[bimjo]

I just wishes I had a nickel fer every time either one of these rules has been broken.

[Manel Brand]

Wow! Imagine that on your live view screen!

Ideally, as a photographer, that would be (more or less) your frame of mind (you shouldn't need it on the VF).

[Manel Brand]

perhaps someone who's studied this properly can say something more convincing.

I told the OP that he should look for it in Atlantis. All that we know, from Assyria, Egypt, Mayas, etc. till today came from there.

He didn't find my hint as serious one and deserving further inquiry (and maybe you don't either... Rest assured that I'm not crazy!)
and I really don't care that much about his fancy discoveries on the public library. I'm used and amused to listen to this kind of "surface scratch theories".

[Gashog]

Ideally, as a photographer, that would be (more or less) your frame of mind (you shouldn't need it on the VF).

Oh good. I wasn't looking forward to replacing my focus screen again.

[Manel Brand]

I wasn't looking forward to replacing my focus screen again.

Yes, save your money for more important stuff...

[asaru]

He didn't find my hint as serious one and deserving further inquiry (and maybe you don't either... Rest assured that I'm not crazy!)
and I really don't care that much about his fancy discoveries on the public library. I'm used and amused to listen to this kind of "surface scratch theories".

Manel, I did not at all dismiss the possibility that the rule of thirds and the golden ration are related. Your plot of thirds vs golden spiral is very suggestive!

On the other hand, classical "good" proportions are usually expressed as unit fractions. Vitruvius did so in his standard first-century book on architecture, it seems.

Consider that one of the canonical ways to front a public building is with a tetrastyle.

Its four columns divide the space into thirds horizontally.

What about vertical proportions? Bear with me, that's a stretch!! If the column spacing further follows the eustyle (and "eu" means "good" or "proper") conventions, then the space between the columns is 2 1/4 column diameters apart [Ref 1]. With an eyeballed cornice of about one-half column width [Ref 2], the total width of the building is giving 11 3/4 (or 12?) column diameters. Meanwhile, vertically, the recommended column height is 9 1/4 diameters [Ref 1]. If the architrave and frieze are each 1 column diameter [Ref 2], and there's a 1/2 diameter cornice [Ref 2: these are all eyeballed from the diagram], that gives a height of 11 3/4 column diameters. So far, so good -- the front is a square. How does it relate to a human being? Well, if the idea is to have two people walk side by side between the columns [Ref 1], that's a 2 1/2 "human width" column separation if we allow a bit of space between. Ah, so the columns are to be approximately 1 human width in diameter! What is the proportion of width to height in the "vitruvian man"? Well, his height is four cubits, his width at the shoulders one cubit [Ref 3]. And we've seen one cubit is one column diameter.

SO NOTE! The height of the buiding is twelve cubits (column diameters) = THREE TIMES the human height.

In other word a human being's head is at one-third the peristyle height.

We have a rule of thirds in architecture --vertically and horizontally -- that's at least FIRST CENTURY BC.

My references:

1. Roman Architecture

2. Entablature - Wikipedia, the free encyclopedia

3. Vitruvian Man - Wikipedia, the free encyclopedia

----

Are these proportions an approximation to the golden spirals and their irrational ( 1 + Root 5) : 2 golden ratio? I don't see why they can't be, based on the little I know. The fact there seems to be a fudge factor (11.75 vs 12, etc.) is as suggestive as the fudge widths of the one-third lines in your diagrams.

In fact, the rule of thirds is just 1+2=3, right? Well, those are the numbers at the start of the sequence 1, 2, 3, 5, 8, 13, 21, 34, 55... where each number is the sum of the previous two. In the limit the ratio between successive numbers becomes exactly the golden ratio. That is, the rule of thirds is the first qpproximation to the golden ratio. I see no reason why it should not have been CONSCIOUSLY done this way, whenever it may have been.

Do the guidelines for photographic composition go back to the architectural canons? I imagine so, through the medium of European painting in the early modern period. I'm no expert in art history, but I do remember reading somewhere that when Western-style painting seeped through to Japan while it was still closed, the Japanese were very taken with the fact there were expected to be standard proportions within the painting.

----

Of course all this is precisely a scratch of the surface. Feel free to dismiss at will. Or is this part of the occult knowledge you're drawing on?

[Manel Brand]

Do the guidelines for photographic composition go back to the architectural canons? I imagine so...

It makes sense. We are dealing with the way our brain perceives beauty. I doesn't matter the medium we are using.

Of course all this is precisely a scratch of the surface. Feel free to dismiss at will. Or is this part of the occult knowledge you're drawing on?

We should think so. After all, this knowledge was (in the ancient times) of a secret nature, not to be disclosed to the non initiated. Hermeticism was the rule back then, being that religion, mathematics, philosophy and so on. That's why drawing conclusions based on the lack of records isn't convincing at all.

If you dig into ancient history, particularly on the origin of mathematics, there are a considerable number of under appreciated documents that could help us rewrite most of our modern notions. To sum it all, we are all closed, to a certain extent, in a modern Eurocentric model about the history of mathematics, disregarding the contributions of India, China, the Mayas, the Egyptian and Mesopotamia civilizations.

[mattdm]

My feeling that you didn't take me very seriously is further supported by your "Sure — it's a good story."

I really didn't mean that badly either. People like a good story. A friend was telling me an interesting new theory about cancer today — that rather than being a "gone haywire" mutation, it's the accidental reactivation of genetic code in cells from a long-ago period before complex multicellular organisms. The early form was something more like lichen — a big lump grows together in parallel with other types of cells, but the "strategy" is simply grow-grow-grow, not taking a measured part in a whole complex creature. The theory is that something gets damaged and bam, that normally-deactivated code gets activated again. There's a tribe in South America which almost never gets cancer (something like 1/100th the incidence of that in the general population), and speculatively, it's because they lack (or have a damaged copy) of the regressive genetic code. Since, until very recent times, people didn't live long enough for cancer to be a major cause of death (as opposed to, say, being eaten by a tiger, or simply dying of a bacterial infection), there's been little evolutionary pressure to select-out this trait completely.

With even no references to the actual study, everyone at the table was nodding along and saying "wow" and "that's so cool!"

That's what I mean by "great story". It doesn't really matter if there's good evidence (yet) — it just feels right! And, I have a personal suspicion that things which are good stories, which simply and elegantly fit the picture, have a tendency to be right. But that may just be my human tendencies getting in the way of my judgment.

We should think so. After all, this knowledge was (in the ancient times) of a secret nature, not to be disclosed to the non initiated. Hermeticism was the rule back then, being that religion, mathematics, philosophy and so on. That's why drawing conclusions based on the lack of records isn't convincing at all.

Absolutely, but with a lack of records and with a lack of artifacts that unambiguously use the ratio, it's a matter of faith.

And, while this applies to the ancient Greeks, it's way less convincing for the Renaissance. There's plenty of writing about the theory of aesthetics, analysis of the works of the masters, and so on. Seems like someone would have at least hinted at it.

If you dig into ancient history, particularly on the origin of mathematics, there are a considerable number of under appreciated documents that could help us rewrite most of our modern notions. To sum it all, we are all closed, to a certain extent, in a modern Eurocentric model about the history of mathematics, disregarding the contributions of India, China, the Mayas, the Egyptian and Mesopotamia civilizations.

It's an excellent point, and it's tragic that we've lost so much of our history.

[Gashog]

Your plot of thirds vs golden spiral is very suggestive!

To me too....of the Mandelbrot Set. Phi to the power of 3

[Class A]

And, I have a personal suspicion that things which are good stories, which simply and elegantly fit the picture, have a tendency to be right. But that may just be my human tendencies getting in the way of my judgment. .

There certainly seems to be evidence in science that theories that are correct are also relatively simple and elegant. Maybe that's only a good story as well. I guess it probably is true to some extent but understandably so because a theory that is simpler will replace a more complicated one provided it explains the same phenomena. Since most scientists happen to be interested in simple and elegant solutions/theories it seems plausible that the respective theories survive and others don't. Too bad that some things (like uniting quantum mechanics with general relativity) seem to be too complex too allow a simple and elegant solution/theory.

There is a saying that goes

"There is always a simple solution to every problem that is evident, plausible, and wrong. "

So yes, maybe my conception about the golden ratio is all wrong.

All I want to say that I appreciate the golden ratio (in the sense of liking work produced according to it) much more than the "thirds". I guess I'm not the only one, but what do I know?

[asaru]

To me too....of the Mandelbrot Set. Phi to the power of 3

I think that's the way it might be supposed to work. The Mandelbrot set is the set of all complex numbers z for which the iteration f(1) = z, f(n+1) = f(n)**2 + z converges. That is, the convergent limit w = w**2 + z if it exists. And for z = -1, w = w**2 - 1, which is the quadratic equation that solves to the golden ratio w = (1 + root 5)/2. Why should z = -1 be important? Well, it's exactly the center point of the smaller "circle" on the Mandelbrot set's left side... Anyway, without going deeper into math I don't understand, it wouldn't surprise me if the golden ratio were somehow embedded into the Mandelbrot set, and the curve on the heart-shaped right side more or less WAS the golden spiral (if defractalled, obviously...).

But, except for pretty snapshots of the Mandelbrot set , that's getting pretty far away from photography!

[Gashog]

Did you guys ever see that movie PI?

[Manel Brand]

Absolutely, but with a lack of records and with a lack of artifacts that unambiguously use the ratio, it's a matter of faith.

The lack of records can be either circumstantial or deliberated, as I've already tried to say to you.

Apparently, you haven't taken in consideration the Archimedes writings that have been recently found; that should have given you a good hint about how things generally stand in relation to what we know about our past.

Atlantis is not lost! It's buried under the ice sheets of Antarctica. You should know that.

More trivia:

A Prayer For Archimedes - Science News

(you shouldn't be using the term faith but the term belief, or rational belief to be more precise (I'm not discussing this matters based on some sort of revelation or mystic intuition.)

Regarding artifacts, we don't know if they existed, or if they were needed. But if they were, that would not be difficult to achieve in antiquity.

You must be aware of the Antikythera Mechanism, right? If not, please look here:

Antikythera mechanism - Wikipedia, the free encyclopedia

You like a good story. How about Atlantis? Don't you think it's as good as many others?

(of course, regarding your interest on the origin of the rule of thirds and the golden rule)

Perhaps you are thinking that's just another legend, like the city of Troy, and I'm a fool on the hill.

[Manel Brand]

Did you guys ever see that movie PI?

Oh yeah! And this one is also very good:

NOVA | Hunting the Hidden Dimension | PBS

[mattdm]

The lack of records can be either circumstantial or deliberated, as I've already tried to say to you.

Nonetheless, without them, any specific claim is indeed a matter of faith, not rational belief.

I'm open to the idea that further evidence will prove me wrong. If I see it, I'll happily change my mind.

But I also find it interesting that no one has any to offer.

Regarding artifacts, we don't know if they existed, or if they were needed. But if they were, that would not be difficult to achieve in antiquity.

You are using "artifacts" in a grand sense here. I mean simply some work of architecture or art where the use of the golden ratio is unambiguous. As stated earlier, the Parthenon is a commonly-cited example, but only works if you draw the lines in an odd way, and accept a great deal of imprecision in the ratio.

You must be aware of the Antikythera Mechanism, right? If not, please look here:

Antikythera mechanism - Wikipedia, the free encyclopedia

You like a good story. How about Atlantis? Don't you think it's as good as many others?

(of course, regarding your interest on the origin of the rule of thirds and the golden rule)

Perhaps you are thinking that's just another legend, like the city of Troy, and I'm a fool on the hill.

I'm not sure exactly what your point is here. Plato wrote about Atlantis several hundred years before this device was constructed.

It's a pretty amazing thing. But it also doesn't have any connection that I'm aware of to the golden ratio. If your point is "wow, the ancient Greeks had some amazing technology", sure. But that's pretty far off topic.