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I see, I haven't yet read that one. But yes, we should be clear what we denote with HH/HT/TT/TH, the coins before, or after the turning of second coin.

Why couldn't the ball I've just got been put into the box on HH? On HH, after we turn the second coin we get HT which is not HH, so a ball is put into the box, no?

I don't want my name to carry respect. I want individual comments evaluated for their validity.

I like this part of your comment a lot! If you don't want to periodically create new accounts, another possibility is regularly changing your name to something random.

Cases clustering at wetmarket, proline at fcs, otherwise suboptimal fcs, out of frame insertion, WIV scientists' behavior after leak (talking about adding fcs to coronavirus in december, going to dinner, publishing ratg13), secret backbone virus not known (for some reason sars not used like in other fcs insertion studies), 2 lineages at market just off the top of my head

You did the same thing Peter Miller did in the first rootclaim debate just for the opposite side: you multiplied the probability estimates of every unlikely evidence under your disfavored hypothesis, observed that it is a small number then said a mere paragraph about how this number isn't that small under your favored hypothesis.

To spell it out explicitly: When calculating the probability for your favored hypothesis you should similarly consider the pieces of evidence which are unlikely under that hypothesis!! Generally, some pieces of evidence will be unlikely for one side and likely for the other, you can't just select the evidence favorable for your side!

As I understand (but correct me if I am wrong), your claim is that we don't feel surprise when observing what is commonly thought of as a rare event, because we don't actually observe a rare event, because of one quirk of our human psychology we implicitly use a non-maximal event space. But you now seem to allow for another probability space which, if true, seems to me a somewhat inelegant part of the theory. Do you claim that our subconscious tracks events in multiple ways simultaneously or am I misunderstanding you?

Relatedly, the power set does allow me to express individual coin tosses. Let be the following function on :

In this case is measurable, because (minor point: Your is not the powerset of ), same for . Therefore is actually a random variable modeling that the first throw is head.

Regarding your examples, I'm not sure I'm understanding you: Is your claim that the eventspace is different in the three cases leading to different probabilities for the events observed? I thought your theory said that our human psychology works with non-maximal eventspaces, but it seems it also works with different event spaces in different situations? (EDIT: Rereading the post, it seems you've adressed this part: if I understand correctly, one can influence their event space by way of focusing on specific outcomes?)

Wouldn't it be much simpler to say that in 1, your previous assumption that the coinflips are independent from what you write on a paper became too low probability after observing the coinflips and that caused the feeling of surprise?

I'm afraid I don't understand your last paragraph, to me it clearly seems an alternative explanation. Please, elaborate. It's not true that any time I observe a low-probability event, one of my assumptions gets low-prob. For example, if I observe HHTHTTHHTTHT, no assumption of mine does, because I didn't have a previous assumption that I will get coinflips different from HHTHTTHHTTHT. An assumption is not just any statement\proposition\event, it's a belief about the world which is actually assumed beforehand.

To me your explanation leaves some things unexplained: for example: In what situation will our human psychology use which non-maximal event spaces? What is the evolutionary reason for this quirk? Isn't being surprised in the all heads case rational in an objective sense? Should we expect an alien species to be or not be surprised?

For my proposed explanation these are easy questions to answer: We are not surprised because of the non-maximal event spaces, rather, we are surprised if one of our assumptions loses a lot of probability. The evolutionary reason is that the feeling of surprise caused us to investigate and in cases when one of our assumptions got too improbable, we should actually investigate the alternatives. Yes, being surprised in these cases is objectively rational and we should expect an alien species to do the same on all-heads throw and not do the same on some random string of H/T.

I don't know.. not using the whole powerset when is finite kinda rubs me the wrong way. (EDIT: correction: what clashes with my aesthetic sense isn't that it's not the whole powerset, rather that I instinctively want to have random variables denoting any coinflip when presented with a list of coinflips yet I can't have that if the set of events is not the powerset because in that case those wouldn't be measurable functions. I think the following expands on this same intuition without the measure-theoretic formalism.)

Consider the situation where I'm flipping the coin and I keep getting heads, I imagine I get more and more surprised as I'm flipping.

Consider now that I am at the moment when I've already flipped coins, but before flipping the th one. I'm thinking about the next flip: To model the situation in my mind, there clearly should be an event where the th coin is heads and another event where the th coin is tails. Furthermore, these events should have equal (possibly conditional) probabilities yet I will be much more surprised if I get heads again.

This makes me think that the key isn't that I didn't actually observe a low probability event (because in my opinion it does not make sense to model the situation above with a -algebra where the th coin being tails is grouped with the th coin being heads because in that case I wouldn't be able to calculate separate probabilities for those events) rather the key is that I feel surprise when one of my assumptions about the world has become too improbable compared to an alternative: in this case, the assumption that the coin is unbiased. After observing lots of heads the probability that the coin is biased in favor of heads gets much greater than that of it being unbiased, even if we started out with a high prior that it's unbiased.

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