andrewk

I think Nietzsche would be a natural philosopher to turn to for such arguments. His philosophy seems to me to be about embracing your passions rather ...

Please Nooooooo! Let's not do that. I reserved the symbol L many pages ago for the maximum possible value ('Limit') in the player's prior distribution...

That's a different metric than the ones I quoted. Mine is in dollars while yours, if I'm reading the PHP correctly, is the dollars divided by the tota...

Most of my languages are very old - Fortran, BASIC, Pascal, C, Simula, LISP, Prolog. These days I mostly use R, and am toying with Python in case that...

I've just been hit by the consequences of some of the issues raised in my Bayesian note. I didn't notice them before, but they're in there. The first ...

Perhaps you are referring to the fact that variable names have no meaning and can be freely swapped, a fact regularly used in physics when we want to ...

What do you mean by a meta-language? In FOPL all we have are a language, logical axioms and rules of inference.

Syntactically equivalent means that the symbol strings, once any language-extension abbreviations have been replaced by their equivalents in the core ...

We have to be careful using the word 'meaning' in logic, because in natural language 'meaning' is associated with 'semantics', but semantics in logic ...

I think it's asking the student to prove that universal quantifiers commute with one another, which is not given as an axiom in most logical systems, ...

It depends on what logical system you are using. In many axiomatisations of first-order predicate logic there is an axiom schema of Universal Quantifi...

I have to go to bed now. I'll look in again tomorrow if time permits.

The question is ill-defined. To answer it, you'd have to specify your algorithm, which you have not done. If we take srap's PHP program as the algorit...

As described in the post immediately above, that setup does not reflect the player's knowledge and expectations.

I did my best to read your code. Although I don't speak much PHP I think I can see what it's doing. It appears to me that it does not reflect the info...

It's a meaningless question. 'on average' is not a meaningful statistical concept. We can only meaningfully talk in terms of expected values. The expe...

I don't answer questions based on false premises. Have you stopped beating your wife?

Do you have another question? If so, what is it?

It bears no resemblance to the analysis. For a start the analysis is about expectations, and your statement doesn't mention them. If you believe it fa...

If the distinction between 'maximise expected winnings' and 'what she should do' is irrelevant (which it is if we accept the implicit assumption that ...

Yes, I imagine they would aim to maximise their expected increase in utility, not their expected monetary gain. So for instance if the envelope contai...

I don't believe that description correctly represents the analysis.

I don't understand how your question relates to the quote. Can you elaborate?

I covered that on the first page, but that was before you joined the discussion. What the player 'should do' depends on her utility function, and none...

That is correct, but has no bearing on the problem. The problem asks about the player's expectation, not the game host's expectation, which is what th...

What evidence do you have for that claim? By all means present it and we can discuss it.

I suspect you are basing that claim on some computer simulation. Firstly, a computer simulation cannot prove anything in probability theory. Secondly,...

That doesn't prevent us from modelling our uncertainty about it by representing it as a random variable. In Bayesian analysis we model a fixed, unknow...

Eliminating Y is making X the numéraire. That's why you need to address the numéraire issue, as explained in this post. When we use X as numéraire, th...

What do you mean by 'exhaustive disjunctive possibilities'? That's all correct, but is not inconsistent with my note. Nowhere does it say that 5 and 2...

We agree on that. Y and X are interdependent. That's why I define Y as \quad\quad\quad\quad\quad Y = X\cdot (1+B) where B is a Bernoulli random variab...

Can you justify that 'since'? There is no justification provided in the sentence in which it occurs, because the words following it have no logical re...

Those results are both correct, and it's because each is done from the point of view of observing that envelope - two opposite points of view. It's an...

I haven't seen any genuine absurdities in the thread so far. Assertions of absurdity, yes, but not real ones. In general, it's best to avoid arguments...

I think it must be somebody else that said that. I can't see it in what I wrote.

The difference between these two is not mysterious. Calculation (a) is done from the point of view of the game host, who knows the value of X, and so ...

Try! Do or do not is a false dichotomy.

You think that's bad. What about 'She is hungry'? The problem is with the verb 'to be', which is a jumble of vagueness and equivocations. That's why s...

I've finally found time to work out my full Bayesian analysis of the problem. For those that are interested, it is here. Non-Bayesians may not like it...

All the better - then you have the perfect mindframe to willingly accept the glorious uncertainty of the universe, and not chase after such meaningles...

I suspect you are thinking of physicsforums. Topic like this are shut down there as soon as they come up because it is speculation, not physics. Specu...

I'm still not sure I understand your question. You've asked about the minimum possible value of X. Do you mean the minimum that I think is possible fo...

Are you sure that was me? It doesn't sound familiar, but maybe I've just forgotten. Can you link the exchange? FWIW I'm imagining X can be any real nu...

I agree with both of these. The point about the maximum possible amount has been made before, but has been lost in the length of the thread. I mention...

Dormez bien, mon ami.

It's not about the games mistress's sample space. She doesn't have one. She has two amounts that she has always intended to put into the envelopes. It...

To me, to say 'B is possible' means 'I would not be astonished if I discovered B to be the case'. If I have 10 and somebody opens the other envelope, ...

I would say yes I do. I feel a discussion over the meaning of 'possible' may be approaching, but let's see where this goes.

Sorry, still not following you. One of what?

I mean that I know my envelope has 10 and that the other envelope has either 5 or 20. I don't know what you mean by 'one of them must be in the distri...