Pragmatically, if I non-blindly pick some representation of turing machines that looks simple to me (e.g. the one Turing used), I don’t really doubt that it’s within a few thousand bits of the “right” version of solomonoff, whatever that means.
Why not?
So is there then a pragmatic assumption that can be made? Maybe we assume that if I pick a turing machine blindly, without specifically designing it for a particular output string, it’s unlikely to be strongly biased towards that string.
Solomonoff Induction is supposed to be a formalization of Occam’s Razor, and it’s confusing that the formalization has a free parameter in the form of a universal Turing machine that is used to define the notion of complexity.
I’m very confused about this myself, having just read this introductory paper on the subject.
My understanding is that an “ideal” reference UTM would be a universal turing machine with no bias towards any arbitrary string, but rigorously defining such a machine is an open problem. Based on our observation of UTMs, the more arbitrary simplifications a Turing Machine makes, the longer its compiler will have to be on other UTMs. This is called the Short Compiler Assumption. Since we can’t agree on a single ideal reference UTM, we instead approximate it by limiting ourselves to a class of “natural” UTMs which are mutually interpretable within a constant. The smaller the constant, the less arbitrary simplification the UTMs in the class will tend to make.
This seems to mesh with the sequences post on Occam’s Razor:
What if you don’t like Turing machines? Then there’s only a constant complexity penalty to design your own Universal Turing Machine that interprets whatever code you give it in whatever programming language you like.
What I’m confused about is this constant penalty. Is it just “some constant” or is it knowable and small? Is there a specific UTM for which we can always write a short compiler on any other UTM?
I’m getting out of my league here, but I’d guess that there is an upper bound on how complex you can make certain instructions across all UTMs because UTMs must (a) be finite, and (b) at the lowest level implement a minimal set of instructions, including a functionally full set of logical connectives. So for example, say I take as my “nonbiased” UTM a UTM that aside from the elementary operations of the machine on its tape, jump instructions, etc. has only a minimal number of instructions implementing a minimally complete operator set with less than two connectives: {NAND} or {NOR}. My understanding is that anything that’s a Universal Turing Machine is going to have to itself have a small number of instructions that implement the basic machine instructions and a complete set of connectives somewhere in its instruction set, and converting between {NAND} or {NOR} and any other complete set of connectives can be done with a trivially short encoding.
1) How can I know whether this belief is true?
Expose it to tests. For example, you might stick your head out a window and look up. The theory that the sky is green strongly predicts that you should see green and only very weakly allows for you to see anything else (your eyes may occasionally play tricks on you, perhaps you are looking close to a sunset, etc.).
2) How can I assign a probability to it to test its degree of truthfulness? 3) How can I update this belief?
If you knew absolutely nothing about skies other than that they were some colour, you would start with a symmetrical prior distributed across a division of colour space. You would then update your belief every time you come into contact with entangled information. For example, every time you look up at the sky and see a colour, your posterior probability that the sky is that colour goes up at the expense of alternative colours. Observing other people describe what they see when they look at the sky and learning about how vision works and the chemical composition of the sky are also good examples of evidence you could use.
In practise, manually updating every belief you have all the time is far to arduous, and most people collect large amounts of beliefs and information prior to learning much about statistics anyway. Because of this, the prior probability you assign to your beliefs will often have to be a quick approximation.
Cue for noticing rationalization: In a live conversation, I notice that the time it takes to give the justification for a conclusion when prompted far exceeds the time it took to generate the conclusion to begin with.
I think the condition from the beginning is that you’re picking a unique girlfriend who knows all microphysical facts about your universe, including the content of any letters you have or will ever write.
I think that was an unfair clipping. The context of that quote was the OP’s statement about the usefulness of getting clarification of language usage.
Let’s suppose that this usage is in fact more common than the two that I cited as “correct”. It seems to be either false or meaningless. What is Bob saying here?
You said in the OP that the more common usage takes the phrase to refer to any exception. So from that, Bob probably means that the brown bear you saw is an exception.
How does Rationalist Taboo help us?
Seeing as how Bob probably means that the brown bear is an exception, his argument is poor. So I would then say something like, “since you agree that there is an exception, you should agree that not all bears are black or white”. If he disagrees, then he isn’t using the common meaning after all and I would ask him to taboo the phrase “exception that proves the rule” to find out what he does mean.
This is my thought as well. Every one of the examples given I would attribute to dialectal differences between common usage and the more technical and jargon-filled language used by scientists and science fans. SaidAchmiz even admits that for some of these, the usage he doesn’t like is more common, which is a big hint. My understanding is that speakers very rarely adopt usage which will be misunderstood by the language group they typically speak with.
“hmm, is that really what you meant to say?” is often met with absurd arguments to the effect that no, this phrasing is not nonsensical after all, these words mean what I want them to, and who the hell are you to try to legislate usage, anyway?
Isn’t this exactly why we have the technique of Rationalist Taboo? It doesn’t matter whether the meaning someone ascribes to a word seems stupid to you, once you understand what they mean by the word, and they understand what you mean by the word, you can move on. The best ways I’ve found to do this are to coin two new words (I like to prepend the word in question with the name of the person whose meaning we are trying to capture), or to always replace the word with its intended substance for the rest of the discourse.
The point I was making is that you attempt to maximise your utility function. Your utility function decreases when you learn of a bad thing happening
I think you’re still confused. Utility functions operate on outcomes and universes as they actually are, not as you believe them to be. Learning of things doesn’t decrease or increase your utility function. If it did, you could maximize it by taking a pill that made you think it was maximized. Learning that you were wrong about the utility of the universe is not the same as changing the utility of the universe.
I believe APMason’s point is that your benchmarks are testing for anti-non-mainstreamism
The flaw I’d point out is that Clippy’s utility function is utility = number of paperclips in the world not utility = number of paperclips Clippy thinks are in the world.
Learning about the creation or destruction of paperclips does not actually increase or decrease the number of paperclips in the world.
As near as I can tell I’m -want/+like/-approve on both wireheading and emperor-like superiority.
My general feeling has been that we explicitly declare Crocker’s Rules or act as though they are an implicit norm so frequently that we might as well add the declaration to the site banner. I always considered this to be a byproduct of a community whose group knowledge includes acknowledgment of emotional biases, debate-as-warfare conceptual metaphors, etc.
I’ve never understood how severe food yield issues from overpopulation are supposed to come about. If the population is increasing far faster than we can increase the food yields, wouldn’t the price of food massively increase and stop people from being able to afford to have children? Is the idea that the worldwide agricultural system would be gradually overtaxed and then collapse within a short period? If not, what were all the people eating the day before catastrophic overpopulation is declared?
Wow, you guys did an awesome job. Very funny to read through and the music is hilarious.
snicker Vampire Thomas Nagel knows what it’s like to be a bat
I took the survey. Thanks for putting this together.
The accuracy has been doubled!
Extensive use of abbreviations and acronyms was primarily a convenience for writers, when writing was done by hand and then by typewriter, there is less justification for it now when most writing is done by computer.
I don’t agree. My impression is that the popularity of abbreviations and acronyms is being driven by the rise in popularity of text messaging, which is usually done from phones with tiny, unusable keyboards; instant messaging, which is done in real time; and social networking site based communication, which often has hard limits on message length (e.g. Twitter).
Daily I measure weight and workout performance.
Monthly I look at my receipts and spending and whether there were any large deviations from my budget.
Every six months I pick an unexceptional week and log everything I do by category (e.g. sleeping, preparing food, working, studying). I create summary tables for the typical week and use them to choose two or three improvements to implement in the next iteration.