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The central limit theorem in terms of convolutions

Key questions for me. 

1. Under what assumptions is the CLT valid? There seem to be many real world situations where it is not valid. E.g. finite variance is one such assumption. 

2. How easily can one check that the assumptions are valid in a given case? The very existence f fat tails can make it hard to notice that there are fat tails and easy to assume that tails are not fat.

2. Even when valid, how fast does the ensemble distribution converge, in particular how fast does the "zone of normality" spread? Even when CLT applies to the mean of the distribution it may not apply to the far tails for a long time.

Covid 11/12: The Winds of Winter

Specifically on the Pfizer press release. Due to various medical conditions I have been following medical research, press releases, government policy etc for many decades and have read cubic meters of medical research papers, textbooks, statistics texts etc.

TL;DR and one thing I have learned : A press release from a pharmaceutical company saying <thing> is very weak evidence that <thing> is true.

In any case realistically a vaccine rollout is extremely unlikely to be done before the end of 2021. This is a best case scenario. And we do not know the extent of the economic damage. 

The Born Rule is Time-Symmetric

For the benefit of others reading this, in Shankar's book referenced below, this is said to not be a full symmetry i.e. not always valid.

There is no reason to think that the evolution of the conjugate function will be the same as the evolution of the original function. 

Also there is no time-reversed Copenhagen measurement process in the theory which he implicitly requires.

Think about a massive object like a planet moving from L to R. It is massive so quantum effects can be ignored. It is clearly not true that the planet would be measured as being in the same place 10 minutes ago and 10 minutes hence. So the statement "All possible futures are also possible pasts" is wrong.

What could one do with truly unlimited computational power?

I suppose I would test out the claim by getting it to mine a few hundred $million of bitcoin for me.

Then crack all the interesting crypto data that is floating around. 

Then brute force search for proofs/solutions of all the big problems such as Riemann Hypothesis, factoring etc. Try all texts shorter than say 100 terabytes and see if they solved the problem.

Work out the implications of all the human genes by calculating out how the human body works. This would include things like solving protein folding.

Find the best/shortest algorithm for all the AI/ML challenges that delivers near perfect results. 

Then simulate the body with various chemical compounds added to cure cancer, infections etc. Design vaccine + cure for coronavirusV2 and also machines to make them.

I guess you could create a model of the brain and then run all sorts of experiments on the simulation to work out how it works. 

Simulate atoms and molecules and brute force ways to build things that would build arbitrary nanotech engines.

At what point would you get worried about AI safety?

Does BioNtech's vaccine result of 90% disease prevention mean that 90% of the vaccinated can't pass the virus to other people?

It means that they have put out a press release. I would be waiting for the paper and hopefully more data. I have found that such press releases often subtly and unsubtly overstate how good the results are. 

From the reports, it looks like 90% of the infections were in the control group. Make of that what you will. It does sound encouraging. We don't know if the "uninfected" were shedding virus at any given time.

IMHO headless posts like this should be removed. By headless posts I mean things like "Link! Check it out!". 

Why should we listen to this? What is it even about?

We are all snowed under by things we might watch or listen to or read. You need to provide good reasons for people to devote their time to something.

Here is the blurb on the podcast. For something that goes for almost 2 hours.

"We discuss the future, legal systems very different from our own, how technology drives progress, and what the future might look like. "

Please steelman the accusations of election fraud

HIlarious the way they quote the NYT on the high incidence of voter fraud, a view they may not entirely adhere to nowadays.

Please steelman the accusations of election fraud

Here is one attempt. I have not evaluated it in any detail.


Interestingly he dismisses the Benford's Law arguments with links that provide what look like cogent reasons.

Bet On Biden

I got heavily downvoted for suggesting that Nate Silver's credibility was not strong enough to make this a good bet.

The most you could say at this point (late in the night on election day) is that it looks like the election is very close. This suggests to me that those people saying that betting on it at 65% odds for Biden was a huge steal, were overconfident. People were quoted who thought Biden's P(win) was 96%. 

I am interested in any suggestions about what went wrong. I can't think of a lot of edifying reasons. 

1. Rationalists don't win

2. Dunning-Kruger effect

3. General overconfidence

4. Saying Trump had a chance runs the risk of signaling that you are a "Trumptard".

5. Stating high confidence is one way to signal high intelligence. "Uh I'm not sure" doesn't sound too smart. 


Bet On Biden

> What do you mean by this?

 I mean that given he won, the actual odds of him winning were actually better than 10%. 

I cannot prove this externally but  - before the election in 2016 I said to several people, who remember this, that it would be somewhere between a narrow Clinton win and a strong Trump win. So it was not outlandish to think Trump could win. The main reason I had was what is now known as the "shy Trump voter" effect. People did not want to get cancelled for admitting that they were a 'fascist'.  

> Look at Nate's track record

If Trump wins this one, as looks fairly likely at the moment, NS will be 3/5 for Presidential elections, no better than chance.

My main beef with the argument from credibility is a) NS does not have a long strong track record in this field of presidential elections, b) Credible is different than totally accurate. I pointed out if he was wrong by a few tens of percents, like last time, his view is not strong evidence that there is a winning bet here. 

Funnily enough NS reduced his P(Biden) to about 50% on election day (or maybe the day before). 

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