Qvyre retweeted
TERENCE TAO SAYS MATHEMATICIANS ARE NOW HIDING THEIR IDEAS FROM EACH OTHER BECAUSE OF AI
"we are getting answers at the cost of insight." they used to share their best research directions openly, now they're afraid "someone with an AI will input their research ideas into frontier model" and get there first
in the video he explains why AI breakthroughs leave even him with nobody to ask
Tao won the fields medal at 31 and is often called the greatest living mathematician
and it already happened. in september OpenAI claimed its AI cracked part of Navier-Stokes, one of the 7 Millennium Prize problems. days later NYU mathematician Tristan Buckmaster asked if they took the idea from his work, and the company admitted it couldn't fully rule out an indirect link
an answer tells you what's true, understanding tells you what to ask next
would you still share your best idea at work if an AI could finish it before you do?
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In 1940 a reporter abandoned his car on this bridge and crawled 500 yards to escape. Your physics textbook probably explains why it fell wrong
Most books say the wind matched the bridge's natural frequency, like a singer shattering a glass. But the wind that day was a steady 42 mph. It had no rhythm to match
The Tacoma Narrows Bridge opened on July 1, 1940, and was so bouncy people nicknamed it Galloping Gertie. Four months later, on November 7, it started to twist
Leonard Coatsworth, an editor at the Tacoma News Tribune, was thrown against the curb, left his car and crawled to the towers. His daughter's dog Tubby was still inside
The real killer was flutter. Once the deck twisted a little, the wind hit it at a new angle and twisted it further. Every swing fed the next one, until the center span tore loose and dropped 190 feet into Puget Sound
Tubby was the only death. In 1991 two engineers, Billah and Scanlan, published a paper calling the textbook story wrong. Plenty of books still teach it
Should textbooks keep the simple wrong story because it's easier to teach, or is a wrong explanation worse than none?
In 1940 a reporter abandoned his car on this bridge and crawled 500 yards to escape. Your physics textbook probably explains why it fell wrong
Most books say the wind matched the bridge's natural frequency, like a singer shattering a glass. But the wind that day was a steady 42 mph. It had no rhythm to match
The Tacoma Narrows Bridge opened on July 1, 1940, and was so bouncy people nicknamed it Galloping Gertie. Four months later, on November 7, it started to twist
Leonard Coatsworth, an editor at the Tacoma News Tribune, was thrown against the curb, left his car and crawled to the towers. His daughter's dog Tubby was still inside
The real killer was flutter. Once the deck twisted a little, the wind hit it at a new angle and twisted it further. Every swing fed the next one, until the center span tore loose and dropped 190 feet into Puget Sound
Tubby was the only death. In 1991 two engineers, Billah and Scanlan, published a paper calling the textbook story wrong. Plenty of books still teach it
Should textbooks keep the simple wrong story because it's easier to teach, or is a wrong explanation worse than none?
Qvyre retweeted
A Soviet cosmonaut spun a wingnut in space in 1985 and watched it flip over by itself. The USSR reportedly kept it quiet for 10 years
The rumored reason: if a spinning object can flip with nothing touching it, what stops the Earth from doing the same?
In the video it's a T-handle on the ISS. Watch it spin, flip 180 degrees, spin, flip back, with nothing pushing it
The cosmonaut was Vladimir Dzhanibekov, on the mission to bring the dead Salyut 7 station back to life. The effect now carries his name
Mathematicians had the equations since the 1800s. Anything with three different axes, a phone, a book, a tennis racket, gets unstable when it spins around the middle one. Toss your phone spinning in the air and you'll see it
In 1991 a team of mathematicians published it as a new discovery about tennis rackets. The cosmonaut's version still wasn't widely known
A wingnut, a racket and your phone all do it. The Earth spins around its most stable axis, so it doesn't
If the Soviets really hid this for 10 years, was it real fear, or just the Cold War habit of classifying everything?
A Soviet cosmonaut spun a wingnut in space in 1985 and watched it flip over by itself. The USSR reportedly kept it quiet for 10 years
The rumored reason: if a spinning object can flip with nothing touching it, what stops the Earth from doing the same?
In the video it's a T-handle on the ISS. Watch it spin, flip 180 degrees, spin, flip back, with nothing pushing it
The cosmonaut was Vladimir Dzhanibekov, on the mission to bring the dead Salyut 7 station back to life. The effect now carries his name
Mathematicians had the equations since the 1800s. Anything with three different axes, a phone, a book, a tennis racket, gets unstable when it spins around the middle one. Toss your phone spinning in the air and you'll see it
In 1991 a team of mathematicians published it as a new discovery about tennis rackets. The cosmonaut's version still wasn't widely known
A wingnut, a racket and your phone all do it. The Earth spins around its most stable axis, so it doesn't
If the Soviets really hid this for 10 years, was it real fear, or just the Cold War habit of classifying everything?
Two Cambridge physicists saw this video and wanted to teach it in a school course. Then they realized they couldn't explain it
Nothing is pulling this chain up. It leaps out of the jar on its own and holds an arch in mid-air
Watch the top of the arch. 8,000 metal beads from an office blind, no magnets, and the chain stays above the rim the whole time it pours out
Steve Mould filmed it in 2013, and it's now known as the Mould effect
In 2014 John Biggins and Mark Warner published their answer. Every link acts like a tiny stiff rod. When the moving chain yanks one end up, the other end jams into the pile below, and the pile kicks it back up. Drop the chain from higher and the arch climbs higher
Then other physicists ran their own tests and argued the kick barely matters, and what really counts is how the chain is piled in the jar
Over a decade later, the experts still don't fully agree on why a chain from an office blind jumps
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Every time you talk to an AI, it's playing one game: guess the next word. That's it
But to get good at that one game, it read more than you could read in 2,600 years, and ran so much math that a computer doing a billion calculations a second would need 100 million years to finish
Nobody teaches it anything directly. It starts as a pile of random numbers that spits out gibberish. Then it reads a sentence, guesses the last word, gets told how wrong it was, and adjusts. Trillions of times
The big jump came in 2017, when Google researchers made it read a whole text at once instead of word by word. Now every word can look at the words around it, so "bank" next to "river" stops meaning money
And the people who build these models can't fully explain why it gives the exact answer it gives. They design the machine, but what it ends up knowing grows on its own
7 minutes, save it for tonight
If it only guesses the next word and still writes better than most people, is that real understanding, or have we been overrating our own?
Every time you talk to an AI, it's playing one game: guess the next word. That's it
But to get good at that one game, it read more than you could read in 2,600 years, and ran so much math that a computer doing a billion calculations a second would need 100 million years to finish
Nobody teaches it anything directly. It starts as a pile of random numbers that spits out gibberish. Then it reads a sentence, guesses the last word, gets told how wrong it was, and adjusts. Trillions of times
The big jump came in 2017, when Google researchers made it read a whole text at once instead of word by word. Now every word can look at the words around it, so "bank" next to "river" stops meaning money
And the people who build these models can't fully explain why it gives the exact answer it gives. They design the machine, but what it ends up knowing grows on its own
7 minutes, save it for tonight
If it only guesses the next word and still writes better than most people, is that real understanding, or have we been overrating our own?
Nobody told these blocks about pi. They count it out anyway
Same weight, 3 hits. Make one 100x heavier, 31. Then 314. Then 3,141. Every time the big block gets 100x heavier, the collisions spell out one more digit of pi.
Gregory Galperin discovered this in 1995. No circles in the setup, no geometry, just two blocks, a wall and a counter.
It's also the worst way ever invented to calculate pi. For 20 digits the heavy block would need about 10 times the mass of the black hole at the center of our galaxy, and you'd have to count 31 billion billion collisions.
The reason is hidden in energy. Write the energy of both blocks as one equation and it's secretly a circle. Each collision moves you one small step around it, so counting the hits is the same as measuring an angle, and angles on a circle lead straight to pi.
If pi shows up in two blocks that have never heard of a circle, did humans invent math, or did we just find something that was already there?
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The shortest path down is a straight line. Watch it finish last
In 1696 a Swiss mathematician dared all of Europe to find the fastest one. He gave them six months. Isaac Newton did it in one night
Johann Bernoulli asked a simple question: what shape of ramp gets a ball from A to B in the least time? The deadline passed and only Leibniz had sent an answer
On 29 January 1697 the letter reached Newton. He came home from the Royal Mint at 4pm, stayed up, and had it solved by 4am. He mailed it back without his name. Bernoulli read it and said he recognized the lion by its claw
The answer is a cycloid, the curve traced by a point on a rolling wheel. It drops steeply at first so the ball picks up speed early, then spends that speed on the long flat stretch. The straight line is shorter, but the ball crawls down it gaining speed the whole way
The curve has one more trick. Release balls from any height on a cycloid and they all reach the bottom at the same moment
The shortest path down is a straight line. Watch it finish last
In 1696 a Swiss mathematician dared all of Europe to find the fastest one. He gave them six months. Isaac Newton did it in one night
Johann Bernoulli asked a simple question: what shape of ramp gets a ball from A to B in the least time? The deadline passed and only Leibniz had sent an answer
On 29 January 1697 the letter reached Newton. He came home from the Royal Mint at 4pm, stayed up, and had it solved by 4am. He mailed it back without his name. Bernoulli read it and said he recognized the lion by its claw
The answer is a cycloid, the curve traced by a point on a rolling wheel. It drops steeply at first so the ball picks up speed early, then spends that speed on the long flat stretch. The straight line is shorter, but the ball crawls down it gaining speed the whole way
The curve has one more trick. Release balls from any height on a cycloid and they all reach the bottom at the same moment
This looks like one pendulum. It's a million of them, all released less than a degree apart.
Each one starts 1/100,000,000 of a radian from its neighbor. Same rods, same gravity, same equations, no randomness anywhere. For a few seconds they swing as one, then the gap keeps doubling until no two of them are anywhere close.
In 1961 Edward Lorenz hit the same wall with a weather simulation. He restarted a run and typed 0.506 instead of 0.506127, and within a few simulated months the two forecasts had nothing in common.
That rounding error became the butterfly effect, and it's why even a perfect computer could never forecast the weather more than about two weeks ahead.