The author obviously really dislikes his subject, Buckminster Fuller, but even accounting for some personal bias, the guy does sound like a bit of an idiot:
> he found the number pi distasteful. “I’d learned at school that in order to make a sphere, which is what a bubble is, you employ pi, and I’d also learned that pi is an irrational number. To how many places, I wondered, did frustrated nature factor pi? And I reached the decision right at that moment that nature didn’t use pi,” reads his objection in a New Yorker profile.
There’s a great book on Mathematical Cranks where one of the recurring themes is that the intuition must always be correct, and anything that seems counterintuitive is abhorrent and must be wrong.
I think this is an okay belief to have if you approach it from the bottom up instead of the top down. If something is counterintuitive, then you shouldn't write it off as a hacky asterisk in your head, you should improve your understanding of the domain in question so that it becomes intuitive.
Well, we don't really know if nature/reality has an infinite precision. Perhaps you don't need an irrational Pi to compute everything up to maximum accuracy. That said, the irrational number Pi in its mathematical abstraction is extremely useful and just as "real" in its abstract mathematical domain.
Not every step of math has to be mapped to something physically real in order to math to be useful to describe the real world.
Imaginary numbers per se may not have a direct mapping to any physical magnitude, but complex numbers nevertheless are very useful to accurately describe real world phenomena. You just don't need to focus in the wrong detail and lose the bigger picture off sight.
> Perhaps you don't need an irrational Pi to compute everything up to maximum accuracy
"For JPL's highest accuracy calculations, which are for interplanetary navigation, we use 3.141592653589793. Let's look at this a little more closely to understand why we don't use more decimal places. I think we can even see that there are no physically realistic calculations scientists ever perform for which it is necessary to include nearly as many decimal points as you present."
I especially like that pi to 40 or so decimals places would be sufficient, theoretically, to calculate the dimensions of the observable universe to within the diameter of a hydrogen atom.
Well, a lot of the stuff that goes wonky when you get to ultra-small scales looks an awful lot like the type of quantization errors you get when you try to model things in a digital computer.
Does that mean that it is a digital computer? No. But it's reminiscent of it.
This is a popular myth, but it isn't true. Some very specific things in physics, like atomic energy levels, are quantized, and everything else is continuous. And atomic energy quantization emerges from a continuous model of space and time.
Except that the molecules that make up the bubble are not infinitely small.
To expand a bit:
Yeah, on a human scale, the bubble looks spherical, but when you look at it on a small enough scale, you start to see behaviors that are far removed from the continuous functions that one would expect from Newtonian mechanics.
So a bubble is unary in that it represents pi with single molecules in a circle. Then, forces tug at it--like gravity a tiny bit, but moreso wind and especially the hyperlocal flow of air driven by eg temperature (and particle concentration) that want it to not be spherical. But the bubble membrane wants to be spherical because that's its most stable shape. Here we're thinking of big huge bubbles, those exemplify this more, bubbles like 20 cm in diameter. So it's a tug of war between the air and the bubble, with the air tending to infinitely deformed and therefore inescapably burst bubble and the bubble tending to pi.
It does seem wrong that nature would use irrational numbers - the fault is more likely in our concepts. Our mathematics may be more parochial than we realize - than we can realize. Alien mathematics may have taken a different route.
The second sentence claims Fuller invented the word synergy. m-w.com says synergy has been in use since the 17th century. This author is not off to a good start.
Coming from a rich family helps, but today in tech and finance we see tons of successfull people from more modest means. i think times have changed and family wealth not as important.
> he found the number pi distasteful. “I’d learned at school that in order to make a sphere, which is what a bubble is, you employ pi, and I’d also learned that pi is an irrational number. To how many places, I wondered, did frustrated nature factor pi? And I reached the decision right at that moment that nature didn’t use pi,” reads his objection in a New Yorker profile.