contested. Both the PhD scholars and the "self-proclaimed experts" are unanimous on this. Dr. Constance Rodriguez has a background in Jungian Theory and a doctorate in Depth Psychology. Is that good enough for you? Tchoutoye 02:18, 24 May 2007 (UTC)

Not good. Just as doctorate in rocket science, biology or venereal diseases not good either. Experts to be quoted in articles are required to be recognized experts in the topic of the article. `'mikka 04:20, 24 May 2007 (UTC)
I think it's fairly obvious that this background is not sufficient to make one an expert in ancient history, which is the relevant field here for her assertion. Presumably she gives a citation for her quote. I would suggest looking at that instead. Furthermore, it would be best to incorporate the reliably sourced materials on vesica piscics as a symbol for the yoni in either this article or the yoni article. At the moment, it seems the discussion is rather odd as you two are discussing the inclusion of a see also link with no content explaining the relevance of the link in either articles. --C S (Talk) 02:52, 24 May 2007 (UTC)
I assume that the opponent is going to expand either of the article in question from the mentioned references. Since I am not an expert here, my sole concern in this and some related articles is proliferation of unreferenced texts. Knowing that there is lots of fantasies are around the internet, my sole action here is to keep the text reasonably referenced. `'mikka 04:20, 24 May 2007 (UTC)

I've added a note to the Vesica_piscis#Mystical_and_religious_significance section, mentioning the yonic interpretation and specifically labeling it a new age interpretation, and including the above references. This is clearly a common interpretation, as attested by the references, and hence should be mentioned, but I don't know if research shows that yonic is a traditional interpretation. Nbarth (talk) 00:32, 20 November 2007 (UTC)

[edit] Vandalic attitude from User:Mukkaderat

I've had it. This user keeps deleting the diagram and the description that show the geometric construction of this figure, even when this it not in the least a controversial issue, even after having been repeatedly warned in the revert summaries, and even after plenty of references for it have been provided both in the article and in this talk page (e.g., the MathWorld entry for this shape which I had provided above). So from now on I consider that this user is vandalizing this article and have left him a warning to the effect in his talk page. Uaxuctum 12:04, 6 June 2007 (UTC)

Colleague, The drawing and its description are deleted, as repeatedly explained, because they introduce unreferenced association of vesica piscis with ichthys in tthe history of christianity. Just the same, I may start pushing the theory that vesica piscis is the thape of the eye of a japanese woman and all the remaining pieces of the circles and surrounding boxes are crow's feet around these eyes, referring to mistical influence of oriental women on Europeans. Excluding the "fish tail" the description and picture are redundant, because the ones already given in the introduction describe and show the shape completely. Mukadderat 15:46, 6 June 2007 (UTC)
Do you know what the very name of this shape vesica piscis means in Latin? It means "the bladder of the fish", because the shape was thought in relation to the full shape with the two extensions forming the "tail" that resembles that of a fish. And do you know what the Greek word ichthys means? It means "fish". If you want to remove references to Christianity because of concerns about verifiability, even though it is not hard in the least to understand why a geometric figure that was associated with the shape of a fish could come to be associated with Jesus which was also associated and represented by the shape of a fish, do it if they really are not supported by the many references already provided. But any case, do it without removing the info about the geometric construction of this shape, which is clearly supported by many references including the MathWorld entry and most certainly is not "pushing a theory". If you remove this non-controversial and already well-referenced geometric construction diagram and section one more time, I will report you as a vandal. So you have already been warned, twice. Uaxuctum 16:10, 6 June 2007 (UTC)
You persistently do not provide the required reference. No need to threaten me. I know fish and fish. There are many fish and words related to fish The point is that the text does not provide the required association within christian beliefs. MathWorld does not draw fish tails. Mukadderat 16:23, 6 June 2007 (UTC)
The reference to the shape of a fish is in the very name of the shape vesica piscis, it needs no further sourcing. I told you you can remove the association with religious beliefs if it is not supported by references (although the association with Christian symbolism is already supported by at least one peer-reviewed reference), but not the geometric construction diagram nor the fact that this shape was named as it was named because it was seen as a portion of a fish shape. Uaxuctum 16:56, 6 June 2007 (UTC)
Oh, and removing reliable sources such as articles published in peer-reviewed journals is a very serious vandalic act. Uaxuctum 16:18, 6 June 2007 (UTC)
Which one? I also would advice you to avoid using the word "vandalism"; see wikipedia:Vandalism. It is not an argument in discussion, only an indication of you being angry about our disagreement. Mukadderat 16:23, 6 June 2007 (UTC)
The article "Musings on the Vesica Piscis" is a fully-referenced scholarly work published in a peer-reviewed journal. Removing all or significant parts of pages, such as removing the info and diagram about the geometric construction of this shape and removing a reliable source, is considered vandalism according to the definition of blanking given in Wikipedia:Vandalism. Uaxuctum 16:56, 6 June 2007 (UTC)
"Musings" are musings by an amateur, not a recognized expert neither in Christianity nor mythology, nor history. This argument is standard all over wikipedia, please see similar example. Mukadderat 18:50, 6 June 2007 (UTC)
The supposedly "similar" example you provide does not apply. Rachel Fletcher is not "an amateur", she is an expert in the issue of the uses and symbolism of geometry in design, having curated several museum exhibits on the matter:
"Rachel Fletcher is a geometer/theatre designer and restoration planner, with a B.A. from Hofstra University, M.A. from S.U.N.Y. Albany, and M.F.A. from Humboldt State University. She is the curator of two museum exhibits on geometry, Infinite Measure and Design By Nature, co-curator of the exhibit Harmony by Design: The Golden Mean and author of the exhibition catalog The Golden Mean as a Design Tool. In conjunction with these exhibits, which have traveled to Chicago, Washington, D.C., and New York, she teaches geometry and proportion as a design system to architects and designers, and has developed a hands-on geometry curriculum for school-age children. She is an adjunct lecturer at the New York School of Interior Design. Her essays have appeared in the Nexus Network Journal, Design Spirit, Parabola, Via, Building Design, the Lindisfarne Letter, and The Power of Place. Her design/consulting credits include an outdoor mainstage for Shakespeare & Co. in Lenox, Massachusetts and the Marston Balch Theatre at Tufts University." [5]
Many books on architecture talk about the religious symbology in buildings and the authors do not need to be scholars of Christianity, mythology or history to produce scholarly works on this issue relevant to architecture. Architects can and do use other references to get the information they need for their studies of religious symbolism in architecture, and it is unlikely that a scholar of biblical studies would produce a better reference for the religious symbolism in buildings than a scholar of architecture specialized in the issue. Same for studying the symbolism in geometric forms, for which someone who has been the curator of several museum exhibits on geometry in design, and who provides plenty of respectable sources in her paper, is a valid reference, especially since her paper has been peer-reviewed and published in a serious journal on geometry, not on some general-purpose magazine nor self-published. Uaxuctum 22:44, 11 June 2007 (UTC)
You convinced me that this person may provide useful and reliable references. No more objections for her in reference list. Mukadderat 00:06, 12 June 2007 (UTC)

Please be aware that your edit war without providing valin references into deleted unreferenced text about questioned statements, per wikipedia:Attribution may lead you to blocking. Mukadderat 16:33, 6 June 2007 (UTC)

Plenty of references have been already provided both in the article and in this talk page, but you have consistently refused to have a look at them and even tried to remove a peer-reviewed journal source from the article. Uaxuctum 16:56, 6 June 2007 (UTC)
I don't refuse. I checked them and even added one more, to a book of internationally known scholars, which confirm article's staements about "153" number. I deleted one reference to essay of a person without credentials in the area of religion, history or mythology. Mukadderat 18:55, 6 June 2007 (UTC)

[edit] Mandorla confusion

In the intro, it says “The shape is called a mandorla ("almond") in India”. This text makes it seem like “mandorla” is an a term for almond in some Indian tongue. Mandorla is in fact the Italian word for “almond”, and the term itself is most commonly used in Western culture when describing traditional Christian art. It has nothing to do with India. There is a term called Mandala (which derives from early Sanskrit for “circle”) that is used in India and is of importance to several of the Dharmic religions. I wonder if this is what Jossi was thinking when he made the edit. In any case, I think it should be removed (and I’ll do it if no one objects within a few days).

[edit] Euclid

I see that no one's posted on the talk page in a while. It may be useful to note that this shape is used in Euclid's first proposition in Elements, where he uses it to construct an equilateral triangle. Call the two centers of the circles A and B and one of their intersections C. Connect A, B, and C to form a triangle. In 2 (flat) dimensions, the triangle is equilateral because AB, BC, and AC are of equal length (they are each the radius of at least one of two circles of equal size). A nifty little proof and an interesting historical context. Just a suggestion. —Preceding unsigned comment added by 67.189.199.47 (talk) 04:51, 17 April 2008 (UTC)