Agreed; my professors did use Planck's trick to introduce quantization, but made it very clear that he was just fitting the data and thought the discretization would disappear with further analysis.
Seemingly also the Wikipedia article (https://en.wikipedia.org/wiki/Ultraviolet_catastrophe) claims the pop-sci ordering: “As the theory diverged from empirical observations when these frequencies reached the ultraviolet region of the electromagnetic spectrum, there was a problem.[3] This problem was later found to be due to a property of quanta as proposed by Max Planck: There could be no fraction of a discrete energy package already carrying minimal energy.”
When systems (think "automated" systems like computer programs, mathematical axioms, formal systems, etc, where conclusions can be drawn/calculated "mechanically" from a few starting points) get large enough, they gain the ability to become self-referential. That is, they become expressive enough to encode statements about themselves. A hallmark of this are "incompleteness theorems" like those of Godel or the Turing halting problem.
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.
I can appreciate a book being obscure or dragging things out when it is trying to give the reader an aesthetic experience. But this point seem to be one that would easiest be communicated clearly and succinctly.
Or is the point "there is so much mystery in these systems that perhaps there is room for an explanation for consciousness"? Maybe then I would be more sympathetic.
Or perhaps I should just read the book before condemning it :)
the point of the book is to give supporting evidence and guide the reader to the conclusion through testimony of thought and historical anecdote.
in other words, GEB tries to coax the reader into a eureka moment, which is exactly why it has so many fans; it convinced each and every one of us that we were genius for just a split second.
Good summary. Examples of GEB’s “fluff” are missing from this comment section, so I wanted to jump in and add one of my favorite. Bach encoded his own name in music notes in a piece, and when discussing that, Hofstadter encodes a sentence in the first letter of each paragraph in that chapter.
I am becoming convinced that sugar, although not exactly a drug to which we could apply the concepts of addiction and withdrawal (like tobacco, alcohol, or opioids), nevertheless creates habits that are really hard to break.
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.
I have actually become less convinced after learning Buffett his eating habits. He and Munger couldn’t have eaten much worse than they did and exercised less. Still they are both alive in their 90s. What are the chances of that? Also, I’ve had a spare time job driving elderly people around. The fittest pensioner I ever met was in his 90s and he, upon asking, claimed that he never in his life did much exercise.
So what do these three people have in common? I think it’s a lack of chronic stress. Buffett and Munger are living pretty relaxed lives and the pensioner I met was also surprisingly happy. He told me at a random point during the drive that he was very happy. He told me: "I just met a new girlfriend a few months ago. I’m 94. Amazing huh?" and said this with the most cinsere happiness I’ve seen.
Contrast this to books like Why Zebras Don’t Get Ulchers by Sapolski. The book goes into all the ways in which a body under chronic stress starts to break down. Simply put, if you stress a lot then the body is in survival mode and cancels recovery processes.
So that’s why I think that stress levels have more influence on health than food or exercise. As long as stress is reasonably short-lived, the body will just recover from most things. I’m happy to hear counterarguments to this theory of mine
According to themselves, they are wealthy because they are patient and not they other way around. In Buffett’s own words: "The stock market is a device to transfer money from the 'impatient' to the 'patient'." Being patient requires keeping your emotions under control, including stress. Also, keeping a calm mindset is a common topic under value investors such as Monish Pabrai and Guy Spier.
I don't have such a habit. My parents were never into similar stuff, neither our extended family nor was it common generally where I grew up. I could start doing it as adult living away from them but decided not to, after seeing how affection for sweet junkfood messes up with women en masse and how utterly weak they are against these cravings. And there are some guys in same boat too.
Same for sodas btw, we generally didn't have them, and later I've never found sparkling-anything appealing, remove the bubbles and drinks become oversweetened sewage. Same for champange/prosecco compared to good white wine for 1/2 the price. Best beer lagers from the bottle I've tasted are those Bavarian treasures that have comparably little co2, which messes up tastes badly. If I anywhere get over-co2 beer I know they don't care about quality, just cheap filler.
My best friend's parents bought a machine that was putting co2 into tap water, never grokked why the heck do they go through all the effort to make something so bad in taste compared to original.
Do your kids a favor, don't make sweet stuff some great thing deserved after hardship. You may extend their lifespan by a decade or two and make them overall stronger humans.
On a shorter timescale, I also really like using mouthwash to prevent snacking. A well timed rinse leaves a nice minty flavor in my mouth and also somehow completely suppresses the urge to eat carbs.
Good point. I tried asking ChatGPT to write the numbers from 1 to 10 in 1 sec intervals and it couldn't.
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.
Interesting, this test can be worked both ways then: ChatGPT will answer quickly and with different cadence than a human AND it will, at least for now, struggle with precision in timed events.
Inspired by this, in my PhD we actually used a quantum computer to do classical logic to investigate if that can lead to energy savings [1]. Quantum machines are (in principle) reversible, so they may avoid Landauer's principle.
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].
Interesting, I suppose you'd use reversible logic for the computation? I think non-reversibility is relatively common in computing, but surely a significant fraction of operations could be made using reversible logic. Fourier transforms are a good example. Sorting a simple example of an operation destroying information (log2(n!) roughly ~ n log2(n) bits). Algorithms would need to be redesigned significantly I suppose if it ever came to reversible computing being energy advantageous.
You could also think of reversible blocks. For example, if you had an half-adder, you each constituent gate could be thought of as doing something like erasing in normal operation. If instead the half-adder was reversible, and you perform the operation, save the outputs, reverse it, and then erase the inputs, at least you only have to pay the Landauer tax on the input bits (rather than each intermediary bit). The bigger the block, the more you save.
All of quantum computing is done with strictly reversible logic. But this is not a reduction of power. The Toffoli gate is an example of a reversible 3-bit logic gate that is universal. You can transform any classical circuit into a reversible one using this gate.
The trick? You have some input/output wires in your circuit that start with initial value 0 or 1, and some that end up in a 'garbage' state. You don't care about what they end up with, they strictly exist to maintain reversibility.
As an concrete example, the binary operator a OR b is not reversible - it destroys information. But if we make it a three-in three-out operator f(a, b, c) -> (a, b, c XOR (a OR b)), then it is reversible. Here f is it's own inverse, because applying it twice you'd end up with c XOR (a or b) XOR (a or b) = c.
Yet if you start with c in an initial 0 state, you can now compute the binary OR of two variables a, b in a reversible manner.
Is there any reason to think that quantum computing can fundamentally do more computation than classical computers? Consider this a leading question rather than a stupid one.
> In truth, anything that a QC can calculate, a classical computer can calculate as well, given exponentially more time: for example, by representing the entire wavefunction, all 2n amplitudes, to whatever accuracy is needed. That’s why it was understood from the very beginning that quantum computers can’t change what’s computable, but only how efficiently things can be computed.
No. Scott Aaronson makes this point repeatedly in his blog. Quantum computers are much faster than conventional computers on a few problems, and practically useless for all the others. That's the whole story.
So, for your first questions, you can definitely entangle as little or as many qubits as you want. In practice, it gets harder the more qubits you want to entangle. But a state like the GHZ state can entangle all qubits in your system.
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.
