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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. Th
by ithkuil 4y ago
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.
- civilized 4y agoWhat's baffling to me is the idea that nature manipulates numbers but not irrational ones. This only makes sense if you assume nature must be a digital computer.
- Turing_Machine 4y agoWell, 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.
- civilized 4y agoMaybe in pop quantum mechanics but not in the real thing.
- Turing_Machine 4y agoThere's nothing "pop" about it. On a human scale, a soap bubble may look perfectly spherical. But it isn't. The closer you look at it, the lumpier it gets.
- civilized 4y agoI don't know how you get from "lumpy" to "looks like quantization error".
- cratermoon 4y ago> 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." https://www.jpl.nasa.gov/edu/news/2016/3/16/how-many-decimals-of-pi-do-we-really-need/ https://www.jpl.nasa.gov/edu/news/2016/3/16/how-many-decimal...
- nuclearsugar 4y agoIncredible! Thanks for sharing this.
- cratermoon 4y agoI 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.
- Turing_Machine 4y ago> Well, we don't really know if nature/reality has an infinite precision. Certainly just about everything appears to be quantized at some level.
- civilized 4y agoThis 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.