How Many Decimals of Pi Do We Really Need? | Hacker News Reader

How Many Decimals of Pi Do We Really Need?

jpl.nasa.gov

26 pointssanj10 comments

I really appreciate the straight forward explanations. It does a good job at putting things into scale/perspective. However, I'm not convinced that discrepancies this small are always "close enough". Consider the Patriot Missile Failure [1] (which has been discussed plenty here on HN [2]). The system's clock was off by about 0.000000095 decimal, but that was enough to result in catastrophic failure. I'm sure that this NASA post is intended for the layperson (which is good), but I'd hope that engineers have a bit more "involved" way of determining the appropriate number of decimals for any given applicaiton?

[1] https://www-users.cse.umn.edu/~arnold/disasters/patriot.html

[2]https://hn.algolia.com/?dateRange=all&page=0&prefix=false&qu...

The article doesn't mention it but adding precision doesn't help for another reason: space isn't flat. If you calculate the surface area of the earth or sun or whatever with pi you're off. Doesn't matter how many decimals you use. You're off because gravity distorts space.

" The answer is that you would need 39 or 40 decimal places."

No, no, no!

The answer is 42... 42 decimal places -- sorry couldn't resist.

I guess that I can finally formulate it: the scale of the universe, from the entire thing down to an atom is about 40 magnitudes of size.

I'm not sure how close to the middle humans are.

1 meter is about 27 orders of magnitude down from 100 Gly, and 12 up from 1 pm (approximately the proton radius). So we are closer to the small side.

Aren't electrons about 3 orders of magnitude smaller than a sub-atomic particles like protons? And I can't find an estimate of the diameter of a neutrino easily from google (do we even have one?), but it seems like neutrinos are even smaller still. And I think we still have a lot to discover in this area.

So maybe it's more like, about 40-50 orders of magnitude, but potentially much more as we explore the "extremely tiny" portion of the scale?

Quarks are supposed to be tiny. Why is the Top quark so gigantic?

As I understand it, it's believed that elementary particles (such as electron), don't have size.

> I'm not sure how close to the middle humans are.

Well, that does depend on the human, technically...

Actual title is “How Many Decimals of Pi Do We Really Need?”. Also, it's from 2016.

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