9 ms·
Summarized answer from the article. > For JPL's highest accuracy calculations, which are for interplanetary navigation, we use 3.141592653589793 > by cutting
by Hayvok 4y ago
Summarized answer from the article.
> For JPL's highest accuracy calculations, which are for interplanetary navigation, we use 3.141592653589793
> by cutting pi off at the 15th decimal point… our calculated circumference of the 25 billion mile diameter circle would be wrong by 1.5 inches.
The author also has a fun explanation that you don’t need many more digits to reduce the error to the width of a hydrogen atom… at the scale of the visible universe!
- anigbrowl 4y ago- hey space nerds, check out my new result - oh yeah what ya got math kid - new digits of Pi. Such fast, very precision! - not this shit again - it's so cool, *look at it* - tl;dr - but it's the key to the universe - ok ok, look we have to do actual space stuff - laugh now fools, while I grasp ultimate power
- louloulou 4y agoIt's a good metric to determine how advanced a civilization it. Would be cool to just compare pis with the aliens, and then whoever has the longest pi takes over, rather than fighting to extinction.
- metadat 4y agoIs 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. :~(
- s0teri0s 4y agoMy inner 12 year old laffed.
- myle 4y agoWell done for a 10 year old!
- dotancohen 4y agoThat was neither low-effort nor immature. The elusive high quality, mature penis joke is well appreciated.
- secondcoming 4y agoThe joke was great. The disclaimer at the end ruins it.
- metadat 4y agoWell, it's just the way HN PTSD plays out.
- secondcoming 4y agoDon’t worry about your internet points
- metadat 4y agoI don't, and totally agree; they're absolutely worthless. I do however get annoyed when decent comments get murdered and become invisible to most of the population.
- karolist 4y agoThe joke was good, but your fear of downvotes and attempt to prevent them by adding the disclaimer is :|
- metadat 4y agoThis is why we can't have nice things (because of me). Sorry!
- belter 4y agoYour fear is irrational...
- MonkeyClub 4y agoHN pinoia aside, it was a pretty good one. However I doubt that a civilization that has survived long enough to invent some (local) sort successful space travel would budge. There are two extremes that would bring balance: mutually assured destruction (but the power comparison must allow for a delicate balance of terror to be believable on both sides); or a mutually beneficial alliance (which can work with a well-meaning advanced civ encountering a less progressed one - the “there there’re, little one” case). That being said, I’m not convinced that searching for universal others isn’t a dead end. But even if it is, it sure can stretch our understanding a bit. E.g. look at the Kardashev scale, with which we can sort of stretch imagination and think of Dysom spheres instead of solar panels. I mean, even if we don’t find aliens, with a roadmap like Kardashev’s it won’t be (too) long before we become the aliens many of us hope for/aspire to.
- DonHopkins 4y agoIt's not how long your pi is, it's the circumference that counts.
- euroderf 4y ago... 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 !
- Grimburger 4y ago> our calculated circumference of the 25 billion mile diameter circle would be wrong by 1.5 inches JPL uses imperial units?
- Hayvok 4y agoJPL 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.
- dotancohen 4y ago> It’s an education article Then it should use the actual units that the students will use for engineering and scientific calculations. Saying "it's education" is not an excuse to not teach.
- ebingdom 4y agoI wonder why they don't just use the highest precision possible given whatever representation of numbers they're using? I know these extra digits would be unlikely to ever matter in practice, but why even bother truncating more than necessary by the hardware? (Or do they not use hardware to do arithmetic calculations?)
- OscarCunningham 4y agoThey 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 https://float.exposed/0x400921fb54442d18
- ternaryoperator 4y agoThis calculation demonstrates how our current 64-bit FP operations are wide enough for almost all physical world needs. But to make the point even clearer: in one 2^-64th of a second, an object moving at the speed of light would not cross the diameter of a hydrogen atom. c in 2^64 = 1.625 × 10-11 m/s; width of a hydrogen atom: 2.50 ^10-11 m
- saagarjha 4y agoDouble precision floating point gives you 53 bits of significance.
- vlovich123 4y agoNot to mention that your error grows with any mathematical operations you perform and all sorts of other numerical precision issues.
- stephencanon 4y agoThis happens for integer arithmetic as well, as soon as you step off the happy path of trivial computations and onto the things we use floating-point for. You cannot exactly solve most differential equations, even if your underlying arithmetic is exact. These errors (“local truncation error”) then carry through subsequent steps of the solution, and may be magnified by the stability characteristics of the problem.
- slyall 4y agoAccording to Wikipedia LIGO is detecting gravitation waves was small as 10^-22 metres.
- stephencanon 4y agoDouble represents values smaller than 10^-300. 10^-22 is no problem, so long as you don’t need more than about 16 digits after the first non-zero.
- 4y ago
- suifbwish 4y agoIf pi is truly infinite wouldn’t it eventually express a sequence of information which would be self aware if expressed in binary in a programmatic system?
- tlonny 4y agoMy 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.
- mormegil 4y agoYes, it doesn't necessarily follow, but it is indeed conjectured that pi is a normal number, meaning all digits appear with the same frequency, but it is not known yet. https://en.wikipedia.org/wiki/Normal_number https://en.wikipedia.org/wiki/Normal_number
- rrobukef 4y agoThe same frequency does not imply every subsequence appears. Consider the modification which rewrites every sequence of 123 to 132. All digits will have the same frequency but 123 will never appear.
- sebzim4500 4y agoIf pi is shown to be normal in every base then every finite sequence must appear in it.
- ithinkso 4y agoYou haven't read the link you posted though. Every digit appearing with the same frequency means a number is simply normal and it is not enough to get you what you want in this case (as pointed out by sibling comment). Normal number is a number where every possible string of length n has the same frequency of 10^(-n)
- metadat 4y ago> The author also has a fun explanation that you don’t need many more digits to reduce the error to the width of a hydrogen atom… at the scale of the visible universe How many more, though? <Perfectionist>1.5in of error per few billion miles seems a bit sloppy, even though I'm sure it fits JPLs objectives just fine.</>
- dskloet 4y agoCalculating 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.
- rrobukef 4y agoBut 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.
- chrisseaton 4y ago> So I don't find this argument very convincing. You think the NASA JPL is mistaken about how accurate they need Pi to be?
- Perseids 4y agoSaying "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.
- noSyncCloud 4y agoHopefully JPL will finally be able to accomplish something once they start taking advice from internet randos.
- MikeDelta 4y ago