“The laws of nature should be expressed in beautiful equations.”
- Paul Dirac
“It is, indeed, an incredible fact that what the human mind, at its deepest and most profound, perceives as beautiful finds its realisation in external nature. What is intelligible is also beautiful. We may well ask: how does it happen that beauty in the exact sciences becomes recognizable even before it is understood in detail and before it can be rationally demonstrated? In what does this power of illumination consist?”
- Subrahmanyan Chandrasekhar
“I often follow Plato’s strategy, proposing objects of mathematical beauty as models for Nature.”
“It was beauty and symmetry that guided Maxwell and his followers.”
- Frank Wilczek
“Beauty, is bound up with symmetry.”
- Herman Weyl
"Still twice in the history of exact natural science has this shining-up of the great interconnection become the decisive signal for significant progress. I am thinking here of two events in the physics of our century: the rise of the theory of relativity and that of the quantum theory. In both cases, after yearlong unsuccessful striving for understanding, a bewildering abundance of details was almost suddenly ordered. This took place when an interconnection emerged which, thought largely unvisualizable, was finally simple in its substance. It convinced through its compactness and abstract beauty – it convinced all those who can understand and speak such an abstract language."
- Werner Heisenberg
Maybe (just maybe) these things (whatever you want to call them) will (somehow) gain access to some "compact", beautiful, "largely unvisualizable" "interconnection" which will be the self-evident solution. And if they do, many will be sure to label it a statistical accident from a stochastic parrot. And they'll right, for some definitions of "statistical", "accident", "stochastic", and "parrot".
Donald Knuth is an extremal outlier human and the problem is squarely in his field of expertise.
Claude, guided by Filip Stappers, a friend of Knuth, solved a problem that Knuth and Stappers had been working on for several weeks. Unfortunately, it doesn't seem (from my quick scan) to have been stated how long (or how many tokens or $) it took for Claude + Stappers to complete the proof.
In response, Knuth said: "It seems that I’ll have to revise my opinions about “generative AI” one of these days."
Seems like good advice. From reading elsewhere in this comment section, the goalposts seem to be approaching the infrared and will soon disappear from the extreme redshift due to rate at which they are receding with each new achievement.
What goalposts do you think are being moved? I constantly see AI enthusiasts use this phrase, but it’s not clear what goalposts they have in mind. Specifically, what is it that you want opponents to recognize that you believe they aren’t currently?
We now have a tool that can be useful in some narrow domains in some narrow cases. It’s pretty neat that our tools have new capabilities, but it’s also pretty far from AGI.
Imagine hearing pre-attention-is-all-you-need that "AI" could do something that Donald Knuth could not (quickly solve the stated problem in collaboration with his friend).
The idea that this (Putnam perfect, IMO gold, etc) is all just "statistical parrot" stuff is wearing a little thin.
It’s time. According to my doctors. All further treatments are pointless. So, please donate so my kids can create a funeral worthy of my keyboard, Pixelbreaker! So I can make a worthy entrance for reuniting with my one true love, Jennell Jaquays.
My daughter Cynthia Elizabeth Heineman, will be making the arrangements
Von Neumann's mathematical fluency, calculation speed, and general problem-solving ability were widely noted by his peers. Paul Halmos called his speed "awe-inspiring." Lothar Wolfgang Nordheim described him as the "fastest mind I ever met". Enrico Fermi told physicist Herbert L. Anderson: "You know, Herb, Johnny can do calculations in his head ten times as fast as I can! And I can do them ten times as fast as you can, Herb, so you can see how impressive Johnny is!" Edward Teller admitted that he "never could keep up with him", and Israel Halperin described trying to keep up as like riding a "tricycle chasing a racing car."
He had an unusual ability to solve novel problems quickly. George Pólya, whose lectures at ETH Zürich von Neumann attended as a student, said, "Johnny was the only student I was ever afraid of. If in the course of a lecture I stated an unsolved problem, the chances were he'd come to me at the end of the lecture with the complete solution scribbled on a slip of paper." When George Dantzig brought von Neumann an unsolved problem in linear programming "as I would to an ordinary mortal", on which there had been no published literature, he was astonished when von Neumann said "Oh, that!", before offhandedly giving a lecture of over an hour, explaining how to solve the problem using the hitherto unconceived theory of duality.
A story about von Neumann's encounter with the famous fly puzzle has entered mathematical folklore. In this puzzle, two bicycles begin 20 miles apart, and each travels toward the other at 10 miles per hour until they collide; meanwhile, a fly travels continuously back and forth between the bicycles at 15 miles per hour until it is squashed in the collision. The questioner asks how far the fly traveled in total; the "trick" for a quick answer is to realize that the fly's individual transits do not matter, only that it has been traveling at 15 miles per hour for one hour. As Eugene Wigner tells it, Max Born posed the riddle to von Neumann. The other scientists to whom he had posed it had laboriously computed the distance, so when von Neumann was immediately ready with the correct answer of 15 miles, Born observed that he must have guessed the trick. "What trick?" von Neumann replied. "All I did was sum the geometric series."
> Von Neumann's mathematical fluency, calculation speed, and general problem-solving ability were widely noted by his peers
I'm impressed by LeBron's basketball skills. I'm not sure what that has to do with IQ.
Certainly von Neumann's quickness helped him solve problems faster, but I'm not sure what this has to do with the discussion at hand. The story of Polya is not dependent upon von Neumann's speed, but it certainly makes it more impressive. The quote says "unsolved problem." It would be impressive if a solution were handed back in any amount of time.
“Our clients understand that a two- to three-minute ad load is more valuable than a nine-minute ad load,” says Mark Read, head of WPP, the world’s largest ad company and Groupm’s parent firm.
It's appropriate that even the chief of the purveyors of advertisements uses the same language ("load") that clinicians use for viral infections.
Then it's a shame that society has largely decided to discard as outdated longstanding philosophies whose tenets do teach the intrinsic value of each human independent of their economic output.
But pushing aside those outmoded ways of thinking did make it easier to sell people useless goods and services which can't fill the hole where dignity and self-respect could instead reside.
And on top we've built the artifice of "social" media (the most shameless oxymoron imaginable) producing sufficient anxiety ensuring that the hole remains unfilled despite all effort.
A fair summary (based on information from Open Secrets) would be that the vast preponderance of contributions were to Democratic and/or progressive candidates or funds ($36,846,356), plus relatively insignificant ($240,200) contributions to Republicans who were (in one way or another) anti-Trump.
"Solidly Democrat/Liberal"
Rank 6
Contributor FTX.US, Washington, DC
Total Contributions $39,884,256
Total Hard Money $1,047,256
Total Outside Money $38,837,000
To Democrats $36,846,356
To Republicans $240,200
"In addition, Bankman-Fried wired maximum individual donations to Boozman and incumbent Republican Sens. Susan Collins of Maine, Richard Burr of North Carolina, Bill Cassidy of Louisiana, John Hoeven of North Dakota and Lisa Murkowski of Alaska throughout the election cycle."
Collins, Burr, Cassidy, and Murkowski are strongly aligned against Trump.
Boozman received his contribution(s) during his primary against Jake Bequette, a strongly pro-Trump Republican.
Hoeven likewise during his primary race against Rick Becker, another strongly pro-Trump Republican.
"Stabenow noted that she is working with her Republican counterpart on the committee, Sen. John Boozman (R-Ark), and regulators to finalize the Digital Commodities Consumer Protection Act (DCCPA) bill in preparation for a committee vote. DCCPA gives power to the Commodity Futures Trading Commission (CFTC) to regulate the trading of digital commodities. This bill was backed by Sam Bankman-Fried, co-founder of the crypto exchange FTX."
Your post did not contest no donations going to progressive or left-wing causes. That is the primary problematic part.
FTX as far as the public is aware is 2/3 Dem 1/3 Repub donations. You only brought up SBF. I was talking about FTX as a whole. Sibling comment notes this as well.
> “Bankman-Fried pledged to spend upwards of $1 billion”
Yes, please. Thank you. I'm not sure which is the better argument: that they are a safety menace due to distraction from driving (video billboards?) or that they are profoundly ugly (including but not limited to aesthetically). Either would suffice for me. The quicker the better.
“The laws of nature should be expressed in beautiful equations.”
- Paul Dirac
“It is, indeed, an incredible fact that what the human mind, at its deepest and most profound, perceives as beautiful finds its realisation in external nature. What is intelligible is also beautiful. We may well ask: how does it happen that beauty in the exact sciences becomes recognizable even before it is understood in detail and before it can be rationally demonstrated? In what does this power of illumination consist?”
- Subrahmanyan Chandrasekhar
“I often follow Plato’s strategy, proposing objects of mathematical beauty as models for Nature.”
“It was beauty and symmetry that guided Maxwell and his followers.”
- Frank Wilczek
“Beauty, is bound up with symmetry.”
- Herman Weyl
"Still twice in the history of exact natural science has this shining-up of the great interconnection become the decisive signal for significant progress. I am thinking here of two events in the physics of our century: the rise of the theory of relativity and that of the quantum theory. In both cases, after yearlong unsuccessful striving for understanding, a bewildering abundance of details was almost suddenly ordered. This took place when an interconnection emerged which, thought largely unvisualizable, was finally simple in its substance. It convinced through its compactness and abstract beauty – it convinced all those who can understand and speak such an abstract language."
- Werner Heisenberg
Maybe (just maybe) these things (whatever you want to call them) will (somehow) gain access to some "compact", beautiful, "largely unvisualizable" "interconnection" which will be the self-evident solution. And if they do, many will be sure to label it a statistical accident from a stochastic parrot. And they'll right, for some definitions of "statistical", "accident", "stochastic", and "parrot".