Trying to read the math behind quantum chemistry, it is never clear to me which parts are fundamental, which parts are tricks, which parts are needed just for close form expressions, which parts are computational approximations, and which are the limitations? For a subject that should be fundamental for future technological advances, and highly dependent on the growth of computation resources, it seems to me exceptionally opaque and I suspect not well presented?
In a nutshell, the only approximation in Hartree Fock is the assumption that the electronic wave function has a very specific form. Namely, that it is a Slater determinant of orbitals, and that each orbital is a linear combination of atomic orbitals from a fixed basis set.
The linear coefficients of the orbitals are then solved for via the (exact) variational method.
Of course, the true wave function is generally not a Slater determinant. In particular, electrons in a Slater determinant with different spins are uncorrelated.
The standard approach to resolving this is density functional theory. In that model, the main approximation is the choice of an “exchange correlation functional” which approximates the electron exchange and correlation energy. The choice of a functional is unfortunately a dark art in the sense that they can only be evaluated empirically rather than from first principles.
Hi, thanks for the recommendations.
I looked a little at the book, basically at the end we can compute some properties for small molecules sitting alone in space?
What about arbitrary molecules, interacting? Or computing reaction rates? In a solvent? My understanding is that there are some algorithms for all of these, and there is probably progress made, but I never seen (online) anyone complaining that we cannot compute even this basic chemistry. I feel like we should care more about this problem.
If electricity is cheap enough, you can take CO2 from air and make fuel (not sure what is the threshold? 5-10 times cheaper then now?). then you can use that fuel where you need its energy density. I agree that it seems pretty dumb to ignore China (and soon India) CO2 emissions. Again, if you manage to make nuclear cheap enough, you could just gift reactors to everyone that needs them. It can be argued that cheap and safe nuclear was not really tried.
Well, it is quite difficult indeed, but I am curious what will happen in the next 20 years, with China very interested in this, and some renewed interest in the west too. I am also not sure which is more unrealistic, cheap nuclear or fusion.
Yea, I mean.. the point isn't the price imo. We can build out nuclear and sequester CO2 without it being super cheap. We can do massive projects like that anyway.
Not sure how helpful it is, but:
Words or concepts are represented as high-dim vectors. At high level, we could say each dimension is another concept like "dog"-ness or "complexity" or "color"-ness. The "a word looks up to how relevant it is to another word" is basically just relevance=distance=vector dot product. and the dot product can be distorted="some directions are more important" for one purpose or another(q/k/v matrixes distort the dot product). softmax is just a form of normalization (all sums to 1 = proper probability). The whole shebang works only because all pieces can be learned by gradient descent, otherwise it would be impossible to implement.
"Bro please just give me the Sudetenland. I swear bro just let me take the rest of Czechoslovakia and I'm done. It's my last territorial demand bro I promise. Just one more annexation and the Treaty of Versailles is fixed. Please bro it's just for the living space."
"Bro please just let me take Kyiv. I swear bro just one more special military operation and the security buffer is complete. It's not a war bro it's denazification. Just give me the Donbas and the land bridge and I'll be chill. One more mobilization and the multipolar world order is saved bro please."
"Bro please just acknowledge the Nine-Dash Line. I swear bro just let me have Taiwan and the great rejuvenation is complete. It's totally an internal matter bro. Just one more island chain and the century of humiliation is over. Please bro just let me cross the strait."
"Bro please just let me bring them freedom. I swear bro just one more regime change and the region is stable. It's about democracy bro it's not about the oil reserves I promise. Just let me install an interim president. Please bro just one more coup."
Is is code a form of AST rewrite rules for optimization? This operation still looks like a incomprehensible wall of code 40 years later (I looked in the past inside the C++ compiler).
It means that the colors should be correct. The sky on tv should look like the sky. The grass on tv should look like grass. If I look at the screen and then I look outside, it should look the same. HDR screens and sensors are getting pretty close, but almost everyone is using color grading so the advantage is gone. And after colors, don't get me started about motion and the 24fps abomination.
> It means that the colors should be correct. The sky on tv should look like the sky. The grass on tv should look like grass.
It is not as clear cut as you think and is very much a gradient. I could send 10 different color gradings of the sky and grass to 10 different people and they could all say it looks “natural” to them, or a few would say it looks “off,” because our expectations of “natural” looks are not informed by any sort of objective rubric. Naturally if everyone says it’s off the common denominator is likely the colorist, but aside from that, the above generally holds. It’s why color grading with proper scopes and such is so important. You’re doing your best to meet the expectation for as many people as possible knowing that they will be looking on different devices, have different ideas of what a proper color is, are in different environments, etc. and ultimately you will still disappoint some folks. There are so many hardware factors at play stacked on top of an individual’s own expectations.
Even the color of the room you’re in or the color/intensity of the light in your peripheral vision will heavily influence how you perceive a color that is directly in front of you. Even if you walk around with a proper color reference chart checking everything it’s just always going to have a subjective element because you have your own opinion of what constitutes green grass.
In a way, this actually touches on a real issue. Instead of trying to please random ppl and make heuristics that work in arbitrary conditions, maybe start from the objective reality? I mean, for the start, take a picture, and then immediately compare it with the subject. If it looks identical then that's a good start. I haven't seen any device capable of doing this. Of course you would need the entire sensor-processing-screen chain to be calibrated for this.
Everything I talked about above applies even more so now that you’re trying to say “we’ll make a camera capture objective colors/reality.” That’s been a debate about cameras ever since the first images were taken. “The truth of the image.”
There is no such thing as the “correct” or “most natural” image. There is essentially no “true” image.
I completely agree. Theoretically you could capture and reproduce the entire spectrum for each pixel, but even that is not "true" because it is not the entire light field. But I still think that we can look at the picture on phone in the hand and at the subject just in front, and try to make them as similar as possible to our senses? This looks to me like a big improvement to the current state of affairs. Then you can always say to a critic: I checked just as i took the picture/movie, and this is exactly how the sky/grass/subject looked.
Well, I know what you mean, color is complicated. BUT, I can look at a hundred skys and they look like sky. I will look at the sky on the tv, and it looks like sky on the tv, not like the real sky. And sky is probably easy to replicate, but if you take the grass or leaves, or human skin, then the tv becomes funny most of the time.
> I will look at the sky on the tv, and it looks like sky on the tv, not like the real sky.
Well for starters you’re viewing the real sky in 3D and your TV is a 2D medium. Truly that immediately changes your perception and drastically. TV looks like TV no matter what.
Trying to read the paper... I guess if you ignore the difference between finite and infinite tape Turing machine, and if all physical constraints are outside the scope of the paper, then it is easy to prove the universe can simulate itself.
Sorry, I don't understand what you are saying. What do you mean by "something reasonable, that reality is virtual"? In many ways, by definition, reality is what is real not virtual. I have other questions, but this is a good start :)
When I say that reality isn't "real" (which is awkward for sure) what I'm referring to is that we have a perception of space and time which is absolute and inviolable, when it's likely space and time (as we understand them) are artifacts of our perceptual lens, and "reality" is based on something more akin to consensus than immutable laws. From this perspective you could view physics more as a communication/consistency protocol for consciousness than the raw nature of the universe.
Hm, from what I know about physics, time and space are actually much more absolute and inviolable than our imperfect perceptions. the laws are quite different than our intuition, but everything is water-tight and there is no room for any deviation. the smallest of deviations would mean multiple nobel prizes, so ppl are searching really hard to find any, without success. On the other hand, if we talk about our perception, the things we see around us are of course a virtual reality constructed by our brain to model the input from our sensors, but this is normal because there is no alternative. But it seems to me you are saying smth different?
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