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The Holy Algorithm

Actually, the Easter 2021 date is in May for some Eastern communities: see

https://www.thebostonpilot.com/article.asp?ID=189602

Base rate of RCT from developing countries finding unexpected effects

The rapid availability of third world originated studies to internet searches by those living elsewhere, which has happened because of internet publishing and especially in the last three years because of openly searchable preprint sites such as medrxiv, is a new enough thing in science that I doubt there has been enough time to get a valid such likely future failure rate, especially if you are including preprints.

To get an approximate base rate you would need to check the years prior to open internet medical paper publishing. At minimum you would need to read the older years of paper versions of those nation's journals, likely in their medical schools, and count the studies fitting your criteria over the past ten years or more, ideally even including the studies rejected by such journals if you are including preprints in your questions about the Covid-19 studies. Not an easy project, so best to take the studies you mention as proposing a hypothesis, perhaps to be tested in the future via reproducibility. Just like most other clinical studies published by anyone else anywhere.

A Simplified Version of Perspective Solution to the Sleeping Beauty Problem

From a completely subjective view, there can be no single answer as to what day of the week it is. It is whatever weekday  I decide it is. Who could gainsay it?

As soon as we allow an objective view of what day of the week it is, we implicitly allow an over-ride of the subjective viewpoint by the objective one, and the 1/3 probability becomes the better choice.

An argument for personal identity transfer.

One advantage to a thought experiment is that it can be scaled without cost. Instead of your  sorites series, let us posit a huge number of conscious humans. We alter each human to correspond to a single step in your gradual change over time, so that we wind up performing in parallel what you posit as a series of steps. Line our subjects in "stage of alteration" order.

Now the conclusion of your series of steps corresponds to the state of the last subject in our lineup. Is this subject's consciousness the same as at start? If we assume yes, then we have assumed our conclusion, and the argument assumes its conclusions.

If we assume for sake of argument the subject's consciousness at the end of our lineup differs from the start of the lineup, then we can walk along the line and locate where we first begin to notice a change. This might vary with groups of subjects, but we can certainly then find a mean for where the change may start. This is possible even if in series we cannot perceive a difference between the subject from one step to another.

An argument for personal identity transfer.

Almost all gradual-brain-to-device replacement arguments are indeed sorites arguments. You assume:

Plucking one or three hairs from a beard that has 10000 hairs beard is too small an action to change a beard visibly

Plucking 2 hairs from a beard with 9998 hairs is too small a change to see (true)

Plucking 2 hairs from a beard with 9996 hairs is too small a change to see (true)

...

plucking 2 hairs 4000 times from a beard is too small a change to see (false)

Examples of Measures

Read this online classic paper about geometric measure theory, because it's really entertaining:

https://www.maths.ed.ac.uk/~tl/docs/Schanuel_Length_of_potato.pdf

Sleeping Julia: Empirical support for thirder argument in the Sleeping Beauty Problem

I think that OP is confusing expected value with probability.

The  expected value formula is the probability of an event multiplied by the amount of times the event happens: (P(x) * n).

This explains the P(B) = 1.5 the OP put above-- he means the expectation is 1.5, because P(waking with any one coin flip result) = 1/2 and the times it occurs is 3.

So the halfers believe the expectation is 1/2 for waking with heads and 1/2 for waking with tails.

The thirders have the expected values right:  1 for waking with heads, 2 for waking with tails.

Born as the seventh month dies ...

This is correct, if you are excluding the case where both are boys both born on Tuesday. Otherwise you would not subtract p(A and B). But, you did not say only one, you said _at least_ one.

Born as the seventh month dies ...

I don't think you have the dependencies quite right, because you can actually use more of the information than you do above to restrict the population from which you draw.

The real underlying population you should draw on seems to to be the population of fathers with exactly two children, of which one might be a boy born on Tuesday.

p(a two boy family given one brother was born on Tuesday) = (p(one brother born on Tuesday in a in two-boy family)) (p(two boys in 2 person families)) / p(out of all two person families, having one be a boy born on Tuesday)

which is if we say Tuesday birth is 1/7 and boy is 1/2,

(2/7) (1/4) / (2/14) = 1/2 so the Tuesday datum drops out.

Do any mammal species exhibit an immune response in some of the herd in response to the infection in other herd members?

It is not a crazy question at all. In fact it has a variety of answers: I will summarize with a "no," a "yes," and a "no."


1. No, exposure of others to Covid-19 may cause them to become specifically immune to that virus, but it will not cause us to also become specfically immune unless we are similarly exposed to virus components themselves, not just the persons involved.


2. Yes, the fact that people near us are in distress because they are sick will probably cause us, as we too are distressed by the situation, to secrete stress hormone and related responses that will somewhat alter our immune system, for example by raising the count of neutrophilic white cells in our blood somewhat.


3. No, that particular kind of nonspecific change in our stress hormones and related effects on our immune calls is not likely to prevent Covid-19 infection in us.

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