6 ms·
sin(x) ~~ x only in radians, so honestly that's reason enough. Once in a while we get programmers wanting to disrupt mathematical notation for whatever reason.
by doliveira 4y ago
sin(x) ~~ x only in radians, so honestly that's reason enough.
Once in a while we get programmers wanting to disrupt mathematical notation for whatever reason... Worst I've seen so far was one arguing that equations should be written with long variable names (like in programming) instead of single letters and Greek letters. Using turns because it's a little easier in specific programming cases is just as short-sighted, I'd say, it doesn't "scale out" to the myriad of other applications of angles.
- MayeulC 4y agoThat's only for small angles though (stems from Taylor's expansion). With other units, you have a conversion factor, but it remains true enough at small angles.
- fbanon 4y agoOr just defining the result of division by zero as zero "for safety": https://www.hillelwayne.com/post/divide-by-zero/ https://www.hillelwayne.com/post/divide-by-zero/ It boggles the mind, truly!
- jgwil2 4y agoAre you claiming the author is incorrect that x/0 = 0 is mathematically sound?
- littlestymaar 4y agoDepends how you define “soundness”, but the idea of prolonging a function out of its definition domain with an arbitrary value that doesn't make it continuous is arguably a curious one. From an algebra perspective (the one given in the blog post) it may be fine, but from a calculus perspective it's really not. The lack of continuity really hurts when you add floating points shenanigans into the mix, just a fun example: When you have 1/0 = 0 but 1/(0.3 - 0.2 - 0.1) = 36028797018963970. Oopsie, that's must be the biggest floating point approximation ever made.
- fluoridation 4y agoBut for 1/x you have that issue anyway. If x is on the negative side of the asymptote but a numerical error yields a positive x, you'll still end up with a massive difference.
- RunSet 4y agoI don't know about "mathematically sound" but I would rather retain the convention that any number divided by itself equals 1.
- hutzlibu 4y agoWhats wrong with long variable names?
- doliveira 4y agoTry to solve the Schrodinger Equation for even an infinite well using long variable names. I'm not talking about using it in code, I'm talking about someone arguing that books and articles should do it as well.
- achn 4y agoYou can use whatever notation you want for your own work, but documenting with, at least, formal variable definitions would be a significant boon for math literacy.
- Olreich 4y agoIf you go watch math lectures, there's a bunch of "x means Puppy Constant" or, "let's substitute in k for the Real component", or "let's signify <CONCEPT> by collecting these terms into a variable". My argument wouldn't be to replace ALL the variables with meaningful names, just the ones with a lot of meaning that a reader might not understand. It'd also be great if constants, variables, and functions all got naming conventions. Lowercase letters are variables, all caps for constants, etc. It saves a little bit on writing to shorten the variable names, but if the goal of math is to share and spread knowledge within the community or without, better naming and less-memorization would both help. You can also rename things for the working out and use friendlier names for the final equations, just tell people how you're renaming them and everyone will follow along and the programmers will stop trying to sell you one readable code. Most importantly the flat dismissal and horror that many express when someone brings up adjusting the symbolic traditions of Maths should be investigated. Engage with why you feel so strongly that anything other than rigid adherence to tradition is sacrilege. Based on what I've heard, in order to be a great Mathematician, you need to hold onto tradition lightly and think outside the box. Rigid adherence to tradition doesn't sound like that to me.
- doliveira 4y ago
- Aardwolf 4y agoThose perfect radians use 2*pi, aka tau, though, a different math notation issue, where mathematicians have chosen the wrong option (imho) and a case for disrupting that part of math notation, to make radians easier to teach: 1/4th of a circle could be tau/4 radians, 1/8th could be tau/8, etc..., instead of confusing halved factors with radians expressed as amount of pi. Regarding long variable names: I'd rather have long variable names, than a mathematician using some greek symbol in formulas without telling what the meaning of it is (and it could be different depending on their background). But I have no issues with the single letter variables if they're specified properly.
- throwaway9870 4y agoJust out of curiosity, where did tau come from? I never heard of it used for 2pi, and frankly, it seems like a poor choice because in engineering it is one of the most common symbols used (time constant tau).
- airblade 4y agoLook up the Tau Manifesto: it’s all explained there.
- grey_earthling 4y agohttps://tauday.com/ https://tauday.com/ is a good entrance to this particular rabbit-hole.
- nkurz 4y ago
- ncmncm 4y agoThat is the way to do the math, but not the way to write the code. That said, I would like for my compiler to combine any multiplications involved down to one factor for input to the fastest sin/cos operations the machine has. And, to treat resulting multipliers close enough to 1, 1/2, and 1/4 as exact, and then skip the multiplication entirely. But the second part is a hard thing to ask of a compiler.
- doliveira 4y agoYeah, seems to me that languages should allow way more semantic expression than most do today. I wish I had done CS, those kinds of compiler optimization sounds so fun. I'd love to work on that
- ncmncm 4y agoGood news, optimization is engineering, not CS. CS is all about what a program would eventually do, if you were ever to run it. Once you run it, you have moved to the domain of technicians. Engineering is about making it run better.
- xchip 4y agoLOL
- RunSet 4y ago> Worst I've seen so far was one arguing that equations should be written with long variable names (like in programming) instead of single letters and Greek letters. That could never work. If anything the words comprising mathematical texts should be defined once and thereafter truncated to their first letter to reduce cognitive burden and facilitate greater comprehension. c = "could"; d = "don't"; f = "for"; g1 = "go"; g2 = "great"; i = "it"; i2 = "i"; m = "me"; s = "see"; w = "works"; w2 = "what"; w3 = "wrong" i w g2 f m; i2 d s w2 c g1 w3.
- chucksmash 4y agoReference Error: s is not defined.
- RunSet 4y agoThanks for the correction. I will be sure to credit you in the acknowledgements.
- NohatCoder 4y agoWhat really bothers me is that mathematicians seemingly never distinguish between doing and presenting mathematics. You can do your own scribbles with single letters, so do I, it works fine. But when you present maths in a scientific article, maths book, Wikipedia article or similar, your convenience as a writer should be secondary. Your task is to present information to someone who does not already know the subject. Presenting an equation as six different Greek letters mashed together means that the equation itself convey almost no information. You need a wall of text to make sense of it anyway.
- aaaaaaaaaaab 4y agoUh oh. I see you didn’t yet encounter the Einstein-notation for tensors :-)