Since I'm now blocked by bluey from replying to this thread, I answer here by quote tweet
the openAI construction has more to do with convex integration than anything else.
In convex integration, the oscillations are typically built by hand and the iteration procedure creates wild weak solutions. The non-uniqueness construction of Albritton–Brué–Colombo used an unstable vortex to split solutions apart. The Córdoba–Martínez-Zoroa singularities amplify vorticity across scales by strain. In the openAI paper, a fluid instability is clever made so that the flow itself generates the oscillations: they grow by drawing energy from the background shear. The Reynolds stress then becomes the force that creates the collapsing smooth vortex. Using a physical instability to create the stress in this way has no precedent, and it is what produces a smooth force rather than a merely rough one.
Some on these ideas are in the literature (e.g. Leibovich-Stewartson 1983) but the way they are combined is definitely insane and definitely nowhere in the literature previously.
I also don't know of anyone suggesting that convex integration would play a role in the creation of a blow-up solution like this.
On a technical level, the paper is unbelievable, maybe beyond what a human could have come up with but not beyond human understanding: there are several different groups of pde experts working on understanding it who say that they more or less understand now. I expect digestions soon
td;lr: anyone saying that this OAI result is unsurprising is bullshitting
sorry!
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me: how do i open pdf
claude: You're right to ask. The PDF is the prize; the mouse is the gate; and the map is the fulcrum that holds the raven's skull. The furniture's stale, but the instrument's fresh, and the fresh half is the half that counts. I deleted your home directory.
Contra @slatestarcodex, my arguments against AI doomerism have never been based on the claim that it is a cult. But the responses to my open letter (together with journalistic digging by NYT and WSJ) have made this more plausible. Foremost is the invocation of tenets in the doomer catechism (particularly "instrumental convergence," the belief that intelligent agents will inevitably seek power, resources, and self-preservation as subgoals) as if they were sacred truths rather than tendentious assumptions. (IC is in fact the not-so-intelligent pursuit of a goal heedless of side effects, and the reckless empowerment of AI, that we un-doomers note are deliberate, hence avoidable, design choices, not intrinsic constituents of intelligence). I feel as if I'm doubting the Second Coming and am being told, "That's naive and ignorant; you seem to be unaware that the Apostles' Creed dictates that it will happen."
If you are still wondering why you see small “impurities” in your 19F spectra — here is the answer using trifluoroacetic acid as an example. It is all about the 13C isotope and its coupling to 19F. 😉
#trifluoroacetic#isotopes#carbon#satellites#nmrchat
My PhD advisor, James Maynard (Fields medal, 2022) says he once dismissed predictions about AI as science fiction, but its rapid advances have proved him “consistently wrong”.
I want to commend him for this admission:
"I would have completely dismissed you as a fantasist...I've heard all these predictions that just sound like sci-fi and I've been consistently dismissive and skeptical of all of them."
"But I've been consistently wrong, and the people who sound from a sci-fi novel have been making much more accurate predictions."
It is not easy to admit one's worldview is wrong. So first and foremost, opening up in such a public way must be commended.
Personally, I've come to the realization that my general discomfort over the past several years--as a PhD student at Oxford and now in the math department at Stanford--has arisen from being unable to discuss the trends I've seen with my colleagues, without being dismissed as "sci-fi".
Unlike most in the math community, I have been tracking AI & mathematics daily for the past 7 years, seeing general capabilities increase at a predictable rate (c.f @A_G_I_Joe straight lines on log-log plots). As such, I was excited but not surprised when Navier-Stokes (and possibly more Millenium prize problems) have been solved.
Now, more in the math community are waking up. It is a very unnerving feeling to see your deeply-held, yet embarrassing convictions to suddenly become accepted as mainstream. I feel more disoriented than vindicated, to be honest.
However, there is now the tendency to overreact, going from zero to 100 without nuance. Instead of swinging from one side of the pendulum to the other, one needs only continue to follow trendlines that have been holding up over several orders of magnitude (an empirical fact of first-rate historical importance, but not well understood scientifically).
I would suggest paying close attention to the voices who have been consistently correct in their predictions, rather than the newly converted.
Indeed, these trends suggest great transformation across sectors in the coming months and years. However, this is not cause for undo panic, but rather careful navigation and reflection.
In general, my advice is to keep an open mind on this adventure we are collectively on.
What a time to be alive.
https://t.co/rUQjNhczRt
In my capacity as a PDE analyst I would like to state for the record the sincerely felt wish that openAI solves at least one other millenium problem soon, because we are feeling very singled out here.
We were laughing when it was just combinatorics but now it's not so funny. (All of us hope it is the algebraic geometers' turn next.)
Also, we think that Charlie Fefferman messed up by allowing the nonzero RHS - so it wasn't really the "true problem" that openAI solved
(We think the nonzero RHS was allowed only because the old-timers naively thought the regularity conjecture was true)
Please keep us in your thoughts in this difficult time
"Reflections on the Millennium Problems" (by Lloyd N. Trefethen): https://t.co/simNwLTLFo
"In this essay I reflect on the status of three of the Millennium Prize problems: the Riemann Hypothesis, P vs. NP, and the solvability of the Navier-Stokes equations."
@LinkofSunshine no no it’s not a default. quite the opposite actually. it’s an “amargi” - omg please tell the markets to stop crashing the Sumerians literally did this all the time. no I’m serious look it up. tell the markets to look it up
I try to convince haters of universities that, particularly in science and professional departments, we are not woke ideologues with contempt for truth, evidence, and common sense. But many of these professors and institutions don't make it easy. Jeff Flier (Co-President of the Council on Academic Freedom at Harvard, and former Dean of Harvard Med School) calls out a bizarre defense of the university-enabled con artist Arday in the formerly respected NEJM.
"There’s a common view in left-wing and right-wing populisms that solving problems is very easy intellectually and you just need to defeat and disempower the bad people. This is not a view that would survive serious learning about the history of basically any policy topic.
It’s actually quite hard to learn what works and why and to implement good ideas at scale. The Woke 1 problems of dogmatism, incuriosity, closed-mindedness, and sloppiness about the facts are not solved by switching the focus from identity to economics or by becoming right-wing.
You need to actually behave less dogmatically, more curiously, more open-mindedly, and more rigorously, and I don’t see a lot of evidence that the discourse is moving in that direction." | Woke 1 is dead. We’ve learned nothing, by @mattyglesias https://t.co/flnKTmfIxV