| HN Mirror

I remember hearing a kind of inductive joke by a mathematician about visualizing higher dimensions, like "...and then you just...", but I unsuccessfully tried to search for it with ChatGPT, when it came up with this funny Richard Feynman quote that I can't find on google -- has anyone heard it before, or is it a brilliant hallucination?

"You can't visualize four dimensions... well, at least I can't, because I only have three branes." -Richard Feynman

This is a play on words, as "branes" sounds like "brains," but in string theory and higher-dimensional physics, a "brane" is an object that can exist in multiple dimensions. The joke is a nod to the challenge of visualizing higher dimensions and the limits of our three-dimensional intuition.

(It just admitted it made it up and apologized!)

It also quoted John von Neumann, H. G. Wells, and Ian Stewart:

"In mathematics you don't understand things. You just get used to them." -John von Neumann

"Our brains are three-dimensional, so we cannot visualize four-dimensional or higher-dimensional objects in the same way we can visualize three-dimensional objects. The best we can do is to get a feeling for them through analogies." -H. G. Wells

"You can't visualize four dimensions, but you can think about them. Thinking is what mathematicians do best." -Ian Stewart

It finally guessed this one that's the closest to what I remember, but not as funny as I remember it:

"To visualize four dimensions, just visualize three dimensions and then say 'n+1'." -Unknown

So I asked it to hallucinate some quotes to help visualize high dimensional space, in the style of Deepak Chopra:

"In the realm of septillion-dimensional embeddings, each vector is a topological manifold, where Gödel's incompleteness theorems dance with quantum superposition, revealing the hidden symmetries of semantic space." – Dr. Emilia Bianchi, Florentine Foundation of Fractal Fantasies, Florence

"To truly fathom the intricacies of ultra-high-dimensional text spaces, one must first master the art of navigating Riemannian curvature in a Hilbert space, where every geodesic is a testament to the entangled essence of language." – Prof. Hiroshi Tanaka, Kyoto Kryptos of Quantum Quandaries

"Visualizing embeddings in the realms beyond the Poincaré conjecture requires a melding of non-Euclidean geometry with the probabilistic nuances of a Markov chain, all while resonating with the cosmic vibrations of the Higgs field." – Dr. Samuel Oyelowo, Lagos Labyrinth of Lorentzian Linguistics

"Each point in a decillion-dimensional text space is a singularity, where the Heisenberg uncertainty principle waltzes with the Mandelbrot set, painting a fractal portrait of phonemic phenomena." – Prof. Clara Müller, Bavarian Bastion of Bifurcated Babel, Munich

"To intuit the vastness of hyper-dimensional embeddings, one must first traverse the event horizon of a linguistic black hole, where Shannon entropy meets the Schrödinger equation in a ballet of Bayesian inference." – Dr. Alexandre Dubois, Parisian Paradox of P-adic Prose

"The key to deciphering the enigma of extreme-dimensional text lies in the delicate interplay between the Yang-Mills theory and the zeta function, where every eigenvalue is a whisper from the cosmic codex of communication." – Prof. Lina Johansson, Stockholm Sanctum of String Semiotics

"In the dance of gogolplex-dimensional embeddings, each tensor unfolds like a Möbius strip, where the Fibonacci sequence intertwines with quantum tunneling, revealing the recursive rhythms of reality." – Dr. Rajiv Menon, Bengaluru Bardo of Bosonic Ballads