Confirmation the prophecy isn’t about Neville:
Neville Longbottom… who took this test in the Longbottom home… received a grade of Outstanding.
Harry raised the parchment with its EE+, still silent.
The Defense Professor smiled, and it went all the way to those tired eyes.
“It is the same grade… that I received in my own first year.”
AND THE DARK LORD WILL MARK HIM AS HIS EQUAL
If the set of Universe States is finite, then yes, there will be a computable utility function for any VNM-rational preferences (the program can be just a lookup table).
Ooops, not totally correct, because the probabilities in the lotteries could be uncomputable.
Some utility functions can be found by randomly putting agents into various universes and seeing what happens
The universe is computable.
Therefore, all utility functions are computable.
3 does not follow from 1 and 2.
If the set of Universe States is finite, then yes, there will be a computable utility function for any VNM-rational preferences (the program can be just a lookup table).
If the set of possible Universe States is countably infinite, and you can meaningfully encode every universe state as a finite string, then no, not every utility function is computable. Counterexample: number the possible universes and assign a utility of $1 to every universe whose number describes a halting turing machine, and $0 for every universe whose number describes a non-halting turing machine.
If the set of possible Universe States is uncountably infinite, or you cannot meaningfully encode every universe state as a finite string, then no, the utility functions might not be remotely computable.
What does Morality Modeling Language do? If you allow it to describe only computable utility functions, then you can make it describe only computable utility functions!
It was a good article, thank you!
Who chooses the Featured Articles of the week?
Let the record show that Bitcoins lost 21% of their value the day after this article was posted.
I think roystgnr’s comment was meant to be parsed as:
“Hmm… I can prove that this is in NP, and I can prove it is not in P and is not in NP-Complete. But that’s not worth any points at all!” (crumples up and throws away paper)
Corollary:
...they shouldn’t have crumpled that piece of paper.
Salesmanship
“Write a polynomial-time algorithm for X, or prove X is NP-Complete. For extra credit, do both.”
But there are problems with this. First, there are many possible TMs that could run such programs. We need to choose one—but such a choice contradicts the “inevitable” nature that Platonism is supposed to have.
The choice of your turing machine doesn’t much matter, since all turing machines can simulate each other. If you choose the “wrong” turing machine, your measures will be off by at most a constant factor (the complexity penalty of an interpreter for the “right” machine language).
Since you’re talking about a game most people haven’t played before, presenting a concrete example is important to do early. I recommend the mystery passage should (a) be blockquoted so it stands out more and (b) moved to before you start talking about heuristics.
Thank you for taking the time to write and edit a post.
Meta
Presenting polemics against something an in-group is already predisposed against really rubs me the wrong way. Putting down someones book can be great as a means to explain a broader point, but shouldn’t be an end unto itself. The article “How not to say stupid things about undecidability” could be a cool; it might point out a flaw in my understanding of the consequences of the halting theorem or something. The article “A post-modernist wrote an argument for God, and it contains some flawed reasoning” isn’t likely to surprise me, or to help me correct my thinking.
The great-grandparent comment did make me consider unbreakable vows as a theory of what happened on Halloween. E.g. to prevent one of his Horcruxes from later killing him, Voldemort made an unbreakable vow not to magically interact with his alter egos (this causing Harry’s sense of Doom around Quirrell). Doesn’t seem necessary, though.
Assuming the only states are married and unmarried. I’m not sure if I would call a widow unmarried, in the same way I’m not sure if I would call a man with a surgically reattached foreskin uncircumcised.
I’m introducing the term Friendly User Interface to complement Friendly AI as a possible area of interest for the LessWrong community.
Speaking only to this. Every new piece of jargon comes with −100 points. Does the usefulness of this term overcome −100 points?
It’s cool, but I doubt as impressive as it looks. If you connect the inputs and outputs the right way, I bet you could make a car out of a toaster oven controller.
In other words, open threads die after about 4 days.
The Pythagorean theorem hasn’t been mentioned in HPMOR. Given this, would anyone bet me at 100-to-1 odds that future chapters will reveal that Harry rederived the Pythagorean theorem, in secret, while a student at Hogwarts, before April, and had fun?