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Thread: Constellations in the art of Leonardo da Vinci

  1. #31
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    Quote Originally Posted by Robert Tulip View Post
    There are broader cultural questions here, as to why Leonardo would have done this, and why he would have kept it a secret.
    I'm going to accept the motive, and secrecy, as plausible. But not proved at all.

    However, your "fit" and calculation of probability is ridiculously bad, from my point of view. I just don't see it at all--and no one else either, it seems. I think that's the only reason that anyone else is mentioning the other avenues of possible proof--comments by the artist, or surviving sketches--which don't seem to exist.

  2. #32
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    Quote Originally Posted by grapes View Post
    However, your "fit" and calculation of probability is ridiculously bad, from my point of view. I just don't see it at all--and no one else either, it seems. I think that's the only reason that anyone else is mentioning the other avenues of possible proof--comments by the artist, or surviving sketches--which don't seem to exist.
    Quite. There seems to be an assumption the Leonardo did this and then the matching of symbols could make sense (even if still not unique). How do we know Leonardo did it? Look at the matching of the symbols! A classic circular argument.

  3. #33
    Leonardo da Vinci made an interesting comment that there are three kinds of people, those who see, those who are shown and those who do not see. Art is full of hidden images and concealed intentions. Here we have a painting that puts astronomy at the centre of western culture.

    Going through the twelve associations with the twelve apostles, from right to left, they are

    Aries: hands
    Taurus: hands
    Gemini: arms
    Cancer: head and arms
    Leo: hands
    Virgo: hand
    Libra: arms and hands
    Scorpio: head, body, hand and sword
    Sagittarius: whole body
    Capricorn: head and hands
    Aquarius: head, left arm and body
    Pisces: hands, arms and shoulder clasp

    If we take these twelve parts of the picture and ask which star patterns they most resemble, the answer is unequivocal that they match the ecliptic stars in the same order as in the sky. It is all about embedding a secret message.

    Jens earlier commented that Christ matches to Pisces. This is true. If we look at another painting that Leonardo helped with, the Baptism of Christ, a similar motif is seen with the shape of Christ's hands and arms matching to the shape of the constellation Pisces, while the shape of John the Baptist matches the constellation Aquarius. Again, it is more than coincidence that these matches accord with teachings that have been somewhat hidden from public view.

  4. #34
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    Quote Originally Posted by Robert Tulip View Post
    Leonardo da Vinci made an interesting comment that there are three kinds of people, those who see, those who are shown and those who do not see. Art is full of hidden images and concealed intentions.
    I guess he missed a fourth group, that I seem to fall into here: those who have been shown, and still don't see.

    If we take these twelve parts of the picture and ask which star patterns they most resemble, the answer is unequivocal that they match the ecliptic stars in the same order as in the sky.
    I disagree, I think this thread contains plenty of equivocation. What would we have to do to convince you? What sort of test could we perform? There have been some suggested, would they work?

  5. #35
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    The obvious test would be for someone to take the constellations in a shuffled order and find equally good matches to the figures (or better still, several people taking given different random orders). Ideally, Robert would do this and use some sort of distance measure to show that his preferred matches are better than any other possible configuration (not that I think that is possible). I was going to do it but I really can't be bothered!

  6. #36
    I would like to follow up on this testing suggestion, but it would need to be done double blind, with participants who had not been exposed to the idea that perhaps Leonardo intentionally embedded the constellations in the same order as in the sky.
    Given that I am effectively claiming this is the actual Da Vinci Code, it might be hard to keep this secret between you me and the doorpost. Previous claims about coded messages in The Last Supper have tended to go viral. However, knowing the famous skepticism of BAUT readers I have little worry of that happening.

    Further to the correspondence between the figure of Jesus Christ and the constellation Pisces, there is an apparent correspondence between the ring of stars in Pisces known as 'the circlet' and Jesus's right hand. It is surprising that the holy grail is missing from this painting. The circlet marks the current position of the March equinox. Viewed from the Southern Hemisphere, it has a striking resemblance to Leonardo's Vitruvian Man.

    I looked further at discussion of hidden images in paintings. Holbein's painting of the skull in The Ambassadors is among the most famous. There are also claims of images embedded in work of Van Gogh, but for the life of me these appear far less obvious than the claims I am making here.

  7. #37
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    Quote Originally Posted by Robert Tulip View Post
    I would like to follow up on this testing suggestion, but it would need to be done double blind, with participants who had not been exposed to the idea that perhaps Leonardo intentionally embedded the constellations in the same order as in the sky.
    That's not really the kind of test I had in mind. More like take the set of zodiac constellations, and see if we can fit them to the original USAn colonies, or something like that.

  8. #38
    Quote Originally Posted by Robert Tulip View Post
    Given that I am effectively claiming this is the actual Da Vinci Code, it might be hard to keep this secret between you me and the doorpost. Previous claims about coded messages in The Last Supper have tended to go viral.
    What is the "actual Da Vinci Code"? I thought it was just a novel. Is there actually some code that Leonardo made, and if so, about what?
    As above, so below

  9. #39
    Quote Originally Posted by Jens View Post
    What is the "actual Da Vinci Code"? I thought it was just a novel. Is there actually some code that Leonardo made, and if so, about what?
    The story in Dan Brown's novel goes back to a book called Holy Blood Holy Grail that claims Jesus Christ married Mary Magdalene and she sailed to Marseilles and gave birth to the Merovingian Dynasty. So, the holy grail, the 'san greal', is supposedly the holy blood line of the messiah, the 'sang real', shifting one letter. My view is that this is pure legend. The link to Leonardo's The Last Supper is the claim in The Da Vinci Code that the figure sitting at Jesus's right is actually Mary Magdalene, and that Jesus and Mary form an M. My point was that if the zodiac shapes are actually embedded secretly in the painting, then it does actually contain a coded message, not the legendary one that Brown has popularised.

  10. #40
    Quote Originally Posted by grapes View Post
    your "fit" and calculation of probability is ridiculously bad
    Let me take you through the "fit" step by step.

    1. Open this diagram http://www.bautforum.com/attachment....0&d=1299724331 (Posted at #10 above.)
    2. Consider each of the twelve ecliptic constellations one by one on the star map.
    3. Apply the same transformation to the constellation as I have applied to the corresponding letter of the alphabet - eg for Taurus (B) rotate 150° left, for Leo (E) rotate 30° right and flatten, for Pisces (L) rotate 120° right, etc.
    4. Observe how these twelve transforms appear in the shape of each of the twelve apostles in The Last Supper.

  11. #41
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    Quote Originally Posted by Robert Tulip View Post
    Let me take you through the "fit" step by step.

    1. Open this diagram http://www.bautforum.com/attachment....0&d=1299724331 (Posted at #10 above.)
    2. Consider each of the twelve ecliptic constellations one by one on the star map.
    3. Apply the same transformation to the constellation as I have applied to the corresponding letter of the alphabet - eg for Taurus (B) rotate 150° left, for Leo (E) rotate 30° right and flatten, for Pisces (L) rotate 120° right, etc.
    4. Observe how these twelve transforms appear in the shape of each of the twelve apostles in The Last Supper.
    Regarding 3, how did these transformations come about? I'm assuming trial and error to find a fit. Or am I mistaken?

    2a. Shuffle the constellations into a random order
    3a. Apply transformations of your own choosing to each constellation
    4a. Observe how these can be matched to your choice of hands, hair, face, clothing or pose of each the twelve apostles

    Do you really not see that you are creating an arbitrary fit and then using it as evidence of something? Do you really think they couldn't be matched in any other way? Why is this any more valid than my fitting the first seven letters of the alphabet to the Seven Samurai?
    http://www.bautforum.com/attachment....4&d=1300193725

    Some of your "matches" are pretty awful as well: Gemini, you have one star on each hand (not even the two end stars) and the rest looped around underneath; Aquarius and Scorpio, randomly scattered over two people, Cancer, superimposed on a pair of hands but not with any real relationship; and so on. Actually, the more I look, the less convincing it gets. On the other hand, those Samurai...

    So, the holy grail, the 'san greal', is supposedly the holy blood line of the messiah, the 'sang real', shifting one letter. My view is that this is pure legend.
    Not even legend, now we know the identity of the person who made it up and faked the evidence.

  12. #42
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    I'm sorry, Robert, but the 'correlations' you describe do not seem to be there, as far as I can see.

  13. #43
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    Now if Aquarius had been carrying a water-pot, Sagittarius holding a teapot, Pisces some fish, and so on, we might be in business...

  14. #44
    Quote Originally Posted by Strange View Post
    Regarding 3, how did these transformations come about? I'm assuming trial and error to find a fit. Or am I mistaken?
    Now Strange, I enjoy your extreme skepticism, but it is really easy to answer. As I have explained several times, I looked to see how the constellations are embedded in the natural order in the painting. Initially I made some mistakes, accepting a site that had Scorpio and Sagittarius reversed, and also with Cancer, not seeing how Leonardo actually shows it. However, the explanation I have just provided in my most recent comment is completely rigorous.
    2a. Shuffle the constellations into a random order
    No, not random, actual, as observed in the sky.
    3a. Apply transformations of your own choosing to each constellation
    No, not of my choosing, but as actually appear in The Last Supper.
    4a. Observe how these can be matched to your choice of hands, hair, face, clothing or pose of each the twelve apostles
    Not my choice, but seeing how Leonardo has placed these shapes in his painting in order.
    Do you really not see that you are creating an arbitrary fit and then using it as evidence of something?
    I am astounded that you cannot see something so simple, as obvious as the refutation of geocentrism. There is nothing arbitrary about any of the fit.
    Do you really think they couldn't be matched in any other way?
    Sorry, that is irrelevant, I am talking about how Leonardo actually did match them. They cannot be matched in any other way, any more than upper case and lower case letters of the alphabet could somehow be matched other than with each other.
    Why is this any more valid than my fitting the first seven letters of the alphabet to the Seven Samurai? http://www.bautforum.com/attachment....4&d=1300193725
    Very amusing, but totally irrelevant. Just for a start, I am not saying that letters are embedded, but constellations, as they are actually observed in the sky, but artfully concealed. Also, the correlations I explain are vastly more prominent than the arbitrary comparison you make with letters. Either hands, arms or whole figures, not silly correlations such as between eyes and the letter B.
    Some of your "matches" are pretty awful as well: Gemini, you have one star on each hand (not even the two end stars) and the rest looped around underneath;
    As we see Gemini, it consists of two parallel lines of stars ending in Castor and Pollux. The third figure in the Last Supper has arms in parallel, a feature not shared by any of the other twelve. Yes, Gemini has Castor and Pollux next to each other, while Leonardo offsets the hands, but the basic shape is there. I don't know what you mean by 'looped around underneath'.
    Aquarius and Scorpio, randomly scattered over two people,
    Aquarius has his left arm draped around Capricorn, matching the constellation shape. I think you are mixing up Scorpio and Sagittarius. Scorpio is the most vivid and exact of the twelve, with Peter's sword matching the scorpion's sting, the curve of his arm matching the back of the scorpion, and his head matching the scorpion's head. Judas partly obscures Peter, with Judas' head right in front of the position of Antares at the heart of the scorpion. Sagittarius is a blobby constellation, and Judas is equally blobby, but still we can see a match between his arms and star lines in the constellation.
    Cancer, superimposed on a pair of hands but not with any real relationship;
    I initially made a mistake with Cancer which I have corrected since. I first thought that Leonardo had just used the hands, but as I recently explained, the Y shape of the constellation matches the whole figure, with the same transform as I show for the letter D. I have not yet corrected this on the copy of the twelve associations here but will replace this soon.
    and so on. Actually, the more I look, the less convincing it gets. On the other hand, those Samurai...
    I'm glad you are so able to convince yourself Strange. Thanks for posing such excellent questions.
    Not even legend, now we know the identity of the person who made it up and faked the evidence.
    Are you talking about the Priory of Sion? There is actually some legendary material, for example it is claimed that "Medieval lore has it that Mary Magdalene along with Mary Jacobe and Mary Salome (mothers of the two James’s of the Gospels) landed in a frail barque near Roman Marseille with Martha, Lazarus and their black servant Sara". I don't think the Magdalene stories of France are just modern inventions.

  15. #45
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    Quote Originally Posted by Robert Tulip View Post
    Do you really think they couldn't be matched in any other way?
    Sorry, that is irrelevant,
    No, it is extremely relevant. You calculated a probability to show that there was a very small chance of any other match. However, if other matches are possible, or probable, that negates your probability argument. Which is pretty much all you got, since there doesn't seem to be any historical evidence.

    As you seem to be saying, you started with other (erroneous) matchings before you got the right ones. Didn't those others seem to work as well?

  16. #46
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    Quote Originally Posted by Robert Tulip View Post
    As I have explained several times, I looked to see how the constellations are embedded in the natural order in the painting.
    Or how you think/see them to be embedded. There is no independent confrimation of your fitting of these patterns.

    Initially I made some mistakes, accepting a site that had Scorpio and Sagittarius reversed, and also with Cancer,
    Doesn't that mean that you were able to fit those constellations to the picture in the "wrong" place. And you were quite happy with that until you found the order was wrong? Does that tell you something?

    No, not random, actual, as observed in the sky.
    No, not of my choosing, but as actually appear in The Last Supper.
    I think you missed my point. I wasn't saying that is what you have done. I mean that is what someone else could do with an equal degree of "success".

    Not my choice, but seeing how Leonardo has placed these shapes in his painting in order.
    You keep saying this as if you had done it and then checked it against the "right answer" as provided by Leonardo. But (unless I have completely missed something here) you are checking your results against ... your results.

    I am astounded that you cannot see something so simple, as obvious as the refutation of geocentrism. There is nothing arbitrary about any of the fit.
    And I am equally astounded that you can't see it is completely arbitrary!

    Sorry, that is irrelevant, I am talking about how Leonardo actually did match them.
    No, you are talking about how you think he matched them.

    Very amusing, but totally irrelevant. Just for a start, I am not saying that letters are embedded, but constellations, as they are actually observed in the sky, but artfully concealed.
    But that is my point. Take 12 patterns of random dots and twelve Disney characters - anyone would be able to do exactly what you have done here.

    Also, the correlations I explain are vastly more prominent than the arbitrary comparison you make with letters.
    I'm afraid I just don't see that. Sorry.

    Either hands, arms or whole figures, not silly correlations such as between eyes and the letter B
    Why is that a "silly" correlation? I'm quite hurt

    The third figure in the Last Supper has arms in parallel, a feature not shared by any of the other twelve.
    I looked at the image carefully to look for parallel arms and, to my eye, characters 1, 3, 10 and 12 have equally parallel arms. (I had actually forgotten which character you mentioned and assumed it was 10 as they are the most obvious.) But this is all purely subjective. You would need to do some formal image analysis to identify structures in the picture and measure how parallel they were to really answer that.

    I'm glad you are so able to convince yourself Strange. Thanks for posing such excellent questions.
    I think it is fascinating that it is so obvious to each of that there is something there ... or not!

  17. #47
    Quote Originally Posted by grapes View Post
    you seem to be saying, you started with other (erroneous) matchings before you got the right ones. Didn't those others seem to work as well?
    I made two mistakes.

    The first arose from looking on the internet for previous evidence of this correlation. The only source I found was an imaginative reading which correctly states that the apostles match the signs from right to left but wrongly mixes up Judas and Peter. BAUT readers kindly corrected this error. This error was not in the identification between figures and stars, but just in the names of the apostles. This mixing of Peter and Judas is not to the point of this thread.

    My second error was regarding the fourth figure from the right, in its match to Cancer. This was a simple mistake on my part. I took the asterism just south of the ecliptic, now known as the head of the snake Hydra, as Cancer, as shown in the Dendera Zodiac. In fact Leonardo used the ecliptic stars. I have corrected this error precisely because my initial reading did not actually match the evidence and did not 'work as well'.

    I should mention, it took me a while to find all the matches. Leo, fifth from the right, is somewhat distorted, as shown in the distortion of the letter E in my decoder. Analysis of the shapes shows that the figure's cocked left hand matches the mane of the lion with Regulus at the wrist, and his right hand matches the group around Denebola. Also Capricorn, third from left, contains two main triangular shapes the same as the stars of Capricorn, made either of the hands and head or of the hands and right arm.

    Leonardo's artistry in concealing his source requires some effort to decode, but once the key is understood all the material appears in a consistent and clear way.

  18. #48
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    Also Capricorn, third from left, contains two main triangular shapes the same as the stars of Capricorn, made either of the hands and head or of the hands and right arm.
    So basically you are looking at the constellations, as shown on modern constellation maps, identifying basic shapes then looking for those shapes on the painting, then declaring a match even if those shapes are distorted. Can't you see several errors in that procedure?

    Here's Capricorn from the Uranometria, published 100 years after the Last Supper was painted, but probably similar to any map Leonardo may have had access to. Where are your triangles here?
    http://www.sciencephotolibrary.com/i...g?id=867000415

  19. #49
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    The reason why I mentioned the possibility of 'Aquarius...carrying a water-pot, Sagittarius holding a teapot, Pisces some fish, and so on' in an earlier post is because that is the way symbolism in pictures like this tends to work. Drawing shapes onto paintings and trying to interpret those shapes seems to be a modern obsession, rather than an Renaissance (or a Classical) practice. Paintings like The Ambassadors include many objects with symbolic significance, but no hidden patterns of geometry.

  20. #50
    Quote Originally Posted by eburacum45 View Post
    So basically you are looking at the constellations, as shown on modern constellation maps, identifying basic shapes then looking for those shapes on the painting, then declaring a match even if those shapes are distorted. Can't you see several errors in that procedure?

    Here's Capricorn from the Uranometria, published 100 years after the Last Supper was painted, but probably similar to any map Leonardo may have had access to. Where are your triangles here?
    http://www.sciencephotolibrary.com/i...g?id=867000415
    Thanks. If you look at the stars of Capricorn, ignoring all fanciful sea-goat imagery, as per the link in my statement that you quoted, you can readily see the triangle. In the Last Supper, Leonardo used alpha and beta for the head, gamma and delta for the right hand, and the unnamed stars at the base of the triangle for the left hand. The only distortion here is that the constellation stars are rotated left about 45 degrees. The stars as observed in the sky have not changed since ancient times except for minimal proper motion and precession.

    The compelling basis for this correlation is that all twelve of the figures match to the stars in similar ways as described here for Capricorn in the same order that the constellations appear in the sky.

  21. #51
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    The stars as observed in the sky have not changed since ancient times except for minimal proper motion and precession.
    But the idea that the stars in Capricorn form a triangle is a modern one, and is not supported by the diagrams in the Uranometria.

  22. #52
    I'm not sure where you get the idea that the Capricorn triangle is modern. I earlier copied the Dendera Zodiac, dating to ancient times which contains the sea-goat, derived from observation. The sea-goat picture has always derived from the triangle. You can see it in the sky quite clearly. I will look into this further.

  23. #53
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    Quote Originally Posted by Robert Tulip View Post
    Let me take you through the "fit" step by step.

    1. Open this diagram http://www.bautforum.com/attachment....0&d=1299724331 (Posted at #10 above.)
    2. Consider each of the twelve ecliptic constellations one by one on the star map.
    3. Apply the same transformation to the constellation as I have applied to the corresponding letter of the alphabet - eg for Taurus (B) rotate 150° left, for Leo (E) rotate 30° right and flatten, for Pisces (L) rotate 120° right, etc.
    4. Observe how these twelve transforms appear in the shape of each of the twelve apostles in The Last Supper.
    Dude: you're not even using the original painting: the thing you link to is some sort of cartoon copy--it's completely different than original....

    http://en.wikipedia.org/wiki/File:Da...2_nowatmrk.jpg

  24. #54
    Quote Originally Posted by Warren Platts View Post
    Dude: you're not even using the original painting: the thing you link to is some sort of cartoon copy--it's completely different than original....

    http://en.wikipedia.org/wiki/File:Da...2_nowatmrk.jpg
    Hi Warren, nice to hear from you, and thank you for posting the link to the reproduction of the restored original of Leonardo's Last Supper.

    You are incorrect that the two versions of the painting are materially different. I used the simplified version only because it is easier to see all the figures. It is a bit harder in the original to see whose hands belong to whom. If you had bothered to compare the two you would have seen that the postures of all the figures are exactly the same. The observation I have made stands without change. I'm really quite surprised you would resort to the 'roll-eyes' condescension when you are utterly wrong.

    That one was easy.

  25. #55
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    Well ! you say easy. I say wrong.
    Leonardo De Vinci did not have star charts or astrology in mind when he set out that image...
    Where have you gotten this absurd idea from ? I would suggest researching this great mans writings and come back to me with his interpretation of his image... I think it had relevance to some religious event involving a super and some symbolisms about bread and wine.... where you get this idea he wants to tel us something else is a bit of a mystery to me...

  26. #56
    Quote Originally Posted by astromark View Post
    Well ! you say easy. I say wrong.
    Leonardo De Vinci did not have star charts or astrology in mind when he set out that image...
    Where have you gotten this absurd idea from ? I would suggest researching this great mans writings and come back to me with his interpretation of his image... I think it had relevance to some religious event involving a super and some symbolisms about bread and wine.... where you get this idea he wants to tel us something else is a bit of a mystery to me...
    Astromark, I have not suggested that Leonardo had astrology in mind. I have actually noted that Leonardo condemned astrology. The suggestion I have raised here has nothing to do with astrology. You are the one who makes that association. What Leonardo did apparently have in mind however, was scientific observation of the night sky.

    I have made several references in this thread to Leonardo's Notebooks. Interestingly, he appears to support the heliocentric theory, long before Copernicus. He does not provide any explanation that I have found about interpretation of the Last Supper.

    Your comment about whether Leonardo explained it has been discussed already in this thread. Obviously he did not explain it, otherwise people would have discussed his explanation. As I pointed out earlier, there are clear reasons why Leonardo would not have explained it. This search for an explicit explanation equates to saying that if we cannot find an explicit statement by Holbein that a skull can be seen in The Ambassadors, then no skull exists.

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    You are saying that there is a unique match between the constellations and the figures, correct? Lets call this Axiom 1.

    Rather than spend/waste my time demonstrating that all 12 could just as easily be matched to any of the figures, lets just concentrate on Capricorn discussed above. You match this to the triangle formed by hands and head of the third figure.

    Therefore, by axiom 1, you must be saying that there are no other figures where a triangular relationship between any parts of the figure can be identified (after allowing any stretching, scaling and rotation of the triangle). Is that correct?

  28. #58
    Andrew Capricorn.gif
    Capricorn.gif
    Quote Originally Posted by eburacum45 View Post
    the idea that the stars in Capricorn form a triangle is a modern one
    Here is a picture from Skygazer 4.5 of the traditional outline of Capricorn and the mythological figure, showing stars to magnitude 4. The triangular shape dates to the ancient world. The head is alpha and beta Capricorni, the tail is gamma and delta Capricorni and the legs are omega and psi capricorni.

    And here for comparison is the overlay on the figure of Andrew, with stars shown without correction for magnitude. We see that the angles of the triangle head-left hand-right hand are much the same as the corresponding angles of the traditional constellation shape.
    Quote Originally Posted by Strange View Post
    You are saying that there is a unique match between the constellations and the figures, correct? Lets call this Axiom 1. Rather than spend/waste my time demonstrating that all 12 could just as easily be matched to any of the figures, lets just concentrate on Capricorn discussed above. You match this to the triangle formed by hands and head of the third figure. Therefore, by axiom 1, you must be saying that there are no other figures where a triangular relationship between any parts of the figure can be identified (after allowing any stretching, scaling and rotation of the triangle). Is that correct?
    Not quite. The existence of a causal correlation does not exclude the existence of a different non causal correlation. I am saying there is a causal correlation between the actual order of the stars in the sky along the path of the sun and the order of the figures in The Last Supper, because Leonardo used the stars as his template, embedding each star pattern in each figure. In the example you gave, looking for triangles, we can see that the Hyades, the head of the bull in Taurus, form a well known isosceles triangle. So, looking at the figure second from right, we see the isosceles triangle in the shape of the left hand, while the right hand matches the Pleiades. The same applies to the isosceles shape of Pisces, appearing in both the left most and central figures as discussed above with Jens. This is as expected. It is also possible to see other triangles, given that the triangle is such a common figure, but there are none anywhere near as exact a match to Capricorn, especially regarding the quite accurate match to the angles, as the one that is in the same position as Capricorn.

  29. #59
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    Quote Originally Posted by Robert Tulip View Post
    Not quite. The existence of a causal correlation does not exclude the existence of a different non causal correlation. I am saying there is a causal correlation between the actual order of the stars in the sky along the path of the sun and the order of the figures in The Last Supper, because Leonardo used the stars as his template, embedding each star pattern in each figure.
    How do you know this? Because you have found a way of correlating the stars with the figures.
    How do you know your correlation is correct? Because it matches that used by Leonardo.
    How do you know what correlations Leonard used? Because they are the same as the ones you have found.
    How do you know your correlation is the one by Leonardo? Because it matches that used by Leonardo.
    How do you know what correlation Leonard used? Because they are the same as the ones you have found.
    How do you know your correlation is the one by Leonardo? Because it matches that used by Leonardo.
    How do you know what correlation Leonard used? Because they are the same as the ones you have found.
    ....

    In summary, there is a causal correlation because you have matched them this way. If you match them any other way it is non-causal, correct?

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    Quote Originally Posted by Robert Tulip View Post
    I'm not sure where you get the idea that the Capricorn triangle is modern. I earlier copied the Dendera Zodiac, dating to ancient times which contains the sea-goat, derived from observation. The sea-goat picture has always derived from the triangle.
    The 'seagoat' figure in the Endera Zodiac resembles the Uranometria figure quite closely, which is in itself quite a remarkable survival. But both images are monstrous hybrid creatures with the tail of a fish and the head and forequarters of a goat. This centaur-like figure is roughly L-shaped, so it seems the ancients saw Capricornus as an L-shape made up of two sides of the triangle rather than a complete triangle. So I'd be looking for an L-shape in Leonardo's painting if it were up to me.
    .

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