/sci/ - Science & Math

>>12398108
I am the person who posted the problem. So far you're the closest one to the actual solution.
The most important point here is that this is a PHILOSOPHICAL problem, not a mathematical problem. The answer to this problem lies almost completely in the way you translate it into an actual mathematical problem.
>On average, I.e. if you did the experiment many times
This is very important. We don't know what happens if we repeat this experiment many times.
It's a one off event, and therefore the expectation is much less relevant than if we were allowed to repeat this experiment infinitely many times.
However, even to define the probability and expectations, some assumptions need to be made, we need to mathematically model the situation.
There's a problem in that there are many different models. It could be that one envelope contains $10 and the other contains $20, and we condition on the even that you chose the $10 envelope. Alternatively you could have $10 and $5. Another alternative is that you have $10 and half of the time the other envelope has $5 and the other half it has $20. It's not at all clear which algorithm of the three you would write to simulate the probabilities, since each algorithm satisfies equally well the problem statement, and hence the description of the situation is too vague to talk about the probabilities involved, without additional assumptions. In the wikipedia explanation for the version of the problem where you do not see what's in the envelope, their model assumes that the total sum of the envelopes is always the same, hence the expectation comes out to be 0.
This is a general problem in probability: a description of a one-off event is rarely enough to form a probabilistic model of what's happening.

Good morning /mg/!
Let's let go of the low IQ gorilla problems from lost redditors and instead here's a bit more interesting problem: If a function f:R->R is continuously differentiable and uniformly continuous, does it follow that the derivative f' is bounded?

>>12214253
Algebra! I recommend Stillwell's Elements of Algebra.

It is reasonable to believe in free will.

1. If some fact or statement is immediately perceived to be true then it's reasonable to belief the statement is true unless your perception is challenged by a valid reason why it could be wrong.
Examples: I remember that yesterday I drank a cup of coffee. There are no valid reasons to believe my perception is wrong and that in fact I didn't drink any coffee yesterday. In absence of such counterevidence, it's reasonable to believe that I actually drank coffee yesterday. I do not need to come up with a mechanism for how my memory works to believe it, nor do I need to give precise technical/philosophical definitions of memory and the word "drank" for it to be reasonable for me to believe this fact. My immediate perception of this fact is enough for it to be reasonable, in absence of evidence or reasons to the contrary.
2. I immediately perceive my own free will (the ability for me to make choices, i.e. influence the future).
I perceived it when I was a child and I still perceive it. In fact, my own perception in free will has been central to the way I live and the way I think about the world. I regularly spend time thinking about how to improve my own future which would make no sense in a worldview where I am not able to influence my own future (for example, in a worldview where everything is already predetermined).
3. The only reason I'm aware of that attempts to challenge my perception of free will is the notion of determinism. That is, the state of the universe at one point in time completely determines how it will look at all subsequent points in time, which is theoretically predictable.
If you have any other reasons for me to doubt free will that are unrelated to determinism feel free to point them out in this thread, I'd be happy to discuss.
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