Claiming you can't have a perfect circle because pi is irrational makes no sense. The physical world isn't built on the decimal system. Similarly, the golden ratio being an irrational number has no bearing on the article's claims at all.
The article really shouldn't have led off with that. Its much stronger point is that the only reason we think of the golden ratio as a design principle is confirmation bias and wishful thinking.
Either keep comparing lots of things to each other until you get a ratio that's about 1.6 (I mean, seriously? The height of some guy's navel?), or just Photoshop a spiral onto anything with a ratio between 1.3 and 2. Golden ratio confirmed!
And I particularly like how the one with Cape Cod completely misses the spiral of Long Point by like 30 miles, and just spirals in toward some arbitrary point in Massachusetts Bay.
"Claiming you can't have a perfect circle because pi is irrational makes no sense. The physical world isn't built on the decimal system."
Irrationality does not depend on the base it is expressed in. It means that a number can not be expressed as a ratio of two integers. Even if you declare yourself to be in "base pi", in which pi is "10" (if it is anything at all, irrational bases get... weird. or, if you prefer, "fun"), pi is still irrational.
Edit a few seconds later: On a whim, look what pops up as the first hit in Google for "irrational base": http://en.wikipedia.org/wiki/Golden_ratio_base Synchronicity strikes again, sorta.
> It's pedantic, sure. Isn't 1.16180 close enough? Yes, it probably would be...
For some reason he didn't see fit to delete that section of the article after realizing it was pointless. Which is too bad, because the rest of it is pretty solid.
I didn't interpret that sentence the way you did I guess. It made sense to me when in context of whether the target of the golden ratio mattered in the first place.
In other words, the golden ratio is an irrational number. Given limits of decimal precision being unreachable by realistic building standards, it'd be a silly target to go to far into the decimal points to perfect your structure. But it doesn't matter anyway because the ratio isn't 'golden,' its 'perfection' is subjective and therefore not meaningful to constrain your projects to.
It has nothing to do with decimal systems or irrational numbers. It is impossible to exactly build something to any number. Choose 1. Can't do it, not with perfect accuracy. It's no harder to make something exactly the golden ratio than to make it pi, sqrt(2), or 6.
Yep. Pretty much any measurement you make in the real world is actually going to be irrational. We just round them to the closest significant figure we have. https://www.youtube.com/watch?v=Swm8tTLWirU
I'm also interested in subatomic particles like quarks. They're usually represented as spheres. Are they really spherical?
Similarly, the gravity of a neutron star probably compresses its own mass pretty damn closely to a perfect sphere. Though I suppose its rotation might deform it?
There's a huge amount of unproven (and possibly unprovable) assumption in that statement. There's no evidence the universe is actually continuous rather than discrete at Plank scales. No evidence in either direction, so far as I know. And given the nature of physics at Plank scales, it might be impossible to devise an experiment which could distinguish between them.
But if that's the case, it would mean it's not wrong (and not right, either) to declare that the universe is discrete, meaning all measure are in fact rational numbers.
As we're talking about design, therefore human perception, we just need to know how the resulting figure is sampled and interpreted by the human eye and mind. If you can't tell dots close together aren't continous, but discreet - then for the purpose of this discussion they are not discreet...
Discrete and continuous are not necessarily mutually exclusive. You can have discrete processes that exhibit continuous behavior. It's really important that you have clear definitions and well-described models when using these general kinds of terms.
See also Vi Hart's "Doodling in Math: Spirals, Fibonacci, and Being a Plant", starting at https://www.youtube.com/watch?v=ahXIMUkSXX0 It covers how the Fibonacci is seen in more places than it actually exists, which is closely related to the golden ratio. (This point is made at the end of part 2 and part 3 is all about it.)
The golden ratio is easy to demystify for journos or non-designers observing the continuos wave of photoshopped crap trying to $ fit --force the spiral inside random images/works. But designers of school (industrial, architectural, engineering etc), know that it has been used for ages. It's there in the books, even in ancient books, period. And it is just another tool for achieving pleasant proportion and cadence.
Design has been prostituted lately, specially with the boom in the software industry, and seems like fitting the spiral in works that weren't built using the tool properly in the first place are destroying its real utility/credibility as design pattern. Fact is that fibonacci (as a mathematical pattern) is useful and can actually be found in several fields from the stock market [0] to physics [1][2]... so it's not just a "design thing".
Is it the "holy number" that many people praise in order to sell their designs? definitely not...
Is it useful as a design tool and could it be an unexplored and practical numerical constant? definitely yes...
Interesting that you give the example of the stock market, since Technical Analysis (which fibs are a part of) is often criticised for confirmation bias and lack of scientific proves of it working.
Pretty much parallel to how the golden ratio is criticised in the OP.
The writing style of this article is antagonistic, childish, and generally offputting.
The concept is interesting, and I would love to learn more about this topic, but the person who wrote this article should consider carefully the tone in which he/she continues to write in the future.
I know John's style since a long time. He might be easy to dismiss as a bitter writer, if you single out one of his pieces. He's not, that's part of his broader take on journalistic style. Anyway, I'm not his lawyer, just make what you want with it.
I find the comments to be much more interesting, though. You touch something that some people consider sacred, and there you go...
Had the author bothered to read Livio's book, he might appreciate that the reason it is so easy to see the golden ratio in designs is not DNA, but math: anytime you divide a measurement into two parts, one larger than the other, the ratio of the larger part to the whole is always closer to the golden ratio than the direct ratio of the smaller part to the larger part.
Slightly OT, but do the words "Here's why." make anyone else cringe when reading a headline? I feel like it's everywhere now, like everywhere, as though it's the secret key to having your article go viral.
So.. it's just four pictures? Am I missing something? I see some black rectangles between the pictures, are those supposed to be embedded videos that aren't loading or ads?
It should be mentioned that in German usage the golden ration (Goldener Schnitt) refers more to the proportions of the spaces separated by the cutting line than to the proportions of the surrounding rectangle. Its common application is basically a finer form of the rule of thirds.
It shouldn't go unmentioned that William Hogarth already proposed a similar system, based on a serpentine line [0] (and, more important, in its three dimensional form, on a spiral) in his "The Analysis of Beauty. Written with a view of fixing the fluctating Ideas of Taste." [1] in 1753. Sidenote: While Hogarth observes this as an important regulating idea in the work of Michelangelo, he explicitly complains the lack of any notion thereof in Leonardo's contemporary "Trattato della Pittura".
I actually think that the article's example using Dali's The Sacrament of the Last Supper sort of disproves itself.
Part of why the painting is so elegant is because of its balanced composition: the arms along the top of the golden spiral, the table edge along the top of the inner spiral, etc.
The golden ratio is algebraic, and can be easily constructed with straightedge and compass. So the first point the author starts with is pure bullshit. That's like saying sqrt(2) is "impossible" despite it being the diagonal of a unit square.
Exactly. Too bad nobody else pointed that out. On the contrary, Pi is transcendental and therefore cannot be constructed.
I hope it is the journalist and not the Stanford math teacher who got it wrong ;-)
