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”
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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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out of curiosity… does that first fact account for the continued expansion of the universe?
It works at the current 93 billion light years of observable universe (46ish in every direction)
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?
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
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…
And then you’re using C++ and they scold you for including cmath for just M_PI because it increases compilation times.
We’re talking about engineers here! We’re using MATLAB or Python if we’re programming at all.
Your not writing regular python code, your writing a special subset of python intended for engineers and scientists called “bad python code”
Your not writing
Coder/engineer confirmed.
As a comp sci that interacts a lot with engineers, I feel this in my soul.
You can’t say that for all engineers. I’m one and the biggest part of my job is programming in C++
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.
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…
“is not like you do calculations by hand anyway”
… get off my lawn, whippersnapper.
They do? Why not provide some explanation?
Somebody else already said it, but that’s what the title is.
Longform: a lot of calculations that happen in astro deal with distances so large so large that only order of magnitude changes actually meaningfully affect the end result. To connect to a more common topic, here’s a joke.
“Whats the difference between a million dollars and a billion dollars?”
“About a billion dollars”
This joke works for the same reason; 1 billion is so many orders of magnitude larger than 1 million that (1,000,000,000 - 1,000,000 = 1,000,000,000) is only incorrect by ~0.1%, even though substituting 0 for 1 million in that equation seems ridiculous on the face of it. Substituting 1 for pi has similarly minimal errors (tbh it usually matters waaaaaaaaay less than .1% error) in a lot of astro math
Also how you get classical physics from relativity.
Astronomy often has pretty high error bars on their measurements (distance, size of stuff, etc).
In astronomy, the important part of the number is often just how big it is (that is, the exponent). Multiplying by pi doesn’t change much in that.
The explanation is in the title.
It isn’t an explanation
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
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 usually a constant (or several ones with varying degrees of accuracy and size)
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
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.
I guess n would be infinite in the limit I’m looking for. I’m looking at this in like a “musing about theoretical complexity” angle rather than actually needing to use or know how to use pi on modern systems.
For the record, I realize how incredibly pedantic I’m being about the difference between the irrational pi and rational approximations of pi that end up being actually useful. That being said, computational complexity has enough math formalism stink on it that pedantry seems encouraged
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)
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.
Good news for her. Cheese cake is a pie not a cake.
You sound like an involved and caring father. Rock on, dude
Theres a YouTube video where the presenter demonstrates DOOM running (or not) with varying values of Pi that’s quite interesting: Non Euclidean DOOM
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/
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.
Using 1 is fun. That means the circumference of a circle is equal to its diameter.
Euclidean geometry enjoyers in shambles
Isn’t this functionally true for objects on the infinite focal plane? I.e. a star? Betelgeuse might actually be huge in absolute terms, but from earth, and even in a large telescope, it’s still a pinpoint whose circumference is not meaningfully distinct from its diameter.
This image is a two-panel meme utilizing a blurry, chaotic photo of individuals seemingly engaged in a mock fight and a separate photo of a person appearing to conduct a science experiment with a small flame, possibly under the influence of poor judgment.
In the left panel, the text “MATHEMATICIANS DEFINING PI” is superimposed over two individuals engaged in a dramatic physical altercation, one holding the other back. A third person, who is uninvolved but present, is labeled “ENGINEERS JUST USING 3 BECAUSE IT’S WITHIN TOLERANCE.” This suggests a hierarchy of concern regarding the numerical precision of π (pi), with mathematicians caring deeply, engineers demonstrating relaxed standards, and general chaos ensuing.
In the right panel, a shirtless person crouches and conducts a questionable experiment involving a lighter and a small pipe. The caption “ASTROPHYSICISTS” is positioned above their head, and below is the phrase “PI = 1.” This implies a level of approximation so extreme it borders on parody, indicating astrophysicists allegedly use such simplifications in the name of cosmic-scale practicality.
The overall composition is an exaggerated commentary on varying standards of numerical precision in different disciplines, presented through low-resolution imagery and humorous juxtaposition.
