Pythagoras' Theorem. Evidence of elsewhere or our ingenuity.

[JimC]

Well, I'm aware that I can annoy the fuck out of people with my questions, so I'll bow out and let you guys enjoy the discussion.

Not at all, FBM. In fact, you have been a very definite stimulus and catalyst for my thinking in this thread tonight...

And well done Audley for starting it and MiM too! This sort of thread makes up for a lot of gun club and political crap...

[JimC]

I do appreciate all this.

Re: Fuzziness, it would be because each component is still part of a larger single deterministic process right?

I don't believe in determinism, and I have argued about it here before. Quantum randomness ultimately destroys determinism on all levels. I think I used the examples of radiation induced cancer and atomic bombs, but it also would make something like the exact moment for a star to go supernova impossible to predict. Add chaos theory to that, and the universe will never be like God imagined at the outset.

There may not be an absolute determinism, but there are at least ways to make good predictions. All we need to avoid is the hubris of earlier models of a clockwork universe...

[MiM]

I do appreciate all this.

Re: Fuzziness, it would be because each component is still part of a larger single deterministic process right?

I don't believe in determinism, and I have argued about it here before. Quantum randomness ultimately destroys determinism on all levels. I think I used the examples of radiation induced cancer and atomic bombs, but it also would make something like the exact moment for a star to go supernova impossible to predict. Add chaos theory to that, and the universe will never be like God imagined at the outset.

There may not be an absolute determinism, but there are at least ways to make good predictions. All we need to avoid is the hubris of earlier models of a clockwork universe...

Agreed! Lost a few posts of the discussion there. Might as well not have posted that.

[Xamonas Chegwé]

Jim, how do you factor in gas giants in your definition of the discreteness of planethood? It is possible to consider them as nothing but atmosphere! Just asking...

[MiM]

Hmm, as I recall the discussion was about whether discreteness exists in the physical universe, not about trying to find some discreteness classification for every different kind of terrestrial body

That said, even a gas giant is an extremely strongly localized agglomeration of mass, on a cosmological scale.

[Clinton Huxley]

Gravity is universal and electrons all "know" the state of every other electron so we are just a big blob of stuff.

[Audley Strange]

Wait. Let me try and get this straight. At a macro level our mathematical models describe a mechanistic universe but at the micro or rather nano level it's all totally random crazy shit?

[Audley Strange]

Well, I'm aware that I can annoy the fuck out of people with my questions, so I'll bow out and let you guys enjoy the discussion.

Not at all, FBM. In fact, you have been a very definite stimulus and catalyst for my thinking in this thread tonight...

And well done Audley for starting it and MiM too! This sort of thread makes up for a lot of gun club and political crap...

And thanks to you and everyone else, it's been a great thread so far.

[Clinton Huxley]

Hijacked blobs of quantum foam forced to walk the Planck.

[MiM]

Wait. Let me try and get this straight. At a macro level our mathematical models describe a mechanistic universe but at the micro or rather nano level it's all totally random crazy shit?

No. As Jim pointed out, there are some (in fact a lot of) processes we can predict very well at the macro level, but chaos theory flutters its wings also here. On the quantum level we can also predict lots of things, but only in a statistical sense.. We cannot predict the path of a single photon, or when a single radioactive atom will decay. Still there are cases where single events on the micro level will have even drastic effects on the macro level (like the single hit of a high energy photon to the tuma of a human cell that is already on its way to become cancerous, and pushes it to full cancer - or the spontaneous fission of a single Pu nucleus in a nuclear bomb that is on the brink of criticality, that makes the device fizzle and drastically reduces its yield). This inability to predict all events at the quantum scale will then also make even the almighty unable to fully predict the macroscopic future of the universe.

[Azathoth]

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

Does the set of all sets contain itself, is that one of them?

Sets can contain themselves. Power sets are the set of all subsets of a set, the empty set and the set itself. It just doesn't work properly with the universal set. A power set has to have higher cardinality than the set that it is a power set of. The power set of the universal set and the universal set itself are the same set giving equal cardinality. That is one paradox.

[Robert_S]

10 minutes and counting. Helluva piss.

Okay.

@Robert S

You may be unsurprised to know I know about Indra's net. It's a great concept. However you seem to be saying that even if it is a map, it is only a map of our internal processes, in so far as we are mapping perceptual data along with inference and bias which are products not of external reality but our consciousness. That such "truths" as the theorem are objective as a function of our minds rather than external physical reality. That the platonic forms are archetypes, products of neurology

Is that about it?

(We should get into a convo about mysticism sometime, perhaps this is going there anyway, we shall see.)

No, I'm not surprised you know of Indra's net. It's a nice concept to have while looking our mental maps as well as everything else. Just like Trin Tragula' fairy cake or...



I think most of my disdain for Plato's Forms (which seems to be seeping out in this thread) is that I'm always skeptical of notions of perfection. Is the circle with all the points equidistant from the center the best circle, or merely the most simple and generic one conceivable?


I don't think I'm a solipsist in any of the definitions under Wikipedia. I'm actually quite confident that there is an objective reality that is quite independent of what I think of it. I influence it in a lot of ways, but I don't think the mind creates it.

But our minds do create, using the brain and various inputs, a map of it. Since there are so many layers of interpretation we have a map of a map of a map of.... reality. There is a reality at one end of it that we start with, but our perception of it is very indirect. Therefore it's going to be distorted and sloppy. And some stuff we do create. Like "green". Without eyeball bearing critters, there is no green, just some EM radiation of a certain band. Likewise, without an observer at some point on the planet there is no objective sunset in the sense we usually mean when we speak of it. Without a certain kind of observer it's just the passing terminator.

But to get back to the question in the thread title:

Somehow, on some intuitive level, the irrationality of C when A and B are happily equal speaks of either no creator or a diabolical one. Even more so with the discrepancies between Even Temperament and Just Intonation in music.

It may seem strange, but one of the things that helped smash out the last bits of theology in me was that there is no perfect tuning for the 12 note scale. It seemed a dirty compromise at the core of one of the things that I love the most. I can happily live with it if we're in a world where we're humans making what we can of an uncaring universe, but not if we're in a universe with an almighty and benevolent creator.

It's a joy and a wonder to a rising ape, but a salted jagged wound to a falling angel.

[Xamonas Chegwé]

I think most of my disdain for Plato's Forms (which seems to be seeping out in this thread) is that I'm always skeptical of notions of perfection. Is the circle with all the points equidistant from the center the best circle, or merely the most simple and generic one conceivable?

It's worse than you might think. To truly conceive of a perfect circle, sphere, line, right-angle, etc., you must first conceive the idea of a perfectly stable, flat portion of the universe and that is only possible if there is no matter whatsoever anywhere in that universe!

Have fun.

[Robert_S]

I think most of my disdain for Plato's Forms (which seems to be seeping out in this thread) is that I'm always skeptical of notions of perfection. Is the circle with all the points equidistant from the center the best circle, or merely the most simple and generic one conceivable?

It's worse than you might think. To truly conceive of a perfect circle, sphere, line, right-angle, etc., you must first conceive the idea of a perfectly stable, flat portion of the universe and that is only possible if there is no matter whatsoever anywhere in that universe!

Have fun.

This implies that perfectionism is a more dangerous tendency that previously believed.

[Xamonas Chegwé]

I think most of my disdain for Plato's Forms (which seems to be seeping out in this thread) is that I'm always skeptical of notions of perfection. Is the circle with all the points equidistant from the center the best circle, or merely the most simple and generic one conceivable?

It's worse than you might think. To truly conceive of a perfect circle, sphere, line, right-angle, etc., you must first conceive the idea of a perfectly stable, flat portion of the universe and that is only possible if there is no matter whatsoever anywhere in that universe!

Have fun.

This implies that perfectionism is a more dangerous tendency that previously believed.

And one way in which maths differs from empirical science. Maths starts from perfection and struggles to apply itself to the world. Science works from the other end.