I get the impression this is not at all confined to Stanford and is really just everywhere in the country at the moment. Not sure the word 'coward' is right though. Feels more like... people are far more interested in being 'normal' than ever before. Maybe a side effect of there being so much economic opportunity in regular jobs and career trajectories that nobody considers riskier paths?
I honestly think it’s the opposite cause. The odds of success have gotten way narrower than they used to be. When kids at Stamford are afraid of failure that says to me that failure is way more likely for everyone. People are taking safe options because the unsafe ones can lead to bottomless pits that even Stanford grads are concerned they cannot climb out of.
I agree they're right to be scared. The culture has regressed. When I was a teenager / in my early 20s I didn't really believe that was possible, and I thought the older folks were just bitter. But now that I'm older and have a firmer grasp of history (both from what I've read, and my own lived experience) it is so obviously the case that the cracks in this decadent society continue to grow bigger over time. Sadly younger generations will repeat the same error I did and waste their precious time taking poorly calculated risks, trusting the wrong people, and suffering the very real, sometimes permanent, consequences. It's a positive feedback loop that only gets more ruthless as the decades pass. Don't stick your neck out, it's not worth it, freedom of speech isn't real. The silver lining is, freedom of thought is real. There are ways to bend your speech to avoid persecution, and reach the people you want to reach. It's a skill that takes time to master. Some people have mastered it. They have been mentioned by name elsewhere in this thread.
What does it look like where some intentional effort is made by society to help people like this get what they are using these models to get, but in a healthy way? That is: how does society reconfigure itself so that people do not end up so lonely and desperate that an AI model solves a emotional problem which is hopelessly unsolved otherwise?
It is not "they go to therapy" because that's cheating; that answers the question "what can they do?" not "what can society do?" (and i think it's a highly speculative answer anyway)
One of the defining features of many such people, by nature or disposition or practice, is they are not easily able to offer in return the meeting of the same needs in another person. At least, not in a way that's easy to understand. People do not gravitate to what is or seems to be one-sided. It seems they are still wired to want a certain level of attention, though, so it's not as though we can just pair them off and expect it to work. What they want and what they can give are not in balance.
Counseling can help with this to some degree and everyone can make some amount of progress. The question is what we do with those whose "ceiling" remains lower than is tenable for most relationships. For those, there is not a better solution than robots.
However, the always-available, always-validating robot is not a valid psychological need. It is a supernormal emotional stimulus. It is not healthy and, like other supernormal stimuli, builds invariably tolerance, desensitization, and dependence. Fast cycling of discontent -> open app -> validation is a huge contributor, the same way that the constant availability and instant nature of vaping make it incredibly addictive.
People with severely disordered attachment _will_ seek out humans, again and again, to fill those unfulfillable needs, and leave bodies and psyches in their wake.
So I think there is a case to be made for harm reduction.
> how does society reconfigure itself so that people do not end up so lonely
The answer no one wants to hear on HN is get rid of capitalism as it is currently.
You, ajkjk, are a product. When you are not working I need you to be looking at a screen full of ads and clicking on things. Don't worry, you won't have anything else to do because everyone else is also doing the same. If your doing things with friends and spending your attention on them, you're not spending your attention on my latest product, and that's pretty anti-capitalist of you. Thinking about going to the bar, you can't afford it, VC bought up all the property and bars and raised the price 400%. Trying to find some other 3rd place to hang out at? Don't exist, nobody can afford people that show up and don't spend anything.
We have designed modern society to push us toward an AI that can give us our undivided attention because everyone else is so busy doing nothing they don't have time for friends.
i don't disagree with the gist of your revolutionary sentiment, but let me remind you that (a) you don't know anything about me, and (b) what you described is a complaint, not an idea.
like, a good looking person will get the occasional comp on the basis of that, but you'll never be friends with the staff on the basis of that. whereas anyone can be friends with the staff, if they are friendly and earnest about it.
well it's hard to formally define them, but it's not hard to say "imagine that all these decimals go on forever" and not worry about the technicalities.
An infinite decimal expansion isn't enough. It has to be an infinite expansion that does not contain a repeating pattern. Naively, this would require an infinite amount of information to specify a single real number in that manner, and so it's not obvious that this is a meaningful or well-founded concept at all.
I don't quite get what you mean here. While you need to allow infinite expansions without repeating patterns, you also need to expansions with these pattern to get all reals. Maybe the most difficult part is to explain why 0.(9) and 1 should be the same, though, while no such identification happens for repeating patterns that are not (9).
Imagine you have a ruler. You want to cut it exactly at 10 cm mark.
Maybe you were able to cut at 10.000, but if you go more precise you'll start seeing other digits, and they will not be repeating. You just picked a real number.
Also, my intuition for why almost all numbers are irrational: if you break a ruler at any random part, and then measure it, the probability is zero that as you look at the decimal digits they are all zero or have a repeating pattern. They will basically be random digits.
> Maybe you were able to cut at 10.000, but if you go more precise you'll start seeing other digits, and they will not be repeating. You just picked a real number.
A reasonably defensible inference would be that adding a finite amount of precision adds a finite number of additional digits. That is a physically realizable operation. There's no obvious physical meaning to the idea of repeating that operation infinitely many times, so this is not clearly a meaningful way of defining or constructing real numbers. If you were trying to use this construction to convince a skeptic that irrational real numbers exist, you would fail -- they would simply retort that arbitrary finite precision exists and that you have failed to demonstrate infinite non-repeating, non-terminating precision.
What are you talking about? Infinite decimals give reals, do they not? Repeating decimals give rational which are a subset of the reals.
The colloquial phrase 'infinite decimal' is perfectly intelligible without reference to whether it's an infinite amount of data or rigorously defined or whatever else.
There's a lot of trickery involved din dealing with the reals formally but they're still easy to conceptualize intuitively.
“What I’m taking about” is that they are not easy to conceptualize intuitively.
If I were a skeptic of real numbers, I’d tell you that talking about an infinite decimal expansion that never terminated and contains no repeating pattern is nonsense. I’d say such a thing doesn’t exist, because you can’t specify a single example by writing down its decimal expansion — by definition. So if that’s the only idea you have to convince a skeptic, you’ve already failed and are out of the game. To convince the skeptic, you’d have to develop a more sophisticated method to show indirectly an example of a real number that is not rational (for instance, perhaps by proving that, should sqrt(2) exist, it cannot be rational).
I guess we are talking about different things. It seems to me that it's trivial to imagine then conceptually. They go on forever and most of them never repeat? Sounds good to me. Sqrt(2) never repeats? sure, whatever. I never found the proofs of this stuff very interesting.
Now, I am a skeptic of their use in physics / science. But that's a different question, and more about pedagogy than the raw content of the theories.
With that approach, all anyone has to say is that you'd have to provide infinite information to specify an example and that the way these objects interact is completely undefined; therefore you haven't defined or done anything at all. You are indeed simply imagining something -- and nothing more. You can imagine whatever you want, but nobody else is inclined to believe that what you imagine exists or behaves in the intended manner.
Beyond that, if a skeptic were inclined to accept the existence of objects with "infinite information content" by definition, they could then ask you to simply add two of them together. That would most likely be the end of it -- trying to add infinite non-repeating decimal expansions does not act intuitively. To answer this type of question in general, you would have to prove that the set of all infinite decimal expansions, if we grant its existence, has a property called completeness, as you would eventually discover that you would have to define addition x+y of these numbers as a limit: x+y = lim_{k -> infinity} (x_k+y_k) where {x,y}_k = the rational number obtained by truncating {x,y} after k digits. You must prove this limit always exists and is unique and well-defined. And even having done all that work, you still couldn't give a single example of one of these numbers without additional nontrivial work, so a skeptic could still easily reject all of this.
This is far beyond what you could reasonably expect the typical middle school student or even general member of the adult population to follow and far more difficult than simply defining complex numbers as having the form x+iy.
yes, I am describing imagining something. Imagine taking decimals and letting them go on without ending. That is conceptualizing them intuitively. It is easy.
I don't really know what you're arguing about. You are describing the sorts of things that have to be solved to construct them rigorously. But I don't know why. No one is talking about that.
I was talking about that, specifically, the relative difficulty of defining reals from rationals vs complex numbers from reals. You replied to me. :)
Moreover, I disagree that you have imagined real numbers. I don’t think you’ve imagined a single real number at all in the manner you describe. Why should I believe you've even described anything that isn't rational to begin with? For instance, 0.999... is the same as 1. Why should I not think that whatever decimal expansion you're imagining is, similarly, equivalent to a rational number we already know about? Occam's razor would reasonably suggest you're just imagining different representations of objects already accounted for in the rationals. After all, an infinite amount of precision captured by an infinite nonrepreating string of digits could easily just converge back to a number we already know.
I am very confused why you are continually talking about rationals as if they are not real. every real number is also a rational number, in the usual conception of things, are they not? Perhaps you are distinguishing the two? like regarding 1.000 as an equivalence classes of cauchy sequences is not the same as 1.000 as the equivalence class of a/a?
because when I picture 1.000 I am clearly imagining a real number. Likewise if I imagine pi, as defined any way you like.
My language was sloppy, but I'll admit I thought it was pretty obvious that we were talking about defining the rest of the reals starting from the rationals -- obvious enough that it didn't need clarification. I can't edit my prior comment, but you may imagine it has been amended in the obvious way with that clarity made explicit rather than implicit and reply to it again if you're interested in continuing the conversation.
> I doubt anyone could make a reply to this comment that would make me feel any better about it.
I am also a complex number skeptic. The position I've landed on is this.
1) complex numbers are probably used for far more purposes across math than they "ought" to be, because people don't have the toolbox to talk about geometry on R^2 but they do know C so they just use C. In particular, many of the interesting things about complex analysis are probably just the n=2 case of more general constructions that can be done by locating R inside of larger-dimensional algebras.
2) The C that shows up in quantum mechanics is likely an example of this--it's a case of physics having a a circular symmetry embedded in it (the phase of the wave functions) and everyone getting attached to their favorite way of writing it. (Ish. I'm not sure how the square the fact that wave functions add in superposition. but anyway it's not going to be like "physics NEEDS C", but rather, physics uses C because C models the algebra of the thing physics is describing.
3) C is definitely intrinsic in a certain sense: once you have polynomials in R, a natural thing to do is to add a sqrt(-1). This is not all that different conceptually from adding sqrt(2), and likely any aliens we ever run into will also have done the same thing.
> but anyway it's not going to be like "physics NEEDS C", but rather, physics uses C because C models the algebra of the thing physics is describing.
Maybe it’s just my math background shouting at me about what “model” means, but if object X models object Y, then I’m going to say that X is Y. It doesn’t matter how you write it. You can write it as R^2 if you want, but there’s some additional mathematical structure here and we can recognize it as C.
Mathematicians love to come up with different ways to write the same thing. Objects like R and C are recognized as a single “thing” even though you can come up with all sorts of different ways to conceive of them. The basic approach:
1. You come up with a set of axioms which describe C,
2. You find an example of an object which follows those rules,
3. That object “is” C in almost any sense we care about, and so is any other object following the same rules.
You can pretend that the complex numbers used in quantum mechanics are just R^2 with circular symmetries. That’s fine—but in order to play that game of pretend, you have to forget some of the axioms of complex numbers in order to get there.
Likewise, we can “forget” that vectors exist and write Maxwell’s equations in terms of separate x, y, and z variables. You end up with a lot more equations—20 equations instead of 4. Or you can go in the opposite direction and discover a new formalism, geometric algebra, and rewrite Maxwell’s equation as a single equation over multivectors. (Fewer equations doesn’t mean better, I just want to describe the concept of forgetting structure in mathematics.)
You can play similar games with tensors. Does physics really use tensors, or just things that happen to transform like tensors? Well, it doesn’t matter. Anything that transforms like a tensor is actually a tensor. And anything that has the algebraic properties of C is, itself, C.
> if object X models object Y, then I’m going to say that X is Y
If you haven't read to the end of the post, you might be interested in the philosophical discussion it builds to. The idea there, which I ascribe to, is not quite the same as what you are saying, but related in a way, namely, that in the case that X models Y, the mathematician is only concerned with the structure that is isomorphic between them. But on the other hand, I think following "therefore X is Y" to its logical conclusion will lead you to commit to things you don't really believe.
> But on the other hand, I think following "therefore X is Y" to its logical conclusion will lead you to commit to things you don't really believe.
I would love to hear an example… but before you do, I’m going to clarify that my statement was expressing a notion of what “is” sometimes means to a mathematician, and caution that
1. This notion is contextual, that sometimes we use the word “is” differently, and
2. It requires an understanding of “forgetfulness”.
So if I say that “Cauchy sequences in Q is R” and “Dedekind cuts is R”, you have to forget the structure not implied by R. In a set-theoretic sense, the two constructions are unequal, because you use constructed different sets.
I think this weird notion of “is” is the only sane way to talk about math. YMMV.
I think the problem with insisting on using "is" that way is that you then can't distinguish between two things you might reasonably want to express, i.e. "is isomorphic to"/"has the same structure as" and "refers to the same object". I totally agree that math is all about forgetting about the features of your objects that are not relevant to your problem (and in particular as the post argues things like R and C do not refer to any concrete construction but rather to their common structure), but if you want to describe that position you have to be able to distinguish between equality and isomorphism.
(Of course using "is" that way in informal discussion among mathematicians is fine -- in that case everyone is on the same page about what you mean by it usually)
> I think the problem with insisting on using "is" that way is that you then can't distinguish between two things you might reasonably want to express, i.e. "is isomorphic to"/"has the same structure as" and "refers to the same object".
It’s reasonable to want to express that difference in specific circumstances, but it would be completely unreasonable to make this the default.
For example, I can say that Z is a subset of Q, and Q is a subset of R. I can do this, but maybe you cannot—you’ve expressed a preference for a more rigid and inflexible terminology, and I don’t think you’re prepared to deal with the consequences.
Tensor are much less unequivocal to me. They seem to follow naturally from basic geometric considerations. C on the other hand is definitely i there but I'm not sure it's the best way to write or conceptualize what it's doing.
I think the issue with "modeling" is really a human one, not a mathematical one.
It's helpful sometimes to think of our collective body of mathematical knowledge as like a "codebase", and our notations and concepts as the "interface" to the abstractions at play within. Any software engineer would immediately acknowledge that some interfaces are FAR better than others.
The complex numbers numbers are one interface to the thing they model, and as you say, in a certain sense, it may be the case that the thing is C. But other interfaces exist: 2x2 antisymmetric traceless matrices, or a certain bivector in the geometric-algebra sense.
Different interfaces: a) suggest different extensions, b) interface with other abstractions more or less naturally, c) lend themselves to different physical interpretations d) compress the "real" information of the abstraction to different degrees.
An example of (a): when we first learn about electric and magnetic fields we treat them both as the "same kind of thing"—vector fields—only to later find they are not (B is better thought of as bivector field, or better still, both are certain components of dA). The first hint is their different properties under reflections and rotations. "E and B are both vector fields" is certainly an abstraction you CAN use, but it is poorly-matched to the underlying abstraction and winds up with a bunch of extra epicycles.
Of (d): you could of course write all of quantum mechanics with `i` replaced by a 2x2 rotation matrix. (This might be "matrix mechanics", I'm not sure?) This gives you many more d.o.f. than you need, and a SWE-minded person would come in and say: ah, see, you should make invalid states unrepresentable. Here, use this: `i = (0 -1; 1 0)`. An improvement!
Of (b): the Pauli matrices, used for spin-1/2 two-state systems, represent the quaternions. Yet here we don't limit ourselves to `{1, i, j, k}`; we prefer a 2-state representation—why? Because (IIRC) the 2 states emerge intuitively from the physical problems which lead to 2-state systems; because the 2 states mix in other reference frames; things like that (I can't really remember). Who's to say something similar doesn't happen with the 2 states of the phase `i`, but that it's obscured by our abstraction? (Probably it isn't, but, prove it!)
I have not given it much more thought than this, but, I find that this line of thinking places the "discontent with the complex numbers in physics" a number of people in this thread attest to in a productive light. That dissatisfaction is with the interface of the abstraction: why? Where was the friction? In what way does it feel unnecessarily mystifying, or unparsimonious?
Of course, the hope is that something physical is obscured by the abstraction: that we learn something new by viewing the problem in another frame, and might realize, say, that the interface we supposed to be universally applicable actually ceases to work in some interesting case, and turns out to explain something new.
I can't entirely follow the details, but apparently quantum mechanics actually doesn't work for fields other than C, including quaternions. https://scottaaronson.blog/?p=4021
That makes sense, but it assumes that the thing you would replace C with is a field. If physics' C is sitting inside a larger space I imagine that that space will not be a field (probably a lie group or something instead).
> The C that shows up in quantum mechanics is likely an example of this--it's a case of physics having a a circular symmetry embedded in it (the phase of the wave functions) and everyone getting attached to their favorite way of writing it
No, it really is C, not R^2. Consider product spaces, for example. C^2 ⊗ C^2 is C^4 = R^8, but R^4 ⊗ R^4 is R^16 - twice as large. So you get a ton of extra degrees of freedom with no physical meaning. You can quotient them out identifying physically equivalent states - but this is just the ordinary construction of the complex numbers as R^2/(x^2 + 1).
> but rather, physics uses C because C models the algebra of the thing physics is describing.
That's what C is: R^2, with extra algebraic structure.
Yes I know and agree with that. But still I think physics can be described with either. There will, I expect be a physical meaning to that quotient. Maybe the larger space without the quotient is also physically meaningful too.
my own brand of yimbyism at least respects that. there's nothing wrong with quiet neighborhoods and loud neighborhoods. the sort of things i want to allow in neighborhoods like yours are locally-owned corner stores and cafes and wine bars and walkable development like cut-throughs and bikelanes. part of the problem with the urbanism debates is that no one has quite figured out how to allow "the good stuff" while keeping out "the bad stuff" because as soon as you upzone, like, walgreens and gas stations and corporate high rises are expected to start showing up. IMO this is something of a "social technology" problem: if we can't figure out how to allow healthy development without stopping unhealthy development, that's a problem to solve systematically.
the other issue with urbanism debates is that everyone's version of Yimbyism is different and you end up not trusting any of them because some people really DO think that you should shut up and allow high rises. They have a moral reason for that too---because housing really is at a shortage and costs too much and some people getting their fancy neighborhoods while others have access to nothing is sorta unfair. But that position is basically untenable, if you try to enforce it you just make an enemy of everyone. But it seems to me that the happy medium, the "build good stuff and not bad (carefully)", is an everyone-wins situation (except for a few crotchety people I suppose). That goal is to break the equilibrium of "some (established) people get to govern what happens to almost-everybody" and replace it with something more generally democratic, but without letting in all the repugnance of how the free market will build things if you don't govern it at all.
(this is all very idealistic of course. The problem is that a random anti-development suburban neighborhood that likes being that way has no incentive to let anyone change at all, and is probably basically right that the urbanism program doesn't benefit them at all. I imagine that only really systematic way around that is to end up in a higher-trust version of society where towns are mostly nice, instead of mostly not, so that people actually crave this sort of development instead of reacting negatively to it.)
I don't have a problem with little corner stores, though I don't think they would be very sustainable in most suburban areas. I just drive for 5-10 mins to a grocery store and get pretty much everything I need there.
The bigger issue I have is that people seem to think that suburban areas can be required to be urbanized, but urban areas could never be suburbanized (from a zoning/setbacks/etc. perspective). That is, they don't seem to think that areas can be forced to change, in general. They seem to think that forcing urbanization is fine, but it's a one-way ratchet.
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