you actually do need one thousand different graphic tshirts to survive and dont listen to anyone who tells you different
More you might like
pasta expands and spinach shrinks. if we could have them mate we may be able to creayte a food which does not change at all when cooked
Oh, so those are your tags.
Where does the -1/12 come from? I'm not familiar with this math equation/proof.
Edit. Well, not -1/12, but whatever they are talking about here.
Idk how much background you have so I'll just go over everything
This is all about what's called the Riemann zeta function. (It's important because of its properties relating to prime numbers but that's not really relevant to this.) It's a function that equals the sum of 1 over all positive whole numbers to the s power
When s is a positive number this works out, since even though you're adding up infinitely many numbers, the exponent in the bottom of the fraction means they're getting smaller and smaller, so the total converges towards a finite final answer. One cool fact is that when s equals 2, the final sum actually equals pi squared over 6
The problem is that this all only applies when s is greater than 1. (Or, for a complex number, if the real part of s >1. If you don't know what that means then don't worry about it.) If s were a negative number, then the numbers you're adding up would actually be getting larger and larger (since a negative exponent in the denominator is the same as a positive exponent in the numerator) and the sum would grow infinitely large
This is why the function isn't defined this way when s is less than or equal to one. Mathematicians have agreed on a different (much more complicated) way of calculating what the function is supposed to equal for smaller values of s, and it's not the same as the infinite sum from earlier. (Extending the definition of a function outside of the domain where it originally works like this is called analytic continuation)
The "1+2+3+..." sum arises when you try to plug in s=-1 using the infinite sum definition. That is just the equivalent of adding up every positive whole number, which of course would just be infinite. It just so happens that the actual accepted value of the function when s=-1 is -1/12, so that's where this supposed equivalence comes from. In case it wasn't clear, they're not equal
I believe this misconception was popularized by a Numberphile video, which didn't go into that much detail and didn't highlight some important caveats. Basically, they didn't make it clear enough that "1+2+3+...=-1/12" isn't actually true and that the proofs they showed relied on some false assumptions. (Deliberately false ones I'm sure, these guys aren't stupid! Numberphile's videos are usually still pretty good for a general audience, not trying to slander them or anything)
What's interesting though is that for a different way of calculating the infinite sum (Ramanujan summation) you actually do get -1/12. The analytic continuation from earlier that defines the function differently also gives -1/12. So there definitely is some sort of connection to the sum of all positive whole numbers, but it's way more complicated and less memeable than (the obviously wrong) "the sum of infinitely positive whole numbers is a negative fraction"
If you want to learn more about exactly how this comes about this video gives a pretty good breakdown
And if you want a more in-depth look at the function itself and the idea of analytic continuation there's this one. I just love this guy's videos so much
i made a free, open source, web-based chip’s challenge (1+2) emulator a bit ago
features include:
- works both on a computer and on a phone… more or less
- comes with ~800 community levels, plus it can load levels in any format (including from the commercial games, either the classic version or the ones on Steam)
- built-in level editor where you can make your own levels and share them with just a link
- totally original art, sounds, and music, though you can load in the classic tileset if you really want to
- undo and rewind
- now you are a fox solving puzzles for fun, instead of bill gates being kind of weird about a girl
- a couple tiny emulation bugs still, oh well
✨ Lexy’s Labyrinth ✨
am i insane or should masks be mandated for hospitals as a permanent installation. a forever institution. always. covid is an irrelevant factor when hospitals are always full of both very sick and very immunocompromised people..?
0x4468c7a6a728 asked:
do you have a favorite programming language
daemonhxckergrrl answered:
PHP xD
okay no, uhhh not really ? languages are languages. from what i’ve used and seen used (i do enjoy a good programming stream) i’ve come to the conclusion that aside from a few real fucking useful features pretty much everything is just window decoration.
i dislike static memory allocation and having to realloc arrays, but otherwise i find C is great. it does what it does and it does it well. i imagine i would fine C++ tolerable if i tried it, but i really don’t care much for OOP.
weirdly enough, despite having classes and being all microsoft, C# actually looks decent. i’ve not used it (or mono) first-hand but the semantics seem comfy and the syntax is just regular curly-brace stuff.
i love the concept of stack-based languages, but if i’m completely honest the paradigm of an imperative language that’s explicit is way more comfy.
POSIX sh is hell though. i use it for compatibility reasons (otherwise i would actually learn all the cool features of zsh) but the moment you wish to have anything resembling a proper utility you either gotta switch to python and import one of those GNU flag parser modules, or you’re rewriting entirely in C.
so yeah, no i don’t have a favourite. maybe i will someday, maybe i will never.
yeah idk if i really have a favorite either, there are certainly languages i prefer for specific tasks (like i usually use python if i want to write a quick script, or rust if i want to do something lower level for example), but i don't think i could actually pick a favorite
It's Python for me, just because it's the right language for most of the stuff that I do (data analysis, machine learning, and goofy little math toys.) I'm very aware of its faults, it's just that I very rarely do things where a different language has appreciable benefits. And the depth of third party libraries for it is freaking enormous.
If I needed speed and like, proper hackeriness instead of just "mathematician in a hacker Halloween costume" I'd probably learn rust. Maybe C#.
python is great ! my dislike of having to switch to it bc a shell script grew out of hand is a limitation of POSIX sh and not an issue w/ python. such an easy language to grok and to just shove data into.
rust is a language i never understood why people thought it hard until i started learning proper compiled languages and then watched people try to make rust projects and now yeah i think rust is cool but wow that's a lotta stuff you have to get to use it well.
i do think it's good that rust forces you to catch pretty much all cases and possibilities though ! like no you gotta expect that might return an invalid value to pass to this function. you may get a value you may get nothing. you need to make sure you're not affecting other functions that may need an unmauled version of this data.
there's something in me that can't get past wanting to write a script first in POSIX sh (i refuse to use bashisms and my login shell is zsh) and then when it's too difficult bc you gotta process more complex data do i switch to python.
my resnvim script started life as a shell script and only moved to python so i could use some level of flag and argument handling. which i do badly xD trying to write an arg parser that can properly handle all flags and their options as complies w/ GNU and BSD and POSIX standards in pure POSIX sh is hell and you should never do it. use python. or C if it's gonna be a proper utility.
i have python installed on my phone. that probably says something about the level of the kind of projects i tend to do in python; but it's perfect for those.
i'm a rare breed for not entirely disliking pure C, and am a fan of "simpler" assembly languages (stuff like 6502 or z80).
job is C# tho and that's entirely reasonable too, especially for bigger projects (it's a shame the microsoft tools suck tho). honestly as long as i don't have to touch too much javascript i'm happy.
if feels like every language has it's purpose, and if you use them for their intended purpose every language is fine.
that last part !! I think you described some of the C hate. people trying to use it in places it isn't suited.
python on your phone ?? now I'm intrigued :3
ALTpython on my phone. pydroid3. it sucks and is awesome just like my life.
