> 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)
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 without open source something similar might have happened to a lot of software, but instead of becoming Open, they'd become gratis (free/zero cost), or almost so. The heart of the matter is that software has near-0 cost of distribution, so making 1 trillion is basically the same cost (to the developer) as making 1 unit. So since developers have free economies of scale, they are highly incentivized to lower the price to capture most of the market, I think. Software also requires relatively little maintenance, it doesn't rot[1] -- good software basically lasts forever with some minor up-keeping. Add in competition, and the tendency is for cost to go to near 0, at least for relatively popular software. But then there are two problems:
(1) If the company goes under, the software is lost, or rather it could be reverse engineered with huge difficulty and some information loss about the actual code.
(2) The incentives are still not well aligned with users. The makers are incentivized to rely on advertisements, get (and sell) user data, make their software addictive, and more.
On (1), FOSS software guarantees the source will be available and can be ported to new systems, basically becoming a common good. On (2), the incentives are very well aligned for FOSS, development can become a community effort, and in the rare case a developer would turn to collecting and selling user data or dark patterns, the software can be forked for example. In particular Open source funded by grants, donations and community/voluntary work is very aligned with public interest.
I get the downside that it could be unfair that developers aren't being paid as much, but I believe it wouldn't be much of a difference in income (for those kinds of software), and we can and should as a community donate to open source efforts (and since it's clearly in the public benefit I think governments, companies and all sorts of organizations would be wise to do so).
Finally, you're basically still free to create and sell closed source software, you just have to compete with community and volunteer efforts. I think it's well within your right (and it might make sense in some cases, say niche software). But I think it's worth considering carefully wether it's best for the product, for you and for the community to have it closed or open.
(also, indeed you can sell FOSS, but to be honest I don't know of many success stories in this regard (anyone share some examples?); I know arduino which is open software/hardware was very successful selling their genuine boards/having a pay request on download that you can dismiss. On Linux package managers make this difficult, although Flathub recently added donation buttons!).
[1] There are some issues popularly called "software rot", but it's basically some relatively minor (compared to the rot of many physical goods) compatibility issues when interacting systems change.
Something I think is worth pointing out: this is happening in the Netherlands, i.e. their jurisdiction. I think most people here aren't from the Netherlands. I think they should be free to try out the legislation they want, and people elsewhere don't need to agree. It's good that different countries can try different things, and if that doesn't work it's a lesson for other places, and if it works that's even better. People on the internet tend to focus too much on uniformity and conformity, as if we lived everyone in the same place.
I think another model could help here. Like an automatic/anonymous micropayment when you access a website. This could be a fraction of your internet subscription reserved for micropayments. It should be possible, and cryptocurrencies aren't necessary either (although similar cryptographic constructions may be used, no need for proof of work).
You might enjoy some of my writings on formalizing meaning (see here[1] and follow the links). In some way, although not always reliable, you can say that if you feel A is more meaningful than B, that is already some kind of evidence for this assertion even if perhaps unreliable in some ways.
So there isn't necessarily some huge crisis that you need to justify: in some ways reality just is (and this includes subjective reality;).
Say if you ask why do the laws of physics conserve energy locally, you can actually argue that if it were otherwise actually life would be extremely more unlikely, as that tends to increase instability in various systems (both energy divergence and going to 0 makes life unlikely); but still I'm almost certain you could conceive of forms of life in non-energy-conservative systems (something like Conway's Game of Life, but maybe with more advance rules if you prefer). So while it makes sense that the physics in our universe is approximately locally conservative (maybe not exactly in GR?), in totality it's just kind of a brute fact, an experimental observation. Our theories help us devise say better experiments to test e. conservation, and in a way map out the landscape of consistent physical laws. But they don't tell you which realization of consistent or admissible laws you'll find yourself in.
Other way to phrase it, what you feel is in a way real. So if you feel in some fundamental way better reading A than B, then that simply reflects a property of reality and needs no further explanation. The only problem is that in some cases our judgement can be distorted, like by substances or maybe overwhelming blinding desires (that fail to reflect fundamental experiences) or by limitations of our memory, etc.. But if we assume this isn't the case (i.e. some pathological reason for your preference), then your feeling is valid irrespective of a wordy justification. I think some things really are subjective, but also believe in a fundamental and very complex way subjectivity is actually as objective as anything else. I think the fact that one experience is actually (with some important caveats and necessary context) better than another in what might be called essentially an objective sense, is one of the most counterintuitive things we will come to accept about the human mind. We tend to mistaken complexity (it's very complex to compare experiences) to impossibility (it's impossible to judge experiences objectively).
I believe in principle there might be the equivalent Laws of Physics (say Newtonian mechanics) for the human mind, but I suspect we're still very far from it, because it might require analyzing the network of n=100 trillion synapses in our brain. I think one day we might get there, but that would probably require something like a computational effort maybe at least several times n, or even on the order of n², or some other poly(n), and also poly(n) memory. If we think of one of the major objectives of physical law is to make predictions, and explain behavior, and say to aid in engineering and designing structures, I think one of the main objective of the laws of the mind would be say to predict whether say an experience or mental state is good or not, and explain why it is so; and then perhaps allow improving a little the design of things so that we have better experiences, that is, a better life. I guess this is already what say psychology, various spiritual traditions, philosophy and arts try to achieve (and I think gets already in many cases pretty close, maybe increasingly closer, to the still inaccessible extremely complicated reality of the human mind and brain).
Regardless, we often have to do our best with what we have today, which is our best-effort subjective judgement, aided by language various human disciplines :)
If you have a very high enough refresh rate display, then yes: just flash alternatingly black-over-white and white-over-black text (i.e. invert it). We perceive essentially a low-pass filtered visual input (with limitations like neural firing rate), eventually it should appear as just uniform gray. Maybe adding some confusing elements might make it feasible at lower refresh rates.
I am not a super experienced coder or anything. But I like thinking about it[1].
The way I've been thinking about it is about organization. Organize code like we should organize our house. If you have a collection of pens, I guess you shouldn't leave them scattered everywhere and in your closet, and with your cutlery, and in the bathroom :) You should set up somewhere to keep your pens, and other utensils in a kind of neat way. You don't need to spend months setting up a super-pen-organizer that has a specially sculpted nook for your $0.50 pen that you might lose or break next week. But you make it neat enough, according to a number of factors like how likely it is to last, how stable is your setup, how frequently it is used, and so on. Organizing has several advantages: it makes it easier to find pens, shows you a breath of options quickly, keeps other places in your house tidier and so less cognitively messy as well. And it has downsides, like you need to devote a lot of time and effort, you might lose flexibility if you're too strict like maybe you've been labeling stuff in the kitchen, or doing sketches in your living room, and you need a few pens there.
I don't like the point of view that messiness (and say cognitive load) is always bad. Messiness has real advantages sometimes! It gives you freedom to be more flexible and dynamic. I think children know this when living in a strict "super-tidy" parent house :) (they'd barely get the chance to play if everything needs to be perfectly organized all the time)
I believe in real life almost every solution and problem is strongly multifactorial. It's dangerous to think a single factor, say 'cognitive load', 'don't repeat yourself', 'lesser lines of code', and so on is going to be the single important factor you should consider. Projects have time constraints, cost, need for performance; expressing programs, the study of algorithms and abstractions itself is a very rich field. But those single factors help us improve a little on one significant facet of your craft if you're mindful about it.
Another factor I think is very important as well (and maybe underestimated) is beauty. Beauty for me has two senses: one in an intuitive sense that things are 'just right' (which capture a lot of things implicitly). A second and important one I think is that working and programming, when possible, should be nice, why not. The experience of coding should be fun, feel good in various ways, etc. when possible (obviously this competes with other demands...). When I make procedural art projects, I try to make the code at least a little artistic as well as the result, I think it contributes to the result as well.
[1] a few small projects, procedural art -- and perhaps a game coming soon :)
Also, more to the point of your observation: we should be indeed very careful about any extreme and any maximization, because I presume when we maximize a lot we tend to bump into limitations of the metric or theories employed. So we should only maximize up to a region of fairly high philosophical confidence, and this is why we need progress in philosophy, psychology, philosophy of arts, philosophy of culture, neurophilosophy, etc.. in lockstep with technological progress -- because technology tends to allow very easy maximization of simplified models of meaning, which may rapidly break down.
I think one example might be that in medieval times maximizing joy and comfort could be a pretty good heuristic in a harsh life of labor. Those days we actually perhaps have to seek out some discomfort now and then, otherwise we'd be locked in our homes or bed ridden with all affordances some of us have; we have to force ourselves to exercise and not eat comfort food all the time; etc.. I think some hard drugs are a good example as well, a kind of technology that allows maximizing desire/pleasure in a way that is clearly void and does not seem associated with overall good experiences long term. An important fact is that our desires do not necessarily follow what is good; our desires are no omniscient/omnibelevolent oracles (they're simply a limited part of our minds).
We need to put thought/effort into discovering and then enacting what is good in robust, wise, careful (but not too careful), etc. ways. Let's build an awesome society and awesome life for all beings :)
More to come. In summary, I became confident that we can, if we're careful, know those things and do something like 'maximize happiness' (as I said, I prefer more general terms than happiness! There's a whole universe of inner experiences beyond just the stereotypical smiley person, I think -- I tend to think of 'maximizing meaning' or 'maximizing well-being').
The basic fact that allows this process to make sense, I guess, is that our inner experiences are real in some sense, and there are tools to study them. Not only are our inner lives real, they make part of the world and its causal structure. We can understand (in principle almost exactly, if we could precisely map our minds and brains) what causes what feelings, what is good and what isn't (by generalizing and philosophically querying/testing/red teaming/etc.), and so on for every facet of our inner worlds.
In fact, this (again in principle) would allow us to make definite progress on what matters, which is our inner lives[1]. I think Susanne Langer put it incredibly well: (on the primacy of experiences as the source of meaning)
"If nothing is felt, nothing matters" (Susanne K. Langer)
This is an experimental fact, we as conscious beings experimentally see this fact is true. So in a way the mind/brain is kind of like a tool which allows us to perceive (with some unreliability and limitations that can be worked with) reality, in particular inner reality.
We can actually understand (with some practical limitations) the world of feelings and what matters. To that we simply experiment, collect evidence and properties about feelings and inner lives, try to build theories that are consistent, robust to philosophical (that is, logical in a high level sense) objections; and then we simply do what is best, or if necessary try out a bunch of ways of life and live out the best way according to our best theories.
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Addendum: Let's take the benzene ring as an illustrative example of our procedure. Someone claims 'a benzene ring is the happiest thing in the Universe, and we therefore must turn everything into a sea of benzene rings. Destroy everything else.'. Is that claim actually true? Let's explore.
It isn't, I claim: if "Nothing is felt, nothing matters". When you are asleep (and not dreaming or thinking at all, let's suppose) or dead, you don't feel anything. No, thoughts are, and must be, associated with activity in our brain. No information flowing and no brain activity, no thoughts. No thoughts, no inner life. Moreover, thoughts require a neural (and logical) infrastructure to arise. It's logically consistent with how we don't observe ourselves as rocks, gas clouds, mountains, benzene molecules, or anything else: we observe ourselves as mammals with actually large brains. There are immensely more rocks, gas particles, benzene molecules, etc.. then there are mammals in the universe. Yet we experience ourselves as mammals. Benzene molecules, rocks and gas clouds just don't have enough structure to support minds and experience happiness.
That's a cute story, I certainly like its tone of mystery.
However, the premise seems a bit wrong (or at least the narrator is wrong). If your brain actually degenerates from usage of the ring (and is no longer used in daily life, acting only reflexively), the premise that you are the happiest from following the ring might be flat out wrong. I think happiness (I tend to think in terms of well-being, which let's say ranks every good thing you can feel, by definition -- and assume the "good" is something philosophically infinitely wise) is probably something like a whole-brain or at least a-lot-of-brain phenomenon. It's not just a result of what you see or what you have in life. In fact I'm sure two persons can have very similar external conditions and wildly different internal lives (for an obvious example compare the bed-ridden man who spends his day on beautiful dreams, and the other who is depressed or in despair).
What the ring seems to do is to put you in situations where you would be the happiest, if only you were not wearing the earring.
The earring that actually guides you toward a better inner life perhaps offers only very minimal and strategic advice. Perhaps that's what the 'Lotus octohedral earring' does :)
No worries :P It's just a way to try to avoid showing the most popular, instead you'd choose randomly from a curve from most popular to least popular, with the chosen index given by i. An easier idea to understand is to pick randomly from the top say 50 websites instead of just showing the most popular ones, avoiding "winner takes all" effects.
This is pretty cool! If I may suggest something, on the explore view, avoid showing most popular (I think it can lead to rote behavior!)
If I may suggest another algorithm, something like picking from most popular to least with probability ~1/(rank+k)^p, where p is any number >1, for example set p=1.5, k=10.
It can be implemented the following way (by computing the integral of the probability distribution):
(1) Have sorted index by popularity with n items
(2) Pick a random (double) r between 0 and 1
(3) The chosen index is (if I did my integrals right;round to nearest integer):
i = ( k^(p-1)*(n-1+k)^(p-1) / ( (r+1)*(n-1+k)^(p-1) - r*k^(p-1) ) ) ^ 1/(p-1) - k
> Can you think of other activities that require this?
Well, reading books (and other documents). I also am suspicious of screens (and specially spending too much time on them... I'm certainly guilty), but the existence of books is somewhat confusing in this regard. However, I really don't think the population as a whole was reading quite as many books/documents as we today use digital devices or social media. That could be cutting into other things, like sun exposure, exercising, perhaps face-to-face social relationships, social support networks.
Something I've noticed since about that time as well is a growing unease and pessimism with our collective future (and even present!). Some things are bleak (like climate change, uncertainty with technologies, etc.), but there's a sense of little hope that definitely should have an impact on the youth. I remember the 90s as a quite hopeful time and that definitely had an impact on my mood. My personal contribution would be spreading more hope about life.
My favorite author w.r.t. this right now that I recommend is Jane Goodall:
> 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 :)
https://archive.bridgesmathart.org/2014/bridges2014-111.pdf