All the links to your blog are broken.
(e.g. "abstracting compassion" leads to "http://lesswrong.com/2010-12-05" instead of "http://www.jefftk.com/news/2010-12-05.html")
I think Eliezer's reply (point '(B)') to this comment by Wei Dai provides some explanation, as to what the decision theory is doing here.
From the reply (concerning UDT):
I still think [an AI ought to be able to come up with these ideas by itself], BTW. We should devote some time and resources to thinking about how we are solving these problems (and coming up with questions in the first place). Finding that algorithm is perhaps more important than finding a reflectively consistent decision algorithm, if we don't want an AI to be stuck with whatever mistakes we might make.
And yet you found a reflectively consistent decision algorithm long before you found a decision-system-algorithm-finding algorithm. That's not coincidence. The latter problem is much harder. I suspect that even an informal understanding of parts of it would mean that you could find timeless decision theory as easily as falling backward off a tree - you just run the algorithm in your own head. So with vey high probability you are going to start seeing through the object-level problems before you see through the meta ones. Conversely I am EXTREMELY skeptical of people who claim they have an algorithm to solve meta problems but who still seem confused about object problems. Take metaethics, a solved problem: what are the odds that someone who still thought metaethics was a Deep Mystery could write an AI algorithm that could come up with a correct metaethics? I tried that, you know, and in retrospect it didn't work.
The meta algorithms are important but by their very nature, knowing even a little about the meta-problem tends to make the object problem much less confusing, and you will progress on the object problem faster than on the meta problem. Again, that's not saying the meta problem is important. It's just saying that it's really hard to end up in a state where meta has really truly run ahead of object, though it's easy to get illusions of having done so.
From the "About" page:
The header image is a mashup [full size] of Wanderer above the Sea of Fog by Caspar David Friedrich and an artist's depiction of the Citadel from Mass Effect 2.
OK, let’s look at this: The prisoner receives 2 pieces of information from the warden at the beginning:
Assuming that the warden's claim is true, there are 5 possible outcomes:
Death at noon of Mon, Tue, Wed, Thu or Fri.
Assuming furthermore that the prisoner has no other information that and that he uses probability theory, he will construct the following uniform probability distribution:
P(Death at noon of X.)=1/5 where X can be Mon, Tue, Wed, Thu or Fri.
Furthermore he can now also infer the conditional probabilities
P(Death at noon of X.|Not dead after noon of Mon.)=1/4 for X = Tue, Wed, Thu or Fri.
P(Death at noon of X.|Not dead after noon of Tue.)=1/3 for X = Wed, Thu or Fri.
P(Death at noon of X.|Not dead after noon of Wed.)=1/2 for X = Thu or Fri.
And finally:
P(Death at noon of Fri.|Not dead after noon of Thu.)=1
Thus the prisoner will now be not 'surprised' only by a death at noon of Friday. As in: The occurring event had P>1/2.
Is this the proper notion of 'surprise'?
I don't think so. - Surprise should be always measured quantitatively.
But observe that in the 'death at noon of Friday' scenario there is no surprise whatsoever. It is qualitatively absent under the condition that the warden speaks the truth:
P(Death at noon of Fri.|Not dead after noon of Thu., The warden speaks truth.)=1 P(Death at noon of Fri.|Death at noon of Fri.)=1 (duh) There is no updating.
The second piece of information from the warden is:
What does this mean, anyway? Can we actually alter our probability distribution based on this datum?
I highly doubt that, but the prisoner in the canonical treatment certainly does update: As it holds that:
P(Death at noon of Fri.|Not dead after noon of Thu.)=1
He concludes:
P(Not dead after noon of Thu. AND The prisoner will be surprised by his death.)=0
And:
P(Death at noon of Fri.|Not dead after noon of Thu., The prisoner will be surprised by his death. )=0
As a special case of 'P(Anything.|Contradiction.)=0'
He then runs a few iterations and concludes that all outcomes have the P=0 under all conditions.
Here the background assumption is still that the warden's words are true. This assumption however is contradictory if the updating procedure of the prisoner is correct. But we can easily see that the new belief structure of the prisoner will be surprised by any of the outcomes; rendering the warden correct. Thus the paradox.
The solution is simply that the prisoner's updating procedure is incorrect.
The datum 'The prisoner will be surprised by his death.' does not warrant the update. The warden's statements are contradictory if the original belief structure is retained and if the only remaining outcome is death at noon of Friday. However, after the first change of the belief structure by the prisoner this no longer holds. The further 'iterations' make even less sense and the whole 'update' is unstable, as our simple reflection shows - now the prisoner will be surprised by any outcome.
So obviously, this is not Bayesian updating.
The prisoner tried to reason. Concluded that he couldn't be killed without proving the warden wrong. Changed his probability distribution over outcomes to reflect this. Thus changing the prerequisites for his initial conclusion. He did not examine the implications of the changed prerequisites. Ensuring that the warden could always be right.
He thus updated wrongly - his believes do not reflect reality.
Observe that the outcome 'The warden was correct.' and it's negation 'The warden was incorrect.' regarding the proposition 'The prisoner will be surprised by his death.', given 'He will be killed at noon of one day of the next five days.' depend solely on the belief structure of the prisoner.
Given that a belief structure is normally used by an agent to maximize utility and yet the prisoner is not an agent (he lacks a utility function), the belief structure is inconsequential apart from proving the warden right or wrong. The shaping of the structure is the only choice given to the prisoner and as such it can be hardly called a structure of belief at all.
If there was a non-constant utility function over 'The warden was correct.' and 'The warden was incorrect.', this would be a 'belief-determined problem' which is likely an inconsistent class of problems by itself - an agent trying to maximize such a problem would have to simultaneously represent the problem and 'believe' in things which generally contradicting this representation in order to maximize the payoff, thus making the 'belief' something indistinguishable from a 'mere' decision.
Nevertheless, in the canonical treatment the prisoner ensured by 'incorrect' updating that the warden was always right.
Likewise, we can construct an 'incorrect' belief structure that ensures that the warden will always be incorrect:
P(Death at noon of day #(N).|Not dead after noon of #(N-1).)=1
This structure will be 'surprised' by any survival, as it expects certain death each day.
Of course, this is total BS from the perspective of probability theory, but so is the original updating scheme.
Once again Harry's voice shrieked "Stupefy!", and later on, when she was remembering this, she could never quite believe she'd managed to do it, but she slashed out with her blade of light like it was a Beater's bat, and hit the stunbolt back at Harry who just barely managed to twist out of the way.
Seems more like just a further Star Wars reference to me.
Well, even if she was somehow protected, note that she was not passively protected (not like a shield spell) - she still had to move to deflect and:
They were both moving slowly, and Hermione guessed that the spell was taking a lot of strength out of them.
So she probably did not have the agility to deflect another shot - especially in the middle of a block or similarly.
Also: A reflected or friendly-fired Somnium could harm neither Harry nor Neville, so there was really little harm in trying - even if Harry came to your hypothesis, he still should have tried it – right after he made sure that she wouldn’t be cut in half subsequently.
As for the other Sunshine soldiers blocking it - I confess that I do not remember how exactly the first-year Contego shields work and what their limitations are (I do not think this has been elaborated upon), but Daphne seems to be out of the main Sunshine cluster here (if there still is one), wielding a sword, as is Neville (so other would tend to distance themselves - they already have, before). She should be quite hard to protect. Of course, there might not be any Sunshine cluster anymore, if Sunshine rushed in-between the enemies, as they planned. But it rather seems to me that that plan failed before it was even initiated. (Their formation is not mentioned in the chapter.)
Also, everyone seems to be shouting their incantations, which seems just dumb.
Harry could have also just Somniumed Daphne, after she has reflected his first Stunner and was currently cumbersomely battling Neville – it would cost him just the magical cost of a Sleep Hex itself. Instead he risks Neville getting heavily fatigued or even stunned and chats on.
Hi, there! Trying to get through the sequences. And past akrasia...
How is it even reasonable to expect some arbitrarily visitor to notice (or guess correctly) your gender?
Do you evaluate your writing style or your expressed thoughts to be so typically female as to yield to no other conclusion? Or do you count on the “obvious” connotations of a name like “Alicorn” - for it is surely obvious that anyone naming oneself thus must be thinking about some fluffy, girly sparkling unicorn instead of, for example, making a reference to the Invisible Pink Unicorn - or something (especially on a rationality website!).
There is no personal information on the user pages here on LS, and decidedly no gender marks on top of the posts themselves. Also, you are obviously not willing to provide any info to make you identifiable in RL and yet expect all people to infer that you are female anyway, even given the prior probability distribution (“there are no girls on the internet”, “a contributor on some intellectual/academia website”)?
Even when one does not think of people on the internet strictly as male, it is simply usually a better guess to refer to them as “he”, given that i) one is unwilling to use “he/she” or a similarly artificial form, and ii) there is no other information one is willing to look up.
Thus I conclude that as long as you do not change your nickname into something like “Alicorn(female!)” or change your expectations, you will be sad like this time and time again. [ :( ]
Oh, how convenient, isn’t it? Well, then what about a self-deception in order to increase a placebo effect; in a case where the concerned disease may or may not be life-threatening?
If his explanation about the nature of the patronus was believed, the active patronuses should dispel. So if he demonstrated and convincingly explained his patronus and chose not to destroy the dementor he would be the sole person in the room with control over the creature.
EDIT: The trouble is, that even if he manages to control the Wizengamot in this way, he can only control them for so long, as they remain in the room.
So he probably would have to rely on their status and/or 'Most Ancient Tradition' keeping them from fleeing the room or calling in reinforcements, while he threatens to release the dementor and/or the information.
(Note that he wouldn't have to reveal his dementor-destroying ability this way, just his 'perfect shield'.)