Context: I haven’t thought of how to construct an Ansatz in a framework built from an arbitrary metaphysic
Comment 1: “I have. There’s almost nothing to it, if Ansatz means nothing more than some guessed-at mathematical descriptions turning out to be right.. and that is the . description of Ansaztz you give here:- (etc) ..then, so long as some things are mathematically describable, some mathematical descriptions will describe them, even if guessed randomly”
Response 1: Hang on, what I mean is, constructing an Ansatz completely from scratch, without any assumed structure doesn’t sound like something there would be ‘nothing to it’ - I would expect that if you have one, you’d need to be careful not to accidentally smuggle in an assumed concept from the get-go, which hasn’t been demonstrated yet—it’s hard to come to any logical machinery or systems from scratch without assuming something, without any structure or rules or symbols at all. Even if it is very simple, you have to start from somewhere. I tried to keep mine very general, and a few items of structure were added as minimally as possible. But what I mean is, the very concept of an Ansatz itself is automatically couched in some framework—I don’t think one can have a concept unless one at least has a framework for the concept to be part of, or to exist in, so I would assume to even invoke the concept, a framework (even a skeleton one) has been assumed.
Comment 2: “(We don’t know where Ansatze come from in a detailed way, but it’s hard to see why that would need a supernatural/metaphsyical explanation, since we don’t know where “think of a number comes from”, but don’;t doubt that it is an ordinary psychological process. The whole rhetoric surrounding Ansatz, or guessing as I like to call it, is overblown, IMO).”
Response 2: In terms of where Ansatze come from, I don’t think we do know quite where it comes from but we don’t need to know for the purpose of this investigation yet—it’s simply enough that we require logic to exist, and for there to be an abstract concept that can be invoked—very little else in the proof was assumed. The supernatural explanation (again, being careful to define what I mean here by supernatural, that is being outside the physical universe) comes about naturally, with only some minimal rules of logic being invoked. We might not know ‘where’ “think of a number” comes from, but we do know that the number is consistently definable, it ‘exists’ (that’s taken based on an MR viewpoint though), and it gets instantiated a lot, in the physical universe—ie the physical objects obey (and have an intimate relationship with) these mathematical objects.
In terms of the psychological process by which we access it, the psychology would be developed from brain structures, and those are based on proteins, based on info from genes, on chemistry, on physics, down to the smallest particle, so at every level, we have seen a great deal of natural processes are respecting mathematics, and we can write down these laws. So it would come at no surprise that our brains are also structured and follow processes. But, you wouldn’t argue that if the brain was destroyed, that the concepts being referred to by some maths would be destroyed, nor would an atom being destroyed mean the concepts of mathematical groups an equations of motion would be destroyed. Surely those are just all instances but not the thing being referred to itself. (ie they are not the mathematical truths themselves, as those truths turn up in all sorts of places).
Apologies if the rhetoric seems overblown—can you specify in what way? As above, I haven’t quite got your view in mind re mathematical truths. It seems you can’t have no metaphysic, we all have a metaphysic in mind, just it might be undeclared or unexamined—so I am interested to learn yours—it seems yours, to you, seems preferable, but I am unclear of your statement of it.
Comment 3: “But Wigner brings in further issues—the issue that a guessed-at mathmaticlal structure which is intended that is intended to describe one phenomenon, can be applicable to others. And you mention , in relation to Dirac’s relativistc wave equation, the ability to make successful novel predictions.. The various sub-problems have various possible solutions. ”
Response 3: What are the issues raised by Wigner issues for? ie it seems consistent with the metaphysic I have adopted. Many different mathematical mechanisms can be applied to describe processes. It happens all the time in particle physics. There’s a concept of a ‘Representation’ of a group. Subatomic particles are arranged into Groups, which have a certain mathematical structure. But a group is quite general, and you can represent a group in different ways. One particular group might have many different representations, one using matrices, one using complex exponentials, all sorts. These representations have the group structure, but they add more, adding specificity, and are called vector spaces. You could use one machinery to look into a physical phenomenon, or you could use another. Both could apply. Hence why it is hard to have a prescription for how to ‘select just the mathematical truths’ applicable to the physical universe so as to bolt them on and get a consistent P+M Universe (hence why I don’t go down that route).
Comment 4: “An ontology where the universe is based on a set of small set of rules explains the unreasonable effectiveness well enough: since each rule has to cover a lot of ground, each rule has multiple applications. And such an ontology is already fairly standard.”
Response 4: The universe being ‘based’ on a set of rules is an interesting phrase, as it does seem similar to my version of MR—ie that there are rules, and those can be talked about in a meta way, regardless of physical universe, and then the physical universe can be talked about as following those rules. I also agree, since it is the view I was expounding, that this leads to an explanation of the unreasonable effectiveness, but the way I said it was different—I just counted the countably-infinite number of possible abstractions that could apply to a phenomena in a physical universe, and the seemingly ‘smaller’ (more restricted) countably-infinite number of abstractions applying to phenomena that also are extant in a universe, and found them to be of the same Cantor cardinality.
Comment 5: “There’s also an underlying problem that saying “I can solve X” has two meanings: “My assumptions are the only solutions to X” and “I have the latest in a long line of putative solutions” It is not enough to succeed, others must fail.”
Response 5: It is true that a phrase like ‘I can solve X’ can have an ambiguity. I take it to mean the latter though, in other words, taking some assumptions, and working through some steps, one can arrive at a valid solution—which in and of itself has merit, without stating whether other approaches can get to the same point. One might point out the neatness (less ‘epicycles’) or more (or less) in line with Occam’s Razor to evaluate a purported solution after it is given—but I wouldn’t say that means a solution hasn’t been given. Certainly in my work I don’t state it’s the only way, it’s much smaller than that, as a claim—just that this way seems to hold up, seems neat, a lot of things fall out of it ‘for free’ (ie it solves the problem with low entropy, without over-engineering extra unnecessaries) and it also seems to align with thinking drawn from multiple different fields of knowledge which is usually a detective’s ‘hint’ in the right direction, during an investigation.
Responses:
Comment 1: “I have. There’s almost nothing to it, if Ansatz means nothing more than some guessed-at mathematical descriptions turning out to be right.. and that is the . description of Ansaztz you give here:- (etc) ..then, so long as some things are mathematically describable, some mathematical descriptions will describe them, even if guessed randomly”
Response 1: Hang on, what I mean is, constructing an Ansatz completely from scratch, without any assumed structure doesn’t sound like something there would be ‘nothing to it’ - I would expect that if you have one, you’d need to be careful not to accidentally smuggle in an assumed concept from the get-go, which hasn’t been demonstrated yet—it’s hard to come to any logical machinery or systems from scratch without assuming something, without any structure or rules or symbols at all. Even if it is very simple, you have to start from somewhere. I tried to keep mine very general, and a few items of structure were added as minimally as possible. But what I mean is, the very concept of an Ansatz itself is automatically couched in some framework—I don’t think one can have a concept unless one at least has a framework for the concept to be part of, or to exist in, so I would assume to even invoke the concept, a framework (even a skeleton one) has been assumed.
Comment 2: “(We don’t know where Ansatze come from in a detailed way, but it’s hard to see why that would need a supernatural/metaphsyical explanation, since we don’t know where “think of a number comes from”, but don’;t doubt that it is an ordinary psychological process. The whole rhetoric surrounding Ansatz, or guessing as I like to call it, is overblown, IMO).”
Response 2: In terms of where Ansatze come from, I don’t think we do know quite where it comes from but we don’t need to know for the purpose of this investigation yet—it’s simply enough that we require logic to exist, and for there to be an abstract concept that can be invoked—very little else in the proof was assumed. The supernatural explanation (again, being careful to define what I mean here by supernatural, that is being outside the physical universe) comes about naturally, with only some minimal rules of logic being invoked. We might not know ‘where’ “think of a number” comes from, but we do know that the number is consistently definable, it ‘exists’ (that’s taken based on an MR viewpoint though), and it gets instantiated a lot, in the physical universe—ie the physical objects obey (and have an intimate relationship with) these mathematical objects.
In terms of the psychological process by which we access it, the psychology would be developed from brain structures, and those are based on proteins, based on info from genes, on chemistry, on physics, down to the smallest particle, so at every level, we have seen a great deal of natural processes are respecting mathematics, and we can write down these laws. So it would come at no surprise that our brains are also structured and follow processes. But, you wouldn’t argue that if the brain was destroyed, that the concepts being referred to by some maths would be destroyed, nor would an atom being destroyed mean the concepts of mathematical groups an equations of motion would be destroyed. Surely those are just all instances but not the thing being referred to itself. (ie they are not the mathematical truths themselves, as those truths turn up in all sorts of places).
Apologies if the rhetoric seems overblown—can you specify in what way? As above, I haven’t quite got your view in mind re mathematical truths. It seems you can’t have no metaphysic, we all have a metaphysic in mind, just it might be undeclared or unexamined—so I am interested to learn yours—it seems yours, to you, seems preferable, but I am unclear of your statement of it.
Comment 3: “But Wigner brings in further issues—the issue that a guessed-at mathmaticlal structure which is intended that is intended to describe one phenomenon, can be applicable to others. And you mention , in relation to Dirac’s relativistc wave equation, the ability to make successful novel predictions.. The various sub-problems have various possible solutions. ”
Response 3: What are the issues raised by Wigner issues for? ie it seems consistent with the metaphysic I have adopted. Many different mathematical mechanisms can be applied to describe processes. It happens all the time in particle physics. There’s a concept of a ‘Representation’ of a group. Subatomic particles are arranged into Groups, which have a certain mathematical structure. But a group is quite general, and you can represent a group in different ways. One particular group might have many different representations, one using matrices, one using complex exponentials, all sorts. These representations have the group structure, but they add more, adding specificity, and are called vector spaces. You could use one machinery to look into a physical phenomenon, or you could use another. Both could apply. Hence why it is hard to have a prescription for how to ‘select just the mathematical truths’ applicable to the physical universe so as to bolt them on and get a consistent P+M Universe (hence why I don’t go down that route).
Comment 4: “An ontology where the universe is based on a set of small set of rules explains the unreasonable effectiveness well enough: since each rule has to cover a lot of ground, each rule has multiple applications. And such an ontology is already fairly standard.”
Response 4: The universe being ‘based’ on a set of rules is an interesting phrase, as it does seem similar to my version of MR—ie that there are rules, and those can be talked about in a meta way, regardless of physical universe, and then the physical universe can be talked about as following those rules. I also agree, since it is the view I was expounding, that this leads to an explanation of the unreasonable effectiveness, but the way I said it was different—I just counted the countably-infinite number of possible abstractions that could apply to a phenomena in a physical universe, and the seemingly ‘smaller’ (more restricted) countably-infinite number of abstractions applying to phenomena that also are extant in a universe, and found them to be of the same Cantor cardinality.
Comment 5: “There’s also an underlying problem that saying “I can solve X” has two meanings: “My assumptions are the only solutions to X” and “I have the latest in a long line of putative solutions” It is not enough to succeed, others must fail.”
Response 5: It is true that a phrase like ‘I can solve X’ can have an ambiguity. I take it to mean the latter though, in other words, taking some assumptions, and working through some steps, one can arrive at a valid solution—which in and of itself has merit, without stating whether other approaches can get to the same point. One might point out the neatness (less ‘epicycles’) or more (or less) in line with Occam’s Razor to evaluate a purported solution after it is given—but I wouldn’t say that means a solution hasn’t been given. Certainly in my work I don’t state it’s the only way, it’s much smaller than that, as a claim—just that this way seems to hold up, seems neat, a lot of things fall out of it ‘for free’ (ie it solves the problem with low entropy, without over-engineering extra unnecessaries) and it also seems to align with thinking drawn from multiple different fields of knowledge which is usually a detective’s ‘hint’ in the right direction, during an investigation.