But of course, this doesn’t work. “The claim that a program can function as a description” is not an extraordinary claim at all; it is merely a restatement of how programs work: they take some input, perform some internal manipulations on that input, and produce an output. If the input in question happens to be the observation history of some observer, then it is entirely natural to treat the output of the program as a prediction of the next observation; there is nothing extraordinary about this at all!
Emphasis added. You haven’t explained how a programme functions as a description. You mentioned description, and then you started talking prediction, but you didn’t explain how they relate.
So the attempted reversal of the burden of proof fails; the “extraordinary” claim remains the claim that the universe cannot be described by any possible program, regardless of length,
The length has nothing to do with it—the fact it is a programme at all is the problem.
On the face of it, Solomonoff Inductors contain computer programmes, not explanations, not hypotheses and not descriptions. (I am grouping explanations, hypotheses and beliefs as things which have a semantic interpretation, which say something about reality . In particular, physics has a semantic interpretation in a way that maths does not.)
The Yukdowskian version of Solomonoff switches from talking about programs to talking about hypotheses as if they are obviously equivalent. Is it obvious? There’s a vague and loose sense in which physical theories “are” maths, and computer programs “are” maths, and so on. But there are many difficulties in the details. Neither mathematical equations not computer programmes contain straightforward ontological assertions like “electrons exist”. The question of how to interpret physical equations is difficult and vexed. And a Solomonoff inductor contains programmes, not typical physics equations. whatever problems there are in interpreting maths ontologically are compounded when you have the additional stage of inferring maths from programmes.
In physics, the meanings of the symbols are taught to students, rather than being discovered in the maths. Students are taught the in f=ma, f is force, is mass and a is acceleration. The equation itself , as ours maths, does not determine the meaning. For instance it has the same mathematical form as P=IV, which “means” something different. Physics and maths are not the same subject, and the fact that physics has a real-world semantics is one of the differences.
Similarly, the instructions in a programme have semantics related to programme operations, but not to the outside world. The issue is obscured by thinking in terms of source code. Source code often has meaningful symbol names , such as MASS or GRAVITY...but that’s to make it comprehensible to other programmers. The symbol names have no effect on the function and could be mangled into something meaningless but unique. And a SI executes machine code anyway..otherwise , you can’t meaningfully compare programne lengths. Note how the process of backtracking from machine code to meaningful source code is a difficult one. Programmers use meaningful symbols because you can’t easily figure out what real world problem a piece of machine code is solving from its function. One number is added to another..what does that mean? What do the quantifies represent?
Well, maybe programmes-as-descriptions doesn’t work on the basis that individual Al symbols or instructions have meanings in the way that natural language words do. Maybe the programme as a whole expresses a mathematician structure as a whole. But that makes the whole situation worse because it adds an extra step , the step of going from code to maths, to the existing problem of going from maths to ontology.
The process of reading ontological models from maths is not formal or algorithmic. It can’t be asserted that SI is the best formal epistemology we have and also that it is capable of automating scientific realism. Inasmuch as it is realistic , the step from formalism to realistic interpretation depends on human interpretation, and so is not formal. And if it SI is purely formal, it is not realistic.
But code already is maths, surely? In physics the fundamental equations are on a higher abstraction level than a calculation: generally need to be ” solved” for some set of circumstances, to obtain a more concrete equation you can calculate with. To get back to what would normally be considered a mathematical structure, you would have to reverse the original process. If you succeed in doing that, then SI is as good or bad as physics...remember, that physics still needs ontological interpretation. If you don’t succeed in doing that.. which you you might not, since there is no algorithm reliable method for doing so...then SI is strictly worse that ordinary science, since it has an extra step of translation from calculation to mathematical structure, in addition to the standard step of translation from mathematical structure to ontology.
Emphasis added. You haven’t explained how a programme functions as a description. You mentioned description, and then you started talking prediction, but you didn’t explain how they relate.
The length has nothing to do with it—the fact it is a programme at all is the problem.
On the face of it, Solomonoff Inductors contain computer programmes, not explanations, not hypotheses and not descriptions. (I am grouping explanations, hypotheses and beliefs as things which have a semantic interpretation, which say something about reality . In particular, physics has a semantic interpretation in a way that maths does not.)
The Yukdowskian version of Solomonoff switches from talking about programs to talking about hypotheses as if they are obviously equivalent. Is it obvious? There’s a vague and loose sense in which physical theories “are” maths, and computer programs “are” maths, and so on. But there are many difficulties in the details. Neither mathematical equations not computer programmes contain straightforward ontological assertions like “electrons exist”. The question of how to interpret physical equations is difficult and vexed. And a Solomonoff inductor contains programmes, not typical physics equations. whatever problems there are in interpreting maths ontologically are compounded when you have the additional stage of inferring maths from programmes.
In physics, the meanings of the symbols are taught to students, rather than being discovered in the maths. Students are taught the in f=ma, f is force, is mass and a is acceleration. The equation itself , as ours maths, does not determine the meaning. For instance it has the same mathematical form as P=IV, which “means” something different. Physics and maths are not the same subject, and the fact that physics has a real-world semantics is one of the differences.
Similarly, the instructions in a programme have semantics related to programme operations, but not to the outside world. The issue is obscured by thinking in terms of source code. Source code often has meaningful symbol names , such as MASS or GRAVITY...but that’s to make it comprehensible to other programmers. The symbol names have no effect on the function and could be mangled into something meaningless but unique. And a SI executes machine code anyway..otherwise , you can’t meaningfully compare programne lengths. Note how the process of backtracking from machine code to meaningful source code is a difficult one. Programmers use meaningful symbols because you can’t easily figure out what real world problem a piece of machine code is solving from its function. One number is added to another..what does that mean? What do the quantifies represent?
Well, maybe programmes-as-descriptions doesn’t work on the basis that individual Al symbols or instructions have meanings in the way that natural language words do. Maybe the programme as a whole expresses a mathematician structure as a whole. But that makes the whole situation worse because it adds an extra step , the step of going from code to maths, to the existing problem of going from maths to ontology.
The process of reading ontological models from maths is not formal or algorithmic. It can’t be asserted that SI is the best formal epistemology we have and also that it is capable of automating scientific realism. Inasmuch as it is realistic , the step from formalism to realistic interpretation depends on human interpretation, and so is not formal. And if it SI is purely formal, it is not realistic.
But code already is maths, surely? In physics the fundamental equations are on a higher abstraction level than a calculation: generally need to be ” solved” for some set of circumstances, to obtain a more concrete equation you can calculate with. To get back to what would normally be considered a mathematical structure, you would have to reverse the original process. If you succeed in doing that, then SI is as good or bad as physics...remember, that physics still needs ontological interpretation. If you don’t succeed in doing that.. which you you might not, since there is no algorithm reliable method for doing so...then SI is strictly worse that ordinary science, since it has an extra step of translation from calculation to mathematical structure, in addition to the standard step of translation from mathematical structure to ontology.