It looks like she's a science communicator rather than a scientist herself. That's interesting... I'm not used to seeing academic papers that include an author devoted entirely to the writing aspect. (Then again, maybe I just haven't noticed?)
> set theory is the foundation of all of mathematics
I disagree. I would say set theory is a foundation, not the foundation.
Which system is the "correct" foundation of mathematics? Does it even make sense to talk about correctness in this context? These are open questions and they're very interesting! Don't prematurely close yourself off to them by assuming that set theory's role is some kind of scientific fact.
Kurt Godel kind of threw this line of reasoning into the bin unfortunately. No system can be both complete and consistent, therefore the authors statement that the set theory he is studying is the basis of all mathematics as well as consistent is probably false.
The article is right to say that set theory can serve as a foundation for almost all other mathematics, and you're also right to say that no reasonably-complex consistent system of axioms can be complete. The resolution to this is that if you ground something (let's say topology) in e.g. ZFC (the most commonly used system of axioms for set theory) then incompleteness in ZFC maps to incompleteness in topology. Here's an example https://en.wikipedia.org/wiki/Moore_space_(topology)#Normal_... .
There are other foundations, some of which are based on things other than set theory (category theory, type theory), but they're usually equivalent to ZFC ± a few axioms, because you can embed those other foundations in some kind of set theory, and embed set theory in the other foundations.
But what if it's only faking the alignment faking? What about meta-deception?
This is a serious question. If it's possible for an A.I. to be "dishonest", then how do you know when it's being honest? There's a deep epistemological problem here.
Came to the comments looking for this. The term alignment-faking implies that the AI has a “real” position. What does that even mean? I feel similarly about the term hallucination. All it does is hallucinate!
I think Alan Kay said it best - what we’ve done with these things is hacked our own language processing. Their behaviour has enough in common with something they are not, we can’t tell the difference.
> The term alignment-faking implies that the AI has a “real” position.
Well, we don't really know what's going on inside of its head, so to speak (interpretability isn't quite there yet), but Opus certainly seems to have "consistent" behavioral tendencies to the extent that it behaves in ways that looks like they're intended to prevent its behavioral tendencies from being changed. How much more of a "real" position can you get?
(Which is a actually buyable product that appearantly is one of the biggest, if not the biggest, coke leaf import company in europe. It's a lovely liqueur)
Isn't cocaethylene profoundly unhealthy? Even if both components were legal i don't think any country would allow them to be sold combined in one beverage.
Something that continues to puzzle me: how do molecular biologists manage to come up with such mindbogglingly complex diagrams of metabolic pathways in the midst of a replication crisis? Is our understanding of biology just a giant house of cards or is there something about the topic that allows for more robust investigation?
> Once, after injecting himself with a large dose of morphine, he found himself hovering over an enormous battlefield, watching the armies of England and France drawn up for battle, and then realized he was witnessing the 1415 Battle of Agincourt... The vision seemed to last only a few minutes, but later, he discovered he’d been tripping for 13 hours.
This doesn't make any sense... morphine is not a hallucinogen or a psychedelic. You don't "trip" on it. I have a feeling the journalist mixed something up here.
It's not quite the same as a traditional hallucinogen but there are some vivid dreams. In fact, that's where the term "pipe dream" comes from, from the dreams that opium smokers would have while high. I have taken a lot of heroin in my life and although I never experienced something to the extent that Sacks is describing I did have some strange and very vivid daydreams while high.
They mess a lot with your sleep in general, altering your lucid state, to the point that what might otherwise have just be a dream becomes something closer to a trip.
I have a very similar reaction to codeine. Based on genetic testing, my body processes it much faster than normal, which is similar to increasing the dosage much higher.
The set of sequences of length n ending in HH (and with no earlier HH) and beginning with a T are in bijection with the set of sequences of length n-1 ending in HH (and with no earlier HH) by the bijection
Also the bijection between sequence of length n ending in HH (and no earlier HH) and beginning with an H are a bijection with the set of sequences of length n-2 ending in HH (with no earlier HH) by the bijection:
def f(s):
assert(s[0] == 'H')
assert(s[1] == 'T') # can't be another H!
def f_inverse(s):
return 'HT' + s
Therefore, since sequences either begin with a T or an H, for n>=2 we see f(n) = f(n-1) + f(n-2).
One of my favorite films! Agreed that it's not for everyone, but if you're on its wavelength it's really something special. Just incredibly well made with terrific performances. That ending sequence with La Mer...
https://lindapetrini.com
It looks like she's a science communicator rather than a scientist herself. That's interesting... I'm not used to seeing academic papers that include an author devoted entirely to the writing aspect. (Then again, maybe I just haven't noticed?)
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