(Sorry for the late response, I hadn't checked my LW inbox much since my previous comments.)
If it were the case that such a function exists but cannot possibly be implemented (any implementation would be implementation as a state), and no other function satisfying the same constraints could possibly be implemented, that seems like it would be a case of it being impossible to have the aligned ASI. (Again, not that I think this is the case, just considering the validity of argument.)
The function that is being demonstrated to exist is the lookup table that produces the appropriate actions, yes? The one that is supposed to be implementable by a finite depth circuit?
It seems to make sense that if hiring an additional employee provides marginal shareholder value, that the company will hire additional employees. So, when the company stops hiring employees, it seems reasonable that this is because the marginal benefit of hiring an additional employee is not positive. However, I don't see why this should suggest that the company is likely to hire an employee that provides a marginal value of 0 or negative.
"Number of employees" is not a continuous variable. When hiring an additional employee, how this changes what the marginal benefit of an additional employee can be large enough to change it from positive to negative.
Of course, when making a hiring... (read more)
Not if the point of the argument is to establish that a superintelligence is compatible with achieving the best possible outcome.
Here is a parody of the issue, which is somewhat unfair and leaves out almost all of your argument, but which I hope makes clear the issue I have in mind:
"Proof that a superintelligence can lead to the best possible outcome: Suppose by some method we achieved the best possible outcome. Then, there's no properties we would want a superintelligence to have beyond that, so let's call however we achieved the best possible outcome, 'a superintelligence'. Then, it is possible to have a superintelligence produce the best possible outcome, QED."
In order for... (read more)
Yes, I knew the cardinalities in question were finite. The point applies regardless though. For any set X, there is no injection from 2^X to X. In the finite case, this is 2^n > n for all natural numbers n.
If there are N possible states, then the number of functions from possible states to {0,1} is 2^N , which is more than N, so there is some function from the set of possible states to {0,1} which is not implemented by any state.
If your argument is, "if it is possible for humans to produce some (verbal or mechanical) output, then it is possible for a program/machine to produce that output", then, that's true I suppose?
I don't see why you specified "finite depth boolean circuit".
While it does seem like the number of states for a given region of space is bounded, I'm not sure how relevant this is. Not all possible functions from states to {0,1} (or to some larger discrete set) are implementable as some possible state, for cardinality reasons.
I guess maybe that's why you mentioned the thing along the lines of "assume that some amount of wiggle room that is tolerated" ?
One thing... (read more)
Yes. I believe that is consistent with what I said.
"not((necessarily, for each thing) : has [x] -> those [x] are such that P_1([x]))"
is equivalent to, " (it is possible that something) has [x], but those [x] are not such that P_1([x])"
not((necessarily, for each thing) : has [x] such that P_2([x]) -> those [x] are such that P_1([x]))
is equivalent to "(it is possible that something) has [x], such that P_2([x]), but those [x] are not sure that P_1([x])" .
The latter implies the former, as (A and B and C) implies (A and C), and so the latter is stronger, not weaker, than the former.
Right?
Doesn't "(has preferences, and those preferences are transitive) does not imply (completeness)" imply (has preferences) does not imply (completeness)" ? Surely if "having preferences" implied completeness, then "having transitive preferences" would also imply completeness?
"Political category" seems, a bit strong? Like, sure, the literal meaning of "processed" is not what people are trying to get at. But, clearly, "those processing steps that are done today in the food production process which were not done N years ago" is a thing we can talk about. (by "processing step" I do not include things like "cleaning the equipment", just steps which are intended to modify the ingredients in some particular way. So, things like, hydrogenation. This also shall not be construed as indicating that I think all steps that were done N years ago were better than steps done today.)
For example, it is not clear to me if once I consider a program that outputs 0101 I will simply ignore other programs that output that same thing plus one bit (e.g. 01010).
No, the thing about prefixes is about what strings encode a program, not about their outputs.
The purpose of this is mostly just to define a prior over possible programs, in a way that conveniently ensures that the total probability assigned over all programs is at most 1. Seeing as it still works for different choices of language, it probably doesn't need to exactly use this kind of defining the probabilities, and I think any reasonable distribution over programs will do... (read 578 more words →)
This may be a silly question.
Suppose (I) someone who doesn't have practical experience with machine learning research (but is generally aware of the structure of a number of different NN architectures, has read some papers, has a decent level of mathematical maturity, etc.) has an idea for a (as far as they/I know) novel NN architecture. And, suppose (I) they understand that, given (my) their lack of experience in the topic, and how most ideas from outsiders are unlikely to work, the idea probably will almost certainly not work.
Suppose also that implementing and testing the idea well would either take (me) this person much longer than it would people who are versed... (read 381 more words →)
If you are interested in convincing people who so far think "It is impossible for the existence of an artificial superintelligence to produce desirable outcomes" otherwise, you should have a meaning of "an aritifical superintelligence" in mind that is like what they mean by it.
If one suspects that it is impossible for an artificial superintelligence to produce desirable outcomes, then when one considers "among possible futures, the one(s) that have as good or better outcomes than any other possible future", one would suppose that these perhaps are not ones that contain superintelligences. And, so, one would suppose that the computational process that achieves the best outcome, would perhaps not be a superintelligence.
To... (read 438 more words →)