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#countability
trivalentlinks · 9 months
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does it ever strike you as weird that there are uncountably many real numbers, but only countably many can be named or precisely described in the english language in a finite amount of time?
obviously all rational numbers can be described in a finite amount of time
("53623562112541251251345146*10^2452/426257567257" is something you can say in a finite amount of time)
so can anything that can be built out of roots of integer polynomials ("algebraic numbers")
("square root of 7 plus 38 times the cube root of 17, divided by the seventh root of 2011")
but also there are lots of non-algebraic numbers that can be described in the english language in a finite amount of time
"the circumference of a circle divided by its diameter"
"euler's number"
"the limit of the series \sum 1/10^(n^3+n^n)" (probably, i don't actually know for sure that this one is non-algebraic, but it's definitely irrational)
"the fine structure constant" (i guess it's unknown whether this is rational or algebraic or anything)
but even with all this, we can name and describe so many numbers, not just all the (infinitely many) whole numbers, rational numbers, algebraic numbers, but so many more than that, and yet there's still way more that could never be named
like we can name all the stars, we can name every atom in the universe and infinitely more universes than that, but we can't name all the numbers between 0 and 1?
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mjlxnau8kf7r5 · 1 year
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snail-and-snail · 2 years
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countability
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magpielark · 28 days
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I should be in bed but the gays have captured me again
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latenightsundayblues · 6 months
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Just remembered the time I downloaded an AI image generator app back when the craze started and typed "jesse pinkman in a supermarket"
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Hes just like me fr......
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smuggonifico-lmao · 7 months
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Holy shit you actually made me google and semi-study what magazine pages could look like and what layout is good and what isnt- Im- ehm happy dtiys? anyway!!!! Happy 5k holy shit thats incredible @tangledinink, incredibly incredible even!!!! You deserve it
(also if the quality is shit, i apologize. Not only did my technology put it through the wringer while i was tryna edit some stupid mistakes out, tumblr also decided to make it worse smhhhh)
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lipshits-continuous · 6 months
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Coming up with solutions to maths problems over text whilst half sleepy is a vibe honestly
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kaftan · 5 months
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I literally have not stopped being haunted by amy saying she just wanted someone to hug her one last time
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thefloralmenace · 2 months
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@kaapstadmk @80sdragonbreath Which one of you fixed Wegman's? 😂
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adaptingant · 1 year
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Wanna know an anagram of Banach-Tarski?
Banach-TarskiBanach-Tarski
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angeliteonfridgeduty · 3 months
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so fun fact
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...this is my absolutesolver page. i put absolutesolver there on occasions because i just do. i have owned it for a few months at this point and now i decided i must showcase it to the internet.
congrats, yall can witness my sheer lack of sanity now.
murder drones is consuming my brain
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nordic-language-love · 7 months
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Talking to my Japanese colleague about Japanese vs English and I said how it's not easy to just say 'and' in Japanese and she was really confused. So I was like... y'know, there's と、くて、で、し、や、とか and she was like "oh yes, of course! I never really thought about it like that!" Truly amazing how what we think of as simple and second nature in our native tongue can be unnecessarily, mind-bogglingly complicated to a someone learning that language.
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*opens google* "how to sign of an email in a smart casual way" *google is inept* *opens tumblr* "HOW SIGN OF EMAIL SMART CASUALLY HLEP"
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elavoria · 5 months
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WIP Whenever
Tagged by @boethiahspillowbook, thank you m’dear! I tag @nostalgic-breton-girl, @sheirukitriesfandom, and @dirty-bosmer, with no pressure as always. <3
To set the scene: The command room in Drezen, Anevia and Irabeth have just stepped out, and Isanna thinks she’s going to have some time relatively alone with Regill when a certain someone shows up—
“Hulrun!” Her wings flared outward in excitement—excitement so pronounced that she hardly noticed she had run one of them directly into Regill—and she couldn’t stand up fast enough. She hurried toward him with a grin, wings spread wide and halo burning bright, and stopped short just in front of him, gazing at him with breathless wonder. “Isanna,” he said with equal wonder, unable to take his eyes off her. “You look like you’ve just descended from Heaven itself.” She laughed softly and said, “You said you wanted to fight alongside the angels, didn’t you?” They gazed at each other lovingly, and she added, “You didn’t tell me you were coming.” Then indignantly, recalling Anevia and Irabeth’s timely exit, “No one told me you were coming. Ah, no matter.” Not caring that there were guards present, she took him in her arms and held him close, and as his arms found their way around her lower back, she folded her wings behind her and relaxed into the embrace, only for him to tense and gently push her aside. “What’s this devil worshiper doing here?” he demanded as he brushed past her. She realized he must have spotted Regill over her shoulder, and when she saw that his hand had moved to his sword, she quickly threw herself in front of him and spread her wings again to stop his advance. “Hulrun, no,” she said, her voice a low warning. “Paralictor Regill Derenge is here at my invitation as a trusted ally. You will show him the same respect you show me.” “You invited a devil worshiper to sit at your command table?” he asked. His eyes narrowed, his brow furrowed, and his hand was still resting on his sword, so she summoned all the authority she could even as she felt a flash of irritation. “His expertise has proven invaluable to the crusade,” she said. “It was his strategy that allowed us to take Drezen with minimal losses. Please, he worships Iomedae just as you do.” “What he worships is a heretical caricature of the Inheritor,” he said icily, eyes boring into Regill’s behind her. Seeing that her own piercing stare hadn’t wavered, he added more as a statement than a question, “You trust him.” “I do,” she said, and she felt her heart start to pound. “I trust him implicitly. With my life, and the lives of my soldiers.” His lip curled in disdain, and Regill finally spoke. “Not going to take the word of an angel from your precious Heaven, Prelate?”
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zvaigzdelasas · 11 months
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"AI can make art without human interaction because at the end of the day, it does exactly what humans do with art - break each new piece of art down to the quantifiable basis vectors that you've implicitly constructed about 'art in general' and then faithfully reproduce a new observation of that 'art in general' by smoothly interpolating between observed instantiations of those basis vectors.
You know, like how humans do"
#the joke is that it can be argued that if you do art like an ai youre not necessarily doing art youre producing commodities#assumption being that 'art' stands in an internal tension with a society whose subjectivity is shaped by the commodity form#which i think is pretty inarguable - the argument is over how that tension can be reconciled#i think a salient difference to point out that distinguishes human from ai is the countability of the set of basis vectors#i wouldnt disagree that humans do 'break down' art in some capacity - otherwise 'style' would be entirely singular#the point is really 'how many numbers are there between 0 & 1?'#'how many subcategories are these qualia broken down into?'#i think creativity & externality depend on uncountably divisible qualia#some kind of infinity needs to sneak in somewhere to point to the outside#all this to say @ anon lol for thinking ai is like an ontological evil#but also lol @ anyone who treats the form of AI as isomorphic to the form of human activity#taylor series can absolutely objectively represent certain analytical functions - as long as the error is monotonically negative#ie so long as each subsequent member of the series 'gets closer' to a natural representation of the analytic function#mandatory disclaimer for new followers:#human use of ai for artistic purposes is art - ai cannot generate art without human interaction at some point in the sequence#ideology of the blackbox is the same as the ideology of plug-and-chug#(i know theyre the same because they transform similar inputs to similar outputs!)#& im on mobile so cant move this tag back up but i dont necessarily agree w the maximalist take of 'commodified art isnt art'#but i also think there is a qualitative difference between commodified art & non commodified art#& the ai form is actually pretty isomorphic to the value form in general imo#it cant replace all human labor but it couldnt replace any concrete human labor ...#...if that concrete form of labor hadnt become reducible to that which can be reached through gradient descent#also if u argue that the black box of 'ai breaking down art to make new art' is isomorphic to 'human breaking down art to make new art'#then an implication of that is that ai ***can make art without human interaction***#otherwise if the blackboxes are isomorphic then why have humans in the loop? whats the qualitative difference?#the proper framing is seeing ai as an augmentation of the decision cycle of humans instead of having a 'decision cycle' themselves
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sadmages · 1 year
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THAT ANIMATION IS AMAZING!!!! I LOVE IT SO MUCH!!!!!
(your lipsinc thingy)
also is that jon by any chance?
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Thank you though!!! And no that's my own guy my sweet cheese my oc Glenn who existed long before any jon fanon design and is my strongest soldier for being mistaken for him so often orz
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