A place for majestic STEMLORD peacocking, as well as memes about the realities of working in a lab.
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This is a science community. We use the Dawkins definition of meme.
Meme of two women fighting while a man smokes from a pipe in the background.
The women fighting are labeled "mathematicians defining pi" and "engineers just using 3 because it's within tolerance"
The man smoking is labeled "astrophysicists" and the pipe is labeled "pi = 1"
Using 1 is fun. That means the circumference of a circle is equal to its diameter.
Electrical engineer. Never used 3. Always 3.14. don't really get the joke.
38 digits of pie gives youv an error of less then a hydrogen atom in the circumference of the known universe.
https://www.jpl.nasa.gov/edu/news/how-many-decimals-of-pi-do-we-really-need/
As a retired mechanical engineer, the joke is that we don't really remember the value of Pi, but we think it's somewhere around 3. But maybe we should use 4 just to be safe.
In any case, I have to remember 3.14 because one of my Daughters was born on Pi Day. Which, according her, is the second most important day of the year, just right behind Christmas Day, when she was growing up. So when she got into high school that meant that we had to bring enough pie to be served in each of her math classes on that day. (Oddly enough she prefers cheese cake over pie on her Birthday).
Now I'm not saying being born on Pi Day influenced her life any, but she has a PhD in Mech Engineering.
Theres a YouTube video where the presenter demonstrates DOOM running (or not) with varying values of Pi that's quite interesting: Non Euclidean DOOM
Good news for her. Cheese cake is a pie not a cake.
This made my day.
Solidifies my preference for pie over cake
You sound like an involved and caring father. Rock on, dude
Computer science: pi is O(1)
Is it actually? I'll admit im pretty rusty on time complexity, but naively I'd think that pi being irrational would technically make even reading or writing it from memory an undecidable problem
It's a number and complexity refers to functions. The natural inclusion of numbers into functions maps pi to the constant function x -> pi which is O(1).
If you want the time complexity of an algorithm that produces the nth digit of pi, the best known ones are something like O(n log n) with O(1) being impossible.
If you're trying to calculate it, then it's quite difficult.
If you just want to use it in a computer program, most programming languages have it as a constant you can request. You get to pick whether you want single or double precision, but both are atomic (a single instruction) on modern computers.
Do said atomic instructions produce pi though, or some functional approximation of pi? I absolutely buy that approximate pi is O(1), but it still seems like a problem involving a true irrational number should be undecidable on any real turing machine
The "true value of pi" is too large for any computer to store. Our current understanding of numbers says it's an infinite number of digits. On the other hand, any number you use to multiply with pi is far less than an infinite number of digits. So you get the correct answer, with no worse precision than your input value, using the approximations of pi.
"Modern" is a bit misleading, x87 had fldpi. The whole x87 part of the standard has been deprecated with x86_64 in favour of the whole sse series of instructions and those don't come with pi. You instead load a constant from program memory, just like any other.
As processors (as of yet) still support those legacy modes they will also contain the constant somewhere in probably microcode storage, calculating it on the fly makes literally no sense at all: It's (for x87) 80 bits of data, much shorter than any imaginable program, smaller than any circuitry able to compute it so you'd be spending time to save no space which is pointless.
ARM, RISC-V etc. come from the RISC tradition so they wouldn't be caught dead including such an instruction. Both have zero registers though as zero is an absurdly useful constant, simplifying things drastically, both on the hardware front as well as within the instruction set (move is add zero to source, save to destination, clear is add zero and zero, save to destination)
Now, that's finite constants. In particular, it's about floating point arithmetic, which is a wonder of maths and a deep rat's nest of numerology, but has finite precision, it's not true real arithmetic. Real real arithmetic is undecidable, in particular comparison and expansion to decimal form are undecidable. Printing infinite strings of digits is usually not what we want to do, and limiting precision of comparisons is... not ideal, but better than having limited precision at every operation: You can decide once you're comparing how accurate you want things to be and don't have to worry while writing down your formula (btw Herbie exists, and that's why packages like this exist. In that case pi is not a constant but a formula, which can be expanded as needed. Quite slow compared to floating point hardware but when you need it you need it and even if you don't it's still useful as a sanity check, gives you an idea of how far off the floating point results are without having to call in a favour with a mathematician.
What would be the "n" in that Big O notation, though?
If you're saying that you want accuracy out to n digits, then there are algorithms with specific complexities for calculating those. But that's still just an approximation, so those aren't any better than the real-world implementation method of simply looking up that constant rather than calculating it anew.
It's usually a constant (or several ones with varying degrees of accuracy and size)
It all depends on the precision you need. You could use an infinite series to get to the precision needed but for most use-cases it’s just a double baked into the binary itself, hence O(1)
I use 3 ^16^/~113~
At least do 22/7
(355/113)/ pi = 1.0000000849136...
That's way more numbers to remember than 1/7 above 3
You're a monster. I love it
Only basic math. You can convert Pi even more precise, but I think to 6 decimals is enough.
38 digits of pi can get the circumference of the visible universe to within a single hydrogen atom.
10 digits gets the diameter of the earth to within an inch.
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10 digits gets the diameter of the earth to within an inch.
Put another way, 10 digits means that your error will be caused by your imprecise model of the Earth's shape, rather than imprecision in the value of pi.
The real comment mvp. You deserve every positive vote my post got
And just two digits introduces less error than your average terrible model
Wow, what do you have against models? I mean, I know that the trope is that they aren't very smart, but the same trope applies to firemen, so why pick on models?
Firemen are way hotter
old man voice this must be that ragebait thing the youngsters are always talking about
I heard once π²=10 is fairly accurate approx and thus g=π²=10 in astrophysics where people thinks in order of magnitude, not value.
But my engineering ass is telling assumptions with larger than 50% difference from actual value may cause issues on order of magnitude if the value is used multiple times and isnt it better be like 5=1/2×10?
That's because your engineering ass needs things to be physical and sane. Physics is a field for the mentally unwell to sink further into insanity while incoherently scribbling greek letters on every available flat surface.
On a more serious note, yeah you absolutely have to be careful about where you apply really ambitious simplifications like that. There are plenty of mathematical regimes where you can use natural units (this is the term to look up if your interest extends further) and simplify your reference frame by a hell of a lot though. Setting the speed of light to 1 is also a hell of a drug, and brother I've got an addiction
As an Astrophysicist, I have never seen anybody use pi=1, you just leave the character, it's anyway better to read, is not like you do any calculations by hand anyway. More common is c=hbar=kB=1, but that is not an approximate, is a gauge in another unit system. Also... Astronomy is not astrophysics...
As an astrophysicist, can you read me my horoscope? I'm a scorpion
Sure, give it to me, I can read it for you.
"is not like you do calculations by hand anyway"
... get off my lawn, whippersnapper.
as an engineer, a lot of languages (even proprietary ones) have a built-in constant pi variable because it is so ubiquitous - its easier and more readable to use pi than 3........
I've also never seen a fellow engineer simplify pi to just 3, although I have seen a rise of memes from people who think they do.
I would slap someone if I saw them try that, it's unnecessarily sloppy. 3.14 is the default, and trivial to work with if you're using a calculator (I would also slap someone if I saw them not using a calculator). Unless you just LIKE having all your calculations be off by almost 5%. Then you'll come back wondering why so many of your parts are out of tolerance.