Gordon_Worley
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(I'm catching up, so that's why this is posted so far after the original.)
When I attempted this exercise I tried to think of how I use the word "arbitrary" and came up with a definition along the lines of "Something is arbitrary if its choice from a set makes no difference to the veracity of a particular statement", i.e. arbitrary is a 2-part function, taking as input a choice and a statement, since without a statement to evaluate against calling something arbitrary to me just looks like membership.
But then I read on and realized that I was being too narrow in what I considered to be arbitrary. Perhaps from too much... (read more)
Eliezer,
You know that you can't succeed without the math, and slowing down for posts like this is taking away 24 hours that might have been better used to save humanity. Not that this was a bad post, but I think you would be better off letting others write the fun posts unless you need to write a fun post to recover from teaching.
I agree that it makes no sense, but as I was writing the comment I figured I would take you down the wrong path of what someone might naively think and then correct it. I think that someone who was overly trained in logic and not in probability might assume that if Raven(x)-->Black(x) being true leads to P(B|R) = 1, they might reason that since the reverse implication Black(x)-->Raven(x) is false, it leads to P(R|B) = 0. But based on the comments above, maybe only an ancient Greek philosopher would be inclined to make such a mistake.
Hopefully not taking away anyone's fun here, but to reconcile Raven(x)->Black(x) but not vice versa, what this statement wants to say, letting P(R) and P(B) be the probabilities of raven and black, respectively, is P(R|B)=0 and P(B|R)=1, which gives us that
P(R|B) = 0 P(RB)/P(B) = 0 P(RB) = 0
and
P(B|R) = 1 P(BR)/P(R) = 1 P(BR) = P(R)
But of course this leads to a contradiction, so it can't really be true that Black(x)-/->Raven(x), can it? Sure, because what is really meant by implies (-/->) is not P(B|R) = 0 but P(B|R)<1. But in logic we often forget this because anything with a probability less than 1 is assigned a truth value of false.
Logic has its value, since sometimes you want to prove something is true 100% of the time, but this is generally only possible in pure mathematics. If you try to do it elsewhere you'll get exceptions (e.g. albino ravens). So leave logic to mathematicians; you should use Bayesian inference.
I believe you made a slight typo, Eli.
You said: "Since there's an "unusually high" probability for P(Z1Y2) - defined as a probability higher than the marginal probabilities would indicate by default - it follows that observing Z1 is evidence which increases the probability of Y2. And by a symmetrical argument, observing Y2 must favor Z1."
But I think what you meant was "Since there's an "unusually high" probability for P(Z1Y2) - defined as a probability higher than the marginal probabilities would indicate by default - it follows that observing Y2 is evidence which increases the probability of Z1. And by a symmetrical argument, observing Z1 must favor Y2."
Nothing you said was untrue, but the implication of what you wrote doesn't match up with the example you actually gave just above that text.
For those saying they have nothing to protect or still need to find something to protect, remember that you are human and, unless you have no natural family or reproductive ties, you always have the people you love to protect. It may seem counterintuitive if you've bought into Hollywood rationality, but love is a powerful motivational force. If you think that, in theory, being more rational is good, but don't see how you can effect greater rationality in your mind, consider the many benefits of your increased rationality (again, not Hollywood rationality, but rationality of the type Eliezer describes above).
In my case, I know I'm trying harder than ever to... (read more)
Am I right in thinking that you've now brought the OB audience to where you need them in order to start trying to talk about AI (or "optimizing processes" or whatever terminology is sufficiently abstract to prevent linguistically inferred misunderstanding)?
Let's suppose we measure pain in pain points (pp). Any event which can cause pain is given a value in [0, 1], with 0 being no pain and 1 being the maximum amount of pain perceivable. To calculate the pp of an event, assign a value to the pain, say p, and then multiply it by the number of people who will experience the pain, n. So for the torture case, assume p = 1, then:
torture: 1*1 = 1 pp
For the spec in eye case, suppose it causes the least amount of pain greater than no pain possible. Denote this by e. Assume that the dust... (read more)
Between teaching mathematics to freshmen and spending most of my time learning mathematics, I've noticed this myself. When presented with a new result, the first inclination, especially depending on the authority of the source, is to believe it and figure there's a valid proof of it. But occasionally the teacher realizes that they made a mistake and may even scold the students for not noticing since it is incredibly obvious (e.g. changing something like ||z - z_0|| to ||z - z_1|| between steps, even though a few seconds thinking reveals it to be a typo rather than a mathematical insight).
Sometimes (and for a few lucky people, most of the time)... (read more)
Interesting discussion.
Eli,
First, since no one has come out and said it yet, maybe it's just me but this post was kind of whiny. Maybe everyone else here is more in-tune with you (or living in your reality distortion field), but the writing felt like you were secretly trying to make yourself out to be a martyr, fishing for sympathy. Based on my knowledge of you from past interactions and your other writings I doubt this to be the case, but none the less it's the sense I got from your writing.
Second, I, too, have been through a similar experience. When I was younger, maybe around the age of 11... (read 554 more words →)