AIPedant
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
Your comment is only true if you take an excessively reductive view of "symbol."
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.
[1] Turing computability, lambda definability, primitive recursion, whatever.
I don't know what "the lowest form of intelligence" is, nobody has a clue what cognition means in lampreys and hagfish.
The most depressing thing about AI summers is watching tech people cynically try to define intelligence downwards to excuse failures in current AI.
I think you're being extremely reductive about what neuropsychiatry actually entails.
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.
(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.)
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.
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
And of course it really makes more sense to say human perception is 3+1-dimensional since we perceive the passage of time.
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.
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.
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.)
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.
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.
This is not coherent as written:
If I flip a dime and a quarter, and tell you that one of them is heads, do you have increased chance of knowing if either particular one is heads? This is more liar's dice than it is monty hall.
Specifically: it is not true that the firstborn has a 50-50 chance of being a girl, given you were told that the family has at least one girl. The firstborn has a 2/3rds chance of being a girl. This is the heart of your confusion.
In a broader sense there is an entire class of confusing conditional probability problems like this. Events which are causally independent in reality (e.g. gender of a child, which door Monty Hall hid the car behind) fail to be probabilistically independent when you have extra information. Yet these probability games are contrived in a way that our intuition takes over and we use our causal understanding even when a better probabilistic understanding gives you a better answer.
What the problem is really saying is this:
1) You have a large collection of families with two kids of varying genders.
2) You draw one of them at random. At this point, your only estimate of P(2 girls) is 0.25.
3) Someone tells you that the family you drew has at least one girl.
4) This extra information changes your probability estimate because the possibility of two boys has been ruled out; the naive 1/4 estimate is refined to 1/3.
The way you are interpreting it is this:
1) You have a large collection of families with two kids, at least one of whom is a girl.
2) Then the probability that the other child is a girl is clearly 50%.
As a reminder this is how the original post phrased the question:
Here's the problem: a family has two children. You're told that at least one of them is a girl. What's the probability both are girls?
To get the right answer you must be careful about conditional probabilities (or draw out the sample space explicitly). The crux of the issue is that you are told extra information, which changes your estimate of the probability.
(This question as written is very easy to misinterpret. The Monty Hall problem, which illustrates the same thing, is better since the sample selection is much more carefully explained.)
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.