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.)
Caves of Qud is quite good, though a bit less traditional in being a big open world vs a dungeon. There a few quirks and bugs but the game is very fun and creative, and it has excellent music. I also love the graphics but it is an acquired taste.
I played the Dwarf Fortress roguelike mode several years ago, and it was really more of a toy - nifty to play around with the mechanics but too dry and arbitrarily difficult to be a fun game. But almost all the dev focus was on fortress management, maybe they’ve spruced up the roguelike with the Steam release.
The point is that knowing where your hand is in space relative to the rest of your body is a distinct sense which is directly three-dimensional. This information is not inferred, it is measured with receptors in your joints and ligaments.
Inner ear is a great example! I mentioned in another comment that if you want to be reductive the sensors in the inner ear - the hairs themselves - are one dimensional, but the overall sense is directly three dimensional. (In a way it's six dimensional since it includes direct information about angular momentum, but I don't think it actually has six independent degrees of freedom. E.g. it might be hard to tell the difference between spinning right-side-up and upside-down with only the inner ear, you'll need additional sense information.)
It is simply wrong to describe touch and proprioception receptors as 2D.
a) In a technical sense the actual receptors are 1D, not 2D. Perhaps some of them are two dimensional, but generally mechanical touch is about pressure or tension in a single direction or axis.
b) The rods and cones in your eyes are also 1D receptors but they combine to give a direct 2D image, and then higher-level processing infers depth. But touch and proprioception combine to give a direct 3D image.
Maybe you mean that the surface of the skin is two dimensional and so is touch? But the brain does not separate touch on the hand from its knowledge of where the hand is in space. Intentionally confusing this system is the basis of the "rubber hand illusion" https://en.wikipedia.org/wiki/Body_transfer_illusion
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.
I don't think "so isolated he turned to a chatbot for validation" describes this, or why people get unhealthily attached to chatbots.
1) The man became severely mentally ill in middle age, and he lived with his mother because he couldn't take care of himself. Describing him as merely "isolated" makes me wonder if you read the article: meeting new friends was not going to help him very much because he was not capable of maintaining those friendships.
2) Saying people turn to chatbots because of isolation is like saying they turn to drugs because of depression. In many cases that's how it started. But people get addicted to chatbots because they are to social interaction what narcotics are to happiness: in the short term you get all of the pleasure without doing any of the work. Human friends insist on give-and-take, chatbots are all give-give-give.
This man didn't talk to chatbots because he was lonely. He did so because he was totally disconnected from reality, and actual human beings don't indulge delusions with endless patience and encouragement the way ChatGPT does. His case is extreme but "people tell me I'm stupid or crazy, ChatGPT says I'm right" is becoming a common theme on social media. It is precisely why LLMs are so addictive and so dangerous.
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.
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.