To me, this is a clear example of there being no such thing as an "objective" truth about the the validity of the parallel postulate - you are entirely free to assume either it or incompatible alternatives. You end up with equally valid theories, it's just those theories are applicable to different models
This is true, but there's an important caveat: Mathematicians accepted Euclidean geometry long before they accepted non-Euclidean geometry, because they took it to be intuitively evident that a model of Euclid's axioms existed, whereas the existence of mod...
I have spent a long time looking in vain for any reason to think ZFC is consistent, other than that it holds in the One True Universe of Sets (OTUS, henceforth). So far I haven't found anything compelling, and I am quite doubtful at this point that any such justification exists.
Just believing in the OTUS seems to provide a perfectly satisfactory account of independence and nonstandard models, though: They are just epiphenomenal shadows of the OTUS, which we have deduced from our axioms about the OTUS. They may be interesting and useful (I rather like nonst...
What’s more interesting is that I just switched medications from one that successfully managed the depression but not the anxiety to one that successfully manages the anxiety but not the depression
May I ask which medications?
For macroscopic rotation:
- Blood vessels cannot rotate continuously, so nutrients cannot be provided to the rotating element to grow it.
- Without smooth surfaces to roll on, rolling is not better than walking.
There are other uses for macroscopic rotation besides rolling on wheels, e.g. propellers, gears, flywheels, drills, and turbines. Also, how to provide nutrients to detached components, or build smooth surfaces to roll on so your wheels will be useful, seem like problems that intelligence is better at solving than evolution.
I'm middle-aged now, and a pattern I've noticed as I get older is that I keep having to adapt my sense of what is valuable, because desirable things that used to be scarce for me keep becoming abundant. Some of this is just growing up, e.g. when I was a kid my candy consumption was regulated by my parents, but then I had to learn to regulate it myself. I think humans are pretty well-adapted to that sort of value drift over the life course. But then there's the value drift due to rapid technological change, which I think is more disorienting. E.g. I investe...
This all does seem like work better done than not done, who knows, usefulness could ensue in various ways and downsides seem relatively small.
I disagree about item #1, automating formal verification. From the paper:
9.1 Automate formal verification:
As described above, formal verification and automatic theorem proving more generally needs to be fully automated. The awe-inspiring potential of LLMs and other modern AI tools to help with this should be fully realized.
Training LLMs to do formal verification seems dangerous. In fact, I think I would extend that t...
Correct. Each iteration of the halting problem for oracle Turing machines (called the "Turing jump") takes you to a new level of relative undecidability, so in particular true arithmetic is strictly harder than the halting problem.
The true first-order theory of the standard model of arithmetic has Turing degree . That is to say, with an oracle for true arithmetic, you could decide the halting problem, but also the halting problem for oracle Turing machines with a halting-problem-for-regular-Turing-machines oracle, and the halting problem for oracle Turing machines with a halting oracle for those oracle Turing machines, and so on for any finite number of iterations. Conversely, if you had an oracle that solves the halting problem for any of these finitely-iterated-halting-prob...
That HN comment you linked to is almost 10 years old, near the bottom of a thread on an unrelated story, and while it supports your point, I don't notice what other qualities it has that would make it especially memorable, so I'm kind of amazed that you surfaced it at an appropriate moment from such an obscure place and I'm curious how that happened.
Oh, it's just from my list of reward hacking; I don't mention the others because most of them aren't applicable to train/deploy distinction. And I remember it because I remember a lot of things and this one was particularly interesting to me for exactly the reason I linked it just now - illustrating that optimization processes can hack train/deploy distinctions as a particularly extreme form of 'data leakage'. As for where I got it, I believe someone sent it to me way back when I was compiling that list.
All right, here's my crack at steelmanning the Sin of Gluttony theory of the obesity epidemic. Epistemic status: armchair speculation.
We want to explain how it could be that in the present, abundant hyperpalatable food is making us obese, but in the past that was not so to nearly the same extent, even though conditions of abundant hyperpalatable food were not unheard of, especially among the upper classes. Perhaps the difference is that, today, abundant hyperpalatable food is available to a greater extent than ever before to people in poor health.
In the pa...
This question is tangential to the main content of your post, so I have written it up in a separate post of my own, but I notice I am confused that you and many other rationalists are balls to the wall for cheap and abundant clean energy and other pro-growth, tech-promoting public policies, while also being alarmist about AI X-risk, and I am curious if you see any contradiction there:
This Feb. 20th Twitter thread from Trevor Bedford argues against the lab-escape scenario. Do read the whole thing, but I'd say that the key points not addressed in parent comment are:
Data point #1 (virus group): #SARSCoV2 is an outgrowth of circulating diversity of SARS-like viruses in bats. A zoonosis is expected to be a random draw from this diversity. A lab escape is highly likely to be a common lab strain, either exactly 2002 SARS or WIV1.
But apparently SARSCoV2 isn't that. (See pic.)
Data point #2 (receptor binding domain): This point is rath...
Generalized to n dimensions in my reply to Adele Lopez's solution to #9 (without any unnecessary calculus :)
Thanks! I find this approach more intuitive than the proof of Sperner's lemma that I found in Wikipedia. Along with nshepperd's comment, it also inspired me to work out an interesting extension that requires only minor modifications to your proof:
d-spheres are orientable manifolds, hence so is a decomposition of a d-sphere into a complex K of d-simplices. So we may arbitrarily choose one of the two possible orientations for K (e.g. by choosing a particular simplex P in K, ordering its vertices from 1 to d + 1, and declaring it to be the prototypi...
Thanks, this is a very clear framework for understanding your objection. Here's the first counterargument that comes to mind: Minimax search is a theoretically optimal algorithm for playing chess, but is too computationally costly to implement in practice. One could therefore argue that all that matters is computationally feasible heuristics, and modeling an ideal chess player as executing a minimax search adds nothing to our knowledge of chess. OTOH, doing a minimax search of the game tree for some bounded number of moves, then applying a simple boar...
OTOH, doing a minimax search of the game tree for some bounded number of moves, then applying a simple board-evaluation heuristic at the leaf nodes, is a pretty decent algorithm in practice.
I've written previously about this kind of argument -- see here (scroll down to the non-blockquoted text). tl;dr we can often describe the same optimum in multiple ways, with each way giving us a different series that approximates the optimum in the limit. Whether any one series does well or poorly when truncated to N terms can't be explained by saying "...
I didn't mean to suggest that the possibility of hypercomputers should be taken seriously as a physical hypothesis, or at least, any more seriously than time machines, perpetual motion machines, faster-than-light, etc. And I think it's similarly irrelevant to the study of intelligence, machine or human. But in my thought experiment, the way I imagined it working was that, whenever the device's universal-Turing-machine emulator halted, you could then examine its internal state as thoroughly as you liked, to make sure everything was consistent...
This can’t be right ... Turing machines are assumed to be able to operate for unbounded time, using unbounded memory, without breaking down or making errors. Even finite automata can have any number of states and operate on inputs of unbounded size. By your logic, human minds shouldn’t be modeling physical systems using such automata, since they exceed the capabilities of our brains.
It’s not that hard to imagine hypothetical experimental evidence that would make it reasonable to believe that hypercomputers could exist. For example, suppose someone demonstr...
Apologies for the stark terms if it felt judgmental or degrading!
No worries! I mostly just wrote that comment for the lulz. And the rest was mostly so people wouldn't think I was using humor to obliquely endorse social Darwinism.
I've never heard of anyone doing this directly. Has anyone else? If not, there's probably a reason. I suppose occupational certification programs serve a similar filtering function. Anyway, your suggestion might be more palatable if it were in the form of a deposit refundable if and only if the applicant shows up/answers the phone for scheduled interviews. You would also need a trusted intermediary to hold the deposits, or else we would see a flood of fake job-interview-deposit scams. And even if you had such a trusted intermediary, I suspect tha...
It's really unclear, as a society, how to get them into a position where they can provide as much value as the resources they take.
Harvest their reusable organs, and melt down what remains to make a nutrient paste suitable for livestock and the working poor?
(Kidding! But that sort of thing is always where my mind wanders when people put the question in such stark terms, perhaps because I myself am a chronically unemployed "taker" (mental illness). Anyway, one of the long-term goals of AI and automation research, as I understand it, is to tur...
I'm curious if anyone has recollections of what it was like trying to hire for similar positions in recent years, when the unemployment rate was much higher. That is to say, how much of this is base-rate human flakiness, and how much is attributable to the tight labor market having already hoovered up almost all the well-functioning adults?
I’m not actually sure what to make of that—should we write off some moral intuitions as clearly evolved for not-actually-moral reasons ... ?
All moral intuitions evolved for not-actually-moral reasons, because evolution is an amoral process. That is not a reason to write any of them off, though. Or perhaps I should say, it is only a reason to "write them off" to the extent that it feels like it is, and the fact that it sometimes does, to some people, is as fine an example as any of the inescapable irrationality of moral intuitions.
If we have the m...
• You are not required to create a happy person, but you are definitely not allowed to create a miserable one
Who's going around enforcing this rule? There's certainly a stigma attached to people having children when those children will predictably be unhappy, but most people aren't willing to resort to, e.g., nonconsensual sterilization to enforce it, and AFAIK we haven't passed laws to the effect that people can be convicted, under penalty of fine or imprisonment, of having children despite knowing that those children would be at high ...
“A shy person cannot learn, an impatient person cannot teach”
The translation you linked actually gives "A person prone to being ashamed cannot learn," which is even more on the nose. Does anyone have any advice on how to deal with this issue? I have a pretty severe case of it, especially because I tend to take a lot (a lot) longer than other people to do pretty much every kind of work I've ever tried, independently of how much intelligence I needed to apply to it. Aside from seeking medical advice for that problem (which hasn't helped...
The Wikipedia link on amphibian decline mentioned the effects of artificial lighting on the behavior of insect prey species as a possible contributor. I suppose it’s possible that that’s a factor in the observations from the German study as well, particularly since they only looked at flying insects. But the observations were apparently made in nature preserves, so one would think that artificial lighting wouldn’t be that common in those habitats. There could still be indirect effects, though.
• How to be aware of other people’s points of view without merging with them
...
• How to restrain yourself from anger or upset
• How to take unflattering comments or disagreement in stride
...
• How to resist impulses to evade the issue or make misleading points
...
• How to understand another person’s perspective
It wasn't the reason I got into it in the first place, but I have found mindfulness practice helpful for these things. I think that's because mindfulness involves a lot of introspection and metacognition, and those skills transfer pretty well ...
Toastmasters? Never tried them myself, but I get the impression that they aim to do pretty much the thing you're looking for.
Groups of friends often coalesce around common interests. This group of friends coalesced around a common interest in rationality and self-improvement. That this is possible to do is potentially useful information to other people who are interested in rationality and self-improvement and making new friends.
This is an appealingly parsimonious account of mathematical knowledge, but I feel like it leaves an annoying hole in our understanding of the subject, because it doesn't explain why practicing math as if Platonism were correct is so ridiculously reliable and so much easier and more intuitive than other ways of thinking about math.
For example, I have very high credence that no one will ever discover a deduction of 0=1 from the ZFC axioms, and I guess I could just treat that as an empirical hypothesis about what kinds of physical instantiations of ZFC proofs... (read more)