§ Big list of quotes
If Alice uses abstract algebra to solve problem and Bob uses concrete calculation, Alice's result is more generalizable than Bob's, while Bob's method is more generalizable than Alice's. This is one reason why combining the two approaches is so valuable. You can start with something you know will work but may not unlock a great mystery, and then look for patterns that clue you in to a wider story.
"There are two kinds of scientific progress: the methodical experimentation and categorization which gradually extend the boundaries of knowledge, and the revolutionary leap of genius which redefines and transcends those boundaries. Acknowledging our debt to the former, we yearn nonetheless for the latter"
you can be dead right. (Being right has a time and a place)
Bott also used to say that a cocyle was "something that hovers over a space and when it sees a cycle, pounces on it and spits out a number".
I'm not complaining here, quite the opposite: this story is really quite exciting and the work mentioned is both real and fascinating. We are essentially back to the days when Newton tried to explain the nature of gravity looking at Kepler's laws trying various options and separating what works from what doesn't. I'm only saying that the famous "physicists' intuition", which is so overrated, is actually just the benevolence of Nature. Why should the Nature be so benevolent to us remains a mystery and I know neither a physicist, nor a mathematician, who could shed any light on that. The best explanation so far is contained in Einstein's words "God is subtle, but not malicious", or, in a slightly less enigmatic form, "Nature conceals her mystery by means of her essential grandeur, not by her cunning".
Whoever is meek to the cruel ones, is cruel to the meek.
Treat everybody the same v/s treat everybody fairly.
"Everyone must choose one of two pains: The pain of discipline or the pain of regret.”
“We have two lives, and the second begins when we realize we only have one.” -- Confucius
"Think of yourself as dead. You have lived your life. Now, take what's left and live it properly." - Marcus Aurelius
It is only when a mosquito sits on your testicles do you learn that some problems must be solved without violence.
The threat is greater than the execution. ~ GM Danya
No guest should be admitted without a date of departure ~ Violet, Downton Abbey
Not knowing things isn't dumb; pretending to know is.
magic is when you have expended more effort to achieve a trick than observers think is reasonable. That you've spent hundreds of hours practising with decks of cards, that you've built a secret passageway across your stage, that you've erected an enormous mirror in a public place, etc..
Knuth says something similar (on his web page I think). He says he doesn't read email because email is good for people who want to stay on top of things but he wants to get to the bottom of things.
"In the past everything was better, even the future" (K. Valentin, translated)
You never rise to the occasion, you sink to the level of your training.
"the mark of an enlightened mind is the ability to entertain ideas without accepting them"
The most intelligent creature in the universe is a rock. None would know it because they have lousy I/O.
Now symmetry and consistency are convertible terms - thus Poetry and Truth are one ~ Noether's theorem?
Science is a differential equation. Religion is a boundary condition. (Alan Turing, quoted in J.D. Barrow, “Theories of everything”)
(I really detest the use of the word "training" in relation to professional activities. Training is what you do to dogs. What you should be doing with people is educating them, not training them. There is a big, big difference.) ~ Ron Garret at JPL
“Simulated consciousness" was as oxymoronic as "simulated addition.”
A cylinder will roll like a sphere in one direction but not roll like a cube in the other. That doesn't make it a sphere and a cube at the same time. It makes it something different. (in analogy to wave-particle duality)
Talent hits a target no one else can hit; Genius hits a target no one else can see..
Raising your floor (consistency) is just as important as raising your ceiling (skill)
"The sky is the limit, so lets build rockets!"
The manner in which the mathematician works his way towards discovery by shifting his confidence from intuition to computation and back again from computation to intuition, while never releasing his hold on either of the two, represents in miniature the whole range of operations by which articulation disciplines and expands the reasoning powers of man. (Personal Knowledge, 131)
Everyone knows that putting a untrained business major in charge of a squadron of soldiers would end badly. He might be able skate by until they got into combat, maybe, but after that they wouldn’t listen to him for long. But for some reason we think that putting an mba in charge of an engineering team is a good idea.
"On and on you will go, making sense of the world, forming notions of order, and being surprised in ways large and small by their failure, forever." — Albert Burneko on Wile E. Coyote.
"There is a special providence that protects idiots, drunkards, children, and the United States of America." ~ Otto van bismarck
"Never believe anything in politics until it has been officially denied" ~ Otto von Bismarck
A good proof is one that makes us wiser. -- Yuri Manin
Keep things in their Gauss given order. -- Gilbert Strang
It is interesting to see where people insist proximity to a subject makes one informed, and where they insist it makes them biased. It is interesting that they think it’s their call to make. [in the context of 'as a male, you don't get a say about toxic masculinity' v/s other 'viewpoints' ] ~ medium article link
"Feeding two birds with one scone" Peta recommended version of "killing two birds with one stone"
the first sign of civilization in an ancient culture was a femur that had been broken and then healed ~ Margaret Mead
The mistake of many adults is confusing serious with solemn.
I hate greek drama. You know, where everything happens off-stage. ~Downton abbey, s02e01
you have to speculate to accumulate
It's so reassuring to see the future unfurl, as long as you remember that it bears no resemblance to the past.
Sybil, vulgarity is no substitute for wit. ~ Violet, Downton Abbey
"Why dwell on that now?" "Because I want to feel the pleasure of telling you I told you so".
The law, in its majestic equality, forbids rich and poor alike to sleep under bridges, to beg in the streets, and to steal loaves of bread.”
'The history of transistors is the history of solving Schrödinger's equation in various materials.' -- Leon Lederman
tradition that contested poems would be thrown into a pool. The better poems would float. Now you know why you shouldn't write dense prose. ~ History of india podcast
children cried with hunger. Women plaited their braids without flowers. ~ History of india podcast.
"There is a spooky quality about the ability of mathematicians to get there ahead of physicists. It's as if when Neil Armstrong first landed on the moon he found in the lunar dust the footsteps of Jules Verne" - Steven Weinberg on old math being applied in physics
You can try; trying is the first step of failure ~ GM Ben finegold on mating sequences.
Some folks prefer the carrot, I the stick. So I will use my considerable expertise to stick it to you.
"Machine learning is like money laundering for bias"
Criticism is prejudice made plausible.” - H.L. Mencken
David Marquet's credos from "Turn The Ship Around!". Don't ask "Are we ready?"; instead, ask "How ready are we?". Everything needs to be phrased so as to invite people to express the knowledge they have, rather than demanding what amounts to a declaration of tribal identity.
You can't just go around recognizing what people don't understand. That's what got Socrates killed. You've gotta make them understand what they don't understand without making them want to kill you. That's what makes a great teacher / leader / etc.
'Every work of art is an uncommitted crime.' - Adorno.
Policies are nice but at the end of the day we need folks to set an example (rather than being made an example of)
“The math students dropped out because they could not understand anything. Of course, I didn’t understand anything either, but non-math students have a different standard of what it means to understand something,” Huh said. “I did understand some of the simple examples he showed in classes, and that was good enough for me.” https://www.quantamagazine.org/a-path-less-taken-to-the-peak-of-the-math-world-20170627/
"you're such a dick!". "I'm moby goddamn dick, and you're swimming in my water".
When people thought the earth was flat, they were wrong. When people thought the earth was spherical, they were wrong. But if you think that thinking the earth is spherical is just as wrong as thinking the earth is flat, then your view is wronger than both of them put together.
"Ethereum has said they're moving from Proof of Work to Stake; I'm not surprised, given the Ethereum developers seem to abhor Work in all of its forms, including making progress on Ethereum itself"
The man is nothing, the work is everything. ~ Napoleon L’homme c’est rien–l’oeuvre c’est tout