tag:blogger.com,1999:blog-2999230124118604245.post8862969610209273420..comments2024-03-18T07:23:32.809-04:00Comments on Gurney Journey: Mythbusting the Golden Mean, Part 1James Gurneyhttp://www.blogger.com/profile/01870848001990898499noreply@blogger.comBlogger26125tag:blogger.com,1999:blog-2999230124118604245.post-5544127735638305552020-10-08T22:04:05.054-04:002020-10-08T22:04:05.054-04:00Debunking the Debunked:
I'd make real sure of...Debunking the Debunked: <br />I'd make real sure of the facts before discrediting this. <br /><br />On its front section, the equation length = φ×height is always true. This manifests as a spiral with the analogy α/2α+1, known as the golden ratio, which is a sacred number in the Greek arithmosophy. <br /><br />https://greatestgreeks.wordpress.com/2017/03/08/ictinus-callicrates/#:~:text=Ictinus%20and%20Callicrates%20were%20the,beautiful%20monument%20of%20human%20civilization.&text=Ictinus%20worked%20with%20other%20architects,Greek%20temple%20facing%20the%20north.Dancing Brushhttps://www.blogger.com/profile/00270420964756033888noreply@blogger.comtag:blogger.com,1999:blog-2999230124118604245.post-36879067850274860692020-10-08T21:41:01.183-04:002020-10-08T21:41:01.183-04:00Not quite true - Debunking the Debunked:
https://...Not quite true - Debunking the Debunked: <br />https://greatestgreeks.wordpress.com/2017/03/08/ictinus-callicrates/#:~:text=Ictinus%20and%20Callicrates%20were%20the,beautiful%20monument%20of%20human%20civilization.&text=Ictinus%20worked%20with%20other%20architects,Greek%20temple%20facing%20the%20north.Dancing Brushhttps://www.blogger.com/profile/00270420964756033888noreply@blogger.comtag:blogger.com,1999:blog-2999230124118604245.post-57369857415027087382018-07-17T14:09:14.320-04:002018-07-17T14:09:14.320-04:00Well said, David Simcox.Well said, David Simcox.Matthttps://www.blogger.com/profile/01891803494450719808noreply@blogger.comtag:blogger.com,1999:blog-2999230124118604245.post-55249077445514973972015-08-02T12:34:27.501-04:002015-08-02T12:34:27.501-04:00Except that, guess what!
"Quantum Criticality...Except that, guess what!<br />"Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E8 Symmetry" http://www.sciencemag.org/content/327/5962/177Persephonehttps://www.blogger.com/profile/01354376413593978157noreply@blogger.comtag:blogger.com,1999:blog-2999230124118604245.post-73617430897343031252013-01-17T16:13:43.393-05:002013-01-17T16:13:43.393-05:00I'm so glad you're tackling this. When I w...I'm so glad you're tackling this. When I was in art school this was a topic of fascination for me. Often professors would discuss phi, the fibonacci sequence, etc. But NEVER ONCE did they explain how it was used in art, just that the masters knew the secrets of this geometry. Let's crack this case open I say! Kudos to you!<br /><br />I even created a blog for a school project discussing it. http://www.greatmastersmaterialsandtechniques.blogspot.comMAQ911https://www.blogger.com/profile/16192380393490919809noreply@blogger.comtag:blogger.com,1999:blog-2999230124118604245.post-18201718069461461262013-01-17T14:12:20.936-05:002013-01-17T14:12:20.936-05:00Speaking as one who did her graduate work in neuro...Speaking as one who did her graduate work in neuroscience, I think that whether the Parthenon or other major works or art and architecture perfectly correspond to the Golden Mean is not quite the issue. It might be more useful to say that our visual system has evolved to extract information from a scene by moving our gaze in particular ways. There are certain proportions, certain combinations of lines, that conduct, stop, and start the gaze in patterns that evoke pleasure. (The reasons we perceive these patterns as pleasurable are a discussion for another occasion.) This pleasure is what we call "beauty." The Golden Mean simply moves our eyes and stimulates our perceptual system in pleasure-evoking ways. The proportions don't have to be precise and the correspondence with the Golden Mean doesn't have to be exact, because eye movements aren't precise. Nor does the architect/artist have to consciously understand the mathematics or the biopsychology underlying this principle; he just knows that he is making something beautiful, and the reason it is beautiful is unimportant. But as the human perceptual system has probably not evolved significantly in the past 2500 years, the beauty created in the Parthenon is valid today as it was when it was built.Andrea Kenthttps://www.blogger.com/profile/11060114297081919392noreply@blogger.comtag:blogger.com,1999:blog-2999230124118604245.post-44607957500939948352013-01-15T17:08:09.212-05:002013-01-15T17:08:09.212-05:00(for instance, how do we know that the ISO standar...(for instance, how do we know that the ISO standard paper sizes (A4, A3, etc) follow the Lichtenberg ratio (often mistaken for the golden ratio)? We know it because we have documentary evidence. If you actually measure the paper sizes you can never prove it beyond a doubt because of course there will be a rational approximation to the irrational sizes, both in your measurements and in the manufacturing process, and so the intended "ratio" won't *ever* be actually there)António Araújohttps://www.blogger.com/profile/03059765930331992020noreply@blogger.comtag:blogger.com,1999:blog-2999230124118604245.post-71819375196841277582013-01-15T16:59:45.377-05:002013-01-15T16:59:45.377-05:00Purely out of curiosity, last year I tried to over...Purely out of curiosity, last year I tried to overlay the rectangle over some of my previous works. I just eyeball all of my compositions anyway, but I thought it would be a fun experiment. I found out that it does match in certain configurations, which I found fascinating. It doesn't change how I create my art or designs, but I did find it very interesting.Russell Dickersonhttps://www.blogger.com/profile/12854569325129096817noreply@blogger.comtag:blogger.com,1999:blog-2999230124118604245.post-64886087853577494502013-01-15T16:59:23.875-05:002013-01-15T16:59:23.875-05:00By the way, one must be decent towards the other s...By the way, one must be decent towards the other side also and admit that in the eventual cases where golden ratios or fibonacci numbers do figure in Nature, you cannot argue against them just because the actual measurements don't fit exactly. Why? Because whatever process is there will be perturbed by many other processes (say, in morphogenesis or whatever). So, paradoxically, a lack of a proper fit is also no argument. The true argument is that if you want to claim a relationship is there, then the burden of proof is upon you. Sure, vague measurements can inspire you, but they are not proof of anything. To "prove" it you have to do harder stuff than just staring at clouds and imagining unicorns - you have to make a strong case in probabilities or preferably demonstrate an actual mechanism for the ratio to be there (or in the case of the Parthenon, for instance, you might simply come up with historical documents that proved the intention was there).António Araújohttps://www.blogger.com/profile/03059765930331992020noreply@blogger.comtag:blogger.com,1999:blog-2999230124118604245.post-40238796868822653172013-01-15T16:51:12.135-05:002013-01-15T16:51:12.135-05:00While the idea of the mean has been skewed over th...While the idea of the mean has been skewed over the years and relegated to the laziness of dogma. I think the relevance comes into play during the time of idealization whereas artists were looking for the perfect form. The golden mean repeats, loosely, in nature and art throughout the world. It is not a rule, or a formula to create greatness...it is an observation of an idea...an approximation that I still think holds some merit. <br /><br />Sit in a class of young grade-school students and ask them each to draw a perfect rectangle...you will see a decided preference toward a 1:1.6. This is not precise...but interesting.Anonymoushttps://www.blogger.com/profile/10544148283642045942noreply@blogger.comtag:blogger.com,1999:blog-2999230124118604245.post-31375564677663397072013-01-15T16:47:10.852-05:002013-01-15T16:47:10.852-05:00As far as I can tell, the golden ratio mania is ri...As far as I can tell, the golden ratio mania is right up there ("down" there?) with numerology and astrology. There's a lot of ways that maths can enlighten you with relation to art (perspective, measurement, and a a rational theory of color are a few) but golden ratio mania doesn't seem to be one of them.<br /><br />It really grates me when people measure in such a shabby (or even dishonest) way that they can "prove" anything they like. Another example is those people who divide actual human faces into thirds or into classical proportions or whatever (or, yes, into golden ratios). Such divisions are useful as *reference points*, but are not to be confused with actual realities in the individual sitter or (another fallacy debunked by actual studies) population averages.<br /><br /> I used to have a teacher who went on and on on how wonderful nature is, that it breaks down the face into simple ratios. Wonderful my butt - if you measure in such a sloppy way then you can get simple ratios just because your precision is so low. Yet, curiously, the very same type of person will find golden ratios everywhere, which isn't a "simple ratio" at all, but rather an irrational number, that requires infinite precision to be measured!<br /><br />I guess the golden ratio is an irrational number that tends to be found by irrational people. :p<br /><br />All of this is not to take away from the interesting geometric relations that actually involve golden ratios. Or from the possibility that indeed those relations may figure in Nature in some ways. But wherever they really figure they must be shown to do so with proper arguments, case by case.António Araújohttps://www.blogger.com/profile/03059765930331992020noreply@blogger.comtag:blogger.com,1999:blog-2999230124118604245.post-21668401186296564002013-01-15T15:35:53.972-05:002013-01-15T15:35:53.972-05:00Good old Golden Mean. An attempt to schematise Nat...Good old Golden Mean. An attempt to schematise Nature & Universal Harmony into some mental concept, IMO.<br /><br />Perhaps too schematic to be universally true, but probably not devoid of golden meanings.Richhttps://www.blogger.com/profile/14233420155151875249noreply@blogger.comtag:blogger.com,1999:blog-2999230124118604245.post-36540241333968031382013-01-15T15:07:38.613-05:002013-01-15T15:07:38.613-05:00Oh yeah? Donald Duck has never lied to me before,...Oh yeah? Donald Duck has never lied to me before, and he has those adorable little nephews Huey, Dewey, and Louie. Keith Devlin can't even spell "Botticelli" correctly.<br /><br />Seriously, in the name of aesthetics, I'm willing to go down any rabbit hole one should point out. I do feel, however, that any valid theory of the aesthetic perception of beauty should have some phenomenological justification; in other words, it must be directly and readily visually comprehensible, and that would tend to disqualify complex mathematical relationships.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2999230124118604245.post-61221240077263347272013-01-15T14:37:43.916-05:002013-01-15T14:37:43.916-05:00Fascinating - probaly true for most "rules&qu...Fascinating - probaly true for most "rules" when it comes to art - but the thought that comes to me is that, all the same, the so-called rules help to shake one's mind up - look at things in a certain way. OK, it's not ultimately "true" - but if it helps one consider proportion and placement... ? Could consider the rules to be "crutches" informing (finally, onece discarded) the instinct... ??JonInFrancehttps://www.blogger.com/profile/05623398725744947374noreply@blogger.comtag:blogger.com,1999:blog-2999230124118604245.post-41966534700072126342013-01-15T13:46:11.200-05:002013-01-15T13:46:11.200-05:00The one that always stumped me was the image of th...The one that always stumped me was the image of the Nautilus. I am so glad that one is debunked here as well.<br />I never really saw a "Fit" but I kept saying to myself that "they" must mean "close enough". But really it isn't. I found an example on the web of a nautilus shell with a golden section spiral depicted above it. Interestingly, they did not superimpose the images, which I did in Photoshop. If the width of the 2 images match, then the height does not. If the size of the golden spiral is increased to match the height of the shell, then nothing else matches up. This isn't even "close enough". Why hadn't I actually followed up on my uneasiness in the past and just done that comparison. Too willing to "suspend disbelief", I guess.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2999230124118604245.post-44516789900229086092013-01-15T13:10:52.941-05:002013-01-15T13:10:52.941-05:00Later, the scale of golden ratio was rediscover by...Later, the scale of golden ratio was rediscover by Fibonacci.Scorchfieldhttps://www.blogger.com/profile/08728471910339126509noreply@blogger.comtag:blogger.com,1999:blog-2999230124118604245.post-51090092935758808972013-01-15T13:03:11.563-05:002013-01-15T13:03:11.563-05:00Ha! I knew it! I always thought people just saw wh...Ha! I knew it! I always thought people just saw what they wanted to see, and it never made sense to me. Now I feel better about "not getting it".Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2999230124118604245.post-26102382341101781112013-01-15T11:49:19.903-05:002013-01-15T11:49:19.903-05:00I also find it funny that in every picture of the ...I also find it funny that in every picture of the Parthenon above, the perspective is wrong. To actually test the GR against it wouldn't you need to take the picture from a slightly higher view point; straight on, instead of from underneath?Keith Parkerhttps://www.blogger.com/profile/14579786144772849547noreply@blogger.comtag:blogger.com,1999:blog-2999230124118604245.post-54815478930444700622013-01-15T11:15:02.439-05:002013-01-15T11:15:02.439-05:00Very interesting read. People do seem to get attac...Very interesting read. People do seem to get attached to numbers, and assign strange significance to them...<br /><br />I watched an episode of Nova a few weeks ago about the construction of medieval cathedrals and they worked all kinds of biblical numbers into those buildings on the show...but I was kind of skeptical, because there are so many numbers in the bible...and because they were having to switch between different units of measurement to make it work. Maybe they are right, or maybe they were forcing it because the wanted to find something of interest to report. Isn't that why people read, and watch fiction about explorers and adventurers? Because we want to discover something nobody knows about?Keith Parkerhttps://www.blogger.com/profile/14579786144772849547noreply@blogger.comtag:blogger.com,1999:blog-2999230124118604245.post-26621994918634337132013-01-15T10:47:27.503-05:002013-01-15T10:47:27.503-05:00Like some others have said here, I never quite bou...Like some others have said here, I never quite bought into the theory of the Golden Mean in art and architecture, but to be honest, I'm not sure that (in my case) that was at least partly justification for my glazed-over eyes.<br /><br />That Devlin article is very intersting and fun to read! I never thought I'd find a scholarly mathematical article so entertaining.Tom Harthttps://www.blogger.com/profile/04770238579550226268noreply@blogger.comtag:blogger.com,1999:blog-2999230124118604245.post-2900881706096075602013-01-15T10:37:25.247-05:002013-01-15T10:37:25.247-05:00Looking at the Parthenon almost every day, I never...Looking at the Parthenon almost every day, I never had even a fleeting thought as to the Golden Ratio being used in it's construction. The design has other foundations to it, and plenty of awesome craftsmanship, but no hocus pocus. <br /><br />Plus, if you are actively looking for something (golden ratio, repetition of a number etc) you're bound to find ways of reproducing it.Michael Syrigoshttps://www.blogger.com/profile/12971372428681922832noreply@blogger.comtag:blogger.com,1999:blog-2999230124118604245.post-16509968395718727122013-01-15T10:27:28.271-05:002013-01-15T10:27:28.271-05:00Thanks for this; it makes one take a good look at ...Thanks for this; it makes one take a good look at other unquestioned geometric concepts retained since the 19th century Academy (which was of course still in the shadow of the Classicism before it.) <br /><br />That being said, the golden mean remains a lovely concept. Order out of chaos and all that...Laura G. Younghttps://www.blogger.com/profile/09698929175179994511noreply@blogger.comtag:blogger.com,1999:blog-2999230124118604245.post-66240416096526058132013-01-15T10:11:46.691-05:002013-01-15T10:11:46.691-05:00Wow! Thanks, James, this looks like the start of a...Wow! Thanks, James, this looks like the start of a great series. I've long suspected that the Golden Ratio was overrated. I've done lots of tracing paper overlays on photos of old paintings trying to find it, and I've usually failed to do so. What I have found a great deal of are simple divisions of the picture plane based on the "armature of the rectangle." Craig Banholzerhttps://www.blogger.com/profile/16958933400558297331noreply@blogger.comtag:blogger.com,1999:blog-2999230124118604245.post-92208086504781788062013-01-15T09:13:32.286-05:002013-01-15T09:13:32.286-05:00Thanks for busting this myth! I have to say I roll...Thanks for busting this myth! I have to say I roll my eyes every time I hear it.Matthew Meyerhttps://www.blogger.com/profile/00845265407152518106noreply@blogger.comtag:blogger.com,1999:blog-2999230124118604245.post-12080402821426952842013-01-15T08:37:08.473-05:002013-01-15T08:37:08.473-05:00I was actually amazed on how useful learning to dr...I was actually amazed on how useful learning to draw a dynamic rectangle was, thanks to Myron Barnstone. It's a great way to deconstruct composition and it's even better for measuring proportion in observation.Anonymoushttps://www.blogger.com/profile/17910130194789907176noreply@blogger.com