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Alicorn comments on Open Thread: March 2010, part 3 - Less Wrong
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Here's a puzzle that involves time travel:
Suppose you have just built a machine that allows you to see one day into the future. Suppose also that you are firmly committed to realizing the particular future that the machine will show you. So if you see that the lights in your workshop are on tomorrow, you will make sure to leave them on; if they are off, you will make sure to leave them off. If you find the furniture rearranged, you will rearrange the furniture. If there is a cow in your workshop, you will spend the next 24 hours getting a cow into your workshop.
My question is this: What is your prior probability for any observation you can make with this machine? For example, what are the odds of the windows being open?
Why am I firmly committed to realizing the future the machine shows? Do I believe that to be contrary would cause a paradox and explode the universe? Do I believe that I am destined to achieve whatever is foretold, and that it'll be more pleasant if I do it on purpose instead of forcing fate to jury-rig something at the last minute? Do I think that it is only good and right that I do those things which are depicted, because it shows the locally best of all possible worlds?
In other words, what do I hypothetically think would happen if I weren't fully committed to realizing the future shown?
Agree with the question of why you would be doing this; sounds like optimizing on the wrong thing. Supposing that it showed me having won the lottery and having a cow in my workshop, it seems silly to suppose that bringing a cow into my workshop will help me win the lottery. We can't very well suppose that we were always wanting to have a cow in our workshop, else the vision of the future wouldn't affect anything.
I stipulated that you're committed to realizing the future because otherwise, the problem would be too easy.
I'm assuming that if you act contrary to what you see in the machine, fate will intervene. So if you're committed to being contrary, we know something is going to occur to frustrate your efforts. Most likely, some emergency is going to occur soon which will keep you away from your workshop for the next 24 hours. This knowledge alone is a prior for what the future will hold.