gnramires

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.

> 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 :)

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!)

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)

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.