I think mathematics is (1) valuable as a way to develop human thinking; (2) useful for us to understand in (more or less practical) ways that will remain valid for the foreseeable feature; (3) enjoyable. This to me indicates we should find ways to keep funding mathematics for its own sake, i.e. just let mathematicians do whatever they think is best for their intellectual development, so that we keep enjoying those benefits. I think the question might then become: not how to keep people interested in becoming mathematicians as cited in this article, but how do we select good professionals to enact those benefits in the presence of very capable AI (e.g. just seeing how many theorems one has proven might be a pretty bad metric) -- I guess I'm referring to what we know as academic or research mathematics.
I think offline exams already work pretty well for this, although I think they do tend to favour a bit much a specific kind of student, so other types of exams could be mixed in, like the proposed digestions of Tao et al, maybe giving a lecture and have a student/professional panel give it a pass/fail, and so on (just throwing a few ideas!).
At least, as far as I can tell this is the urgent matter, along with convincing students that being a mathematician is still a valid choice, and funding agencies that mathematicians should still be funded. That last point is where I think the general public should speak in support of keeping funding, I am not sure at what level. I know there are many other issues in society, like people with food insecurity or just hunger in many parts of the world, preventable disease, etc., but I think it's worthwhile to keep professional mathematics (not sure at what level?) because of how much our complex society benefits if not relies on it still.
> to surmise that our universe is computable by a deterministic computer program
Please an expert chime in to complement, but I believe simulation in quantum mechanics is a quite interesting and not so simple topic.
I believe the more correct thing to say is that quantum mechanics is approximable than simply computable. Don't forget, QM and current physical theories use real numbers, which are not digitally representable; although it seems also the case that information is locally bounded. The finite distribution of states and probabilistic dynamics is I believe is fundamentally what makes information bounded, (which forbids for example naive hypercomputation and I think several paradoxes that might arise from unbounded local information) but don't forget in general the dynamics is still based on continuous quantities as far as we know, not discrete quantities like in a computer. QM is about discrete states within a continuum set interacting with continuum dynamics, I think is accurate to say. Quantum field theory probably complicates things more but similar conclusions might be valid. This continuum dynamics can't be computed exactly, at most you could achieve a pretty good approximation; you'd also need to provision probabilities, either from pseudorandomness (which technically would invalidate the probabilistic model, although in practice this invalidation is not feasibly distinguishable by an observer of current human-scale computing power) or gathering environmental noise.
It's really interesting to me how nature is kind of surprising and defiant of simple hypothesis we come up with. But I think each of those characteristics plays a role, is an important part of existence somehow, and we should keep trying to understand why each aspect of nature is the particular way it is for their numerous insights into our condition and existence.
I agree about the continuum only allowing an approximated simulation by Turing computation. But that’s orthogonal to QM, you already get that with classical fields. In Everettian QM, the evolution of the quantum state of the universe is still deterministic, following the Schrödinger equation. There is no probabilistic aspect in simulating it as a whole.
Regarding the continuum, the final word hasn’t been spoken with regard to the physical world, and probably also with regard to mathematics, since there is some level of controversy about the continuum even in the foundations of mathematics. We know for example that the continuum hypothesis is independent of ZFC, so what’s up with that. It might very well turn out that there is no continuum in physical reality. However, it seems highly unlikely that it’ll be anything like the naive conception of a cellular automaton.
While we model our world as continuous quantities, doesn't QM give the necessary leeway here by imposing limits on measurement? If you computed fields as grids with grid points that are half a plank length apart, then added some "quantum noise" (just good pseudorandom noise in the right distribution), could we tell?
For things like light frequencies I believe we are not even sure if they are truly unquantized, so they might be discretely computable for all we know
Time is the tricky one. But if you get away from computing the whole universe and just try to compute the viewpoint of one observer that might be quite solvable
Any text/program/formula describing a real number can be represented as an integer number, therefore there's only a countable amount of real numbers that can be worked with.
> I don't mean the nature of consciousness or internal experience (which is unfalsifiable)
The way I've been thinking about it is not that internal experience is unfalsifiable, along with the modern science connotation that everything that is unfalsifiable is automatically irrelevant (which would be quite absurd, as everything that is dear and meaningful to humans are all simply cognitive phenomena in the end!). It's that it is externally, naively and a-priori unfalsifiable. That is, you can't externally measure or prove it, without having an a-priori theory of what it is and how it happens in the first place. But it is internally falsifiable, in the sense that if we have it, then we know we have it. Note that it's not that "If I have it, then I say I have it", or that "I one has it, he says he has it"; those are all communication to the external world, and for example machines can clearly say they have it without having it, or you can have it before even learning the words that represent it. But if you have it, you can know you do. This actually creates some potential for expanding this knowledge, maybe, in the future, to allow for external verification. We can internally investigate properties associated with consciousness, and from those properties (along with scientific knowledge), maybe one day we will know more about the objective basis which affords consciousness/sentience manifesting or emerging. So I see it like an experimental field where the component of self-assessment or self-experimentation or self-measurement is essential (again along with more conventional scientific notions).
I have been thinking the same way about all properties of life/consciousness, in particular if we think of ethics as a property of (even if you consider the ethics or ideals only pertaining to how it would be ideal to lead your own life) the mind, or of sentience in general. I think of ethics as an inherent property of existence: it stems from the fact that internal experiences/internal life/sentience/etc. are the only thing that could have value, that in fact sentience is experimentally (again taking the point of view of experimental sentience) the only thing that truly matters or has value. If we are minds, we know that only the content of minds can matter; it cannot matter, for example, that a lone rock in some place no one can know about has this or that fate, because there is no mind to interact or perceive and be affected in any way by it. So all of ethics can probably be founded or based upon this kind of observation, and the act of experimental self-observation of consciousness. And I think it's quite important that we collectively recognize those values and what matters to make our lives better (better yet, as good as it can be!) :)
Going further, all of those are currently under the umbrella of metaphysics, which is again a kind of prejudiced-against (often taken as irrelevant, when it contains some of, and in fact many of, the most important things in life) field of science/knowledge. I think metaphysics should just be seen for what it is as a more indirect kind of science. In a way all of science is varying degrees of indirect, we use all sorts of instruments and need to make all kinds of assumptions (that conceivably, but unlikely, could indeed be false) to be able to do any kind of science or assume any kind of validity to results. We need to assume (although indeed many of those assumptions we don't even need to consider, i.e. they're implicit) there aren't any "gremlins" of whatever kind interfering with our measurements. We do our best to cross-verify whatever experiments we have to increase our confidence. Likewise, metaphysics to me is simply about inferring facts and properties with more indirect methods. One of them is what I referred to above, i.e. observations from within your own mind, and proposing properties of cognition from first hand experience. A second (very close to actual physics) is conjecturing what other universes are out there of if there is some larger mechanism our own universe (or all universes) are part of. Another is judging other properties of existence, for example, are our minds completely separate or are we all ultimately part of the "same thing", somehow? How did I come about living as the person I am currently living, am I perhaps a random sample, with some particular distribution, of all living beings? How do those facts influences how we should live together? (I think they all strongly support the notion of valuing everyone, and discredit any absolute notion of primacy of yourself in ethics, i.e. egotism).
The particular problem I have with your take on value is it sets up a future conflict based upon the state that a human has. It's based on a number of presumptions that only a particular set of arrangements of matter, well, matter. And those that matter happen to be watery sacks of meat.
So in your framework you setup a definition of what an external measurement of someones sentience state... Now, someone makes a machine that outputs those states and externally behaves as if it has sentience. What do you then? Upturn the table and get mad because your classification system no longer just contains humans?
Thank you for your reply. I'm not sure I understand your objection perfectly.
> it sets up a future conflict based upon the state that a human has
It's not clear to me it does.
> It's based on a number of presumptions that only a particular set of arrangements of matter, well, matter.
Well, this premise must be true, I think. How could it be otherwise?
> And those that matter happen to be watery sacks of meat.
This I disagree with. My comment contains no such claims that only humans matter.
> So in your framework you setup a definition of what an external measurement of someones sentience state... Now, someone makes a machine that outputs those states and externally behaves as if it has sentience.
So, this is something we need to be very cautious about, I think. First, we don't really know what makes someone sentient. I do not claim to know, and certainly not know with a high degree of certainty (I may have a few incomplete hypothesis).
First, it's clear to me that someone's external behavior does not dictate sentience (positively or negatively). I gave some examples, but I think this can be pretty reliably established. To make things simpler, divide the candidate sentient systems by their "output quantity/quality", from less to more. (1) On the "no output side", it's clear that someone can think a lot and have a wonderful inner life without being able to speak. There are (some medical) cases of people going long periods without speaking by choice or by medical condition. Those people can be sentient just fine, obviously you shouldn't need to speak or "output" anything to be considered having an inner life. (2) On the "human-like output" (or superhuman), the argument becomes more involved. First, clearly just the output itself being indistinguishable from human is not sufficient because it could be for example a simple program that just pastes some verbatim copy of a never seen dialogue. Or very simple chatbots that are quite convincing at appearing human (can fool many judges for a while), but clearly also are not sentient. Even for a for a system that genuinely resembles a real human even with under scrutiny, (with all sorts of similar abilities across all fields), consider the case that this system could be simply one astronomically large (unrealistic, I know) lookup table. Basically, it simply works inside by fetching an indexed piece of data and returns it. This is possible, although this machine would need to be astronomical in scale (so it's more of a thought experiment). It shows to me, convincingly, the actual "internal" or "microscale" even implementation of your thoughts matter critically for sentience. I presume, for example, that even if some small portion of your mental activity (i.e. a kind of "subcircuit" in your brain) were replaced by something like a lookup table, you would lose part of the experience of that mental activity. This is clear when the content of your mind differs when you're trying a (kind of) problem for the first time and when you're solving one for the umpteenth time. The latter (possibly, not necessarily) feels more boring, also normally more automatic with less thinking required as you've built habitual responses.
> What do you then? Upturn the table and get mad because your classification system no longer just contains humans?
I would do no such thing. I would welcome any other kinds of sentience. But it would be important to me to carefully establish and understand what kind of systems are sentient, indeed in large part to protect them.
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My main point is that you kind of need to start with sentient minds to understand what sentience is (and of course, not only that, but sentient minds that are aware of their sentience and willing/keen to study it). If you start without sentience, it doesn't seem like this particular concept would form a necessary basis for a theory of action or motivation. Like you can't prove from elementary mathematical premises that sentience is important, I don't think. We need to start from some knowledge that derives from first-hand experience of being an actual sentient being, and expand, solidify or formalize this knowledge to be able to understand it with scientific precision (or anything close to it).
>some knowledge that derives from first-hand experience of being an actual sentient being
This is where things kind of fall apart. We all agree (hopefully) that humans are sentient. The question is, "what else is sentient". Are all animals sentient? If so that leaves a very, very wide range on what sentience is. If not you have to operate your scientific scalpel with a very high level of subjectivity on what is and isn't counted. At some point in the past there was no sentience, now there is. Was it a click and we have it, or was it a slow awakening to the world bit by bit (this is my take). It would also quite likely miss systems that could operate at a higher level of sentience than humans, for example some types of hive minds.
My take on it is that any sufficiently complex system with memory, the ability to perceive outside information, difference that information from what it's doing versus what's happening outside of its actions, and learn from that behavior is at least somewhat sentiment.
This leads me to think that LLMs are 'kind of' proto-sentient. They are not persistent, their short term memory is tiny, and they don't self learn. Once we get the persistent and self learning parts working this really starts to check a lot of the boxes that we consider sentient. Of course by the time we get that working it seems likely we'll have much bigger problems in dealing with AI and the entire sentience thing might not be the first thing on our plates.
> This is where things kind of fall apart. We all agree (hopefully) that humans are sentient. The question is, "what else is sentient". Are all animals sentient? If so that leaves a very, very wide range on what sentience is. If not you have to operate your scientific scalpel with a very high level of subjectivity on what is and isn't counted. At some point in the past there was no sentience, now there is. Was it a click and we have it, or was it a slow awakening to the world bit by bit (this is my take).
I believe pretty much the same thing. It probably isn't all or nothing.
But for me personally I'm really interested not only in what it is (although I'm very much interested in that), but because the problem is so thorny (as you mention subjective), I am first centrally interested in how (or if) we can actually know it reliably. So subjectivity is part of reality, as the mind is part of reality. In principle, it seems we should be able to understand quite a bit about subjectivity because of this, because it is part of reality. For example, the mind clearly obeys causality and all other principles (that I know of) we observe (elsewhere) in reality.
So I've been studying this along side with ethics, as the two are deeply interrelated, and I think ethics is an important field to develop, and to develop additional certain around (many people find difficulty in finding meaning in life). By ethics I mean what we should do, what is good, and from that also of course how we should behave toward each other.
I believe in a very open science way of working, feel free to contribute :)
That said, I have no formal philosophical training (although I did study so philosophers), but I believe for philosophy as for math and science the soundness of the arguments (as well as consistency with reality/experimental verification) are what is fundamental.
> was it a slow awakening to the world bit by bit (this is my take)
Yes, I usually have been facing this kind of problems using some tools inspired by math and logic. For example, take some supporting arguments (1) it is known that humans undergo significant changes throughout our lives, we gain neurons and neural connection in childhood, and lose those throughout our lives (although I believe the brain as a whole is very dynamic throughout). There didn't seem to be any turn on/off of sentience in my own life; (2) Even my earliest memories point to a gradual awakening; (3) In my discussion with Dagon, he brought I think a central point: probably sentience isn't a single phenomenon or something you turn on/off. It's probably more a whole array of inner sensations (that may compose greater structures, longer lasting sensations), kind of like a zoo of experiences. It's us that desperately want to be a single, or singular thing, which I believe is related to our instincts and notion of ego. So the self or ego seems like it is not a fundamental thing, but simply a way we understand or organize our society, and I do think it's important in practice. I think we're more like a collection of interrelated internal phenomena, which can probably significantly vary in intensity, duration, how good they are (this is a key and tricky point I believe!), etc.. This might be analogous to fields and particles in physics. As far as we currently know, it seems fields are arguably more fundamental than particles (or rather a possible distinct and complete interpretation), and fields are extended and not discrete phenomena. Particles are useful approximations or abstractions of field behavior in this sense. In closure, indeed sentience does not seem like anything like an on-an-off, 0/1 phenomenon, as explained in the cases above.
I really want to know how much can we know about sentience. If my hypotheses above are true, then I think we can establish some elementary facts only about sentience, like you mentioned it seems clear to me as well you need some kind of information processing system, the volume of information probably matters, and its internal structure probably matters as well. Consider that in any object at a temperature above 0K, there is an enormous flux of information corresponding to interaction between particles, essentially thermal flow or local kinetic information. Clearly any piece of matter is not sentient. So clearly what information is being exchanged and how, how it is processed and transformed matters. I think a useful principle in this regard is simply that the information should (as a sufficient, and maybe almost necessary condition) represent certain things and form networks of representation or meaning. Basically, sentience (which gives meaning to life) seems pretty much built on meaning: in the sense of representation and interrelation of abstract concepts, for example, like the state of your body, known persons and ideas, places, and so on (some of this meaning seems quite instinctive and non-verbal, I do not believe human language is a total necessity for those experiences to manifest, I think there are proto-linguistic representations in our minds; so I do believe animals probably do have varying degrees of sentience; indeed many of those meaningful representations many times are just bodily signals like pain, relief (like when you drink water after being thirsty), taste from food, or abstract feelings from music, and so on).
So as we require a more and more complete (e.g. finding more specific necessary conditions for them to manifest, and also more detailed sufficient conditions) conditions for those sentience phenomena, we will I think meet a vast array, a huge number of distinctive phenomena, and those phenomena manifest in different character, intensity and frequency depending on the individual (like comparing what a human experiences with some animal of other species). I think that will find close associations with the study of art. Like we know there is more energetic or more relaxed music, or more melancholic or more upbeat, and those feel different. We already know a whole lot about sentience :)
Now we do come back to the question of whether we can tell say an LLM manifests those phenomena internally. Beside everything I said, I think it's a matter of studying its structure and seeing comparatively how much it transforms and analyzes information (with a certain originality, perhaps, i.e. non-memorization) versus how much its answers are simply kind of rote and non-transformative (basically a high degree of memorization) (like the lookup table example I gave previously). Those are all observations built on our first hand experience of being sentient beings, and couldn't be otherwise -- the "laws of the mind" are not provable in elementary systems of logic (somewhat like the laws of physics are not either). Logic is able to tell only which of a number of candidate theories is internally consistent (note logical consistency itself has an experimental motivation from observing nature! (e.g. logic is related to causality in nature)), but it cannot tell which of candidate consistent theories is the case. For example, someone can claim sentience simply does not exist. There is nothing logically inconsistent in that theory by itself, but its inconsistent with our own experience of the world (I think, therefore I am). I've seen some pretty wild claims on the internet :) which I don't believe are true -- you can find propositions that the meaning of life is this or that (for example, to have power or wealth) -- I reject those propositions in a similar manner to stating "I think, therefore I am" -- sentience is evidently true from personal experience, and it being true, and us essentially being "made out of" sentience or sentient phenomena, all that matters must concern that, and not any external objects like wealth or power. It's clear to me wealth does not automatically determine the character of your sentience, and neither does power.
Another central interest of studying sentience is understanding whether some experience (or set thereof) is good or bad -- for the lack of being aware of a better term, I call this valence (i.e. how much value it has). That is important of course to us, because we don't want to just live, we want somehow to have good lives. This is something else that is experimentally true, I believe: when you suffer or feel intense pain, for example, you can verify that indeed there are bad feelings; and likewise when you have gone through good moments, afterwards you become convinced of their existence. This is kind of tricky because I don't think what we desire is necessarily good, or things we don't desire necessarily bad (i.e. it seems motivation, which is a lot driven by instinct, is distinct from genuine valence). And in general this self-knowing process has many important personal limitations like our limited memories and limited capacity to compare different feelings.
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Finally, it is not clear to me this project (for example, of being able to have some rough scientific measure of how intense and frequent are sentient phenomena (or qualia) of an LLM versus a typical or given human -- say e.g. 50,000x more or less intense) is at all feasible, given the limitations of humanity and technology, it's not clear we can do more than handwave "Something, something information processing, something something meaning!" :) But I do think it's worthwhile to try and see what we can find.
I've written some C code recently, and it came to me perhaps the pointer syntax may not be ideal. I'm not sure what the ideal would be, but I think a different notation for usage and declaration could make it less confusion.
In particular I associate '*' (used as *ptr, i.e. content that ptr points to), with content, as opposed to '&' (from &var, address of var), so again '*' means content thing points to. But in declaration, when you declare 'char *ptr', which is a pointer to a char, you clearly can't read it exactly the same way ("char with content of a pointer"? More like, the content of a pointer is char). So maybe another symbol like @ (denoting "is a pointer"), or just the keyword pointer, might make things clearer, so you'd have 'char pointer ptr' (ptr is a pointer to a char, read backwards) or simply 'char @ ptr'. The shorter '@' would be justified when you have multiple pointer e.g. when working with multidimensional arrays (which are often @@@float, something like that). Just an idea that occurred me ;)
(Although I hadn't thought about pcfwik's principle that it's written as used, that makes somewhat more sense to me)*
Edit: Said otherwise, in usage syntax the convention (or at least my way of thinking) may be left-to-right, "content of" or "address of", while in declaration we read right-to-left, "is an int", or "is a pointer", and it would make sense to me that the symbol for "is a pointer" is different than the symbol for "content of"/"address of".
I thought it was a bit of a miss that C didn't use ^ as the pointer sigil. I mean it's literally pointing. I'm guessing some early terminals didn't have that character on the keyboard.
> I thought it was a bit of a miss that C didn't use ^ as the pointer sigil. I mean it's literally pointing. I'm guessing some early terminals didn't have that character on the keyboard.
That can't be the reason; IIRC Pascal has always used '^' for pointer derefencing (just like git's HEAD^^^)
I think the only significant mistake was having both prefix and postfix operators for types. If they all neatly sat on one side there would be no problem.
Which follows an obvious "if modifier of a base type goes to the left of the type, then the operator that uses this modifier goes to the right in the expression". Just like "array of T/[]T" translates into "arr[index]".
> Math is entirely subjective. "Proof" essentially means "Other educated practitioners have the same experience when trying to understand this."
> The logical steps that proofs are built on all have that common foundation. Our concept of logic based on our subjective experience of "truth." We've built machines that reproduce our subjective processes mechanically, but there is no sense in which this idea of "true" is truly objective. It happens to be computationally convenient, and it has some relationship to experience, but that doesn't make it an independent reality that all possible observers, human and otherwise, would agree on.
I continue to think extensively about truth, but currently I disagree. There are senses in which truth can be well established, and those are quite important. I think the basic essence of truth is how we can make a statement (or a model), and have a system for measuring either reality or just mathematical/abstract objects, and verify the statement through this measurement.
As you note, for current mathematics it seems like all of it (all things we call mathematics at the moment) can in principle be formalized in a logic that is machine-verifiable, that is, essentially objective. We're well on our way to demonstrating this for most of mathematics (already most undergraduate curriculum). I think that's because almost the definition of math is that is has this property: in my opinion mathematics has distinguished itself as being the "science of certainty" as applied to language and abstract thought. The way this certainty is achieved is through agreeing on some fundamental assumptions and how certain rules (which are also assumptions themselves) can act on those assumptions to constitute theorems. Theorems are not necessarily physical-world truths/properties (at least not in a simple way in the universe we currently inhabit), you can study alternate physical laws that aren't compatible with our (approximately) Newtonian world, for example. They are logical/abstract-world truths that result from your assumptions. Pretty much by definition (and in a somewhat limited), then, mathematics (at least as far as things like truth of theorems in certain axiomatic systems) is inherently objective, machine-verifiable even.
What's left to be subjective, I would say, isn't really the notion of truth in mathematics, it's which assumptions we should elect to investigate, and which theorems should we elect to prove within those assumptions. Some mathematicians also have some notion of "absolute truth", and tend to reject systems of assumptions (axioms) that don't match what they regard as true -- basically going in reverse and searching for assumptions that can enable a theorem (which effectively acts as an additional assumption).
This activity needs certain basic premises to make sense, for example if a set of assumptions proves that a property holds, and also that a property doesn't hold; or if they predict a certain value X is the result of a dynamical model, and also predict that a different value Y is the result of such a model/equation, then we reject those premises. In a certain sense we are most interested in premises that have, even if a very weak, correspondence to reality.
I think it's more informative to recognize that it's not that everything is subjective[1], it's that everything is experimental. For example, the claim above that measurements and correct predictions can only have a singular valid value, corresponds to our experience with reality, in which in a certain way is singular; there are not multiple realities; objects have definite positions. Even if you think of quantum mechanics, in which we may say particles follow a distribution instead, we still say then there's a singular distribution a particle might have at any single time. Logic itself isn't random, it's connected to empirical observations about reality, which tends to increase the chance that conclusions for logic (which is made to share some properties with reality) tend to be valid in the physical world, of course often dependent on what additional statements you pile on top.
There is also another interesting lens that mathematics is artistic (and I think this will become increasingly important) -- making maths and learning maths is a kind of satisfying cognitive activity in its own right, and we also tend to chose what to explore mathematics on those grounds (in fact historically, pre-18th century say, this might be one of the main drivers of mathematical development, I believe[2]). But of course this is again just a reflection of the actual real properties of human cognition, and also this interest and satisfaction often becomes connected, if sometimes faintly, with the ability of math to represent reality (in a particularly satisfying way) and its objects of interest (for example patterns in nature). Another description for this aspect is maths as being hobby-like, about solving puzzles, or like a (hopefully enjoyable) game.
Note that for this particular "game", the objectivity (or if you prefer, machine-objectivity or consensus-machine-verifiability) of the rules and their application is a significant bonus, it makes the game much more interesting, increases its potential when everyone can agree and the rules and not "capricious" (simply dependent on whims of other people and judges); this gives practitioners safety and security and enables a wide social reach -- most games strive to have objective rules.
Arguably this kind of activity is valuable for the cognitive and subjective development of people that has lasting importance.
> Animal brains can't abstract like (some of) our brains can. What are the odds our brains are limitless and don't have some similarly crippling limitations from a couple of levels up?
Well, this happens sometimes. In cases where there are phenomena like universality. For example, in any computation machine model (state machines, pushdown automata, etc.) has limitations that we can say makes them less powerful then Turing Machines. But then Turing machines can simulate any other machine, becoming a kind of ultimate or last stage (at least in terms of abstract capability) machine. It may be that our cognition has some bounded universality properties (I think it's likely it does).
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In summary, I still think mathematics has a lot of human potential in terms of (1) high level human guidance, (2) an internal artistic/subjective sensibility to the subject, (3) safeguarding human understanding of the world and associated individual intellectual development.
[1] Again, I just argued that there is a strong sense in which for example mathematics isn't subjective at all, but sure I do believe in a weak sense everything is subjective in the sense that everything is known or filtered or sensed through our minds which have limitations and aren't simple deterministic machines.
[2] For example, I believe for the Greeks geometry was intimately connected to philosophy/aesthetics (e.g. Platonism) and very little to applications. In ancient times and middle ages maths developed a lot from astronomical observations that had some applications but I think were largely cultural and ritualistic. In the late middle ages European aristocracy would fund mathematics largely for its inherent interest as an intellectual activity, and many nobleman enjoyed mathematics as a past time and would challenge each other to puzzles. Japan had Sangaku, in which mathematics was made for fun, aesthetic purposes and possibly bragging rights. No one actually needed to build say spheres in obtuse constructions with certain radii :)
Really cool, and although I am not quite up to date on biology research (relevant here), I believe there were exciting results showing mechanisms like electric fields acting as signals for cells to differentiate in some species, i.e. "telling a cell where it is", and supposedly guiding "what it should do/become", etc.. I believe this was a result from studying Axolotls, the amazing self-regenerating (and severely threatened of extinction in nature) salamanders[1].
Side note: if we needed more reasons to conserve the amazing and enormous spectrum of life, one more reason is this kind of discovery that might enable better understanding (and maybe enhancement one day) of cell growth and regeneration in humans. Also showing that biology in many ways is extremely far ahead of what humans can achieve with current technology or will for the foreseeable future (as much as the automata example is very neat, it's nowhere near self-assembling full working and self-reproducing creatures from a compact genetic code!).
It seems you can donate directly to help Axolotl conservation (which again is critically endangered), seems really important if you can help! [2] (although there are of course many other means to help if you're interested in conservation in general!)
It's not just about the base algorithm. It's also about the memory needed to run it, and the clockspeed. For example, even the hardest problem you can imagine, if it has a verifier algorithm that fits in 4k (which means the solution itself can be much larger than 4k), then you can simply do a basic brute force search over the solution space. That doesn't mean this algorithm is very intelligent; it's only very capable if you have a sufficiently fast computer; although indeed brute force is only feasible for the simplest tasks in practice, so the idea that algorithms (of increasing sizes) enable (greater) intelligence is definitely a part of the story, but not the whole story. You can also think of DNA, which represents a recipe for our bodies and brain, which we then use (essentially as an "algorithm") to learn things, with degrees of freedom (memory) far surpassing what DNA stores.
Now if you had a very good chess program running in very constrained (dynamic/RAM) memory, then that'd be partially more revealing. From a cursory search there's a 1800 ELO engine for the C64, which seems very impressive but very far from the best human players.
I'd be interested to see a curve of ELO x Avaliable RAM for the best chess engines (up to given RAM), and how that compares to other games and activities.
On RAM vs ROM (program size) memory, I think at a high level dynamic memory helps you keep track of search paths in a large tree search, saving you some computation. Program size tends to enable improving the effectiveness of your search heuristic, as well as pre-computing e.g. initial and final game optimal moves (potentially saving arbitrarily much compute). I like thinking about those things because I think the search paradigm is pretty informative of computation (and even intelligence) in general. Almost every problem is basically some kind of heuristic search in some kind of space. And you tend to get better at things by refining your heuristics (usually through some experimental training process or theoretical insight), considering more options, exploring deeper consequences, etc..
I think what really defines humans isn't really our ability to solve problems or play chess well etc. (although that's extremely useful and also enjoyable most of the time), it's really our emotions and inner world. We are not really Thinking Machines in essence, we're Feeling Machines most significantly. The thinking part is a neat instrumental part :) We can delegate thinking to machines but what we cannot extinguish is feeling or the human "soul", because that is the source of all meaning.
I like the idea of some kind of algorithm minimalism, or at least parsimony; but I also think sometimes it might be appropriate? In this case, another approach would simply be randomization, which doesn't favor any name (Aaaaaron Aaaaanderson's blog :P ), this randomization can be consistent (such that you can find something you wish in linear time).
I think equally important is algorithmic transparency, that is, that the algorithm be publicly disclosed (although I think simplicity is a component of transparency: if you just dump a huge incomprehensible algorithmic mess somewhere that's not very helpful), so that you at least know what you are getting into, and better yet have some ability to choose and make educated critique of the current state of things (i.e. does the algorithm just maximize engagement like a slot machine? or does it optimize for some kind of helpfulness?).
This is extremely far from any of my expertises, but I'll offer an answer while no one else did (please correct me!). Basically, all medicine (i.e. drugs) we have are proteins or certain compounds that fit within some of our cell's (or viruses) molecules and does funny stuff to them, like disabling certain parts, acting as a signal to regulate behavior, and so on. Doing funny stuff is basically about fitting into another molecule. So research about how proteins (most molecules (after water) in our body, I guess) interact is incredibly important in basically all medicine, specially in the discovery of medicine (like suggesting compounds (drug) that could fit in certain receptors or perform certain function), and understanding disease/pathologies (which give ideas on how to prevent and treat them).
If folding@home helps to understand and model this behavior of molecules (which I guess tends to be difficult and unreliable to do without the aid of computers), it is extremely helpful. Now I don't know other details like, perhaps molecular biology is the bottleneck and there is scant available molecules to analyze (reducing its impact/marginal sensitivity), or perhaps compute really is a bottleneck in this particular problem. But nonetheless it seems like a great project for which contributions do make a difference.
(Note: although, that said, if you were expecting something like 'compute->miracle drug comes out', I believe that's not quite how it works; research in general rarely works that way, I think because the constraint space and problem space that would require this approach is too large and complicated; and in fact I believe many if not most significant discoveries have resulted from playing around and investigating random molecules, often from (nonhuman) animals, plants and bacteria[1]; although molecular sciences (molecular biology) seem to enable a slightly more methodological approach)
Do you think they used an AI or something? Seems to be answering a question I didn't even ask. The strange performative replies I've had to my question makes me more suspicious about folding@home.
Honestly, I doubt it was an LLM because an LLM would have stuck closer to answering the question (avoiding non-sequiturs is the only thing they do, after all) .
I'm not quite sure what the point of the response was.
This is not a super well thought out position, but I've been leaning towards really disliking AI art in general (without having an opinion on any strong policy action yet).
First, art is, I think, one of the most enjoyable activities we have. One evidence is a lot of people forego higher salaries to choose an art job (although being a job carries additional responsibilities and some inconveniences compared to doing it as a hobby). It's a shame to see it diminished, when I believe we should be diverting efforts to automate other stuff.
Second, most AI art I've seen has been quite substandard compared to human art. We still don't know very well what human emotions are, the origin of sentience and qualia, etc.. But I think humans still lead here in having and probably understanding emotions. While for other tasks most implementation detail is irrelevant (e.g. in code, that it works tends to be most important, vs. minute choices in style), in art every detail is particularly relevant. Knowing this, it bothers me usually when I see this art that it doesn't carry the same knowledge of context and nuance a human would have.
Third, There's also the effect of making me question whether each piece of artwork was made by a human or AI, that didn't exist before. It does carry a bit of a magical feeling I think knowing a real person made every piece of artwork prior to 2018 or so (I think algorithmic art[1] is fine in this regard, because it tends to be more clearly algorithmic, and the involvement of the artist in coding is significant), that is now gone or at risk. Even the thought of imagining say their work day or what they had for lunch or talked to coworkers or friends is pleasant to me (at the risk of romanticizing it too much).
I suppose if AI art actually understood human nature, and specially the specific context of each art piece, better than us some of my arguments might be diminished. But the negatives so far seem to outweigh the positives, and I would like to e.g. give preference to content that doesn't use AI art.
(It is, admittedly, also the case that we lost a similar amount of craftsmanship when the industrial revolution happened, and in return we were able to support a larger population, and greater material conditions for most people. Every object now isn't carefully handcrafted. I think it's different because well, now material conditions are relatively abundant, and second there's no such insatiable, significant and irreplaceable demand for art as there were to common industrialized objects (take shoes for example), at least not to the same extent or vital significance. That is, the ability to have a shoe at all far outweighs it being carefully handcrafted, I believe; while experiencing a poorly made AI movie or artwork might be actually worse than none at all (or simply an older human made movie), and it also gets more cumbersome to evaluate for ourselves whether AI was employed or not. Also, while say shoes only last a limited time and need to be constantly produced, good artwork can last indefinitely (using digital storage), and even if you account for cultural change and relevance, can still last a really long time, motivating investing more into it.)
I'm quite sure that if we're still around in 500 or so years, we'll still be enjoying say Starry Night by Vincent van Gogh (probably as a digital reproduction). Current AI art will probably be largely discarded, so seems largely an unwise investment. Actually this kind of applies to code as well. It seems plausible Linux could still be used in 500 years from now (see how we still value finding Unix v4 50 years after), or at least of some interest. Those durable intellectual goods don't seem like wise places to invest anything but the best of us :) (at least in the cases it's not disposable)
The arguments above also don't seem to apply say in concept stages, or say for bland corporate diagrams that will be disposed of in 1 day, and which a huge quantity is needed. I think the main criteria I would evaluate is (1) Was it enjoyable to produce (for the artist(s))?; (2) Will it have a significant (artistic) impact on who is experiencing it?; (3) Will it last a long time?
[1] W.r.t. algorithmic art (and digital in general) (take bytebeat[2] for example), which is a field I really love, I am not any kind of absolutist about it. I know there tends to be extremely more degrees of freedom for human expression in a manual piece than in an algorithmic piece, so I see it more as a complement and not a substitute for more conventional art. I'd never give up ever hearing human musician player music for bytebeat, just bytebeat is a lovely experimental other dimension of expression. Writing a prompt seems a too few degrees of freedom and context, and too much of an uniform context that is less rich than humans can provide.
I think offline exams already work pretty well for this, although I think they do tend to favour a bit much a specific kind of student, so other types of exams could be mixed in, like the proposed digestions of Tao et al, maybe giving a lecture and have a student/professional panel give it a pass/fail, and so on (just throwing a few ideas!).
At least, as far as I can tell this is the urgent matter, along with convincing students that being a mathematician is still a valid choice, and funding agencies that mathematicians should still be funded. That last point is where I think the general public should speak in support of keeping funding, I am not sure at what level. I know there are many other issues in society, like people with food insecurity or just hunger in many parts of the world, preventable disease, etc., but I think it's worthwhile to keep professional mathematics (not sure at what level?) because of how much our complex society benefits if not relies on it still.
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