Hey! I'm Rémy and my main occupation in real life is mathematics, specifically dynamical systems. This probably contributed a small part to me enjoying the TPD as much as I do, given the importance of the "hierarchical dynamization of one's own structure" within it. My discovery of the TPD was, as probably for many, preceded by years of struggling which I've been recontextualizing within the framework of the theory. It resonated with me in a way very few things ever did and it felt like lots and lots of pieces I new had to be important suddenly fell into place. Since then, I've been doing a lot of reading and thinking on Dabrowski's work.

I discovered this community via the Miscellaneous section on the TPD website run by Tillier. It included a link to Jessie's blog which in turn lead me to this nice place. I'm glad I found my way here and am looking forward to interesting exchanges and discussions!

## Is this seat free?

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Welcome, Rémy! Thanks for sharing a bit about yourself. It's always so interesting to hear how and why people come to TPD.

When you say you do dynamical systems, is that the thing that comes up in my Google search related to condensed matter physics? (It's not well developed at all, but I still have an amateur interest in physics.) Or if not...what

When you say you do dynamical systems, is that the thing that comes up in my Google search related to condensed matter physics? (It's not well developed at all, but I still have an amateur interest in physics.) Or if not...what

*is*a dynamical system?### Re: Is this seat free?

Well, the concept of an abstract dynamical system is fairly general so I could very well imagine connections to condensed matter physics, though personally, I'm mostly on the pure mathematical side of things. The most basic example of a dynamical system is a tuple (X, f) consisting of a set X and a function f:X -> X. One can think of X as the "state spaces" of a dynamical system, i.e., the set of possible states, and of f as describing how these states develop in the course of time, where time is modelled as discrete for the sake of simplicity. This means that if x is a state in X, f(x) is the state of the system one time unit later. From here, you can go on and add structure on X and assume nice properties of f and then you are already in the position to fill books with the study of different notions of "chaos", "attractors", "entropy" etc. for such systems. And a lot of the theory was actually motivated by physics, for example by Boltzmann's work on thermodynamics, who sparked what we now call ergodic theory with his "ergodic hypothesis". But there are also connections to classical mechanics, fluid mechanics, and a lot of other areas where one has some sort of dynamicity.

A little more (though not too) concretely, you could describe a possible connection from my interests to physics as follows: Physical systems often comprise so many individual particles that, even if we forget about Heisenberg and all that quantum stuff, we have no real chance of ever determining the state of the system precisely. Just think of the weather, but even small systems quickly become impossible to handel in such a naive way. Often, all we can really do is make rough measurements (e.g. temperature, air pressure) from which we can then more or less extrapolate the state of the system or at least the aspects of it that interest us. Us being limited to accessing the world via different kinds of measurements (even visual perception is, in some sense, just a measurement) poses lots of interesting questions about how much we can really know about the world if we can only access it via measurements and how we can translate our measurements into properties of the underlying dynamical system. You could say that I'm working on this sort of questions. But to be honest, in the end it's just a mathematical idealization and once you bring in quantum mechanics, among other things, you need to replace commutative with non-commutative structures because of Heisenberg and then things get a lot more complicated. So you need to take it with a grain of salt. Anyways, I hope this gives you some idea of the connections to physics.

A little more (though not too) concretely, you could describe a possible connection from my interests to physics as follows: Physical systems often comprise so many individual particles that, even if we forget about Heisenberg and all that quantum stuff, we have no real chance of ever determining the state of the system precisely. Just think of the weather, but even small systems quickly become impossible to handel in such a naive way. Often, all we can really do is make rough measurements (e.g. temperature, air pressure) from which we can then more or less extrapolate the state of the system or at least the aspects of it that interest us. Us being limited to accessing the world via different kinds of measurements (even visual perception is, in some sense, just a measurement) poses lots of interesting questions about how much we can really know about the world if we can only access it via measurements and how we can translate our measurements into properties of the underlying dynamical system. You could say that I'm working on this sort of questions. But to be honest, in the end it's just a mathematical idealization and once you bring in quantum mechanics, among other things, you need to replace commutative with non-commutative structures because of Heisenberg and then things get a lot more complicated. So you need to take it with a grain of salt. Anyways, I hope this gives you some idea of the connections to physics.

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You bring me back to my college days when I was rooming with two friends who would go on to get a PhD and an ABD in math! Thanks for sharing. It even made a little sense!

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I just joined. Really appreciate the insights here. And I needed to respond to this post.

You stated, 'Physical systems often comprise so many individual particles that, even if we forget about Heisenberg and all that quantum stuff, we have no real chance of ever determining the state of the system precisely. Just think of the weather, but even small systems quickly become impossible to handel in such a naive way.'

So this makes me wonder about the validity of predictions of global warming. I'm not a scientist, in fact I always kid others that I'm much more of a right-brained person. However even *I* have an appreciation for the amazing complexities of our earth's weather systems. And nowadays, there is this huge emotional component attached to weather ... it's almost as if the weather has become a religious topic. One is categorized in relation to their belief about something. In the medieval age, Christians categorized nonbelievers as heretics. I see that happening now, where if you question certain Big Science pronouncements, you are branded with certain capital letters. 'D' for 'Denier'. 'A' for 'Anti-vaccinator' and so forth.

You stated, 'Physical systems often comprise so many individual particles that, even if we forget about Heisenberg and all that quantum stuff, we have no real chance of ever determining the state of the system precisely. Just think of the weather, but even small systems quickly become impossible to handel in such a naive way.'

So this makes me wonder about the validity of predictions of global warming. I'm not a scientist, in fact I always kid others that I'm much more of a right-brained person. However even *I* have an appreciation for the amazing complexities of our earth's weather systems. And nowadays, there is this huge emotional component attached to weather ... it's almost as if the weather has become a religious topic. One is categorized in relation to their belief about something. In the medieval age, Christians categorized nonbelievers as heretics. I see that happening now, where if you question certain Big Science pronouncements, you are branded with certain capital letters. 'D' for 'Denier'. 'A' for 'Anti-vaccinator' and so forth.