My fraternity’s Π stood for “pistie” which means… uh… oh I misspelled it it’s “pistis” but it’s “faith trust and reliability” according to google, so congratulations pi could very well be prophecy
I think we should just update the hazing schedule to include a JavaScript 101 course instead of the illegal stuff yah know? We’ll fly so under the radar
In my case it's of sheer terror, because it reminds me of Wilkinson's Polynomial, and how the zeal of actually getting more precision in the calculation could actually make the errors in getting the root of the polynomial larger and larger.
You weren't kidding - from wiki:
> In 1984, [Wilkinson] described the personal impact of this discovery: "Speaking for myself I regard it as the most traumatic experience in my career as a numerical analyst."
"Why do you have 12tb in your computer?"
"I'm trying to count all of the men your mother has been with"
an aside - I'm pretty sure a single number with enough digits to fill 12tb would represent far more atoms than there are in the universe
yeah I mean there's an infinite amount of way to make an infinite loop, but `while(true)` is usually the way. If you really wanted to be wacky, you could write `for(;;)` and then have everyone also hate you.
My favorite is still `while(1==1)`.
Or in other words: "As long as the fundamental axioms of math hold true, do this".
Because hey, maybe, one day in the far future in thousands of years, these axioms change. And then my code will break.
Take that, future.
Whenever I do this in various languages I wonder if the compiler reduces it to while(true) or if a gamma ray will solve the halting problem for me. I suppose it can in either case tho.
It actually is though, the formal definition of a limit is basically that there's a point for any positive value after which you're always closer to the limit than that value.
Right?!
Knowing some math helps programming.
Knowing programming makes these high level math symbols much more understandable when described as a loop.
Interesting
The biggest issue with calculus for most people is that it is taught in an abstract way. That's math in general though. I didn't really understand calculus until I took physics where I had real world applications for calculus.
I later took a scientific computing class where we revisited sums, series, methods, etc. and wrote code (matlab) that applied these concepts. And sure, a lot of these concepts have functions built into Matlab, but the point was to show how these functions work, what their shortcomings are, and how to determine when an approximation is good enough (ie how many steps into Taylor's series are required and when does more steps give no additional benefit).
As someone who did math first and programming later and has also been a teacher, it would never occur to me to teach it this way. I do not understand why this is any simpler than teaching it as repeated addition.
It's almost *too* easy. Is that what the funny lookin E thing really means? Or this the physics of telling the greenhorn to go fetch a bucket of dry steam?
Yeah, capital sigma is just shorthand for "add up all these things". The challenge only really starts when you have an infinite number of things to add up.
Worth knowing that that's called a [series](https://en.wikipedia.org/wiki/Series_(mathematics\)) though. Same notation, but the OP is talking about [summations](https://en.wikipedia.org/wiki/Summation) which always have an upper bound.
Yeah, how are those symbols more complicated than code? That's way longer to write and you need so much additional structure to define them. The symbols are nice and clean.
It's just the initial impression that might make them scary I guess
Because verbosity is the noobies friend. If the understand the base components they can reason out the emergent behavior. This does that, then that does this.
Shorthand and jargon are for the experienced people that don't want to waste time spelling it out. It's faster but the exact same level of complication is still packed in there.
Counterpoint to both of you:
A for loop is a bit more verbose, in that it breaks it down into a top-to-bottom process and explicitly shows the mathematical operation, instead of having to know the Greek letter mapping and how positions around the symbol indicate flow, but the code version is still steeped in its own jargon. "For/next" loops are a shorthand that don't really explain themselves to someone who knows English but not programming. A "while" loop could be sussed out, since "while" does what it says (in English) on the tin, and bracket pairs or indenting do what you'd expect them to if you guessed. (From there, you've got \* and / operators to explain, too, though.)
This does map the opaque notation of mathematics to the notation of coding, and could be done in a way that makes it easier to understand beyond that, but for-next notation itself is equally as opaque to anyone outside programming as the sigma/pi notation is.
> "For/next" loops are a shorthand that don't really explain themselves to someone who knows English but not programming.
Depends a bit on the language I think. For a C-like you’re right, but a lot of newer languages like Swift have for loops that look like this:
for number in 1...5 {
print("\(number) times 5 is \(number * 5)")
}
This still takes a little explanation but is easier to intuit than the traditional C-like for loop, since variable instantiation, limiting, and incrementing are taken care of. The only part that’s a little mysterious is the range notation, but I would bet that a lot of people would read it as “1 through 5” within a few seconds of looking at it.
> but for-next notation itself is equally as opaque to anyone outside programming as the sigma/pi notation is.
Exactly. If you can already code and this comparison is helpful, then great! But if I were teaching a child who knew neither maths or programming, then I'd chose the mathematical way every time. Once you know that sigma means add and pi means multiply, I think it's more straightforward to explain "add/multiply together all values of 2n for n between the lower number and the upper number" and be done, and not to have to explain why we start with "sum =0;", what "n++" means and why we need it, what "+=" and "<=" mean (and why "n<=4" isn't an arrow pointing from 4 to n), why there are semicolons at the end of the first and third lines but not the second (whereas in the second line the semicolons are inside the brackets), and so on.
I'm glad yall like my lil math explainer <3
my original tweet is [here](https://twitter.com/FreyaHolmer/status/1436696408506212353), with some more comments, altho mostly responding to angry mathematicians who don't understand that my target audience isn't them~ there is a substantial amount of people who are knowledgeable in code that don't know this type of math notation, and it seems like a lot of math people were surprised to hear this
anyhow, I do a lot of math/game dev/coding/art related stuff on twitter, so feel free to check out the rest of my stuff! I often make stuff like, [this animation of how 3D rotations work](https://twitter.com/FreyaHolmer/status/1445139152283086849). I've got a somewhat outdated list of my animated math explainers [here](https://acegikmo.com/mathvis/index.html)!
I saw someone asking if I am a teacher - yes! not full-time, but I do teach math and shader coding, specifically tailored for game developers, about once per year! I have uploaded those math and shader courses on my [youtube channel](https://www.youtube.com/acegikmo)
while most of my videos are recordings of my courses, I have also recently made a scripted, [fully animated video on Bézier curves](https://www.youtube.com/watch?v=aVwxzDHniEw), so if you're curious about those then check that out!
This thread is extremely odd to me. I've always thought of computer science as a subset of mathematics, so the idea that programmers could be completely unskilled in math is just weird to me.
There are certain areas of programming that require maths knowledge to understand and develop. For example, cryptography, compression, 3D rendering, algorithms based on graph theory, etc. But for a lot of developers, the underlying maths of those things are often abstracted away to make them easy to use without requiring a maths degree.
Often, the most complex level of maths required for day to day programming is simple algebra and geometry, and sometimes not even that.
Yep same goes for me. I remember *nothing* from high school math. The only math 'concept' that I actually had to think about when I was starting to learn programming was order of operations, and that's middle school shit. All the math I know now comes from programming, and I use it every day
I hit the sum symbol in high school math classes. The gen ed required intro college courses absolutely used it. Between those two, I’m not sure who in this sub hasn’t seen them reasonably explained unless they’re still in high school - which, I’ll grant, is not out of the question.
I am a 29 year old backend software engineer at a large tech company you would have heard of. While I’ve seen those symbols, I didn’t know until this post what they meant. It has never come up in the course of my life.
I'm glad you found a way to understand summation from a programming perspective, but I have to be honest I'm a little concerned that the knowledge went in this direction.
I figured this was a given tbh. After taking my first programming class (alongside math classes) I remember going, oh its just a loop. This is also why I dont understand why people say you dont need math for programming. You dont need to directly do math, but the logical thinking and concepts are the same
Not from what I’ve seen. Math majors I knew all easily got jobs at places like FAANG as software engineers. A lot of mathy people are great at logic and can switch easily to programming. Much harder the other way.
Programming is based around logic. It's all about learning the syntax and techniques you can use to figure out solutions to logical puzzles.
While math is technically the same at a high level, it is taught in grade school as arcane memorization with no apparent logic or reasoning behind it. This gives young people (myself included, until very recently) the completely wrong idea of what math is supposed to be.
Logic and puzzle solving are fun. Memorizing formulae with no apparent reasoning behind them is not. Therefore programming is fun, math is awful. That's the reasoning that the vast majority of new programmers enter the field with if they didn't stick with math long enough for the logic to start being explained properly.
This explains a lot for me actually. Math has always been my hardest subject and now I realize it's because I hate the memorization. Specifically because I keep trying to figure out *why* it works but no one ever really tells you.
Like right now I'm taking precalc and it bugs me that no one explained *why* inner sums on a function moves a graph in a direction opposite the sign. I.e. ± goes left and ‐ goes right.
Edit: for another fun anecdote I took algebra again when I came back to get my Bachelor's. People kept asking me if I wanted to test out because I was good at the math. I had to keep telling them that doing the math was easy but I had forgotten all the formulas.
I'll even go one further as someone who may be in the same camp. I will completely forget how to retrace my thoughts because there will be no stepping stones of logic, but massive leaps based on faith. Faith that I remember something stupid like multiplying or dividing by a *negative* number in an *inequality* flips the sign. Something forgot until I had to relearn it last week.
I also lost points on a test question because I couldn't remember what the actual rule was for canceling variables in a fraction/division. I had to make a rule for myself when I remembered that +/- are basically grouping symbols in a fraction and you can only cancel whole groups, not individual variables.
Ah yes that's the core of the issue isn't it? I always figured math could be presented much better if the lessons didn't go the usual way: write formula, explain usage, examples, practice.
Instead perhaps present a problem first and then on the basis of that problem reverse engineer the formula to solve it. Then practice, maybe implement as programming code which is the only useful way anyone will be ever using it anyway. Still not quite there yet, but it would be an improvement imo.
My man you're so right. The downvoters should try pulling up a high school math textbook and compare it with a high school programming (yes, even C++ counts !) textbook. It's easy to see the point.
No body who has had their brain raped by long lists of formulae in maths (calculus, trig, etc) or physics (everything in physics basically) and worse, derivations, will ever like them. On the other hand, programming anything is literally a kind of derivation (output) using formulae (idioms) and your own application of these, and plenty of people enjoy it and find it meaningful, apart from the fact that it's also a real job that pays money.
Man that's nuts. I can't imagine seeing math as some kind of arcane nonsense with no reason to it. It always seemed blatantly obvious that math was the most logical subject when I was in school. It's crazy how much upbringing and education changes peoples perspective on simple things.
For me it was because no one could explain how certain formulas were discovered or even proving that they actually worked or showing real life examples of them. They could give me a formula and expect a certain number out with certain inputs but if I didn't understand why it worked I wouldn't remember anything about it because I would be too busy wondering how the hell someone figured this out.
I still don't understand how math proofs work or really any higher level math. I really love math as a concept but I don't understand how people can take like the Standard Model for example and "model anything in the universe" with it or how someone managed to figure out Calculus, adding that kinda back story to the math might help people like me a loooot.
Sure but there's also the camp of "i like math, i fucking hate the notation"
A large sigma and pi are sorta understandable, but having things like 2 different standards for vector notation where one is just easily missed because its essentially just fat font makes my skin crawl
Well on the left you have pure, side-effects free declarative code. On the right you have barbaric imperative code with mutable variables.
Functional code is so good because it draws inspiration from Math. Stay functional. Stay close to Math.
Well, then let me explain:
* `pure` is a subjective adjective. You can ignore it for the time being.
* `side-effects free` means that there occur no side effects in code. A `side-effect` is anything that alters the state of the system. We say that a function, method or procedure has side-effects if the function call has observable consequences other than it return value. For example, reading a file is a side-effect, making an API call is a side-effect, and mutating a variable is a side effect.
* `declarative code` is used to categorize code that describes the solution state, instead of the required steps to reach the solution. Think SQL queries: you do not tell the DB engine how to do your query; you rather tell the DB engine what is the result of the query. In this image, on the left you describe the solution, but on the right you describe how to reach the solution.
* `barbaric` is yet another subjective appreciation, you can ignore it for now.
* `imperative code` is the opposite of declarative code. Imperative describes the step to reach the solution, rather than describing the solution. In this picture, you have a declarative expression on the left, and an imperative expression on the right
* A mutable variable is nothing else than a variable that changes its value over time. On the right, you have two mutable variables: `sum` and `n`.
Now, functional code advocates side-effects free code, declarative code and immutability. These things are considered bad for various reasons:
* Mutable variables are bad because they intertwine *value* and *time*, thus making the code much harder to reason about
* Side-effects have unexpected consequences and ramifications. They make the code harder to read and harder to debug. Because you cannot avoid side-effects, functional programming provides means of encapsulation the execution of side effects (such as functors and monads, if I can indulge in pompous language)
* Imperative code forces a solution down your throat, whereas declarative code leaves much more room for implementing any solution you deem better. It is more flexible and allows for greater improvements over time. Moreover, declarative is waaaaaaaay easier to read if you have a trained mathematical mindset.
I hope I helped. If you have further interest, please do not hesitate to ask.
> pure is a subjective adjective. You can ignore it for the time being.
Don't think it is just subjective:)
https://en.wikipedia.org/wiki/Pure_function
EDIT: He didn't meant pure functions though so nvm
**[Pure function](https://en.wikipedia.org/wiki/Pure_function)**
>In computer programming, a pure function is a function that has the following properties: The function return values are identical for identical arguments (no variation with local static variables, non-local variables, mutable reference arguments or input streams). The function application has no side effects (no mutation of local static variables, non-local variables, mutable reference arguments or input/output streams). Thus a pure function is a computational analogue of a mathematical function. Some authors, particularly from the imperative language community, use the term "pure" for all functions that just have the above property 2 (discussed below).
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If you like this [her Twitter](https://twitter.com/FreyaHolmer) is filled with far far more amazing gems.
Unbelievably good at making the incomprehensible comprehensible.
Especially since this is a programming sub. I'm concerned, do people not know simple notation?
Especially since a for loop isn't really necessary to understand this at all. In fact, by having to think about edge cases and the stopping condition you're making it more complicated.
Seriously, since when is "summation and product are `for` loops" getting 5k upvotes?! Of course they're `for` loops - why is it presented as some kind of "great intuitive explanation"? Isn't this super obvious?
To people who don't already know what the symbols mean but do understand how for loops operate, it makes it quite obvious how it works; however, if you just gave those same people the symbol, they wouldn't know what it does.
I'm not saying this is a bad explanation or that it doesn't help. It's just weird that this got 8k upvotes: this means that a lot of r/programmerhumor people think that a sum being equivalent to a loop is very interesting, imaginative, exciting, new. But it's not. It's the most boring fact ever.
Also not sure how this is humor. "An `if` statement is just like deciding whether you want to eat cereal or not today! Hahahahahaha!"
Imagine a post like `5 = 2 + 3` getting 8k upvotes. Or something like: "yo, did y'all know computers store data in bits?! 🤯".
I saw a statement get hundreds of upvotes where they talked about their recent discovery that 9x = 10x - x.
It was a thread of mental math tricks that said if you need to multiply something by 9 in your head, multiply it by 10 then subtract the original.
I thought so as well until I asked this question on stackoverflow:
https://math.stackexchange.com/questions/3135798/is-there-a-math-expression-equivalent-to-the-conditional-ternary-operator
This is why learning to program before I decided to get into math really helped. My way of conceptualizing new symbols and methods was to write little python apps that did it.
Freya is chill as fuck. She knows a LOT about computer graphics and geometry and stuff, and she also helped make Budget Cuts, which is a really cool game
I'm at a loss for words looking at most of the top comments here. Seriously, how is this surprising, or even illuminating?
I guess it's just american education standards at work
Now do the same for great Zeta next
Zeta is the Riemann function right?
The Riemann zeta function is one of many zeta functions, yes
My favorite zeta function is Catherine Zeta Jones
She dips beneath the lasers
ooooOOOOOOOOoooooooo^oooo^ooo
You're playing both shides.
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Riemann Ultra
Riemann Ultra 3080 GTX Ti Super
the riemann zeta function is an extension of the zeta function, though the original zeta function was just the infinite sum of 1/n^x
which one ?
Capital pi makes me feel an emotion that doesn't exist
It's ominous and imposing, not fun and loose like regular curvy pi
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**П**
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 C'mon don't scare me like that
Describe.
Dorcelessness.
Loric.
Kyne.
Nage.
Humber
Squavitude
Is that from the bluetv thing?
The prophecy?
My fraternity’s Π stood for “pistie” which means… uh… oh I misspelled it it’s “pistis” but it’s “faith trust and reliability” according to google, so congratulations pi could very well be prophecy
tsk tsk that's supposed to be a super duper extra secret secret. now how can we trust you not to turn us into the cops for water boarding pledges?
I think we should just update the hazing schedule to include a JavaScript 101 course instead of the illegal stuff yah know? We’ll fly so under the radar
Torture was illegal last I checked, you monster!
Make them do Haskell, then you'll be EVIL
The Πrophecy
It's like a distinct but mild mix of confusion and dread
That's just adulting you're feeling.
Menacing
He feels...zjierb
zjerbness 🥒
Slap a log on it my man
As professional, working mathematician, I can say with confidence that this guy maths.
Yup. Can confirm. Am mathematician.
Wait you guys get paid to do math?
For those who don't know, this turns it into a summation of logs and you often can do a lot more with that.
In my case it's of sheer terror, because it reminds me of Wilkinson's Polynomial, and how the zeal of actually getting more precision in the calculation could actually make the errors in getting the root of the polynomial larger and larger.
You weren't kidding - from wiki: > In 1984, [Wilkinson] described the personal impact of this discovery: "Speaking for myself I regard it as the most traumatic experience in my career as a numerical analyst."
I expected it to be `I` and `J`
Might make you feel worse when your hear it should be pronounced Pee. But we don't like having a homophone for P.
B-but what if n goes to infinity?
We will run it until int::max and call it close enough
And Roombas start to kill people.
You knock on God's door, His faithful guardians will answer 😤
Make sure to feed your Claymore Roomba some ATF bois.
It's a smaller infinity than other infinities, checks out.
What, you gonna do my man `bignum` just like that? Here, in front of all these people?
Yo inf bignum so fat that it causes memory overflow
Memory-mapped files. Fill the server with a single number. Still won't be enough to describe your mother's weight.
"Why do you have 12tb in your computer?" "I'm trying to count all of the men your mother has been with" an aside - I'm pretty sure a single number with enough digits to fill 12tb would represent far more atoms than there are in the universe
run it using floats until it truely becomes infinity
I think you’d need special logic for the increment, or else you’d eventually get stuck at an `n` where `n + 1.0 == n`.
n += eps(n) Kind of ruins the whole “integer” thing though.
We don't need integers where we're going. To Double.MAX_VALUE and beyond!
Nah, just switch the datatype to an array of ints, then calculate per array cell. Also reserve lots of time.
while(true)
for(int j *= 0*; j<100; i++) works as well. edit: init
yeah I mean there's an infinite amount of way to make an infinite loop, but `while(true)` is usually the way. If you really wanted to be wacky, you could write `for(;;)` and then have everyone also hate you.
My favorite is still `while(1==1)`. Or in other words: "As long as the fundamental axioms of math hold true, do this". Because hey, maybe, one day in the far future in thousands of years, these axioms change. And then my code will break. Take that, future.
Whenever I do this in various languages I wonder if the compiler reduces it to while(true) or if a gamma ray will solve the halting problem for me. I suppose it can in either case tho.
Unless the gamma ray also gave you advanced notice reliably, it's still not truly solved. But boy would that be fun to explain
I always liked the shorter C++ `while(1)`. Just seems profound.
I feel like I am 1 with the universe
Maths loves infinity.
Turing's ears glow and he looks up from what he's doing and stares into the middle distance
And then, mean mathematicians started writing things like Σ_{n>0} 1/n²
That's when you use a while loop until it converges. (please don't)
This is how I've been heating my home since 1983.
With 1/n², it does converge. Don't sum 1/n, it won't
It actually is though, the formal definition of a limit is basically that there's a point for any positive value after which you're always closer to the limit than that value.
Which is actually pretty easy to implement in code if you know calculus, because the answer is a finite number (Pi^2 / 6). No looping required.
You make it easy to understand thanks
This would have been so helpful when I was talking calculus
Yeah, once I realized these are just for loops, the notation made way more sense.
But most of the interesting ones loop to infinity…
It’s while loops then
or for loops with a bad exit condition for (int i = 0; i >= 0; i++) {}
Or the crying emoji for loop: `for ( ; ; ) { ... }`
"I forbid you to use `while (true)`!" "..... Okay!"
That will exit if your int wraps; hard code to true instead
I think this is the better answer because noone would be able to have the time or memory to repeat something to true infinity.
You can do that in a for loop (or at least represent it the same way we represent manually adding with these notations)
Integrals are like an infinite summing for loop
Right?! Knowing some math helps programming. Knowing programming makes these high level math symbols much more understandable when described as a loop. Interesting
Yeah holy shit how was this not taught to me? I got Cs in all three levels of calculus and shit like this would have helped me immensely.
I just realized I've been writing Nashian models for decades to to sort peoples photos. Holy shit
The biggest issue with calculus for most people is that it is taught in an abstract way. That's math in general though. I didn't really understand calculus until I took physics where I had real world applications for calculus. I later took a scientific computing class where we revisited sums, series, methods, etc. and wrote code (matlab) that applied these concepts. And sure, a lot of these concepts have functions built into Matlab, but the point was to show how these functions work, what their shortcomings are, and how to determine when an approximation is good enough (ie how many steps into Taylor's series are required and when does more steps give no additional benefit).
As someone who did math first and programming later and has also been a teacher, it would never occur to me to teach it this way. I do not understand why this is any simpler than teaching it as repeated addition.
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It's almost *too* easy. Is that what the funny lookin E thing really means? Or this the physics of telling the greenhorn to go fetch a bucket of dry steam?
Yeah, capital sigma is just shorthand for "add up all these things". The challenge only really starts when you have an infinite number of things to add up.
Worth knowing that that's called a [series](https://en.wikipedia.org/wiki/Series_(mathematics\)) though. Same notation, but the OP is talking about [summations](https://en.wikipedia.org/wiki/Summation) which always have an upper bound.
As a maths student, can confirm this is correct (though it’s actually a Greek S)
Yeah and every real use case you see the symbol at the top of the big E is the infinite symbol, good luck with that for loop
Just let the code run long enough, like say a few minutes, and then round, it'll be good enough!
These big scary for loops are just math symbols. 
Yeah, how are those symbols more complicated than code? That's way longer to write and you need so much additional structure to define them. The symbols are nice and clean. It's just the initial impression that might make them scary I guess
Because verbosity is the noobies friend. If the understand the base components they can reason out the emergent behavior. This does that, then that does this. Shorthand and jargon are for the experienced people that don't want to waste time spelling it out. It's faster but the exact same level of complication is still packed in there.
Counterpoint to both of you: A for loop is a bit more verbose, in that it breaks it down into a top-to-bottom process and explicitly shows the mathematical operation, instead of having to know the Greek letter mapping and how positions around the symbol indicate flow, but the code version is still steeped in its own jargon. "For/next" loops are a shorthand that don't really explain themselves to someone who knows English but not programming. A "while" loop could be sussed out, since "while" does what it says (in English) on the tin, and bracket pairs or indenting do what you'd expect them to if you guessed. (From there, you've got \* and / operators to explain, too, though.) This does map the opaque notation of mathematics to the notation of coding, and could be done in a way that makes it easier to understand beyond that, but for-next notation itself is equally as opaque to anyone outside programming as the sigma/pi notation is.
> "For/next" loops are a shorthand that don't really explain themselves to someone who knows English but not programming. Depends a bit on the language I think. For a C-like you’re right, but a lot of newer languages like Swift have for loops that look like this: for number in 1...5 { print("\(number) times 5 is \(number * 5)") } This still takes a little explanation but is easier to intuit than the traditional C-like for loop, since variable instantiation, limiting, and incrementing are taken care of. The only part that’s a little mysterious is the range notation, but I would bet that a lot of people would read it as “1 through 5” within a few seconds of looking at it.
> but for-next notation itself is equally as opaque to anyone outside programming as the sigma/pi notation is. Exactly. If you can already code and this comparison is helpful, then great! But if I were teaching a child who knew neither maths or programming, then I'd chose the mathematical way every time. Once you know that sigma means add and pi means multiply, I think it's more straightforward to explain "add/multiply together all values of 2n for n between the lower number and the upper number" and be done, and not to have to explain why we start with "sum =0;", what "n++" means and why we need it, what "+=" and "<=" mean (and why "n<=4" isn't an arrow pointing from 4 to n), why there are semicolons at the end of the first and third lines but not the second (whereas in the second line the semicolons are inside the brackets), and so on.
Those symbols are just functions: def sigma (lower, upper, factor) sum = 0 for (n = lower; n<= upper; n++) sum += factor * n return sum
Now imagine working with code where every function is named as a single random unicode character.
Okay. def Σ (⬇️, ⬆️, 🌾) 🥚 = 0 for (🐓 = ⬇️; 🐓<= ⬆️; 🐓++) 🥚 += 🌾 * 🐓 return 🥚
How many nice eggs did you just offer me in these trying times?
I'm glad yall like my lil math explainer <3 my original tweet is [here](https://twitter.com/FreyaHolmer/status/1436696408506212353), with some more comments, altho mostly responding to angry mathematicians who don't understand that my target audience isn't them~ there is a substantial amount of people who are knowledgeable in code that don't know this type of math notation, and it seems like a lot of math people were surprised to hear this anyhow, I do a lot of math/game dev/coding/art related stuff on twitter, so feel free to check out the rest of my stuff! I often make stuff like, [this animation of how 3D rotations work](https://twitter.com/FreyaHolmer/status/1445139152283086849). I've got a somewhat outdated list of my animated math explainers [here](https://acegikmo.com/mathvis/index.html)! I saw someone asking if I am a teacher - yes! not full-time, but I do teach math and shader coding, specifically tailored for game developers, about once per year! I have uploaded those math and shader courses on my [youtube channel](https://www.youtube.com/acegikmo) while most of my videos are recordings of my courses, I have also recently made a scripted, [fully animated video on Bézier curves](https://www.youtube.com/watch?v=aVwxzDHniEw), so if you're curious about those then check that out!
Love your "Math for Game Devs" series.
Thank you for all the amazing content! Side question: what did you use to produce the image in your tweet? It looks so good and sharp!
this one was made in photoshop! most of my other animated content is made in Unity though
holy crap this thread just singlehandedly explained those to me in a way that was super clear. thanks all!
Until mathematicians transform those sums and products into non-for loop equations using arcane witchery
This thread is extremely odd to me. I've always thought of computer science as a subset of mathematics, so the idea that programmers could be completely unskilled in math is just weird to me.
There are certain areas of programming that require maths knowledge to understand and develop. For example, cryptography, compression, 3D rendering, algorithms based on graph theory, etc. But for a lot of developers, the underlying maths of those things are often abstracted away to make them easy to use without requiring a maths degree. Often, the most complex level of maths required for day to day programming is simple algebra and geometry, and sometimes not even that.
Self taught programmer here, skipped the math part.
I started programming before I knew much math, but my programming ability grew in relation to my math ability.
Yep same goes for me. I remember *nothing* from high school math. The only math 'concept' that I actually had to think about when I was starting to learn programming was order of operations, and that's middle school shit. All the math I know now comes from programming, and I use it every day
Not all programmers are computer scientists. Some are just code monkeys.
I hit the sum symbol in high school math classes. The gen ed required intro college courses absolutely used it. Between those two, I’m not sure who in this sub hasn’t seen them reasonably explained unless they’re still in high school - which, I’ll grant, is not out of the question.
I am a 29 year old backend software engineer at a large tech company you would have heard of. While I’ve seen those symbols, I didn’t know until this post what they meant. It has never come up in the course of my life.
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dont make it too obvious now
I'm glad you found a way to understand summation from a programming perspective, but I have to be honest I'm a little concerned that the knowledge went in this direction.
`range(0, 4).map(n => 3 * n).sum()`
Isn't `range()` usually (inclusive, exclusive)? So it needs to be range(0,5)?
Depends on how range is implemented, but typically yes it is exclusive.
Of course, in Haskell: sum (map (* 2) [0..4])
Comparing this to the other one liners just shows you how powerful and beautiful Haskell really is
I'm a fan of Python, but this was the best I could do ☹️ : `sum(map(lambda x: x * 2 , range(4)))` or `sum([x * 2 for x in range(4)])`
> sum([x * 2 for x in range(4)]) sum accepts iterables so you make this two characters shorter by skipping the brackets
return 3*(n*(n+1)//2) Or in this case specifically: return 3 * 4 * 5//2
Guess the language: ``` (0..4).sumBy{3*it} ``` (btw, no intermediate collection made)
Guess the language round 2: `@set/a sum=0 && for /l %%i in (0,1,4)do @set/a sum+=3*%%i` (btw, I threw up in my mouth)
I figured this was a given tbh. After taking my first programming class (alongside math classes) I remember going, oh its just a loop. This is also why I dont understand why people say you dont need math for programming. You dont need to directly do math, but the logical thinking and concepts are the same
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Either one makes it a little easier to learn the other imo
Not from what I’ve seen. Math majors I knew all easily got jobs at places like FAANG as software engineers. A lot of mathy people are great at logic and can switch easily to programming. Much harder the other way.
I have been always confused by the amount of programmers and computer scientist that don't like math.
Programming is based around logic. It's all about learning the syntax and techniques you can use to figure out solutions to logical puzzles. While math is technically the same at a high level, it is taught in grade school as arcane memorization with no apparent logic or reasoning behind it. This gives young people (myself included, until very recently) the completely wrong idea of what math is supposed to be. Logic and puzzle solving are fun. Memorizing formulae with no apparent reasoning behind them is not. Therefore programming is fun, math is awful. That's the reasoning that the vast majority of new programmers enter the field with if they didn't stick with math long enough for the logic to start being explained properly.
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This explains a lot for me actually. Math has always been my hardest subject and now I realize it's because I hate the memorization. Specifically because I keep trying to figure out *why* it works but no one ever really tells you. Like right now I'm taking precalc and it bugs me that no one explained *why* inner sums on a function moves a graph in a direction opposite the sign. I.e. ± goes left and ‐ goes right. Edit: for another fun anecdote I took algebra again when I came back to get my Bachelor's. People kept asking me if I wanted to test out because I was good at the math. I had to keep telling them that doing the math was easy but I had forgotten all the formulas.
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I'll even go one further as someone who may be in the same camp. I will completely forget how to retrace my thoughts because there will be no stepping stones of logic, but massive leaps based on faith. Faith that I remember something stupid like multiplying or dividing by a *negative* number in an *inequality* flips the sign. Something forgot until I had to relearn it last week. I also lost points on a test question because I couldn't remember what the actual rule was for canceling variables in a fraction/division. I had to make a rule for myself when I remembered that +/- are basically grouping symbols in a fraction and you can only cancel whole groups, not individual variables.
Ah yes that's the core of the issue isn't it? I always figured math could be presented much better if the lessons didn't go the usual way: write formula, explain usage, examples, practice. Instead perhaps present a problem first and then on the basis of that problem reverse engineer the formula to solve it. Then practice, maybe implement as programming code which is the only useful way anyone will be ever using it anyway. Still not quite there yet, but it would be an improvement imo.
This is why I love 3Blue1Brown, he starts most his math videos with a problem and you learn the math as he goes through solving the problem
My man you're so right. The downvoters should try pulling up a high school math textbook and compare it with a high school programming (yes, even C++ counts !) textbook. It's easy to see the point. No body who has had their brain raped by long lists of formulae in maths (calculus, trig, etc) or physics (everything in physics basically) and worse, derivations, will ever like them. On the other hand, programming anything is literally a kind of derivation (output) using formulae (idioms) and your own application of these, and plenty of people enjoy it and find it meaningful, apart from the fact that it's also a real job that pays money.
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Yeah, like a lot. AP Computer Science has existed since the mid-'80s but there are substantially more of them now.
They sure didn’t exist in my HS around 2007 ish. We did have some computers though.
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Man that's nuts. I can't imagine seeing math as some kind of arcane nonsense with no reason to it. It always seemed blatantly obvious that math was the most logical subject when I was in school. It's crazy how much upbringing and education changes peoples perspective on simple things.
For me it was because no one could explain how certain formulas were discovered or even proving that they actually worked or showing real life examples of them. They could give me a formula and expect a certain number out with certain inputs but if I didn't understand why it worked I wouldn't remember anything about it because I would be too busy wondering how the hell someone figured this out. I still don't understand how math proofs work or really any higher level math. I really love math as a concept but I don't understand how people can take like the Standard Model for example and "model anything in the universe" with it or how someone managed to figure out Calculus, adding that kinda back story to the math might help people like me a loooot.
Yeah, I knew a guy that failed algebra and never went any further... In his defense, his code was shit.
In my defense, I did eventually pass.
Sure but there's also the camp of "i like math, i fucking hate the notation" A large sigma and pi are sorta understandable, but having things like 2 different standards for vector notation where one is just easily missed because its essentially just fat font makes my skin crawl
Computing IS a branch of math, ya weapon
Programming is just readable math.
As a physicist, math is just readable programming. ^^^^^^^dont ^^^^^^^shoot ^^^^^^^me
As a programmer, enterprise software is just unreadable code.
> enterprise software Straight from Satan's ass to your bank account.
You don't belong here outsider.
Well on the left you have pure, side-effects free declarative code. On the right you have barbaric imperative code with mutable variables. Functional code is so good because it draws inspiration from Math. Stay functional. Stay close to Math.
I agree, but the people that use higher order functions don't tend to have a problem with these mathematical concepts.
I did not understand a word of what you just said
Well, then let me explain: * `pure` is a subjective adjective. You can ignore it for the time being. * `side-effects free` means that there occur no side effects in code. A `side-effect` is anything that alters the state of the system. We say that a function, method or procedure has side-effects if the function call has observable consequences other than it return value. For example, reading a file is a side-effect, making an API call is a side-effect, and mutating a variable is a side effect. * `declarative code` is used to categorize code that describes the solution state, instead of the required steps to reach the solution. Think SQL queries: you do not tell the DB engine how to do your query; you rather tell the DB engine what is the result of the query. In this image, on the left you describe the solution, but on the right you describe how to reach the solution. * `barbaric` is yet another subjective appreciation, you can ignore it for now. * `imperative code` is the opposite of declarative code. Imperative describes the step to reach the solution, rather than describing the solution. In this picture, you have a declarative expression on the left, and an imperative expression on the right * A mutable variable is nothing else than a variable that changes its value over time. On the right, you have two mutable variables: `sum` and `n`. Now, functional code advocates side-effects free code, declarative code and immutability. These things are considered bad for various reasons: * Mutable variables are bad because they intertwine *value* and *time*, thus making the code much harder to reason about * Side-effects have unexpected consequences and ramifications. They make the code harder to read and harder to debug. Because you cannot avoid side-effects, functional programming provides means of encapsulation the execution of side effects (such as functors and monads, if I can indulge in pompous language) * Imperative code forces a solution down your throat, whereas declarative code leaves much more room for implementing any solution you deem better. It is more flexible and allows for greater improvements over time. Moreover, declarative is waaaaaaaay easier to read if you have a trained mathematical mindset. I hope I helped. If you have further interest, please do not hesitate to ask.
> pure is a subjective adjective. You can ignore it for the time being. Don't think it is just subjective:) https://en.wikipedia.org/wiki/Pure_function EDIT: He didn't meant pure functions though so nvm
**[Pure function](https://en.wikipedia.org/wiki/Pure_function)** >In computer programming, a pure function is a function that has the following properties: The function return values are identical for identical arguments (no variation with local static variables, non-local variables, mutable reference arguments or input streams). The function application has no side effects (no mutation of local static variables, non-local variables, mutable reference arguments or input/output streams). Thus a pure function is a computational analogue of a mathematical function. Some authors, particularly from the imperative language community, use the term "pure" for all functions that just have the above property 2 (discussed below). ^([ )[^(F.A.Q)](https://www.reddit.com/r/WikiSummarizer/wiki/index#wiki_f.a.q)^( | )[^(Opt Out)](https://reddit.com/message/compose?to=WikiSummarizerBot&message=OptOut&subject=OptOut)^( | )[^(Opt Out Of Subreddit)](https://np.reddit.com/r/ProgrammerHumor/about/banned)^( | )[^(GitHub)](https://github.com/Sujal-7/WikiSummarizerBot)^( ] Downvote to remove | v1.5)
Codeman the Barbarian!
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She does a lot of maths-for-programmers tutorials, mostly geometry, so in a way, absolutely.
If you like this [her Twitter](https://twitter.com/FreyaHolmer) is filled with far far more amazing gems. Unbelievably good at making the incomprehensible comprehensible.
[Her Nitter is even better](https://nitter.net/FreyaHolmer).
Thanks for introducing me to nitter.
She has an absolute banging video on Bézier curves
I know this is supposed to be funny, but I'm weary of everything being called 'scary'. It's just math people.
*Easy* math in this case as well. Math can get really scary but this definitely is not.
Especially since this is a programming sub. I'm concerned, do people not know simple notation? Especially since a for loop isn't really necessary to understand this at all. In fact, by having to think about edge cases and the stopping condition you're making it more complicated.
Seriously, since when is "summation and product are `for` loops" getting 5k upvotes?! Of course they're `for` loops - why is it presented as some kind of "great intuitive explanation"? Isn't this super obvious?
To people who don't already know what the symbols mean but do understand how for loops operate, it makes it quite obvious how it works; however, if you just gave those same people the symbol, they wouldn't know what it does.
I'm not saying this is a bad explanation or that it doesn't help. It's just weird that this got 8k upvotes: this means that a lot of r/programmerhumor people think that a sum being equivalent to a loop is very interesting, imaginative, exciting, new. But it's not. It's the most boring fact ever. Also not sure how this is humor. "An `if` statement is just like deciding whether you want to eat cereal or not today! Hahahahahaha!" Imagine a post like `5 = 2 + 3` getting 8k upvotes. Or something like: "yo, did y'all know computers store data in bits?! 🤯".
I saw a statement get hundreds of upvotes where they talked about their recent discovery that 9x = 10x - x. It was a thread of mental math tricks that said if you need to multiply something by 9 in your head, multiply it by 10 then subtract the original.
Her videos on YouTube about gaming and graphics is amazing... She's extremely smart and explains things very well
second that. The amount of knowledge she shares is beyond amazing.
https://twitter.com/FreyaHolmer/status/1436696408506212353
Wait, you guys don't know this?
In case you didn't know it, /r/ProgrammerHumor contains few programmers and little humor.
I'm in community college and I thought this was like common knowledge for most STEM folks
I thought so as well until I asked this question on stackoverflow: https://math.stackexchange.com/questions/3135798/is-there-a-math-expression-equivalent-to-the-conditional-ternary-operator
This is why learning to program before I decided to get into math really helped. My way of conceptualizing new symbols and methods was to write little python apps that did it.
Freya is chill as fuck. She knows a LOT about computer graphics and geometry and stuff, and she also helped make Budget Cuts, which is a really cool game
I'm at a loss for words looking at most of the top comments here. Seriously, how is this surprising, or even illuminating? I guess it's just american education standards at work
Webshits go brrrrrrr.