Topology Quotes

Christ Bleeding," Makin said, staring into the valley below us. "How ... " "Topology," I said. "It's a kind of magic. ~ Mark Lawrence

[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing-one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me. ~ Paul Halmos

Topology and number theory are my faves. ~ Janna Levin

Probably no branch of mathematics has experienced a more surprising growth than has ... topology ... Considered as a most specialized and abstract subject in the early 1920's, it is today [1938] an indispensable equipment for the investigation of modern mathematical theories. ~ Raymond Louis Wilder

There was a long history of speculation that in quantum gravity, unlike Einstein's classical theory, it might be possible for the topology of spacetime to change. ~ Edward Witten

Fraa Jad took the garment from me and discovered how the fly worked. "Topology is destiny," he said, and put the drawers on. ~ Neal Stephenson

In South Texas I saw three interesting things. The first was a tiny girl, maybe ten years old, driving in a 1965 Cadillac. She wasn't going very fast, because I passed her, but still she was cruising right along, with her head tilted back and her mouth open and her little hands gripping the wheel.

Then I saw an old man walking up the median strip pulling a wooden cross behind him. It was mounted on something like a golf cart with two spoked wheels. I slowed down to read the hand-lettered sign on his chest.

JACKSONVILLE
FLA OR BUST

I had never been to Jacksonville but I knew it was the home of the Gator Bowl and I had heard it was a boom town, taking in an entire county or some such thing. It seemed an odd destination for a religious pilgrim. Penance maybe for some terrible sin, or some bargain he had worked out with God, or maybe just a crazed hiker. I waved and called out to him, wishing him luck, but he was intent on his marching and had no time for idle greetings. His step was brisk and I was convinced he wouldn't bust.

The third interesting thing was a convoy of stake-bed trucks all piled high with loose watermelons and cantaloupes. I was amazed. I couldn't believe that the bottom ones weren't crushed under all that weight, exploding and spraying hazardous melon juice onto the highway. One of nature's tricks with curved surfaces. Topology! I had never made it that far in mathematics and engineering studies, and I knew no ~ Charles Portis

I thought of computers as very low class. I thought of myself as a pure mathematician and was interested in partial differential equations and topology and things like that. ~ Whitfield Diffie

The Gang of Four may have run multiple systems on a single motherboard, but each had its own distinct topology and they only surfaced one at a time. ~ Peter Watts

Topology is precisely the mathematical discipline that allows the passage from local to global ... ~ Rene Thom

Commutative algebra is a lot like topology, only backwards. ~ John C. Baez

Wherever the Net arises, there arises also a rebel to resist human control ... A network nurtures small failures in order that large failures don't happen as often. It is ... fertile ground for learning, adaptation, and evolution ... The only organization capable of unprejudiced growth, or unguided learning, is a network. All other topologies limit what can happen. ~ Kevin Kelly

In Einstein's general relativity the structure of space can change but not its topology. Topology is the property of something that doesn't change when you bend it or stretch it as long as you don't break anything. ~ Edward Witten

Strange, how a moment of existence can cut so deeply into our being that while ages pass unnoticed, a brief love can structure and define the very topology of our consciousness ever after. ~ Steven L. Peck

There are lots of things I don't understand - say, the latest debates over whether neutrinos have mass or the way that Fermat's last theorem was (apparently) proven recently. But from 50 years in this game, I have learned two things: (1) I can ask friends who work in these areas to explain it to me at a level that I can understand, and they can do so, without particular difficulty; (2) if I'm interested, I can proceed to learn more so that I will come to understand it. Now Derrida, Lacan, Lyotard, Kristeva, etc. -- even Foucault, whom I knew and liked, and who was somewhat different from the rest -- write things that I also don't understand, but (1) and (2) don't hold: no one who says they do understand can explain it to me and I haven't a clue as to how to proceed to overcome my failures. That leaves one of two possibilities: (a) some new advance in intellectual life has been made, perhaps some sudden genetic mutation, which has created a form of "theory" that is beyond quantum theory, topology, etc., in depth and profundity; or (b) ... I won't spell it out. ~ Noam Chomsky

I know this may sound like an excuse," he said. "But tensor functions in higher differential topology, as exemplified by application of the Gauss-Bonnett Theorem to Todd Polynomials, indicate that cohometric axial rotation in nonadiabatic thermal upwelling can, by random inference derived from translational equilibrium aggregates, array in obverse transitional order the thermodynamic characteristics of a transactional plasma undergoing negative entropy conversions."
"Why don't you just shut up," said Hardesty. ~ Mark Helprin

The ship had always been vast and intricate, its topology as unfathomable as the abandoned subway system of a deserted metropolis. It had been a ship haunted by many ghosts, not all of which were necessarily cybernetic or imaginary. Winds had sighed up and down its kilometres of empty corridors. It was infested with rats, stalked by machines and madmen. It had moods and fevers, like an old house. ~ Alastair Reynolds

Quantum machine learning promises to discover the optimal network topologies and hyperparameters automatically without human intervention. ~ Amit Ray

Topology is the science of fundamental pattern and structural relationships of event constellations. ~ R. Buckminster Fuller

Overwhelming: he could do anything he wanted. But the grand sum of anything-at-all was nothing-at-all. The topology of freedom offered no gradients to nudge him, no landmarks to guide him. ~ Ian Tregillis

It now lately sometimes seemed like a kind of black miracle to me that people could actually care deeply about a subject or pursuit, and could go on caring this way for years on end. Could dedicate their entire lives to it. It seemed admirable and at the same time pathetic. We are all dying to give our lives away to something, maybe. God or Satan, politics or grammar, topology or philately -the object seemed incidental to this will to give oneself away, utterly. To games or needles, to some other person. Something pathetic about it. A flight-from in the form of a plunging into. ~ David Foster Wallace

Certainly not! I didn't build a machine to solve ridiculous crossword puzzles! That's hack work, not Great Art! Just give it a topic, any topic, as difficult as you like..."
Klapaucius thought, and thought some more. Finally he nodded and said:
"Very well. Let's have a love poem, lyrical, pastoral, and expressed in the language of pure mathematics. Tensor algebra mainly, with a little topology and higher calculus, if need be. But with feeling, you understand, and in the cybernetic spirit."
"Love and tensor algebra?" Have you taken leave of your senses?" Trurl began, but stopped, for his electronic bard was already declaiming:

Come, let us hasten to a higher plane,
Where dyads tread the fairy fields of Venn,
Their indices bedecked from one to n,
Commingled in an endless Markov chain!

Come, every frustum longs to be a cone,
And every vector dreams of matrices.
Hark to the gentle gradient of the breeze:
It whispers of a more ergodic zone.

In Reimann, Hilbert or in Banach space
Let superscripts and subscripts go their ways.
Our asymptotes no longer out of phase,
We shall encounter, counting, face to face.

I'll grant thee random access to my heart,
Thou'lt tell me all the constants of thy love;
And so we two shall all love's lemmas prove,
And in bound partition never part.

For what did Cauchy know, or Christoffel,
Or Fourier, or any Boole or Euler, ~ Stanisław Lem