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Comment by scblock | Hacker News Reader

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.

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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!

http://xkcd.com/spiral/ This is pretty strong evidence.

I can't even understand what's going on in #3.

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.

Weirdly, the author even acknowledges this:

> 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.

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.

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...

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.)

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