So according to Cantor a segment has an uncountable infinity of points instead of a countable amount. So you could have always from eternity divided a segment and never in forever get to the end. — Gregory

As you may be suggesting, there has to be an end, lest there be no potency, and, for now, it would be at the Planck size.

This can make us feel large against the background of the massive universe. — Gregory

Until the massive universe makes us feel small. It turns out that the mid-point is about the size of a piece of dust.

But the world, I've been told, doesn't exist as a single extended reality, but has levels of reality. — Gregory

Yes and no, for there are fields behind the field quanta that we call particles. There would also be levels of actions/reality emergent for such as atoms, molecules, cells at their levels.

How can we conceptualize how substance is different in the quantum realm? — Gregory

The field quanta form when there is an interaction, bound by a discrete energy spectrum. The base 'substance' would be covariant quantum fields, whatever they consist of, as themselves.

Yes, whatever they consist of. The Dali Lama is interested in arguing that the quantum world gives rise to the classical world, although it doesn't follow that this is so just because the quantum is smaller. "Emergent" seems to mean the composition is greater than the smaller parts and so have more meaning. Aristotle's "potential infinity" seems to dovetail nicely with seeing the levels energy appears in

"Emergent" seems to mean the composition is greater than the smaller parts and so have more meaning. — Gregory

More is different.

Aristotle's "potential infinity" seems to dovetail nicely with seeing the levels energy appears in — Gregory

"Potential Infinity" only works in math. The specific energy levels, say, as for electrons only being able to jump to certain orbits are due, we suppose, to that the waves still have to connect and can't just get chopped off to fit at any orbit.

The definition of 'infinite', largest or smallest, is not that it is an amount, but that it can never complete, and thus it cannot be.

Nice. I don't think General Relativity will ever be reconciled with Quantum Physics. The geodesics don't work at that level, because space doesn't work the same way. There is force in the atom, despite the attempt to get rid of force in the Newtonian sense

Nice. I don't think General Relativity will ever be reconciled with Quantum Physics. — Gregory

Loop Quantum Gravity is trying to derive quanta of space-time so that General Relativity can be gotten to from quantum principles as an approximation of a finely grained continuum that still operates well at large numbers. It's not easy, but all else has been quantized so far.

So I draw this symbol:



And I tell you that in the "bar" on the left-hand side, there's 5 billion dollars credited to your bank account.

Do you feel rich, or do you think it's just some nonsense I'm making up?

If the classical is not entirely reduced to the "small", if for no other reason than emergent principles, then maybe scientific explanations of our sense organs don't represent the reality at the top (our experience of the world). What we think we see is really an image created in the brain, but.. is it? Is this not reductionism?

Books like The Phantom Brain, Quantum Psychology, and even a Ted Talk I saw argue that we almost hallucinate our own reality. But to prove this from science is to first accept the reality of the nervous system as matter in space. So I don't know what trick that use to get around this. It also, again, seems to deny that the sum is greater than the parts, and forgets that the classical realm comes from but is not reducible to the quantum. Classical physical biology give rise to our spiritual experiences of the world, and that is a structure that has legitimate selfness too.

If the classical is not entirely reduced to the "small", if for no other reason than emergent principles, then maybe scientific explanations of our sense organs don't represent the reality at the top (our experience of the world). What we think we see is really an image created in the brain, but.. is it? Is this not reductionism? — Gregory

Probably, there are many 'smalls' that can lead to the same classical large.

Of course, the sense organs take in what's out there, but ignore a lot, because, I guess, so that we have greater contrast, plus, the brain paints a more useful face on the jumble of waves or whatnot out there.

We only ever 'see' the brain's model, which model also reflects what we already know in forms made by the brain, as proved by dreams, in which not anything comes in through the senses from outside.

Reductionism is popular, but there is something to be said for emergence, such as many connected neurons can do more than just one neuron by itself could do (more is different). We presume that what goes on in Totality is completely relative to the inside of Totality, given that there is no outside to provide any absolutes. Even that as tiny as particles would really be more like that they are hubs of relations, leaving not much to be intrinsic, although Lee Smolin thinks that energy and momentum have to be.

Classical physical biology give rise to our spiritual experiences of the world, and that is a structure that has legitimate selfness too. — Gregory

Seems that at each new level, associated patterns become that operate at that level, and so on.

I've had experiences (which others have told me they have had too) where I see a road or something with trees and all those green leaves, and my mind tells me the reality out there is exactly as it looks. This is not an argument, but still it is a very strong experience, more so maybe than the opposite of hallucinating. I propose Heideggerian being-in-the-world-ness, because the quantum world is possibility processes. Anyway great discussion! I will check out Lee Smolin

This can make us feel large against the background of the massive universe. But the world, I've been told, doesn't exist as a single extended reality, but has levels of reality. — Gregory

Your views are very constructivist. They seek to claim a definite connection between the abstract, Platonic world of infinite set cardinalities and the real, physical world.

From a Platonic view, there may be an elusive connection between mathematical abstractions and the real, physical world, but firm claims about this connection are absolutely not supported. From a formalist point of view, the symbol manipulations in Cantor's theory on transfinite numbers are perfectly consistent and therefore completely accepted. From a structural point of view, infinitary arithmetic extensions leave number-theoretic algebraic structures perfectly undamaged.

Aside from that, mathematics refuses to make definite claims about the real, physical world and limits itself to enforcing consistency in language expressions by governing the permissibility of symbol manipulations using an elaborate bureaucracy of formalisms. Constructivism is a mistake, because the only goal of mathematics is to consistently manipulate fundamentally meaningless and useless symbols. Nothing more.

We seem to be going in the direction where no knowledge can be obtained other than knowledge of ourselves. This is where Descartes started in his Meditations. Nevertheless, Descartes argument that things at a distance look small when they are really large is awkward. Instead of an illusion, we just have perspective, which he didn't seem to understand. Sure the world seems objective in its worldliness. But there are other questions two, like gender. To MANY, it is common sense that there are two sexes, male and female. That these are natures. Modern nominalism says otherwise.

Philosophy is hard

So according to Cantor a segment has an uncountable infinity of points instead of a countable amount. — Gregory

I don't know Cantor, but isn't this just a matter of abstract reasoning, or not?

In the abstract, of course any segment is infinitely divisible. Why wouldn't it be? Outside the abstract, Poetic Universe's mention of Planck scale basically shows Cantor can not be right in that instance (assuming our understanding of Planck scale is accurate and complete).

Philosophy is hard — Gregory

I hear that. Even my 'abstract' answer above is more of a dodge, if I am understanding what you are trying to get at.

Well the infinite divisibility of a geometric object suggested to me that pure geometry doesn't apply to the world of phenomena we know

I want to find something spiritual in all this. The Dalai Lama said that, in the modern world spirituality without quantum physics is an incomplete picture of reality. Also he supported "Nagarjuna’s contention that things only exist by way of designation." Nagarjuna is very interesting when seem in light of Aristotle. The Madhyamaka or Middle Way and the Chittamatrin or Mind Only, likewise teach of the selflessness of phenomena itself. What can this mean?

Well the infinite divisibility of a geometric object suggested to me that pure geometry doesn't apply to the world of phenomena we know — Gregory

Yes, agreed.

If you want to deal with knowledge claims that apply to the real, physical world, then it is preferable to pick them from downstream users of mathematics ("applied"), such as science or engineering, which have real-world semantics and actively seek to develop usefulness. Mathematics itself stays clear of that, if only, not to compete with or needlessly disturb the semantics investigated by its downstream users.