Easy. Let f be a continuous real function that is not differentiable somewhere. Let H be the truth value of the Riemann hypothesis. Define g(x) as "f(x) if not H else 0". Boom.
Reminds me of a homework exercise in theory of computation back in my uni days. Is the function "f(x) is 0 if H else 1" computable? Of course it is. It is either constant 0 or constant 1. We don't know which at this point, but f is a constant function in either case, so it is surely computable.
I visit a friend in Sweden the other day. Her house was built in the 80s, nothing fancy, a simple one family house. There is a ventilation system integrated. Every room has an inlet and the air is sucked out of the bathrooms and kitchen. Even has a heat exchanger. It's a pretty simple system: no cooling and it's not really used for heating except for pre-heating the incoming outside air with the energy in the exhaust air. But it exchanges the houses air multiple times a day. She told me this has been standard there for decades. A few ventilation pipes integrated into the houses construction and that's it. It's even mandatory in multi tenant houses to check air flow every few years.
It's not just the AC crazy US where HVAC is standard. It's just common sense to have such a system if you care about your health.
If your CO2 levels are that high then you should fix the HVAC system and get it up to code or lobby for fixing the code. In many countries, a full air exchange in any office space every X hours is mandatory. In other countries that's optional and they need to get their act together.
> The semantics (or lack thereof) of C and C++ can make this difficult to actually test for because the compiler is allowed to say "test passed" to any input leading to UB.
I get what you are saying but does this actually apply to a test? If the code under test is in one compilation unit and the test harness in another and they are linked together then the UB optimization issue ends at the API boundary and can't possibly make the test pass ..?
The point I was waiting for but never came, so I'll make it here, is: Will LLMs be able to synthesize? Sure they can learn calculi. Lambda, differential, whatnot. But will Claude eventually be able to come up with a genuinely new formalism? A new calculus? Sth that allows us to do things we couldn't do before?
Though this action drive (and the means he has) could be used for so much better. Humankind's top 10 problems don't include the issue of being confined to a single planet. That far down the list. The actual stuff gets you less attention from the tech crowd. Hunger. Poverty. Wars. Droughts. Mass extinctions. Climate change. Transmittable diseases. Cancer. Alzheimers. It's beyond me how one can reasonably argue (or defend somebody who does) that we really ought to focus on becoming multi-planetary.
> For many people the state is inefficient, illogical, evil and goes after them without any reason (ex: think COVID restrictions).
And that is an argument for agreeing to give more ways to go after you to that supposedly evil government?
I'd understand if people have high trust in government and argued "Yeah it could be misused, but I trust the government not to do that". That still misses the part that governments can change, but at least it's somewhat consistent.
If you ask me personally, then no, we don't need to have such a vote.
But if the point is that country wide referendums should only be held for important questions but then exclude Brexit because "it's stupid" then that's an inconsistent argument. Surely the question whether the UK should leave the EU was a very important decision to make. That the vote went a certain way which you don't like does not make it less important of a decision.
Unless the actual point is "referendums should only be held for questions that are important and will go the way I like". You can have that opinion but then please be honest about it instead of disguising it with supposedly neutral musings about democracy. (Hint: Democracy does not mean that only what you want will happen.)
That makes little sense in a highly competitive market where your competitive edge is waning by the minute. Tey dumped billions into creating the new models. Just letting them sit there just to see what the Chineee do makes no sense.
> Mathematically, as lim temperature->0, the distribution gets spikier and spikier, the most likely sample goes to almost-but-not-quite infinity and the rest go to almost-but-not-quite 0.
That's not how limits work. As the temperature goes to 0, the rest goes to 0. That's it. The "almost-but-not-quite" is part of the "goes to".
Let's say f(x) = 3x+1. It's a continuous function. If we let x go to 10, f(x) goes to 31. Not "almost-but-not-quite 31". No, to 31. (If you don't have a continuous function then it's the same argument, but less intuitive to illustrate.)
Reminds me of a homework exercise in theory of computation back in my uni days. Is the function "f(x) is 0 if H else 1" computable? Of course it is. It is either constant 0 or constant 1. We don't know which at this point, but f is a constant function in either case, so it is surely computable.