Is this some kind of a pi-nus measuring contest joke?

Yeah, yeah, go ahead and downvote this one to death. I know we don't like jokes 'round these parts, especially low-effort immature ones. :~(

It's not how long your pi is, it's the circumference that counts.

... and the emcee asks for the fifty zillionth hex digit, but only Team HOOMINZ has the formula for an arbitrary hex digit in isolation of pi !

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.

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

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

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.

if memory serves, the problem with ieee754 fp representation isn't the relative sizes of its largest and smallest possible values, but its uneven representation of the values between

Double precision floating point gives you 53 bits of significance.

It's even more absurd than that:

Anything shorter than about 10^-43 sec is faster than light can travel a Planck length.

According to Wikipedia LIGO is detecting gravitation waves was small as 10^-22 metres.

64bit floating point IEEE754 uses 10bits for exponent, and one bit for the sign. It's not that all 64bits are dedicated for value representation.

If you meant that 64bit long is a rather large 20decimals, indeed it is.

2^-64 has little to nothing to do with 64-bit FP operations and is accurately represented in a 32-bit or even 16-bit float.

My understanding (which might be wrong) is that just because PI is infinite and non-repeating, doesn't necessarily mean that every conceivable pattern of digits is present.

As a contrived example, consider the pattern:

01 001 0001 00001 etc.

This pattern is infinite and never repeats but we will never see two consecutive "1"s next to each other.

We know for a fact that pi is truly infinite, there's no "if" there. But we are not sure whether it contains every sequence of (e.g.) decimal digits.

Either way, your proposition works for "the list (or concatenation) of all positive integers in ascending order" as well. There is no deep insight in it, even if it were also true for pi.

if you accept the premise behind this question (which I wouldn't dispute) then theoretically any information at all would be self aware given the right computer

Bold claim in terms of IT (there exists currently no self-aware system in IT) but of course it contains all the info needed to build a human.

I'd rather say it contains the code to generate itself which should be much easier (= earlier) to find.

What you want is a disjunctive number, also called rich number or universe number.

It is an infinite number where every possible sequence of digits is present, and therefore, such a number contains the code of a self aware program, as well as the complete description of our own universe (hence the name "universe number") and even the simulation that runs it, if such things exist.

We don't know if pi is a disjunctive number, for what we know, though unlikely, the decimal representation of pi may only have a finite number of zeroes. It means we don't have the answer to your question.

Sure, similar argument to a Boltzmann Brain.

They do. This is precisely the number of accurate digits you get when you use a double (i.e. 64 bit floating point). https://float.exposed/0x400921fb54442d18

JPL uses metric for calculations.

It’s an education article, and the author mentions he first got the question from (presumably American) students so it makes sense he would answer in imperial units that an American middle schooler could understand.

At least one more. What else would dang track?

you mean 7:21 given the circumstances

They are wetter.

But it also contains all possible contradictions and negations of all possible secrets - so, you don't know which is the "true" secret.

Or the typewriter’s monkey

Also reminds me of https://xkcd.com/2170/

Obligatory "there truly is an xkcd for everything."

Or even better, it's defined as the smallest positive root of the sine function. Much simpler definition.

JPL needs the number of digits in a double float because JPL needs to use double floats because JPL is performing engineering.

Paradoxically, double floats are engineered to provide more digits than you need because you need more digits than you need when engineering because if you don’t have insignificant digits to drop, you don’t have enough digits.

> Instead, they just show that the "default" number of digits is enough.

The "default" number of digits was chosen and became the default because it's enough for mostly everything.

Well kinda, the size of the mantissa is certainly chosen to be large enough to give the precision scientific computing would "typically" need, but that's considering trade-offs and just being vaguely good enough for most cases. Sometimes we use 80-bit extended precision floating point for example.

> Generally speaking, if you think you need more than double precision, what you really want is double precision and a better algorithm. Generally speaking.

Though a lot of the time, the better algorithm is using an error accumulator-- so 2 doubles. This tends to outperform 80-bit extended precision, double-double, or long double arithmetic... but more precision would often also suffice and use the same amount of space.