The whole argument is like a daydream. Let’s imagine that we have time series for two things that are correlated for no reason except that we assume this. Then let’s throw away the time ordering information so we have two unordered sets of data. Then let’s say that contrasting the uncorrelatability of the unordered sets with the original correlation of time series is a d-separation.
I hardly have even basic knowledge of these techniques of causal inference, but even I can see that you are doing crazy stuff. Think of causal inference analysis as a machine where either it produces an output, indicating a causal connection, or it does nothing, indicating no causal connection. The part where you throw away the time ordering is like smashing the machine; and then you treat the unresponsiveness of the resulting pile of parts, as if it were a null response from an intact machine.
There’s also something dodgy going on, with your need to assume two time series that are correlated. If you start with two time series which, by hypothesis, are not correlated, then even this flawed argument isn’t possible—you can’t even get your alleged separation, because there’s no correlation, either with or without time. Your formal demonstration that time is caused by motion, seems to require consideration of two time series that are correlated by coincidence, which would be a weird and stringent requirement for an argument purportedly demonstrating something about the nature of time in general.
The best diagnosis of the argument I can presently make is that it came about as follows: You were already sympathetic, or potentially sympathetic, to the idea that time is caused by motion. Then you were sort of musing about the formalism of causal analysis in a fashion increasingly detached from the usual context of its use, and eventually ran across a “does not compute” condition, but you interpreted this implosion of the formalism as a message from the formalism, and built it up into a formal demonstration of the metaphysical proposition that time is caused by motion.
If I take a step even further back, I can see this as another example of metaphysics returning in a disorderly way, through the gaps in a formalism which has replaced metaphysics with mathematics. In pre-scientific philosophy, people reasoned using natural language about time, space, causality, reality, truth, meaning, and so forth. In the 20th century, there was an attempt to reduce everything to measurement and computation. Reasoning was replaced with the symbol systems of formal logic, objective physical reality was replaced with observables in quantum mechanics, the study of mind was replaced with the study of behavior and of brains—there might be half a dozen core examples.
In statistics they abandoned causality for correlation. Pearl’s mini-revolution was to reintroduce the concept of causality, but he only got to do it because he found a formal criterion for it. His theory has therefore strengthened, in a small way, the illusion of successful reduction—people can apply Pearl’s procedure and perform causal analysis, without worrying about why anything causes anything else, or about what causality really is.
But people have a tendency to rediscover the issues and problems that the old informal philosophy tackled, and then they try to address them with the intellectual resources that their culture provides. Thus the wavefunction tools of Copenhagen positivism get turned into ontological realities by Everett, and the universe of mathematical concepts becomes the ultimate reality in Tegmark’s neoplatonic theory… and odd manipulations of causal analysis formalism, become Wentworth’s argument for a particular metaphysics of time.
I definitely don’t want to say that every such reinvention of metaphysics from within a formal discourse, is mystical or pathological. The interaction between the modern formalisms and the old issues is a very complicated and diverse process. But in general, to me the process looks healthiest when the formalism is grounded in some old-fashioned informal intuitions—where people can explain the concepts of their formalized physics, logic, etc., in a way that grounds in very simple experiences, thoughts, and understandings. And the problem that modern thought has created, is that it denies the validity, possibility, or existence of many of these informal intuitions.
Modern people have these elaborate rule-based systems available to them, systems for representing or thinking about certain aspects of reality in a very sophisticated way, but they are cut off from the history of informal thought which motivated the formalisms. As a result, when they try to think about reality at a primordial level, they have to improvise as if there had never been such a thing as systematic metaphysical thought, but at the same time they have available to them, these modern intellectual power tools which bear in their design, traces of the abstract issues which motivated their construction. The result is a cargo cult of formalism in which the constructs of modern rigor are stacked up in imitation of philosophical reasoning.
I can talk in generalities like this for a long time, it seems. But I’m not yet at a stage where I can go into the details and say, your formalism assumes this, which is why you can’t use it to do that. Which is why I hoped someone else would work out that part.
Actually, I wasn’t thinking about metaphysics at all. I was trying to demonstrate rigorously that time is the common cause of the observed correlation (which AlexMennen did correctly in another comment). While trying to do this, I realized that even after removing the values of time from the samples, there was still information about time embedded in the ordering of points, so I was trying to not use that information. The rest just fell out of the analysis. I wasn’t sympathetic to any particular metaphysics, and I wasn’t thinking about making metaphysical statements at all. I was thinking about how to incorporate this bizarre case into algorithms for learning causal networks.
After thinking about it, I realized that time is a really bad example. We’re not really interested in the numerical values of time, we’re interested in the association of points in the same sample. In this case the association happens to contain time information, which is why it’s so damn confusing. A clearer example would be a population of mice, where we sample each variable once from each mouse. Then the association is given by mapping each point to the mouse it came from. In that case, it’s much more clear that the association contains information in itself separate from all the numerical values.
The whole argument is like a daydream. Let’s imagine that we have time series for two things that are correlated for no reason except that we assume this. Then let’s throw away the time ordering information so we have two unordered sets of data. Then let’s say that contrasting the uncorrelatability of the unordered sets with the original correlation of time series is a d-separation.
I hardly have even basic knowledge of these techniques of causal inference, but even I can see that you are doing crazy stuff. Think of causal inference analysis as a machine where either it produces an output, indicating a causal connection, or it does nothing, indicating no causal connection. The part where you throw away the time ordering is like smashing the machine; and then you treat the unresponsiveness of the resulting pile of parts, as if it were a null response from an intact machine.
There’s also something dodgy going on, with your need to assume two time series that are correlated. If you start with two time series which, by hypothesis, are not correlated, then even this flawed argument isn’t possible—you can’t even get your alleged separation, because there’s no correlation, either with or without time. Your formal demonstration that time is caused by motion, seems to require consideration of two time series that are correlated by coincidence, which would be a weird and stringent requirement for an argument purportedly demonstrating something about the nature of time in general.
The best diagnosis of the argument I can presently make is that it came about as follows: You were already sympathetic, or potentially sympathetic, to the idea that time is caused by motion. Then you were sort of musing about the formalism of causal analysis in a fashion increasingly detached from the usual context of its use, and eventually ran across a “does not compute” condition, but you interpreted this implosion of the formalism as a message from the formalism, and built it up into a formal demonstration of the metaphysical proposition that time is caused by motion.
If I take a step even further back, I can see this as another example of metaphysics returning in a disorderly way, through the gaps in a formalism which has replaced metaphysics with mathematics. In pre-scientific philosophy, people reasoned using natural language about time, space, causality, reality, truth, meaning, and so forth. In the 20th century, there was an attempt to reduce everything to measurement and computation. Reasoning was replaced with the symbol systems of formal logic, objective physical reality was replaced with observables in quantum mechanics, the study of mind was replaced with the study of behavior and of brains—there might be half a dozen core examples.
In statistics they abandoned causality for correlation. Pearl’s mini-revolution was to reintroduce the concept of causality, but he only got to do it because he found a formal criterion for it. His theory has therefore strengthened, in a small way, the illusion of successful reduction—people can apply Pearl’s procedure and perform causal analysis, without worrying about why anything causes anything else, or about what causality really is.
But people have a tendency to rediscover the issues and problems that the old informal philosophy tackled, and then they try to address them with the intellectual resources that their culture provides. Thus the wavefunction tools of Copenhagen positivism get turned into ontological realities by Everett, and the universe of mathematical concepts becomes the ultimate reality in Tegmark’s neoplatonic theory… and odd manipulations of causal analysis formalism, become Wentworth’s argument for a particular metaphysics of time.
I definitely don’t want to say that every such reinvention of metaphysics from within a formal discourse, is mystical or pathological. The interaction between the modern formalisms and the old issues is a very complicated and diverse process. But in general, to me the process looks healthiest when the formalism is grounded in some old-fashioned informal intuitions—where people can explain the concepts of their formalized physics, logic, etc., in a way that grounds in very simple experiences, thoughts, and understandings. And the problem that modern thought has created, is that it denies the validity, possibility, or existence of many of these informal intuitions.
Modern people have these elaborate rule-based systems available to them, systems for representing or thinking about certain aspects of reality in a very sophisticated way, but they are cut off from the history of informal thought which motivated the formalisms. As a result, when they try to think about reality at a primordial level, they have to improvise as if there had never been such a thing as systematic metaphysical thought, but at the same time they have available to them, these modern intellectual power tools which bear in their design, traces of the abstract issues which motivated their construction. The result is a cargo cult of formalism in which the constructs of modern rigor are stacked up in imitation of philosophical reasoning.
I can talk in generalities like this for a long time, it seems. But I’m not yet at a stage where I can go into the details and say, your formalism assumes this, which is why you can’t use it to do that. Which is why I hoped someone else would work out that part.
Actually, I wasn’t thinking about metaphysics at all. I was trying to demonstrate rigorously that time is the common cause of the observed correlation (which AlexMennen did correctly in another comment). While trying to do this, I realized that even after removing the values of time from the samples, there was still information about time embedded in the ordering of points, so I was trying to not use that information. The rest just fell out of the analysis. I wasn’t sympathetic to any particular metaphysics, and I wasn’t thinking about making metaphysical statements at all. I was thinking about how to incorporate this bizarre case into algorithms for learning causal networks.
After thinking about it, I realized that time is a really bad example. We’re not really interested in the numerical values of time, we’re interested in the association of points in the same sample. In this case the association happens to contain time information, which is why it’s so damn confusing. A clearer example would be a population of mice, where we sample each variable once from each mouse. Then the association is given by mapping each point to the mouse it came from. In that case, it’s much more clear that the association contains information in itself separate from all the numerical values.