Minor quibble which I hope isn't breaking a norm: BetFair did seem to pay out last week, or at least some of the bets on who would win the presidency were settled on 07/11/20.
Do you expect we'll be n the midst of a third wave before the vaccine begins to be doled out? Or just beginning to enter one? Thanks for the post.
Use a fire lighter
The post about Sweden's unusual situation you linked to has updated. The author claims that the reduced death rate is mostly due to younger people getting near all of the covid cases, which is supported by recent data (the figure shows total number of changes between July and 03 Nov). Why that is the case is another issue.
Edit: As always, thanks for the post.
What about Thorium? A back of the envelope calculation suggests thorium reactors could supply us with energy 100-500 years. I got this from a few sources. First used the figure of the 170 GW days produced per metric tonne of fuel (Fort St Vrain HTR) and the availability of fuel (500-2500 ktonnes according to Wikipedia) to estimate 10-50 years out of Thorium reactors if we keep using 15TW of energy. And that's not even accounting for breeding reactors, which can produce their own fuel. So if we do go with the theoretical maximum, then we should multiply this figure by 50. I'm basing that estimate of the (probably peak) fuel efficiency of Thorium from what Carlo Rubia of Cern said (see Wikipedia article above). That is, 1 tonne can provide 200 times more power than 1 tonne of Uranium. Since Uranium produces ~45 GW days per metric tonne of fuel, we get the estimae of 50 times. Then we get the figure of 500-2500 15TW years.
Supposing that we really need four or five times the amount of energy we actually use, leaves us with an upper bound of ten times the naive estimate. So I'd estimate thorium could provide 100-500 75TW years.
Thanks for the reply. Feelings of helplessness sounds about right, and I think you may be right about giving your self the feeling that you are being supported. Only, people with severe chronic pain often suffer from anxiety and depression as well. It seems like it would be a hard battle getting their brains to recognise those aforementioned feelings.
How does this apply for physically painful trauma? I understand that the broader process should work, but I'm curious if you could guess what frame would be the most helpful for such trauma.
Somewhat urgent: can anyone recommend a good therapist or psychiatrist for anxiety/depression in the UK? Virtual sessions are probably required. Private is fine. Also, they shouldn't be someone biased towards rationalist types. The person I'm thinking of has nearly no knowledge of these ideas.
Other recommendations that seem relevant welcome.
I still disagree. You can use Fermat's last theorem rigorously without understanding why it works. Same for the four colour theorem. And which mathematics understand why we can classify finite simple groups the way we do? I'd bet fewer than a percent do. Little wonder, if the proof's 3 volumes long! My point is that there are many theorems a mathematician will use without rigorously knowing why it works. Oh sure, you can tell them a rough story outlining the ideas. But could the prove it themselves? Probably not, without a deep understanding of the area. Yet even without that understanding, they can use these theorems in formal proofs. They can get a machine to check over it.
Now, I admit that's unsatisfying. I agree that if they don't, then they don't have a rigorous understanding of the theorem. Eventually, problems will arise which they cannot resolve without understanding that which they accepted as magic. But is that really so fatal a flaw for teaching students the hyperreals? One only needs a modest amount of logic, perhaps enough for a course or two, to understand why the transfer principle works. Which seems a pretty good investment, given how much model theory sheds light on what we take for grounded.
Now I suppose if you find infinitary mathematics ugly, then is all besides the point. And unfortunately, there's not much I can say against that beyond the usual arguements and personal aesthetics.
Note that I didn't say it's not an aesthetic preference. I just don't think likely to be false --> ugly, though I agree learnings its likely to be false-->uglier than before.
No, to understand why the transfer principle works requires a fair amount of knowledge of mathematical logic. It doesn't follow that you can't perform rigorous proofs once you've accepted it. Or am I missing something here?