268 karma · joined February 9, 2023
High school went up through what we call Algebra II. Calculus is an Advanced Placement (AP) course that most students don't take.
I took physical sciences calc + multivariate calc (1 year including summer), an intro to proofs and set theory course, and then finally a rigorous construction of reals was taught in our upper division real analysis course. So somewhere in my second year as a math major. Though I had already researched the constructions myself out of curiosity.
Apart from the material being extraneous for anyone outside the major, I think they were in a sense trying to be more rigorous by first requiring set theory which included constructions of the integer and rational number systems.
The preamble already contains multiple errors (conflation of general and special relativity, assertion that category theory formalizes the common diagram, assertion that mathematical reasoning underwrites thought itself, assertion physical models are unnecessary/curve fitting is all you need ...)
The intro reminds me that V.I. Arnold once accused his algebraist colleagues (quite unfairly), especially in France, were primarily driven by their inferiority complex with respect to the hard sciences. The book would be much better if it didn't begin in this manner. It's valid to study mathematics (or anything of beauty, anything indispensable) for its own sake, of course.
Putting aside the enormous capital, technical and energetic hurdles - where would the profits come from?
Sam's idea seems to be that governments will have to give people basic income, but he is not really an ally to the UBI movement, because in his vision mainly what needs to be bought is access to OpenAI's computer systems.
To be honest it is the onus of the venture capital class to prove they are not grifters. Talk is extremely cheap compared to the resources at their disposal. And to be fair most of them do not even claim to be altruists.
Math and computer science at their core are more it less the same. Both are concerned with manipulating "digital" equipment that is assumed to respond predictably. Equipment is a prerequisite even for pure mathematics - it is interesting in this case because it is the mathematician themself, who agrees to act that way and respond predictably.
Physics is implicated in this in that it forms the basis of that agreement. Certainly it did historically. In the 20th century serious attempts were made to justify it on the basis of notions like consistency and completeness; the failure of that project is not yet fully absorbed. To be fair, the results are devastating because they can only really be understood by students after they have invested greatly in mathematics with the idea that all but a few "facts" derive from reason - when in fact almost none of them do.
Deep Impact (the only good asteroid movie?)
Jurassic Park + Independence Day (peak Goldblum)
Total Recall + A Scanner Darkly (best Philip K Dick adaptation)
Gravity (great visuals / perseverance story)
Their CEO and board are... extremely unreliable narrators, to put it lightly.
They just raised over $6b at a $157b valuation. The total amount of capital invested to date is astonishing. The fact is that their corporate structure is not really a hindrance - 18 billion should be enough to start "an enduring company", in the sense that it won't disappear next year.
The idea that they need to be a corporation to succeed seems like just another story to sell. It's unlikely they'll get out of this hole.
Boltzmann had originally tried to prove that the second law is a mechanical (statistical) fact and several others tried as well. But Poincaré showed that those systems which, regardless of their initial state, inevitably increase entropy later on inevitably reduce it (his recurrence theorem). There are also in fact reversible processes in nature, so it can't be that mechanics alone implies the procession of time. Something more involved is going on.
Carlo Rovelli has also written a lot about the "thermal time" concept in his books.
My takeaway from them is that you can't really get time out of mechanics by itself (statistical or otherwise). In the same way that you can't get baryon asymmetry. It is intrinsically a selection principle on initial conditions.
I grant the hardware is absurdly expensive at the high end, but I really don't think application wise the comparison is apples to apples.
Hotzs saying literally everything with an io pin or actuator will be driven solely by NN (driven by tinygrad) seems to me maybe 1/3 self promotion, 1/3 mania, some much smaller amount incisive at best.
"Societies have always been shaped more by the nature of the media by which they communicate than by the content of the communication."
"Electric circuitry has overthrown the regime of "time" and "space" and pours upon us instantly and continuously the concerns of all other men."
"In an electric information environment, minority groups can no longer be contained-ignored. Too many people know too much about each other."
"We now live in a global village...a simultaneous happening. We are back in acoustic space. . . Electric circuitry profoundly involves men with one another. Information pours upon us, instantaneously and continuously. As soon as information is acquired, it is very rapidly replaced by still newer information. The world has forced us to move from the habit of data classification to the mode of pattern recognition."
The phase change has already been in full swing for 50+ years. From The Medium Is The Massage, 1967.
"Safety may not at all be the result of decisions that were or were not made, but rather an underlying stochastic variation that hinges on a host of other factors, many not easily within the control of those who engage in fine-tuning processes. Empirical success, in other words, is no proof of safety. Past success does not guarantee future safety. Murphy's law is wrong: everything that can go wrong usually goes right, and then we draw the wrong conclusion."
"Why, in hindsight, do all all these other parts (in the regulations, the manufacturer, the airline, the maintenance facility, the technician, the pilots) appear suddenly "broken" now? How is it that a maintenance program which, in concert with other programs like it never revealed any fatigue failures or fatigue damage after 95 million flight hours, suddenly became "deficient"? Why did none of these deficiencies strike anybody as deficiencies at the time?"
The central idea is not to (stop at) discovering what mistakes were made, but to understand why they didn't seem like mistakes to the individuals making them, and what suppressed the influence of anyone who might have warned otherwise.
In terms of what we may/not be missing out on, I say that because it seems few of the possibilities remaining after a century of investigation (many worlds, relational/information based approaches, etc) contain any new physics or scientific insight.
Eg if we could somehow tell that MW or pilot wave theory is "correct", we would still have nothing to do but shut up and calculate the same things, no?
If unitary evolution continues in some sense, we would still need to throw factors away in order for the theory to remain predictive to us.
Particles are only observed to be in a single place at a single time. My understanding is that it may be that we lose the perspective necessary to see them elsewhere, since we are embedded in the same eigenstate (or something close to it). But the task of science is confined to observables. I question, what are the scientific questions that collapse postulate holds back from being solved?
The "Copenhagen interpretation" as we understand it, in which some thing "collapses" when measured, trades under the same name but was invented later. As a result the original interpretations of Bohr/Heisenberg and their philosophy of science have somewhat exited the discussion, even though they had the only defensible epistemology -- the rest as you say is just ontology.
I agree with others that it is not surprising and is a technicality. If you put that aside then the situation is much closer to your intuition.