You’re conflating between “have important consequences” and “can be used as weapons in discourse”
Amalthea
Karma: 415
What do you mean by example, here? That this is demonstrating a broader property, or that in this situation, there was a tribal dynamic?
Typo, thanks for pointing it out. Also, see here for the physics reference: https://en.m.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_⋯
I’m one of these professional mathematicians, and I’ll say that this article completely fails to demonstrate it’s central thesis that there is a valid intuitive argument for concluding that 1 + 2 + 3 + … = −1/12 makes sense. What’s worse, it only pretends to do so by what’s essentially a swindle. In my understanding, it’s relatively easy to reason that a given divergent series “should” take an arbitrary finite value by the kind of arguments employed here, so what is being done is taking a foregone conclusion and providing some false intuition for why it should be true.
On a less serious note, speaking to the real reason why 1 + 2 + 3 + … = −1/12, that’s actually what physicists will tell you, and we all know one should be careful around those.
Sure, but you’re just claiming that, and I don’t think it’s actually true.
You run into the trouble of having to defend why your way to fit the divergent series into a pattern is the right one—other approaches may give different results.
I think it’s quite unlikely that GPT 5 will destroy the world. That said, I think it’s generally reasonable to doubt prediction markets on questions that can’t be fairly evaluated both ways.
I think the possibility of compute overhang seems plausible given the technological realities, but generalizing from this to a second-order overhang etc. seems taking it too far.
If there is an argument that we should push compute due to the danger of another “overhang” down the line that should be made explicitly and not by generalisation from one (debatable!) example.
Sorry, low effort comment on my side. Still, I think the original link seems misleading in the point it’s purportedly trying to make.
Doesn’t have any bearing historically. Also seems more like a brute force search, where the component of studying the materials properties has been made more efficient (by partially replacing lab experiments with deep learning).
Which document, and in what way?
To be quite frank, you’re avoiding complex numbers only in the sense that you spell out the operations involved in handling complex numbers explicitly—so of course there’s no added benefit, you’re simply lifting the lid of the box...
That being said, as you discover by decomposing complex multiplication into it’s parts (rotation and scaling), you get to play with them separately, which already leads you to discover interesting new variations on the theme.
I don’t understand what you’re trying to say—would you mind trying to illustrate what you mean?
“if I keep having “misunderstandings” with more people who have no past record of similar behavior, after two or three it cumulatively becomes a strong Bayesian evidence that I am actually the bad guy.” It’s not quite that easy. Abuser’s may particularly tend to seek out vulnerable people, and it’s a real effect that when you are already raising a complaint about someone, this may open you up to further abuse by other bad actors, who can now have exploit that you now have spent your social capital. In other words, Bayesian considerations have a place, but you need to be extra careful that you’re not misattributing the correlations.
Fighting dirty can involve looking reasonable to the outside, e.g. being willing to lie or bend the truth and distracting from the key issues of the matter—these can all be done civilly.
I think think it’s also easy to falsely conflate progress in understanding with having achieved some notable level of understanding. Whether one has the latter will likely only become clear after a significant passage of time, so it’s hard to make a judgement right away. That said, it’s fair to say “No idea” is overstating th case compared to e.g. “We understand very little about”.
“The others give humanity a chance to see what is happening and change the rules ‘in flight ’.”
This is possible in non-Foom scenarios, but not a given (e.g. super-human persuasion AIs).
I tentatively agree, but it also seems difficult to think of a better alternative.
I agree. It’s rare enough to get reasonable arguments for optimistic outlooks, so this seems worth for someone to openly engage with in some detail.
Do you have an example for where better conversations are happening?