Very cool presentation. I loved how he says that they improved dict so much that they basically rediscovered database tables with indices.
265 karma · joined December 4, 2017
Maybe a good idea would be to parse the abstract through an LLM to make it more understandable (maybe caching the results so it's not expensive)? Maybe also using some standard style, like starting with a couple of "dumbed-down" sentences of the article for the non-expert, and progressively explaining better.
He was attempting to formalize de Broglie's "particles as waves" concept, which, according to the article, "could obtain the quantization rules of Niels Bohr and Sommerfeld by demanding that an integer number of waves should be fitted along a stationary orbit."
Schrödinger's equation put that claim on firm mathematical grounds. It gave correct predictions. But just what this new "wave function" was remained up to interpretation.
Why? It's not just because of small interactions with the environment that we cannot control. It's that even the apparatuses that we use to control/drive the logical instructions (lasers, electrical transmission lines) should be taken into account if the computer is to be considered isolated. But usually they aren't, and this leads to inevitable losses of reversiblity in the data register.
In other words, unitary (reversible) operations do not come for free.
I think that in quantum computers it is more likely that energy-efficiency will come from some sort of algorithmic advantage.
The book argues that these "strange loops" (of a system onto itself) are behind the emergence of intelligence and consciousness, because physical matter itself gives rise to human intelligence, albeit being a mechanical system.
In other words, we discover what we can invent.
Notice how we train animals with treats: sniffing drugs, attacking robbers, etc. It's a powerful behaviour modulator.
Our brains are no different. In a pavlovian way, we reinforce behaviours that give us a sugary reward. But in our case, the feedback loops are really short. Instead of doing a difficult task, our behaviour to get the reward is simply going to the kitchen and opening a snack.
Do you ever get the feeling, after a meal, that you feel like having "a little something", like a sweet? To me, that's like a learned pavlovian behaviour. And every time we cave, we reinforce that automatic response. It can be anxiety-inducing not to do the behaviour.
The question in my mind is: how do we break this pattern? Because it's easy to do it once, but it's statistically hard to keep it up many times. You will slip up and reinforce the behaviour again.
I am becoming increasingly convinced that we need to change the environment around us, that is, regulate the amount of added sugar in foods.
Edit: Oops, I read the question the other way around. Humans can easily emulate ChatGPT's behaviour in this scenario -- just say that, as an LLM, you cannot do the task.
However, there are subtle energy costs that you can hit before getting to Landauer's. The most interesting to me is that the qubits can become entangled with the wires that control them! This reduces the quality of information, and one way around it is to use a lot of energy [2].
[1] https://arxiv.org/abs/2210.10470
[2] https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.89...
How do you entangle? You can just let two particles interact, so they "mix" their information. Example: you send laser light (photon qubits) to an atom (another qubits). After a short period, there is a probability that the atom absorbed photons, but that probability is not 100%. You just entangled light with an atom. Only measurement can give you information on whether the photons were absorbed or not.
In practice, each platform has its own entangling mechanism. Usually, it entangles only 2 qubits. Many-qubit entanglement can be achieved by pairwise entangling AB, BC, CD, etc.
The first practical example of qubit entangling operation was the Cirac-Zoller gate, you can check it out.
Regarding your second question, you can actually measure just part of the system, and measure the rest later. It will give you a partial collapse. It's called "tracing out", the quantum analogue of marginalization in probability.
Here's a good example of the power of dimensional analysis: how small should the Earth be to collapse into a black hole?
Knowing nothing about the problem, you know it should involve at least two things: the mass of the Earth, M, and the gravitational constant G.
Since F=ma and F=GMm/d^2, we know that GM has units of distance^2 * acceleration (check that). This is equal to distance * (distance/time)^2.
We want a radius, which is a distance. And we almost have it! At least if we can get rid of the (distance/time)^2 factor. But that's a velocity^2! Now, what's a velocity that should be natural in questions about black holes and general relativity? Why the speed of light c, of course.
So, we can guess that the answer is GM/c^2.
Now compare this with the real answer: https://en.m.wikipedia.org/wiki/Schwarzschild_radius
We know that triangles may be displaced, rotated, flipped and scaled while still looking the same. We have a word for this: we say two triangles are congruent when they are the same up to these operations.
This means that there is something intrinsically invariant about triangles. Can we find it? Actually yes! If the sides of a triangle have lengths A, B, C, then the ratios A/B, B/C, etc. are invariant. That is, if you make a triangle twice as big, all sides will multiply by 2, so A/B becomes (2A/2B)=A/B -- it's the same!
So, we can come up with names for these invariant ratios. They're most useful for right triangles. To give names, we need to pick any of the two smaller angles as a reference, call it "a". Now, let C be the largest side, A be the side opposite to the angle and B the adjacent side. Then, the ratio A/C can be called sin(a), B/C can be called cos(a) and A/B can be called tan(a).
Since sin(a), cos(a) and tan(a) are ratios, they only depend on the angle, not how big your triangle is. But if you know some side of the triangle, then you can know all of the other using these values. So sin, cos and than really capture the uniqueness I was talking about!
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Now the applications. I memorized these as the "divide by C" rule.
The Pythagorean theorem says thar A^2 + B^2 = C^2.
Divide by C^2, and you get sin(a)^2 + cos(a)^2 = 1.
Divide by cos(a)^2, and you get tan(a)^2 + 1 = sec(a)^2.
These are all the Pythagorean theorem on disguise.
I still remember that "click".