#math symbols

[slowlygoingnowhere]

An oldie but a goodie: Equality Is Greater Than Division. (sticker | shirt) alienfolklore.net

[er-cryptid]

Physics Symbol Meanings

[lumsel]

chinese room 2

So there’s this guy, right? He sits in a room by himself, with a computer and a keyboard full of Chinese characters. He doesn’t know Chinese, though, in fact he doesn’t even realise that Chinese is a language. He just thinks it’s a bunch of odd symbols. Anyway, the computer prints out a paragraph of Chinese, and he thinks, whoa, cool shapes. And then a message is displayed on the computer monitor: which character comes next?

This guy has no idea how the hell he’s meant to know that, so he just presses a random character on the keyboard. And then the computer goes BZZZT, wrong! The correct character was THIS one, and it flashes a character on the screen. And the guy thinks, augh, dammit! I hope I get it right next time. And sure enough, computer prints out another paragraph of Chinese, and then it asks the guy, what comes next?

He guesses again, and he gets it wrong again, and he goes augh again, and this carries on for a while. But eventually, he presses the button and it goes DING! You got it right this time! And he is so happy, you have no idea. This is the best day of his life. He is going to do everything in his power to make that machine go DING again. So he starts paying attention. He looks at the paragraph of Chinese printed out by the machine, and cross-compares it against all the other paragraphs he’s gotten. And, recall, this guy doesn’t even know that this is a language, it’s just a sequence of weird symbols to him. But it’s a sequence that forms patterns. He notices that if a particular symbol is displayed, then the next symbol is more likely to be this one. He notices some symbols are more common in general. Bit by bit, he starts to draw statistical inferences about the symbols, he analyses the printouts every way he can, he writes extensive notes to himself on how to recognise the patterns.

Over time, his guesses begin to get more and more accurate. He hears those lovely DING sounds that indicate his prediction was correct more and more often, and he manages to use that to condition his instincts better and better, picking up on cues consciously and subconsciously to get better and better at pressing the right button on the keyboard. Eventually, his accuracy is like 70% or something -- pretty damn good for a guy who doesn’t even know Chinese is a language.

* * *

One day, something odd happens.

He gets a printout, the machine asks what character comes next, and he presses a button on the keyboard and-- silence. No sound at all. Instead, the machine prints out the exact same sequence again, but with one small change. The character he input on the keyboard has been added to the end of the sequence.

Which character comes next?

This weirds the guy out, but he thinks, well. This is clearly a test of my prediction abilities. So I’m not going to treat this printout any differently to any other printout made by the machine -- shit, I’ll pretend that last printout I got? Never even happened. I’m just going to keep acting like this is a normal day on the job, and I’m going to predict the next symbol in this sequence as if it was one of the thousands of printouts I’ve seen before. And that’s what he does! He presses what symbol comes next, and then another printout comes out with that symbol added to the end, and then he presses what he thinks will be the next symbol in that sequence. And then, eventually, he thinks, “hm. I don’t think there’s any symbol after this one. I think this is the end of the sequence.” And so he presses the “END” button on his keyboard, and sits back, satisfied.

Unbeknownst to him, the sequence of characters he input wasn’t just some meaningless string of symbols. See, the printouts he was getting, they were all always grammatically correct Chinese. And that first printout he’d gotten that day in particular? It was a question: “How do I open a door.” The string of characters he had just input, what he had determined to be the most likely string of symbols to come next, formed a comprehensible response that read, “You turn the handle and push”.

* * *

One day you decide to visit this guy’s office. You’ve heard he’s learning Chinese, and for whatever reason you decide to test his progress. So you ask him, “Hey, which character means dog?”

He looks at you like you’ve got two heads. You may as well have asked him which of his shoes means “dog”, or which of the hairs on the back of his arm. There’s no connection in his mind at all between language and his little symbol prediction game, indeed, he thinks of it as an advanced form of mathematics rather than anything to do with linguistics. He hadn’t even conceived of the idea that what he was doing could be considered a kind of communication any more than algebra is. He says to you, “Buddy, they’re just funny symbols. No need to get all philosophical about it.”

Suddenly, another printout comes out of the machine. He stares at it, puzzles over it, but you can tell he doesn’t know what it says. You do, though. You’re fluent in the language. You can see that it says the words, “Do you actually speak Chinese, or are you just a guy in a room doing statistics and shit?”

The guy leans over to you, and says confidently, “I know it looks like a jumble of completely random characters. But it’s actually a very sophisticated mathematical sequence,” and then he presses a button on the keyboard. And another, and another, and another, and slowly but surely he composes a sequence of characters that, unbeknownst to him, reads “Yes, I know Chinese fluently! If I didn’t I would not be able to speak with you.”

That is how ChatGPT works.

[division-duplex]

grouping symbols i need to learn... specifically how they work..

[ryllen]

[lorebird]

In which Ford struggles so badly to relate to other people that he wonders if he’s really human at all. The more isolated he becomes, the harder it is to reconcile with his own humanity.

[lilac-dreamxxz]

hii can u do just the full alphabet of cursive capital and lowercase letters? thank u love 🎀

⠀⠀⠀⠀⠀⠀⠀⠀ 𝓐 𝓑 𝓒 𝓓 𝓔 𝓕 𝓖 𝓗

⠀⠀⠀⠀⠀⠀⠀ ⠀𝓘 𝓙 𝓚 𝓛 𝓜 𝓝 𝓞 𝓟 𝓠

⠀⠀⠀⠀⠀⠀⠀⠀𝓡 𝓢 𝓣 𝓤 𝓥 𝓦 𝓧 𝓨 𝓧

⠀⠀𝓪 𝓫 𝓬 𝓭 𝓮 𝓯 𝓰 𝓱 𝓲 𝓳 𝓴 𝓵 𝓶 𝓷 𝓸 𝓹 𝓺 𝓻 𝓼 𝓽 𝓾 𝓿 𝔀 𝔁 𝔂 𝔃

divider ctto !

[fre-sitas]

꒰͡ ͜ @cg1rl ͜ ͡꒱ 𝅄 ࣪

[useless-catalanfacts]

If you visit the Sagrada Família basilica in Barcelona (Catalonia), you might be intrigued by these squares with numbers. Like every detail in the building, it has a symbolic meaning.

These are a very particular kind of magic squares. A "magic square" is a series of numbers on a square grid, placed so that any row, column, or diagonal line always adds up to the same number. Well, to be fair, there is one more rule for the normal magic squares which this one doesn't follow: the squares cannot repeat numbers and must use all numbers from 1 to the number of squares possible (for example, a square of 3x3 would have numbers from 1 to 9, a square of 4x4 would have them from 1 to 16, etc). When this rule is followed, the number that results from the addition will always be the same (in a square of 3x3, the sum of 1+2+3+4+5+6+7+8+9 = 45, and each row, column and diagonal line sums 45/3 = 15; in a 4 x 4 magic square, where the sum of all the numbers from 1 to 16 is 136, the magic constant is 136/4 = 34). For mathematical reasons, the resulting number cannot be chosen, it will always be the same one if we follow those rules.

And here is why this one doesn't follow that rule, and it's on purpose. It doesn’t have all the numbers from 1 to 16 (it is missing the 12 and 16) and some numbers are repeated. And why did they do that? Here's the important bit: the result of the sum isn’t 34 (as would always be in a 4x4 magic square), but 33.

The sculptor who created the Sagrada Família's Passion façade (the artist Josep Maria Subirachs, following architect Antoni Gaudí's vision) took a different spin for these squares. Magic squares have been used as talismans in many cultures for millennia, since ancient cultures including 3rd millennium BC China, Ancient India, Ancient Egypt, Arab, and Greek cultures, among others. For the Sagrada Família (a Christian temple), Subirachs used to hide a number of great significance in Christian symbolism.

Painting Melencolia I by Albrecht Dürer (1514) and a detail from it.

Subirachs adapted a magic square from this engraving by Dürer and changed it so that it would add up to 33: the age that Jesus Christ is traditionally believed to have been when he was executed. A number based on the repetition of another of the most important numbers in Christianity: 3, symbolizing the holy trinity.

The square in the Sagrada Família manages to add 33 by repeating some numbers and skipping others. But it also goes further than adding up 33 in every row, column, and diagonal line. The same number can also be obtained with many other combinations. Here are some of them:

Plus, in the magic square at the Sagrada Família, there is also a sort of hidden subliminal signature: adding up the numbers that repeat and looking at their correspondence in the Roman alphabet, we get the initials INRI (Iesus Nazarenus Rex Iudaeorum = "Jesus of Nazareth King of the Jews" in Latin), which was written on the sign at the top of the cross where Jesus was crucified.

This way, mathematics, art history and religious symbolism all come together in this little symbol.

Photos from Alamy, Martin Leicht, Sagrada Família blog. Text adapted from Sagrada Família blog. All the graphs with the numbers are from that same article.

[sarcasticscribbles]

you have no idea how deep and mysterious I thought I was when I was 16 and posted this to DeviantArt

[majickth]

Me: I should really buckle down and finish all my work before committing to any big proj—

My brain, banging pots and pans together: HEY WHAT IF ETOILES IS A TIRED KNIGHT AND POMME IS THE DRAGON HES SUPPOSED TO SLAY BUT INSTEAD HE ADOPTS HER AND RUNS AWAY TO LIVE IN A COTTAGE IN THE FRENCH COUNTRYSIDE

[lipshits-continuous]

Fuck ÷, all my homies hate ÷

[unnonexistence]

the math secret nobody tells you is you can make anything equal anything else with the power of extremely bad notation

[anistarrose]

went so far down the wikipedia rabbit hole that I found a paper that I think can only be read in the voice of Jonathan Frakes Asking You Things

[ID: a screenshot reading:

"... precise features or to have specific relationships with other models. Would you like to live in a universe where CH holds, but (diamond symbol) fails? Or where (2 to the aleph sub n = aleph sub n plus 2) for every natural number n? Would you like to have rigid Suslin trees? Would you like every Aronszajn tree to be special? Do you want a weakly compact cardinal kappa for which (diamond sub kappa) REG fails? Set theorists build models to order."

End ID.]

[eatsleepcrap]

You can check when your first post was on your blog's archive: yourblogname.tumblr/archive

(apologies for the atrocity that is trying to access tumblr archive on mobile)