This is where you are confused - in fact just plain wrong:
A symbol is a discrete sign that has some sort of symbol table (explicit or not) describing the mapping of the sign to the intended interpretation
Symbols do not have to be discrete signs. You are thinking of inscriptions, not symbols. Symbols are impossible for humans to define. For an analog computer, the physical system of gears / etc symbolically represent the physical problem you are trying to solve. X turns of the gear symbolizes Y physical kilometers.
No, analog computers truly are symbolic. The simplest analog computer - the abacus - is obviously symbolic, and thus is also true for WW2 gun fire control computers, ball-and-shaft integrators, etc. They do not use inscriptions which is maybe where you're getting confused. But the turning of a differential gear to perform an addition is a symbolic operation: we are no more interested in the mechanics of the gear than we are the calligraphy of a written computation or the construction of an abacus bead, we are interested in the physical quantity that gear is symbolically representing.
Your comment is only true if you take an excessively reductive view of "symbol."
Articles like this indicate we should lock down the definition of "computation" that meaningfully distinguishes computing machines from other physical phenomena - a computation is a process that maps symbols (or strings of symbols) to other symbols, obeying certain simple rules[1]. A computer is a machine that does computations.
In that sense life is obviously not a computation: it makes some sense to view DNA as symbolic but it is misleading to do the same for the proteins they encode. These proteins are solving physical problems, not expressing symbolic solutions to symbolic problems - a wrench is not a symbolic solution to the problem of a symbolic lug nut. From this POV the analogy of DNA to computer program is just wrong: they are both analogous to blueprints, but not particularly analogous to each other. We should insist that DNA is no more "computational" than the rules that dictate how elements are formed from subatomic particles.
I understand the broader point but it is not actually constitutionally problematic for the executive branch to assert that a suspect committed a crime - of course they believe that, that's why the suspect was arrested! It is better for an elected official to preface things with "allegedly" "we believe" etc, but the governor is ultimately speaking on behalf of the prosecution, not the judge. The first half of this article is based on a bad-faith misreading of the governor's words.
If you look at my comment history you will see that I don't think LLMs are nearly as intelligent as rats or pigeons. Rats and pigeons have an intuitive understanding of quantity and LLMs do not.
I don't know what "the lowest form of intelligence" is, nobody has a clue what cognition means in lampreys and hagfish.
"Making predictions about the world" is a reductive and childish way to describe intelligence in humans. Did David Lynch make Mulholland Drive because he predicted it would be a good movie?
The most depressing thing about AI summers is watching tech people cynically try to define intelligence downwards to excuse failures in current AI.
Putin and Xi fantasizing about immortality via 3D-printed organs quite starkly illustrated that many adults do not understand the difference between science and science fiction.
Keep in mind that we also have no clue how general anesthesia works! It's not just psychiatry, many medications targeting the nervous system (e.g. muscle relaxants) have unknown mechanisms of action https://en.wikipedia.org/wiki/Category:Drugs_with_unknown_me...
I think you're being extremely reductive about what neuropsychiatry actually entails.
It didn't come completely out of nowhere, Euler and Bernoulli had looked at trigonometric series for studying the elastic motion of a deformed beam or rod. In that case, physical intuition about adding together sine waves is much more obvious. https://en.wikipedia.org/wiki/Euler%E2%80%93Bernoulli_beam_t...
Other mathematicians before Fourier had used trigonometric series to study waves, and physicists already understood harmonic superposition on eg a vibrating string. I don't have the source but I believe Gauss even noted that trigonometric series were a solution to the heat equation. Fourier's contribution was discovering that almost any function, including the general solution to the heat equation, could be modelled this way, and he provided machinery that let mathematicians apply the idea to an enormous range of problems.
On the simplest end of that spectrum, Taylor series are useful because many real-world dynamics can be approximated as a "primarily linear behavior" + "nonlinear effects."
(And cases where that isn't true can still be instructive - a Taylor series expansion for air resistance gives a linear term representing the viscosity of the air and a quadratic term representing displacement of volumes of air. For ordinary air the linear component will have a small coefficient compared to the quadratic component.)
That's not what "coherent computational representation" means in this context. It means being able to reliably apply the rules of Othello / chess / etc to the current state of the board. Any competent amateur can do this without studying thousands of board positions - in fact you can do it just from the written rules, without ever having seen a game - they have a causal, non-heuristic understanding of the rules. LLMs have much more trouble: they don't learn how knights move, they learn how white knights move when they're in position d5, then in position g4, etc etc, a "bag of heuristics."
Notably this is also true for MuZero, though at that scale the heuristics become "dense" enough that an apparent causal understanding seems to emerge. But it is quite brittle: my favorite example involves the arcade game Breakout, where MuZero can attain superhuman performance on Level 1 and still be unable to do Level 2. Healthy human children are not like this - they figure out "the trick" in Level 1 and quickly generalize.
You can say it’s exactly 1 plus or minus some small epsilon and use the completeness of the reals to argue that we can always build a finer ruler and push the epsilon down further. You have a sequence (meters, decimeters, centimeters, millimeters, etc) where a_n is the resolution of measurement and 5*a_(n+1) determines your uncertainty.
However, at each finite n we are still dealing with discrete quantities, i.e. integers and rationals. Even algebraic irrationals like sqrt(2) are ultimately a limit, and in my view the physicality of this limit doesn’t follow from the physicality of each individual element in the sequence. (Worse, quantum mechanics strongly suggests the sequence itself is unphysical below the Planck scale. But that’s not actually relevant - the physicality of sqrt(2) ultimately assumes a stronger view about reality than the physicality of 2 or 1/2.)
The real point is that it takes infinite energy to get infinite precision.
Let me add that we have no clue how to do a measurement that doesn't involve a photon somewhere, which means that it's pure science fiction to think of infinite precision for anything small enough to be disturbed by a low-energy photon.
I am confused why you think the exactness of integers and rationals is unphysical. "This egg carton has 12 eggs" is a (boring) physical statement. "You can make 1/3rd of a carton of eggs without cutting an egg" also seems perfectly physical to me. Your problem with zero-point-three-repeating is a quirk of decimal representation, not a mystical property of 1/3.
Egg cartons might sound contrived but the reals don't necessarily make sense without reference to rulers, scales, etc. And in fact the defining completeness / Dedekind cut conditions for the reals are necessary for doing calculus but any physical interpretation is both pretty abstract and probably false in reality.
It sounds to me like Google is moving to a more typical "technical lead" model where leads have substantial authority and some mentorship responsibilities, but they're essentially an IC and someone else up the chain actually handles proper management. Informally, tech leads can gently chew out less senior devs, but if someone actually needs to be disciplined then the lead needs to talk to the manager.
TLM is an odd role. I understand big tech companies have their own culture but it does seem like a poor management strategy regardless of efficiency.
Beyond codegen, it seems to me that the resolution to this paradox is that ChatGPT is a very popular toy in peoples' home life, but a lot of those very same people are wise enough to not use it for enterprise applications. Or, if they foolishly trusted Satya Nadella, LLM-assisted work eventually blew up in their face and they stopped using it. So gen AI is quite popular, but badly falls short of tech's aspirations.
I hate generative AI and refuse to use it, but I hear of people using it all the time in low-stakes contexts:
1) recipes (the cookies might suck but they won't be poisonous)
2) low-quality infotainment (NotebookLM)
3) OpenAI proudly celebrating that horrible Studio Ghibli crap - unlike dishonest math benchmark scores, garish slop on demand actually brings in customers!
And I've also heard of people using it at work and being severely criticized:
1) ChatGPT-drafted license agreements that the executives would never agree to
2) summarizing documents you were too lazy to read and missing crucial context
3) coworkers being personally offended (or superiors being angry) about a ChatGPT email
Programmers and bottom-barrel creatives have the only reliable success with LLMs if there's real money at stake. Then there are notably but low-margin use cases like dyslexia assistance, Be My Eyes, etc. For everyone else, it's just a nifty doo-dad.
Symbols do not have to be discrete signs. You are thinking of inscriptions, not symbols. Symbols are impossible for humans to define. For an analog computer, the physical system of gears / etc symbolically represent the physical problem you are trying to solve. X turns of the gear symbolizes Y physical kilometers.