#tarski

[tagitables]

Alfred Tarski

[popolodipekino]

fiabe

Romanzo d'avventure e fiaba sono due stili diversi, e attivano in misura diseguale due facoltà diverse, quella della logica e quella dell'immaginazione. Ad Alfred Tarski (1901-1983), che in filosofia era un nominalista materialista, era spesso richiesto di spiegare la presunta contraddizione tra le sue idee e matematica che coltivava, soprattutto teoria degli insiemi, cioè una teoria di cose che egli non credeva esistessero; Tarski rispondeva così: "Io credo che ci sia un valore anche nelle fiabe, e nello studio delle fiabe." da Rapidità, in G. Lolli, Discorso sulla matematica. Una rilettura delle Lezioni americane di Calvino

[prokopetz]

People on this site will put together polls like "The Banach-Tarski Paradox versus Camembert Cheese", then act like the results prove that they're surrounded by idiots.

[somethingusefulfromflorida]

When a mommy skeleton and a daddy skeleton love each other very much they run at each other full-speed and crash into a huge pile of bones and then their disembodied arms start putting themselves back together but they do it wrong so now they've got their skulls on backwards and arms where their legs should be and ribs all over the place and after a few failed attempts they conglomerate into one big two-headed eight-limbed double-skeleton but eventually they get it right and reform back into their separate selves but somehow in the middle of it all enough bones got dropped and misplaced that they have enough spare parts to make a baby skeleton!

[thehumanwiki]

what if we combined the ship of thesues with the banach-tarski paradox. which sphere is the original sphere

[bubbloquacious]

8. Least favorite notation you’ve ever seen?

12. Who actually invented calculus?

52. Do you have favorite math textbooks? If so, what are they?

57. What inspired you to do math?

:)))

From Real's Math Ask Meme.

8. Least favourite notation you’ve ever seen?

Writing a tensor product of bra-ket vectors as |1⟩|2⟩ instead of |1⟩⊗|2⟩, which was standard in the quantum information theory course I took (with @floralfractals :^)) a few years back. This makes an expression like ⟨1|⟨2||3⟩|4⟩ ambiguous! It evaluates to ⟨1|3⟩⟨2|4⟩ if you interpret the juxtaposition as a tensor product, and to ⟨1|4⟩⟨2|3⟩ if you intepret it as scalar multiplication.

10. Who actually invented calculus?

I did! Or I will have done, when I invent my time machine to travel back to the Islamic Golden Age to tell Al-Khwarizmi about category theory. Then they'll all see.

44. Do you have favourite math textbooks? If so, what are they?

I never stick with textbooks long enough for these to be like super well-founded recommendations, but I quite like Jonathan Gleason's Introduction to Analysis, Peter Johnstone's Stone Spaces, and Bochnak, Coste, & Roy's Real Algebraic Geometry.

49. What inspired you to do math?

So besides the fact that from a young age I was intrigued and engaged by puzzles and problem solving, it took quite some time before I realized I wanted to become a mathematician. Sometime during my fourth or fifth year of secondary school we covered logarithms, and that's when it all started to click for me. How addition, multiplication, exponentiation are just operations, and that they can have inverse operations, and that these are all examples of the exact same phenomenon. I started watching Vsauce and Numberphile and Vihart, and the rest is history.

[dramatic-dolphin]

i will always associate the banach-tarski paradox with bdsm and gay sex, for reasons i will not explain <3

[emvisual]

Si la mecánica cuántica te volvía loco, espera a ver lo que dicen las matemáticas. Echa un vistazo a la paradoja de Banach–Tarski, verás que curioso.

¿Puede una esfera descomponerse en un número finito de conjuntos de puntos y volver a montarla en 2 esferas idénticas a la original?

Imagina que lo hacemos con billetes...

[conundrumcomics]

"Sierpinski's Genesis"

[thecrazyalchemist]

For every cursed math, there is math that is even more cursed

math people scare me. math people will be like "math works in mysterious ways TO YOU. i get it though." and they do and it's fucking terrifying.

[galaxacious]

Everyone hold your horses. New Banach-Tarski explanation dropped:

[muchmossymess]

Maths is so fucking stupid

[rlyehtaxidermist]

True, but probably not for the reasons you're saying this.

the only science to really concern itself with the notion of "an ultimate truth" rather than specific answers to specific - if far-reaching - questions is mathematics

mathematics has known that any meaningful definition of ultimate truth is impossible since 1933

one of the best academic paper titles

[teachanarchy]

Does math have a major flaw? - Jacqueline Doan and Alex Kazachek

[janmisali]

Sorry if you've already answered this before, but where would the Banach Tarski Paradox fall in your categories for paradoxes? It feels like it's somewhere between "Counterintuitive fact" and "Math Prank". It's not quite a fact because we can't really do it, but it's not quite a prank because there's proofs about how it works.

depends on your stance on the axiom of choice

[tohruies]

dandelions

sunday mornings

whale watching and the coast

motes of dust that float like gold foil beneath the sun

making kimchi

tic-tac-toe on coffee shop napkins

pomegranates

70mm film

wired earbuds

the banach-tarski paradox

and a very sublime pastry shared over elevenses!