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Thread: Thoughts and Findings related to the Maranatha "Key" Pt. II

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    Quote Originally Posted by jlockest View Post
    OK - what is the difference between geometry and 'Sacred Geometry'?

    What odds all those painters knowing this amazing secret? You know of the Vermeer link to all this, and I'm sure I read somewhere that the person who detected the 'tilted hexagram' in Vermeer had also seen it in various other artists' work. The original site has gone, but this archive is still available: Vermeer's Riddle Revealed - Priory of Sion paintings analyzed for the Grail Geometry.


    So, wouldn't it be just as likely, that instead of being some amazing secret, that geometry used in art is being misread and geometric shapes 'perceived' (that were never intended) by the viewer from other geometric 'proportional' constructs that were used, and intended, by the various artists?

    ge·om·e·try
    jēˈämətrē/Submit
    noun
    the branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogs.
    a particular system of geometry.
    plural noun: geometries
    "non-Euclidean geometries"
    the shape and relative arrangement of the parts of something.
    "the geometry of spiders' webs"
    https://www.google.com/webhp?sourcei...F-8#q=geometry

    Sacred geometry ascribes symbolic and sacred meanings to certain geometric shapes and certain geometric proportions.[1] It is associated with the belief that a god or God is the geometer of the world. The geometry used in the design and construction of religious structures such as churches, temples, mosques, religious monuments, altars, and tabernacles has sometimes been considered sacred. The concept applies also to sacred spaces such as temenoi, sacred groves, village greens and holy wells, and the creation of religious art https://en.wikipedia.org/wiki/Sacred_geometry


    If you'd like want to position a counter-argument, it should be necessary to 1st: read the article I posted. 2nd: to look at the references provided in the article which support the theory. And then 3rd: demonstrate how there is another system at play, (since this is your theory, or at least your query) and then use sources to support that position.

    Yes, I know about that Vermeer study. I don't understand your point in bringing it to attention. That writer's theory is that Vermeer used the "Grail Geometry" to COMPOSE his work, which doesn't support your idea that it is randomly "seen".

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    Quote Originally Posted by hayward View Post
    ge·om·e·try
    jēˈämətrē/Submit
    noun
    the branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogs.
    a particular system of geometry.
    plural noun: geometries
    "non-Euclidean geometries"
    the shape and relative arrangement of the parts of something.
    "the geometry of spiders' webs"
    https://www.google.com/webhp?sourcei...F-8#q=geometry

    Sacred geometry ascribes symbolic and sacred meanings to certain geometric shapes and certain geometric proportions.[1] It is associated with the belief that a god or God is the geometer of the world. The geometry used in the design and construction of religious structures such as churches, temples, mosques, religious monuments, altars, and tabernacles has sometimes been considered sacred. The concept applies also to sacred spaces such as temenoi, sacred groves, village greens and holy wells, and the creation of religious art https://en.wikipedia.org/wiki/Sacred_geometry


    If you'd like want to position a counter-argument, it should be necessary to 1st: read the article I posted. 2nd: to look at the references provided in the article which support the theory. And then 3rd: demonstrate how there is another system at play, (since this is your theory, or at least your query) and then use sources to support that position.

    Yes, I know about that Vermeer study. I don't understand your point in bringing it to attention. That writer's theory is that Vermeer used the "Grail Geometry" to COMPOSE his work, which doesn't support your idea that it is randomly "seen".
    So sacred geometry is no different to normal geometry then - as if I'm an atheist, then all geometry is just geometry? Or if I'm a pagan, then my sacred geometry isn't the same as your sacred geometry? Or if I worship apples then the pip shape is sacred?

    Totally agree that the Vermeer site is written by someone who sees that geometric shape and then assumes that the artist used it to compose his work. BUT, as in all the cases I've seen so far of geometry in paintings, I'm not sure anyone has showed 'intent' by the artist. And I've seen numerous attempts at applying 'geometric' shapes to various artworks - so does that make them all 'true'? So even the ones that you don't agree with that other people see? Just for a laugh, enter 'geometry in poussin' into Google , then pick the images tab on the search results and then see how many different images are returned. Did Poussin then intentionally put ALL those different shapes into his artwork?

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    Quote Originally Posted by jlockest View Post
    So sacred geometry is no different to normal geometry then - as if I'm an atheist, then all geometry is just geometry? Or if I'm a pagan, then my sacred geometry isn't the same as your sacred geometry? Or if I worship apples then the pip shape is sacred?

    Totally agree that the Vermeer site is written by someone who sees that geometric shape and then assumes that the artist used it to compose his work. BUT, as in all the cases I've seen so far of geometry in paintings, I'm not sure anyone has showed 'intent' by the artist. And I've seen numerous attempts at applying 'geometric' shapes to various artworks - so does that make them all 'true'? So even the ones that you don't agree with that other people see? Just for a laugh, enter 'geometry in poussin' into Google , then pick the images tab on the search results and then see how many different images are returned. Did Poussin then intentionally put ALL those different shapes into his artwork?
    You've missed the context of the article, as well as all of the references in the article which show that the historic perspective of these individuals was that such Geometry was viewed as the work of God, of divine nature, or from the hand of a grand architect. Plato's Timaeus describes the Cosmological structure of the Universe as made by the hand of a Demiurge or "divine craftsman". He described how the indication of this "design" is evident through geometry, particularly the regular solids. Pacioli elaborated on this subject in his "On the Divine Proportion" which sought to demonstrate that the proportions of geometry seen through such design was indicative that God was behind their "heavenly" design. Kepler furthered this discussion in his Mysterium Cosmographicum, part of which attempted to demonstrate how this "design of the divine" was proven through the regular solids and how they could be nested within each other, so as to suggest that the "plans" were "embedded" in the geometric materials themselves.

    This is the context of the subject of "Sacred Geometry" in question. Whatever your personal beliefs might happen to be in the present tense have no effect or bearing on the historical context surrounding the subject. If you are Pagan and you don't like the "divine" overtones of the story, that is really your problem, it doesn't change what had been recorded.

    Next,
    The difference between what is "true" --or isn't-- in terms of finding geometry is between what is observable and what isn't Either the geometry is fully justified on all points or sides or it isn't. If it is, this means that each point is justified through intersection or features in the work. When this happens, I would then expect someone to ask "what are the odds" of this occurring in several paintings in such a fashion, with exactly the same degree of tilt to the picture plane?

    There is also an obvious difference between what is coincidence and probable intent.

    For example, the writer of Vermeer's "Grail Geometry" uses an approach that, from my point of view, is process of total coincidence. There is simply not enough indication through either intersection lines or terminating points of the lines revealed in the image to show that the artist had considered justifying all the points of the geometry. This writer's geometry is also usually off of the canvas edge entirely, which shows that "nothing" had aided to complete the image. Yes, anyone can take the tilted hexagram and put it over an image and mark the points where its sides intersects features in the painting. This does not really demonstrate anything since you have the rest of the shape to account for.

    When I take your suggestion and Google "geometry in Poussin", all of these examples also appear to have one or two corresponding points of their geometry matched with points in the image, but then the other points either fall in the middle of nowhere and have no correspondences or justifications in terms of either intersecting lines or distinct objects in the image.

    To a person that actually LOOKS with a keen eye, they can see in the other examples spoken of where each line ends, where they intersect with other lines and which points are being defined through features in the image. Each point is justified, not floating randomly, like the "geometry in poussin" images. That is the difference. When you have no justification, there is no probability that it was intended. But when you have justification in the image and the same things appears in different works, it begins to increase the probability that it was intended.

    You can either accept that this was a random coincidence for it to appear in several works by such artists, or that there was a similar or common reason for doing so.

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    Quote Originally Posted by hayward View Post
    You've missed the context of the article, as well as all of the references in the article which show that the historic perspective of these individuals was that such Geometry was viewed as the work of God, of divine nature, or from the hand of a grand architect. Plato's Timaeus describes the Cosmological structure of the Universe as made by the hand of a Demiurge or "divine craftsman". He described how the indication of this "design" is evident through geometry, particularly the regular solids. Pacioli elaborated on this subject in his "On the Divine Proportion" which sought to demonstrate that the proportions of geometry seen through such design was indicative that God was behind their "heavenly" design. Kepler furthered this discussion in his Mysterium Cosmographicum, part of which attempted to demonstrate how this "design of the divine" was proven through the regular solids and how they could be nested within each other, so as to suggest that the "plans" were "embedded" in the geometric materials themselves.
    I think you said it in the opening line. Geometry was viewed as the work of G_d. My understanding is that geometry (all geometry) was seen as a way of recognising G_d's hand in creation - an aspect of G_d's mind. It wasn't seen that only geometry in some artworks or buildings represented G_d's fingerprint - it was ALL geometry. If, historically, chemistry had been understood better, then G-d may have been seen as the great 'chemist' - and ALL chemistry would have been seen as partially lifting the veil on the mind of G_d. Applying 'sacred' to geometry appears to do the opposite of what was intended - where ALL geometry was seen to indicate G_d's handiwork, suddenly only part of geometry was in some way 'sacred'. It seems to me just to be a way for people, since HBHG, to impart some form of mystery and '....oooooh spooky, look...sacred geometry...' factor.
    So I ask again then - what is the difference between so called 'sacred' geometry and geometry in my house?

    Quote Originally Posted by hayward
    This is the context of the subject of "Sacred Geometry" in question. Whatever your personal beliefs might happen to be in the present tense have no effect or bearing on the historical context surrounding the subject. If you are Pagan and you don't like the "divine" overtones of the story, that is really your problem, it doesn't change what had been recorded.
    It's not my problem at all. You're trying to peddle that some forms of geometry are more 'sacred' than others.


    Quote Originally Posted by hayward
    Next,
    The difference between what is "true" --or isn't-- in terms of finding geometry is between what is observable and what isn't Either the geometry is fully justified on all points or sides or it isn't. If it is, this means that each point is justified through intersection or features in the work. When this happens, I would then expect someone to ask "what are the odds" of this occurring in several paintings in such a fashion, with exactly the same degree of tilt to the picture plane?

    There is also an obvious difference between what is coincidence and probable intent.
    Is there? I have read so many so called exposes of geometry in art - and on artist alluding to women as disciples in some artworks. The people who found THEIR geometric shapes believed they had found the 'hidden' key. As I asked earlier, just Google it and see how many DIFFERENT geometric shapes you get and in different places on the same piece of artwork.
    From recollection, when you were challenged before to say why you selected the points for your construction on a different object, you refused to say. The problem then being H, is that without any good reason to select the specific construction points, who is to say that the constructs actually exist or not? Let alone imply intent.

    Quote Originally Posted by hayward
    For example, the writer of Vermeer's "Grail Geometry" uses an approach that, from my point of view, is process of total coincidence. There is simply not enough indication through either intersection lines or terminating points of the lines revealed in the image to show that the artist had considered justifying all the points of the geometry. This writer's geometry is also usually off of the canvas edge entirely, which shows that "nothing" had aided to complete the image. Yes, anyone can take the tilted hexagram and put it over an image and mark the points where its sides intersects features in the painting. This does not really demonstrate anything since you have the rest of the shape to account for.

    When I take your suggestion and Google "geometry in Poussin", all of these examples also appear to have one or two corresponding points of their geometry matched with points in the image, but then the other points either fall in the middle of nowhere and have no correspondences or justifications in terms of either intersecting lines or distinct objects in the image.

    To a person that actually LOOKS with a keen eye, they can see in the other examples spoken of where each line ends, where they intersect with other lines and which points are being defined through features in the image. Each point is justified, not floating randomly, like the "geometry in poussin" images. That is the difference. When you have no justification, there is no probability that it was intended. But when you have justification in the image and the same things appears in different works, it begins to increase the probability that it was intended.

    You can either accept that this was a random coincidence for it to appear in several works by such artists, or that there was a similar or common reason for doing so.
    https://www.goldennumber.net/art-composition-design/ - is this person seeing the 'truth'? Are his lines correct?
    How did he select his lines compared to you? Did he have a method - a plan? How do you select the points, and measurements, you need for your constructs?

    It seems that up to the 13th century or thereabouts, art wasn't 'structured'. Then, the renaissance (a neo classicist) movement came along and art was taken back to a realism in both shape and form - perspective and relationship became all. This pervaded all art from painting to architecture. You're also aware of how art was taught with the master/apprentice relationship in workshops. As in all trades/guilds of the time, the different groups had their own secrets pertaining to their trades. I don't dispute at all, that artists were taught geometry and applied that geometry to their art. I would 'guess' as well, that they probably found shortcuts in creating aesthetically pleasing (and perspectively correct) works. Their masterpieces would then have to have shown that they had mastered the techniques. Similarities then in structure and construct methods across schools would then potentially follow - and isn't that what is being seen?

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    Quote Originally Posted by jlockest View Post
    I think you said it in the opening line. Geometry was viewed as the work of G_d. My understanding is that geometry (all geometry) was seen as a way of recognising G_d's hand in creation - an aspect of G_d's mind. It wasn't seen that only geometry in some artworks or buildings represented G_d's fingerprint - it was ALL geometry. If, historically, chemistry had been understood better, then G-d may have been seen as the great 'chemist' - and ALL chemistry would have been seen as partially lifting the veil on the mind of G_d. Applying 'sacred' to geometry appears to do the opposite of what was intended - where ALL geometry was seen to indicate G_d's handiwork, suddenly only part of geometry was in some way 'sacred'. It seems to me just to be a way for people, since HBHG, to impart some form of mystery and '....oooooh spooky, look...sacred geometry...' factor.
    So I ask again then - what is the difference between so called 'sacred' geometry and geometry in my house?
    I think you are projecting your own perspective over material which isn't REALLY discussing what you are concerned about. This article is about the relationship between Leonardo Da Vinci's Last Supper, the work of Pacioli through context of Plato's Timaeus and with others such as Kepler. This article IS NOT about whether one form of geometry is "SACRED" and the rest is not. This is YOUR idea, not mine. Nowhere has this article, or have I, stated that one is and the other isn't. You ask for a difference and I gave you common definitions in the modern sense. You can probably appreciate that most people don't really consider regular, mathematical geometry to be special or "Sacred" in any way.

    Quote Originally Posted by jlockest View Post
    It's not my problem at all. You're trying to peddle that some forms of geometry are more 'sacred' than others.
    Never anywhere has that been a subject or issue. This is a product of your own conclusion, that if one mentions the term "Sacred Geometry", then the implication is that every other form of Geometry is not "Sacred". This is nonsense. It is simply presented here as a subject, with context, for the reader.


    Quote Originally Posted by jlockest View Post
    Is there? I have read so many so called exposes of geometry in art - and on artist alluding to women as disciples in some artworks. The people who found THEIR geometric shapes believed they had found the 'hidden' key. As I asked earlier, just Google it and see how many DIFFERENT geometric shapes you get and in different places on the same piece of artwork.
    From recollection, when you were challenged before to say why you selected the points for your construction on a different object, you refused to say. The problem then being H, is that without any good reason to select the specific construction points, who is to say that the constructs actually exist or not? Let alone imply intent.

    Collective hearsay is hardly evidence for anything. But if you look at the examples provided in the google search, there is not enough correspondence for the shape to be considered justified. From recollection, I also remember you being challenged to look at the drawing and see where the points terminated and where they intersected. Since you couldn't report on that, I will assume that you didn't want to bother. This is the only "system" employed. When D presented his Geometry, it was the first thing I did. Opened the image in photoshop and started drawing lines. About the 'Dagobert parchment' Why not just begin by looking at that "device" in the upper left of the page and see where upper line extends to next in the text?


    Quote Originally Posted by jlockest View Post
    https://www.goldennumber.net/art-composition-design/ - is this person seeing the 'truth'? Are his lines correct?
    How did he select his lines compared to you? Did he have a method - a plan? How do you select the points, and measurements, you need for your constructs?

    It seems that up to the 13th century or thereabouts, art wasn't 'structured'. Then, the renaissance (a neo classicist) movement came along and art was taken back to a realism in both shape and form - perspective and relationship became all. This pervaded all art from painting to architecture. You're also aware of how art was taught with the master/apprentice relationship in workshops. As in all trades/guilds of the time, the different groups had their own secrets pertaining to their trades. I don't dispute at all, that artists were taught geometry and applied that geometry to their art. I would 'guess' as well, that they probably found shortcuts in creating aesthetically pleasing (and perspectively correct) works. Their masterpieces would then have to have shown that they had mastered the techniques. Similarities then in structure and construct methods across schools would then potentially follow - and isn't that what is being seen?

    Is this person seeing the 'truth'? Maybe yes, maybe no. The writer's proposition is that the golden ratio was used to compose these artworks. There has been much writing about this idea over time with regard to human anatomy as well, with the reason being that it is "used" or "appears" so often is because it promotes a 'visual harmony' of some sorts. I'm not a huge advocate of this idea, but I will accept the writer's evidence, of which there seems to be an ample amount. The real question for me is that, if this is a proportion so commonly found in nature and in human nature, is it by design or by some "unconscious harmony" that such things are produced? I don't have an answer. But, the tilted hexagram idea is different. It does not appear to be the result of some natural, "harmonic design" like the 'Golden Ratio', which is about spatial division and proportional development. The tilted hexagram appears more deliberate. It is just like an object interjected into the composition. Two different things.

    But I guarantee that throughout the history of human Art, every piece of work you've seen has been 'structured' (better term, COMPOSED). When an artist produces an image, there are decisions being made, observations that are in play, and relational thinking in terms of line and shape are a primary component of that. Even the cave paintings at Lascaux are exemplary of this. In the Renaissance, this 'system' of painting, architecture and sculpture simply took on a more 'refined', developed and academic sensibility.

    I find it odd --and interesting-- that you would rather adhere to some system which is unidentified or completely unknown by yourself to justify the appearance of the geometry rather than to use simple observation. The method I am using here is simply looking at what the artist painted. I am surprised that by now, after having been introduced to the process for such a long time, that the method is still a mystery. D had shown how connecting lines and shapes in the painting produced the geometry. In my last article, I showed how I found the shape step by step in the Maranatha book, by connecting lines and points in the image. Any person can take the image with the geometry shown and verify the results for themselves this way. It is that simple. There is no magic 'system' which stems from any point of calculation or ratio of dividing the image such as the article link you posted.

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    Quote Originally Posted by hayward View Post
    I think you are projecting your own perspective over material which isn't REALLY discussing what you are concerned about. This article is about the relationship between Leonardo Da Vinci's Last Supper, the work of Pacioli through context of Plato's Timaeus and with others such as Kepler. This article IS NOT about whether one form of geometry is "SACRED" and the rest is not. This is YOUR idea, not mine. Nowhere has this article, or have I, stated that one is and the other isn't. You ask for a difference and I gave you common definitions in the modern sense. You can probably appreciate that most people don't really consider regular, mathematical geometry to be special or "Sacred" in any way.
    H,
    I'll come back to the rest tomorrow - BUT just briefly isn't your article entitled '......The Secret and Sacred Geometry of Leonardo’s The Last Supper by Hayward Gladwin......' and don't you go on to say..... '....Yet, as curious these theories might be, there is perhaps another level to the work which could be of deep interest; that being the structure of the work’s visual composition and its relationship to Sacred Geometry.....' and '.....To reflect on what it was that had prompted me to begin a search for Sacred Geometry on The Last Supper was somewhat multi-faceted to begin with.....' , label one of your images as '.....The Last Supper and Revealing Leonardo da Vinci’s Hidden and Sacred Geometry....' and then continue with '....These clues all added up convince me that this sacred geometry was intentional....' , finally labelling another image as '....Kepler’s Sacred Geometry....'?

    Surely the thrust of your article is that 'this geometry' is in some way more 'sacred' than your bog standard, basic geometry? If not, then why keep bothering to stress it?

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    Quote Originally Posted by jlockest View Post
    H,
    I'll come back to the rest tomorrow - BUT just briefly isn't your article entitled '......The Secret and Sacred Geometry of Leonardo’s The Last Supper by Hayward Gladwin......' and don't you go on to say..... '....Yet, as curious these theories might be, there is perhaps another level to the work which could be of deep interest; that being the structure of the work’s visual composition and its relationship to Sacred Geometry.....' and '.....To reflect on what it was that had prompted me to begin a search for Sacred Geometry on The Last Supper was somewhat multi-faceted to begin with.....' , label one of your images as '.....The Last Supper and Revealing Leonardo da Vinci’s Hidden and Sacred Geometry....' and then continue with '....These clues all added up convince me that this sacred geometry was intentional....' , finally labelling another image as '....Kepler’s Sacred Geometry....'?

    Surely the thrust of your article is that 'this geometry' is in some way more 'sacred' than your bog standard, basic geometry? If not, then why keep bothering to stress it?
    For the record, I had never emphasized Sacred Geometry originally in the article, this was by the editor's choice. In fact, my original text never even used "sacred geometry" as a term, I had referred to it simply as "geometry" and that they had considered it as 'Divine'. The references through the historic philosophers and mathematicians were meant to stand as providing this context. Yet, even despite that, I think you are dwelling on something that is rather a distraction in relation to the subject anyway. So you don't like the editor's premise to the reader that the geometry should be presented as being"Sacred", even when considering that, based on the quoted texts of the writers, that they in fact did view such geometry as being "Sacred"? Maybe you should take your argument up with Plato, Pacioli, and Kepler.

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    Hayward, you probably should have just told Sixer13 "NO", and you could have avoided this argument, especially as the entire reason that Sixer13 would have wanted to use the term "sacred" is because it just sounds "more inspiring", because Easter, even though the geometry should have inspired all by itself. I'm not sure what Jlockest hopes to achieve, but it seems that Jlockest thinks that he can disprove your geometry and your entire premise by disproving that "sacred geometry" exists, even though that still leaves the "geometry" part, and a painter might use under-lying geometry in a painting for a number of reasons. Perhaps Jlockest will seek to disprove painting next.
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    Quote Originally Posted by hayward View Post
    For the record, I had never emphasized Sacred Geometry originally in the article, this was by the editor's choice. In fact, my original text never even used "sacred geometry" as a term, I had referred to it simply as "geometry" and that they had considered it as 'Divine'. The references through the historic philosophers and mathematicians were meant to stand as providing this context. Yet, even despite that, I think you are dwelling on something that is rather a distraction in relation to the subject anyway. So you don't like the editor's premise to the reader that the geometry should be presented as being"Sacred", even when considering that, based on the quoted texts of the writers, that they in fact did view such geometry as being "Sacred"? Maybe you should take your argument up with Plato, Pacioli, and Kepler.
    H,
    Well, which of your three replies is 'true'? Your initial repost was to try to belittle, then denial saying you hadn't promoted Sacred Geometry, now that you were forced into using the term and you now seem to be blaming the 'editor'. Obviously the reader has no knowledge of what the 'original article' was - the only thing they see is the article as published on the web site - which for all intents and purposes was written by you.
    Going back to what Plato, Pacioli, and Kepler thought about geometry and its relationship to G_d, it's a bit difficult to ask isn't it? But I would guess that it was along the lines of what I tried to explain - that ALL geometry is seen as being a way of getting a glimpse into the workings of the mind of G_d.

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    Quote Originally Posted by hayward View Post
    .......

    Collective hearsay is hardly evidence for anything. But if you look at the examples provided in the google search, there is not enough correspondence for the shape to be considered justified. From recollection, I also remember you being challenged to look at the drawing and see where the points terminated and where they intersected. Since you couldn't report on that, I will assume that you didn't want to bother. This is the only "system" employed. When D presented his Geometry, it was the first thing I did. Opened the image in photoshop and started drawing lines. About the 'Dagobert parchment' Why not just begin by looking at that "device" in the upper left of the page and see where upper line extends to next in the text?
    H,
    To draw anything, you have to start somewhere. In YOUR article on the Dagobert parchment, you stated that you started with an R (from recollection) and constructed from there. You said:
    '....The Dagobert Parchment of Rennes Le Chateau fame also contains a similar form.

    The steps for finding this are as follows:

    Starting with the raised “R” in the center of the document, use this point as the center point. ...'

    My question was then, and is now. How did you select that R? You then 'decide' on a radius - how?

    The reason for the question is obvious isn't it? Without a reason for selecting the start point (and then the radius - ie the 'size' of the geometric shape) then any shape can be drawn anywhere on that document.

    That is then 'true' of any shape drawn anywhere. If there is no reason for selecting points in the construction, then does the construct actually exist anywhere other than in the mind of the constructor/viewer.



    Quote Originally Posted by hayward
    Is this person seeing the 'truth'? Maybe yes, maybe no. The writer's proposition is that the golden ratio was used to compose these artworks. There has been much writing about this idea over time with regard to human anatomy as well, with the reason being that it is "used" or "appears" so often is because it promotes a 'visual harmony' of some sorts. I'm not a huge advocate of this idea, but I will accept the writer's evidence, of which there seems to be an ample amount. The real question for me is that, if this is a proportion so commonly found in nature and in human nature, is it by design or by some "unconscious harmony" that such things are produced? I don't have an answer. But, the tilted hexagram idea is different. It does not appear to be the result of some natural, "harmonic design" like the 'Golden Ratio', which is about spatial division and proportional development. The tilted hexagram appears more deliberate. It is just like an object interjected into the composition. Two different things.
    I'm not sure that I got my point across. It seems that from the 13th century on, perspective and harmony based on Phi became the 'thing' in art. I would guess that the artists were then taught this as part of their apprenticeships. As with other guilds and trades, I would 'guess' that the artists developed methods and ways of achieving compositions that were both harmonic and perspectively correct in the simplest way. I would then assume that the composition would be planned on the canvass, with the construction lines. So I would expect geometric lines/shapes on the canvass - didn't D allude to pin holes in Poussin's canvass (how did he know that by the way?) being construction points - fine. So I have no issue with geometry in art at all.

    Quote Originally Posted by hayward
    But I guarantee that throughout the history of human Art, every piece of work you've seen has been 'structured' (better term, COMPOSED). When an artist produces an image, there are decisions being made, observations that are in play, and relational thinking in terms of line and shape are a primary component of that. Even the cave paintings at Lascaux are exemplary of this. In the Renaissance, this 'system' of painting, architecture and sculpture simply took on a more 'refined', developed and academic sensibility.
    Fine.

    Quote Originally Posted by hayward
    I find it odd --and interesting-- that you would rather adhere to some system which is unidentified or completely unknown by yourself to justify the appearance of the geometry rather than to use simple observation. The method I am using here is simply looking at what the artist painted. I am surprised that by now, after having been introduced to the process for such a long time, that the method is still a mystery. D had shown how connecting lines and shapes in the painting produced the geometry. In my last article, I showed how I found the shape step by step in the Maranatha book, by connecting lines and points in the image. Any person can take the image with the geometry shown and verify the results for themselves this way. It is that simple. There is no magic 'system' which stems from any point of calculation or ratio of dividing the image such as the article link you posted.
    But H - it's the same issue as the Dagobert parchment isn't it?. YOU are deciding which points are relevant. Is a pointing finger relevant? Yes? Then are all pointing fingers relevant? Do they indicate the centre of a circle or the corner of a square? Do two pointing fingers give a radius or a diagonal or a side or....Who decides on the scale of the geometric shape? Why does your circle have the radius it does?
    You say '..the method I am using...' ...grand - what is that method? Doesn't method imply something you can explain and repeat? BUT that seems to be the opposite of what you're doing - as with the Dagobert parchment, you kept saying that the selection of the point wasn't arbitrary, but then simply refused to say how you selected the point. Is that the same here - or do you really have a 'method/plan/system' for selecting the relevant points?

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