> "I don't know what talking about "Infinity * 0" means in an informal sense means"
I'm not a rationalist, I'm only using their language to make the mapping to their ideology simpler. A comet striking earth would be "infinitely bad". The chance of that happening is, as far as I'm concerned, zero (its not zero, but I round it down.) If you multiply the infinitely bad outcome by the zero percent chance of it happening, you result is that you shouldn't waste your time and emotional resources worrying about it.
Normal people don't phrase this kind of reasoning with math terminology as rationalists do, but that terminology isn't where the rationalists go wrong. Where the rationalists go wrong isn't the multiplication, it's the failure to ignore very unlikely outcomes as normal people would. They think themselves too rational to ignore the possibility of unlikely things, but ironically it is normal people who don't spend their time dwelling on extremely unlikely bullshit have a more rational approach to life.
The rationalists spend hours discussing scenarios like "What if a super AI manipulates people into engineering a super virus that wipes out humanity? Its technically possible; there's no law of physics which prevents this!", to which a normal person would respond by wondering if these people are on drugs, why would they spend so much time worrying about something which isn't going to happen?
Yeah pretty much. If I was to write it out further: "near infinity bad thing could happen but it has a near infinitesimal chance of it happening, what is the amount of finite resources you should spend to prevent it?". The numbers are probabilities and how much of an effect it is. It really is infinity * epsilon but that would confuse more people so I decided to say infinity * 0.
I was very explicit when I said "humanity decided". It doesn't matter if one or the other is the actual formal system math system result either way, it was chosen out of practicality that in this kind of philosophical issue, the more pragmatic thing was to axiomatically choose that "infinity * 0 = 0" when faced with things like this. The rationalists in a more meta/broader sense have decided that it's infinity * epsilon = infinity even if they say it is not on the surface. Their actions show they believe the other direction.
In math infinity * epsilon is indeterminate until you decide what the details of infinity & epsilon is, which I find quite fitting.
I'm not a rationalist, I'm only using their language to make the mapping to their ideology simpler. A comet striking earth would be "infinitely bad". The chance of that happening is, as far as I'm concerned, zero (its not zero, but I round it down.) If you multiply the infinitely bad outcome by the zero percent chance of it happening, you result is that you shouldn't waste your time and emotional resources worrying about it.
Normal people don't phrase this kind of reasoning with math terminology as rationalists do, but that terminology isn't where the rationalists go wrong. Where the rationalists go wrong isn't the multiplication, it's the failure to ignore very unlikely outcomes as normal people would. They think themselves too rational to ignore the possibility of unlikely things, but ironically it is normal people who don't spend their time dwelling on extremely unlikely bullshit have a more rational approach to life.
The rationalists spend hours discussing scenarios like "What if a super AI manipulates people into engineering a super virus that wipes out humanity? Its technically possible; there's no law of physics which prevents this!", to which a normal person would respond by wondering if these people are on drugs, why would they spend so much time worrying about something which isn't going to happen?