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Comment by dskloet | Hacker News Reader

Calculating the circumference of a circle isn't the only thing pi is used for. And small errors at the start of a calculation can become big errors at the end. So I don't find this argument very convincing.

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That's why they are using 15 decimal places, which in reality, is complete overkill. No instrument I am aware of is capable of measure with such accuracy, top of the line is usually at around 9 decimal places. This is a scale at which relativistic and quantum effects have to be considered.

That pi is 6 orders of magnitude more precise. The nice thing about having 6 and not just 1 or 2 (that would be sufficient) is that you don't have to worry too much about the exponential effect of compound error.

So really 15 decimal places is enough not to worry about pi not adding significant imprecision to your calculation, but not so ridiculous as to waste most of your time processing what is essentially random digits.

That it roughly corresponds to the precision of IEEE754 double precision floating-point numbers is probably no coincidence. This is maths that standard hardware can do really well. More than that requires software emulation (slow) or specialized hardware (expensive).

I love the fact that some random dude on HN is telling NASA that their calculations regarding space calculations are not very convincing. Internet can be a beautiful place.

Debate shouldn't be discouraged purely out of deference to the agreed upon authority. Sometimes the random voice in the crowd can say something important.

Probably not in most cases, but this isn't the sort of place we shout people down just for disagreeing. If you disagree with them, present your reasoning, and not just "they're NASA so they must be right!".

There is a difference between "NASA/JPL are doing something wrong" and "NASA/JPL's explanation to a middle-schooler of why they are doing something has an error".

The argument saying we don’t need more than N pi decimals because we could compute the radius of the universe down to an hydrogen atom is indeed not very convincing.

This is also unrelated to NASA’s past or present activities

But the question was answered by NASA and how many decimal places THEY need for THEIR highest level calculations.

If a HN user requires more, as for example they are planning to travel further than Voyager 1 then you’re absolutely right, it’s not very convincing to narrow it down same as NASA had.

> So I don't find this argument very convincing.

You think the NASA JPL is mistaken about how accurate they need Pi to be?

Saying "I don't find the argument the authority gives convincing" is a different statement than "I distrust the authority". And in fact there are many experts, from craftsmanship over engineering even all the way to science that demonstratebly know method to achieve success, but are missing methods to verify their explanatory models or don't really need to care. E.g. for bakeries the microbiological background is often much less relevant than getting the process right.

In the case of this explanation by JPL, they are giving a very dumbed down explanation to visualize the extreme precision of floats to layperson. By necessity it is very incomplete and fails to transmit a deeper understanding to those of us that have an at least passing understanding of numerically analysis. For me that means I want to know more, as there is certainly important nuance missing, and I'd want to know more from the same experts at JPL exactly because I trust their expertise.

Hopefully JPL will finally be able to accomplish something once they start taking advice from internet randos.

The impact of a higher precision in pi depends on the rest of the calculations or simulations; factors like the (roundoff) errors caused by the size of your floats and your other constants, the precision of your calculations (like your sine), or (roundoff) errors in your differential equations and timestep accumulations. And finally, you have uncertainties in the measurements of the world (starting conditions) you use for your simulations. I guess in NASA's case, a higher precision in pi doesn't add to the overall performance of their calculations, or at least not to a relevant one.

But all measurements of weight, length, position/speed have errors multiple orders larger. Errors by second and third approximations will dominate. Let alone unpredictable (unknown) physics playing a role.

Well then the problem isn’t Pi and any number of decimal places.

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