Q: Quantum. Bayesianism isn't the LessWrong official preferred interpretation of QM because....?
In the Sequence, Eliezer made a strong case for the realist interpretation of QM (neo-Everettian many worlds), based on decoherence and Occam's razor. He then, in another point of the Sequence, tied that problem with interesting questions about anthropic probability (the infamous anthropic trilemma), and that cemented MWI as the preferred way to think about QM here.
On the other hand, I think we are still missing the big picture about quantum mechanics: ER = EPR, categorical quantum mechanics, QBism etc. all points us to interesting unexplored directions.
I'm going to contain anything I post to this thread. Just incase it's nonsense. I was just thinking of asking: Is it rational to 'go to Belgium' as they say - to commit suicide as a preventative measure to avoid suffering?
Only in very extreme case. Have you looked up on every alternatives?
I suspect there are cases where a perfectly rational, knowledgeable agent could prefer the suffering of death over the suffering of continued life.
Agents with less calculating power and with less predictive power over their possible futures (say, for instance, humans) should have an extremely low prior about this, and it's hard to imagine the evidence that would bump it into the positive.
The problem with depression is that it skews your entire ability to think clearly and rationally about the future. You're no longer "a rational agent", but "a depressed agent", and it's really bad.
From an outside view, of course only very extreme pain or the certainty of inevitable decline are worth the catastrophic cost of death, but from the pov of a depressed person, all future is bad, black and meaningless, and death seems often the natural way up.
See wikipedia. The point is that T does not just take the input n to the program to be run, it takes an argument x which encodes the entire list of steps the program e would execute on that input. In particular, the length of the list x is the number of steps. That's why T can be primitive recursive.
From the page you link:
The T predicate is primitive recursive in the sense that there is a primitive recursive function that, given inputs for the predicate, correctly determine the truth value of the predicate on those inputs.
Also from the same page:
This states there exists a primitive recursive function U such that a function f of one integer
The claim as stated is false. The standard notion of a UTM takes a representation of a program, and interprets it. That's not primitive recursive, because the interpreter has an unbounded loop in it. The thing that is is primitive recursive is a function that takes a program and a number of steps to run it for (this corresponds to the U and T in the normal form theorem), but that's not quite the thing that's usually meant by a universal machine.
I think the fact that you just need one loop is interesting, but it doesn't go as far as you claim; if an angel gives you a program, you still don't know how many steps to run it for, so you still need that one unbounded loop.
The standard notion of a UTM takes a representation of a program, and interprets it
Nope. The standard notion of a UTM take the representation of a program and an input, and interprets it. With the caveat that those representations terminate!
What you say, that the number given to the UTM is the number of steps for which the machine must run, is not what is asserted by Kleene's theorem, which is about functions of natural numbers: the T relation checks, primitive recursively, the encoding of a program and of an input, which is then fed to the universal interpreter.
You do not say to a Turing machine for how much steps you need to run, because once a function is defined on an input, it will run and then stop. The fact that some partial recursive function is undefined for some input is accounted by the unbounded search, but this term is not part of the U or the T function.
The Kleene equivalence needs, as you say, unbounded search, but if the T checks, it means that x is the encoding of e and n (a program and its input), and that the function will terminate on that input. No need to say for how much steps to run the function.
Indeed, this is true of and evident in any programming language: you give to the interpreter the program and the input, not the number of steps.
I think my go-to here would be Low of Solipsism from Death Note. As an aspiring villain being resurrected, I can't think of anything more dastardly.
That's interesting, you think of yourself as an aspiring villain? What does that entail?
Why is this useful to remember?
Because primitive recursion is quite easy, and so it is quite easy to get a universal Turing machine. Filling that machine with a useful program is another thing entirely, but that's why we have evolution and programmers...
A counterexample to your claim: Ackermann(m,m) is a computable function, hence computable by a universal Turing machine. Yet it is designed to be not primitive recursive.
And indeed Kleene's normal form theorem requires one application of the μ-Operator. Which introduces unbounded search.
Yes, but the U() and the T() are primitive recursive. Unbounded search is necessary to get the encoding of the program, but not to execute it, that's why I said "if an angel gives you the encoding".
The normal form theorem indeed says that any partial recursive function is equivalent to two primitive recursive functions / relations, namely U and T, and one application of unbounded search.
I have read Convict Conditioning. The programming in that book (that is, the way the overall workout is structured) is honestly pretty bad. I highly recommend doing the reddit /r/bodyweightfitness recommended routine.
It's free.
It has videos for every exercise.
It is a clear and complete program that actually allows for progression (the convict conditioning progression standards are at best a waste of time) and keeps you working out in the proper intensity range for strength.
If you are doing the recommended routine you can ask questions at /r/bodyweightfitness.
The main weakness of the recommended routine is the relative focus of upper body vs. lower body. Training your lower body effectively with only bodyweight exercises is difficult though. If you do want to use Convict Conditioning, /r/bodyweightfitness has some recommended changes which will make it more effective.
This is awesome, thank you!
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QBism is very interesting, but still lacks a lot of foundations for it to be taken seriously as a mainstream interpretation: why SIC-POVMs should be preferred? What they can tell us about the ontology of quantum mechanics? Do they exists in all dimensions? How are they related to the Heisenberg picture?