(http://img41.imageshack.us/img41/5600/fossilsnails.jpg)
Fossil molluscs. None of these are Golden spirals. © 2008 by John Holden
Another one for the series of "kill your idols".
Turns out this whole golden ratio/fibonacci/golden spiral shit is mostly swallowed and regurgitated shit without much proof.
- There's no statistical data that shows human aesthetic preference for golden ratios. And the few times some preference does roll out, and the experimental setup is solid, you can't, not with any statistical confidence say whether it's 1.5, 1.618 or 1.666.
- All those pretty pictures of spirals in nature, nautilus shells, spiral galaxies, etc etc. Nobody ever checks them. People like pretty pictures. Usually the ratios aren't even *close* to the golden ratio. And certainly never exact matches as governed by some recurrence relation (the Fibonacci sequence).
http://www.lhup.edu/~dsimanek/pseudo/fibonacc.htm
http://plus.maths.org/content/os/issue22/features/golden/index
Interesting! This is indeed an idol I must kill.
I've been telling my design teachers they're full of shit about this sort of thing for years.
I recently dropped out because I was tired of being showered with their Golden knowledge.
wow that is actually startling
somewhere in mathmagicland, donald duck is angry
(http://www.toplessrobot.com/donaldduck4.gif)
Taking a moderate position, I have noticed that at the very least, the brain tends to find the 2/3 ratio to be fairly pleasing; and the golden ration roughly approximates that.
I'll agree the entire Fibonacci sequence, once created, might have been Lo5'd to fit a generally pleasing aesthetic -- but that doesn't mean the aesthetic doesn't hold up.
Quote from: LMNO, PhD on June 22, 2011, 03:27:21 PM
Taking a moderate position, I have noticed that at the very least, the brain tends to find the 2/3 ratio to be fairly pleasing; and the golden ration roughly approximates that.
I'll agree the entire Fibonacci sequence, once created, might have been Lo5'd to fit a generally pleasing aesthetic -- but that doesn't mean the aesthetic doesn't hold up.
I'd argue that this has more to do with repeating proportions which titillate our robust pattern recognition faculties, rather than any particular ratio in and of itself.
Yeah, I've been using the Golden Ratio a lot in my CG art, but mostly when I have a number in a property (like a light's brightness) that I need to adjust. I multiply it up or down by the Golden Ratio, but it usually requires subtle tweaking from there. Phi is very interesting once you understand the repeatable nature of the operation... but it's not some end-all-be-all ratio. NET, the Design Department really pushed that on you like that?
Thanks for the links.
Quote from: ☄ · · · N E T · · · ☄ on June 22, 2011, 10:07:27 PM
Quote from: LMNO, PhD on June 22, 2011, 03:27:21 PM
Taking a moderate position, I have noticed that at the very least, the brain tends to find the 2/3 ratio to be fairly pleasing; and the golden ration roughly approximates that.
I'll agree the entire Fibonacci sequence, once created, might have been Lo5'd to fit a generally pleasing aesthetic -- but that doesn't mean the aesthetic doesn't hold up.
I'd argue that this has more to do with repeating proportions which titillate our robust pattern recognition faculties, rather than any particular ratio in and of itself.
I agree with this.
Quote from: LMNO, PhD on June 22, 2011, 03:27:21 PM
Taking a moderate position, I have noticed that at the very least, the brain tends to find the 2/3 ratio to be fairly pleasing; and the golden ration roughly approximates that.
I'll agree the entire Fibonacci sequence, once created, might have been Lo5'd to fit a generally pleasing aesthetic -- but that doesn't mean the aesthetic doesn't hold up.
3/2 is also a superparticular ratio (http://en.wikipedia.org/wiki/Superparticular_number), that's a ratio of (n+1)/n. These ratios pop up all the time in musical theory as intervals, for instance. I do believe it has been scientifically established that that intervals such as the octave (1:2), perfect fifth (3:2), etc are more pleasing to the ear than ratios that aren't based on--or close to--small integers. (I should dig up research for that too, but it's way more plausible IMO).
The wikipedia page on superparticular numbers also states that these ratios are used as aspect ratios for "visual harmony", in flags and digital photography.
One thing that I read during all this browsing about was a visual designer that remarked, if you pick a ratio to work with, like 2:3 or 1:0.618 or whatever, and then use it
consistently throughout your design, you will get a strong sense of harmony. I can really get behind that. It doesn't really matter
which rule you pick, but as long as you pick a system, and stick with it, you will create something that somehow makes sense internally, and is therefore appreciated as more beautiful or harmonious.
So there is
something to this idea, but it's quite a bit more complicated than just using the golden ratio whenever, because people automatically perceive it as prettier than other ratios.
Oh! And btw speaking of the Law of Fives, there's this beauty I came across too, while searching about, it's a littlebit off-topic, it's basically a mathematical version of the Lo5 (even though it's not entirely rigorous or serious, just like ours):
http://en.wikipedia.org/wiki/Strong_Law_of_Small_Numbers
http://primes.utm.edu/glossary/page.php?sort=LawOfSmall
http://mathworld.wolfram.com/StrongLawofSmallNumbers.html
It's not
quite like our Law of Fives, but it's also about seeing structures in things that aren't actually there. Except this time they really aren't actually there. There's WAY more big integers than there are small integers (duh). So when you play around with formulas that make crazy patterns with these numbers, especially when they involve prime numbers it seems, you're going to see patterns, and then mistake the pattern for a rule or a theorem. Except then, after many years of searching, there turns out to be some incredibly huge number that breaks the pattern. Click around those links to see some examples. I suppose you have to be a littlebit mathematically-minded to see how wonderful it is, though :)
Thanks, Trip! That's some pretty cool stuff.
re-reading that I think I'll clarify a tiny bit, cause I wrote a mess:
Quote from: Triple Zero on June 23, 2011, 03:03:37 PM
3/2 is also a superparticular ratio (http://en.wikipedia.org/wiki/Superparticular_number), that's a ratio of (n+1)/n. These ratios pop up all the time in musical theory as intervals, for instance. I do believe it has been scientifically established that that intervals such as the octave (1:2), perfect fifth (3:2), etc are more pleasing to the ear than ratios that aren't based on--or close to--small integers. (I should dig up research for that too, but it's way more plausible IMO).
The wikipedia page on superparticular numbers also states that these ratios are used as aspect ratios for "visual harmony", in flags and digital photography.
1- there probably
exists statistical/scientific data that really shows superparticular ratios or ratios made from small integers are more pleasing to the ear
2- I haven't looked for it yet
3- there is probably no scientific data on whether these numbers used as (visual) aspect ratios are more pleasing to the eye or not
4- I should probably look for either
Oh and in case you're getting a kick out of the music & mathematics stuff, LMNO, check these out:
http://en.wikipedia.org/wiki/Music_and_mathematics
http://www.maths.abdn.ac.uk/~bensondj/html/maths-music.html -- dunno if this is the same book I read, but it's a free PDF download, especially chapters 4,5,6 and 9 are about scales and notes and such, which is a subject I find super-interesting, but I'm not very familiar with cause I never learned to play an instrument. The things about frequencies and waveforms and FFT and DSP I know quite a bit about.
Quote from: Triple Zero on June 23, 2011, 04:36:40 PM
http://www.maths.abdn.ac.uk/~bensondj/html/maths-music.html -- dunno if this is the same book I read*, but it's a free PDF download, especially chapters 4,5,6 and 9 are about scales and notes and such, which is a subject I find super-interesting,
It is indeed the same book I read years ago--I just dug it up from my external-HD-o'-backups, seems I read the old 2001 version which comes in eight separate PDF parts.
Anyway, the book is highly recommended and awesome, and seeing that you love music, and you're also not afraid of some maths (understanding your dad's quantum and all), you're probably going to enjoy the fuck out of this book.
That's some cool stuff, Trip :)
Bump. Just came across another PDF on "Misconceptions about the Golden Ratio"
http://laptops.maine.edu/GoldenRatio.pdf
Quote from: Triple Zero on June 23, 2011, 05:22:39 PM
Quote from: Triple Zero on June 23, 2011, 04:36:40 PM
http://www.maths.abdn.ac.uk/~bensondj/html/maths-music.html -- dunno if this is the same book I read*, but it's a free PDF download, especially chapters 4,5,6 and 9 are about scales and notes and such, which is a subject I find super-interesting,
It is indeed the same book I read years ago--I just dug it up from my external-HD-o'-backups, seems I read the old 2001 version which comes in eight separate PDF parts.
Anyway, the book is highly recommended and awesome, and seeing that you love music, and you're also not afraid of some maths (understanding your dad's quantum and all), you're probably going to enjoy the fuck out of this book.
This is really interesting! Thanks much for the pdf link. This thread has expanded my brain :)
Well, this is awesome, Trip. I acknowledge the fractal geometry of natural things because A) they're made up of smaller repeating units and B) fractals are developmentally easier to program. However, I've remained skeptical of these golden numbers. Yes, pi and other perfect and repeated proportions in geometry are very interesting, but how often does anyone see a perfect rectangle or circle or any simple geometric shape outside of mathematical ideals? The living world has always been about "whatever works", and not about what matches are human aesthetic.
I'd also suggest that the reason these ratios seem to match our human aesthetic, at least in part, is because human designers use them everywhere.
eix=cos(x) + i sin(x) gives me a boner
Yes, also eiπ + 1 = 0
:fap:
If we're going there, then
(http://www.physics.udel.edu/~watson/phys208/formulas/maxwell-review.gif)
The glyph φ on the other hand is universally beautiful :fnord: