Painting is the spaces between the lines.

Sculpture is the gaps between the materials.

Music is the intervals between the notes.

Reality is the holes between the quarks.

In all cases, the arrangement is everything and the components are nothing.

Yes, ouch! Your finite intelligence trying to comprehend a potentially infinite problem in an infinite universe. 

Of course your baffled. you may be tempted to use the "G" word. Sometimes it does seem that when we try to figure it all out God presents us with yet another layer of the onion to peel away.

That's why a physicist would hesitate offer an opinion.

We are down to the quarks, gluons, leptons and such, perhaps it will end there.

Watch the news to see if the 'God particle" Higgs boson...  pops up for the Large Hadron Collider (LHC) at CERN.

I suspect that the reason you are baffled is rather that you have tripped over your own unanalysed assumptions, than that your question is based upon any truly deep problems. (All that subject to subdivision and correction of course!)

I cannot be sure of some of the ideas you have in mind, but let's see whether we can dispose of some of the more superficial difficulties.

You ask: "Do all objects contain further subdivisions or does the chain of subdivision end at some ultimately elementary particle." Suppose someone had demonstrated the existence of the ultimon, a particle that he had shown conclusively in practice and principle to be the ultimate indivisible physical particle. He also had demonstrated that, in spite of its practical and theoretically necessary indivisibility, it did not follow that all its aspects were identical. For example, it might behave differently in some orientations from others, conceptually, though not actually exactly, as a tiny bar magnet might behave differently in different fields. In every other way it behaves like a point object. Now, question: we know it cannot be divided, but does that make it in every way "indivisible"? I am afraid that you have certain semantic concepts to clarify and also justify before you may reasonably demand that we treat your question seriously.

In the empirical universe of our experience to date, we seem to have an impressively inductively consistent principle that when we get below a certain size of object under examination, if we want to achieve any greater resolution, we have to apply greater power. This has a great deal to do with why every proposed new field of subnuclear investigation demands yet greater energies. Exactly where such investigations might end, my guess might well be worse than yours, but I bet yours is not worth much! However, if that observation is of fundamental application, then trying to achieve a subdivision that requires more energy than the mass equivalent of nearly the whole universe would seem to present something like the ultimate subdivision. It might well form the basis of the definition of the ultimon, right? If anyone proposed that the ultimon indeed were divisible into smaller parts in principle, if only we had more energy, then how should we or anyone else prove it? Create another universe to consume in the analysis? What would the proposed assertion of divisibility amount to?

I draw to your attention the fact that to date, even the humble electron, observed as a particle, has shown no tendency to behave as other than a point particle. In what way would you propose that we should regard it as other than indivisible?

Now, suppose that we did indeed discover an ultimately indivisible particle, point-like and inscrutable, much like the electron. What makes you think that it must be identical with all other ultimately indivisible particles, point-like and inscrutable? Leptons such as electrons and neutrinos are not the same as all their fellow leptons, and they also are not the only known, apparently point-like particles; there are other particles with different quantum numbers. We have no reason in principle to imagine a zero-dimensional universe, just because some particle or particles are ultimately small and ultimately indivisible.

You speak of "finding the same paradox as above", but I regret to point out that you have neither characterised, supported, nor established any paradox.

Sorry mate, before you can claim to have earned your bafflement, it is back to the drawing board for you!

Hi Dan, I am sorry, but you seem to be contradicting yourself. Consider:

>I had considered that there might be fundemental particles with different qualities.< vs: >I would argue that if any particle has a different quality to another is because it must have different components…<

>The paradox remains.<

As a paradox that is more of a contradiction (or at least confusion) in concepts than contradiction in terms. If you are saying that a particle that has more than one attribute it must have more than one different component, how would you support that logically or experimentally? As far as we can tell, an electron is a point body, but it reacts to various forces; which part of an electron would you say reacts to the weak force, which to the electromagnetic force, which to “spin” and so on; are you suggesting that if we had a powerful enough microscope we could see the bolts holding the different components together that if released, could go off independently, carrying only  their own quantum number with them? Forgive, but that is a big ask! Why would it be any less acceptable to assume that embodying one attribute could entail other attributes?

By way of analogy, consider the fact that a body of gas emitting a given wavelength of light is opaque to that wavelength; do you suppose that this is because apart from behaving as an emitter, the gas must have a distinct barrier to prevent the passage of the light? That it is impossible for an excited gas to have multiple attributes that cannot be located in different parts of a particular mechanism?

I reckon that that idea is more of a fiction than a paradox. I think of Hardin’s first law: you cannot do just one thing. It was coined in a different context, but I reckon that it is hard for a even an indivisible particle, be it never so fundamental, to do just one thing. If you can think of one, whether divisible or not, let me know what it might be and what its one attribute might be.

Whether it has a rest mass of the order of zero, a few electron volts, a million or a billion eV, I still would like to see you distinguish between components and attributes.

Rushing, more later maybe...

I think it is wise to refer to Claude Shannon's view of a world of information. In his view, the fundamental basis of reality is information. I suppose a rough analogue to understand it would be to see it in terms of 1s and 0s, on and offs that a computer uses to compute it's inputs. Here, the arrangement AND the substance matters, equally and profoundly.And for the more philosophically minded people out there, the more interesing and wonderful reprecussion of such a view is the question, "What if the Universe is a giant computer?" But our finite little minds would ask the grand and noble question of "why?" and try so hard, but never get a fulfilled answer in the end.It kind of sucks, but we have limitations too, as fallible, limited, and as Dawkins may say, selfish creatures. But that is only for now. We have come quite far since our dawns from the African Savannahs (as far as our understanding of human evolution goes....). I believe it is safe to assume, and hope, that we can push our boundaries, our barriers that limit our nature, as we explore more and more not just of the Universe, but also of ourselves. And that answer won't just come from one science; each branches of science, can yield wisdom that we can apply elsewhere too. And also interdisiplinary subjects too could help. And this is why it is prudent to understand that no scientific discipline is greater than another.Peace.