Pythagoras' Theorem. Evidence of elsewhere or our ingenuity.

[JimC]

Our very terms "singular" and "discrete" come from observing a complex external world, where some objects are connected to others, and some have a physical separation. In fact, all the terms we use in a philosophical discussion are, at heart, analogies to aspects of our physical bodies interaction with its surroundings, living or non-living. We are rooted in physicality; it is central to our struggle to make the world clear...

[MiM]

Audley, what about the discreteness-countability issue I mentioned?

[cough]I mentioned it on the first page[/cough]

Obviously, if you start to look at the solar system with the tools of quantum mechanics, you will see only myriads of wave functions, that extend out to infinity, and just get denser in certain area, but I very much believe that approach leads to not seeing the forest for all the trees. On a cosmological scale the planets (and their moons...) are perfectly discreet entities, with very well defined boundaries, and wast distances between them. Not accepting that aspect, just because we now also know the other aspect constitutes a kind of blindness, at least in my mind.

[FBM]

Since we're talking countability, is discreteness a fundamental feature of anything in existence, or is it projection of how the brain/mind evolved to effectively analyze experience?

I was getting to it. Honest.

Remember a while ago there was some conversation in which I kept persisting that "universe" by definition was a totality, that no matter what you describe, parallel dimensions, the past, phone books, pornographic drawings of Linus from Peanuts, the letter P, all of it is part of one single thing?

Well there is your discreteness. However there is a problem in that the concept of universe as a unit or an object, is that A) we are part of that object
and B) every experience we have of it is dim and internalised. So it definitely is a projection. However is the projection correct, like a torch in a dark forest, or is it just us looking at hallucinations on the cave walls?

So if the totality is a singular unity, where is the discreteness? What's it discrete from?

The void. The Abyss.

Nothing, then?

[FBM]

Audley, what about the discreteness-countability issue I mentioned?

[cough]I mentioned it on the first page[/cough]

Like I'm going to read the thread.

[JimC]

Audley, what about the discreteness-countability issue I mentioned?

[cough]I mentioned it on the first page[/cough]

Obviously, if you start to look at the solar system with the tools of quantum mechanics, you will see only myriads of wave functions, that extend out to infinity, and just get denser in certain area, but I very much believe that approach leads to not seeing the forest for all the trees. On a cosmological scale the planets (and their moons...) are perfectly discreet entities, with very well defined boundaries, and wast distances between them. Not accepting that aspect, just because we now also know the other aspect constitutes a kind of blindness, at least in my mind.

Yes. We have to be open to using a variety of mental stances when trying to make sense of the Universe, developing an appropriate set of mathematical and conceptual tools for different physical scales. They work brilliantly in their own areas, we use them effectively, and the ways in which they clash at the edges of their domains (e.g. general relativity and quantum mechanics) points to puzzles and discontinuities worth investigating.

[FBM]

Where is the clear, definite, discrete boundary of a planet? Or a star?

[Azathoth]

Since we're talking countability, is discreteness a fundamental feature of anything in existence, or is it projection of how the brain/mind evolved to effectively analyze experience?

I was getting to it. Honest.

Remember a while ago there was some conversation in which I kept persisting that "universe" by definition was a totality, that no matter what you describe, parallel dimensions, the past, phone books, pornographic drawings of Linus from Peanuts, the letter P, all of it is part of one single thing?

Well there is your discreteness. However there is a problem in that the concept of universe as a unit or an object, is that A) we are part of that object
and B) every experience we have of it is dim and internalised. So it definitely is a projection. However is the projection correct, like a torch in a dark forest, or is it just us looking at hallucinations on the cave walls?

So if the totality is a singular unity, where is the discreteness? What's it discrete from?

The void. The Abyss.

Nothing, then?

The idea of a universal set is a handy way to think about things but doesn't work logically. Runs into several paradoxes.

[MiM]

The surface of the planets crust. Get's a little blured if the planet has an atmosphere, but its not important if its a few hundred kilometres off, when you look at distances of lightminutes, between planets (or lightyears, between stars).

[JimC]

Where is the clear, definite, discrete boundary of a planet? Or a star?

In real planetary objects, there will not be the pure mathematical discreteness of a platonic sphere floating in absolute empty space. However, there is a continuous spectrum of "discreteness" from this platonic ideal (never to be seen in its absolute form in a real universe) to the smooth transition shown, for example, when one gaseous compound is in the process of diffusing into a second one.

On that scale, a planet is vastly closer to the discrete end of the spectrum - its tenuous atmosphere is very small beer compared to the surface boundary between it and a dense solid or liquid interior.

[FBM]

The surface of the planets crust. Get's a little blured if the planet has an atmosphere, but its not important if its a few hundred kilometres off, when you look at distances of lightminutes, between planets (or lightyears, between stars).

Would airborne soil count as the planet? I'm thinking that the closer you look, the less discreteness you'll actually find. Is the atmosphere part of the planet? It's gravitational and electromagnetic fields? Are they not integral aspects of the planet's being? And a star...where's its clear cut-off point? You know much better than I that when you get down to the atomic level, things are quite fuzzy indeed. I'm sort of the impression that we make mental models of these things AS IF they had clear, definable boundaries, but that doesn't mean that they actually do.

[MiM]

This is exactly what I was tackling eight posts up ffs, refusing to see the forest for all the trees.

[FBM]

Where is the clear, definite, discrete boundary of a planet? Or a star?

In real planetary objects, there will not be the pure mathematical discreteness of a platonic sphere floating in absolute empty space. However, there is a continuous spectrum of "discreteness" from this platonic ideal (never to be seen in its absolute form in a real universe) to the smooth transition shown, for example, when one gaseous compound is in the process of diffusing into a second one.

On that scale, a planet is vastly closer to the discrete end of the spectrum - its tenuous atmosphere is very small beer compared to the surface boundary between it and a dense solid or liquid interior.

That's pretty close to where I'm going with it. But to say that the magnitude of the impact of the atmosphere is small is a subjective measure, I think.

[FBM]

This is exactly what I was tackling eight posts up ffs, refusing to see the forest for all the trees.

I read that and am disagreeing with it.

Edit: Not the facts you mentioned, but the conclusion you drew from them.

[JimC]

The surface of the planets crust. Get's a little blured if the planet has an atmosphere, but its not important if its a few hundred kilometres off, when you look at distances of lightminutes, between planets (or lightyears, between stars).

Would airborne soil count as the planet? I'm thinking that the closer you look, the less discreteness you'll actually find. Is the atmosphere part of the planet? It's gravitational and electromagnetic fields? Are they not integral aspects of the planet's being? And a star...where's its clear cut-off point? You know much better than I that when you get down to the atomic level, things are quite fuzzy indeed. I'm sort of the impression that we make mental models of these things AS IF they had clear, definable boundaries, but that doesn't mean that they actually do.

Yes, there is a fuzziness, but it is very minor in its nature. A clear lack of discreteness would see an objects density change smoothly from centre to an infinite distance. However, in fact we see massive, sudden changes in density, if not to zero, then a very tiny figure indeed. The discontinuities are not absolute in a mathematical sense of some arbitrary figure for density changing to zero instantly, but that is not a requirement to treat them as discrete objects in many useful ways. Depending on the prediction required, one may or may not need to take into account the minor discrepancies that derive from the solar wind, magnetic fields etc.

[FBM]

The surface of the planets crust. Get's a little blured if the planet has an atmosphere, but its not important if its a few hundred kilometres off, when you look at distances of lightminutes, between planets (or lightyears, between stars).

Would airborne soil count as the planet? I'm thinking that the closer you look, the less discreteness you'll actually find. Is the atmosphere part of the planet? It's gravitational and electromagnetic fields? Are they not integral aspects of the planet's being? And a star...where's its clear cut-off point? You know much better than I that when you get down to the atomic level, things are quite fuzzy indeed. I'm sort of the impression that we make mental models of these things AS IF they had clear, definable boundaries, but that doesn't mean that they actually do.

Yes, there is a fuzziness, but it is very minor in its nature. A clear lack of discreteness would see an objects density change smoothly from centre to an infinite distance. However, in fact we see massive, sudden changes in density, if not to zero, then a very tiny figure indeed. The discontinuities are not absolute in a mathematical sense of some arbitrary figure for density changing to zero instantly, but that is not a requirement to treat them as discrete objects in many useful ways. Depending on the prediction required, one may or may not need to take into account the minor discrepancies that derive from the solar wind, magnetic fields etc.

I wouldn't disagree with any of that, but treating them as if they were discrete is not quite proving that they actually are so, is it?