This is a placeholder to start the discussion of indivisibility, by first going back to why it was an issue for Epicurus in the first place. What questions or positions was he addressing?
Here are some starting points, first from David Sedley's "Lucretius and the Transformation of Greek Wisdom":
From the Cambridge Companion to Epicureanism, Epicurus was responding to Aristitotle's attacks on Atomism:
Here is where the issue of "movement" comes in, from the same source. We need more development of Epicurus' response to this. I am not going to have time to pursue this right now, but there had to have been important reasons for this dispute and we can't analyse the issue without uncovering them:
Jumping from the 20 tenets thread....
Cassius, I was curious about Victor Stenger from reading the SofE post that I indirectly linked to in the tenets thread. From browsing on Amazon, his book God and the Atom looks to be exactly what I'm looking for: a discussion of particle theory from an Epicurean perspective. I think I'll start with that book and see where it leads me.
Oops I crossed posts with your last 2. Is the Epicurean Atomism essay online or just in the CCtoE book?
Godfrey: That is GREAT if you have time to tackle God and the Atom. I recall Alex saying many good things about Stenger and that book in particular. I think I scanned a few pages but that is as far as I got. It would be tremendously helpful if you are able to expand this or related threads with commentary from Stenger.
As far as the clips above those are from the Cambridge books so I don't think there is a full free copy on line.
I know I have read about this in various sources but unfortunately I don't seem to have kept good notes. That was one of the reasons for setting up this forum 
Here's a clip from page 12 of DeWitt's book:
The whole issue of "infinity" is charged with implication, both down (infinite divisibility) and "up" (is it right to say that the universe is "infinite" in size, or is "boundless" perhaps a better word?) Because ultimately there must be no mystery to whether something exists or not.....
And of course those issues lead to the closing of the letter to Pythocles:
All these things, Pythocles, you must bear in mind; for thus you will escape in most things from superstition and will be enabled to understand what is akin to them. And most of all give yourself up to the study of the beginnings and of infinity and of the things akin to them, and also of the criteria of truth and of the feelings, and of the purpose for which we reason out these things. For these points when they are thoroughly studied will most easily enable you to understand the causes of the details. But those who have not thoroughly taken these things to heart could not rightly study them in themselves, nor have they made their own the reason for observing them.
A feature of interest in the discussion is the idea that atoms were not only thought to be physically indivisible: atoms were also thought to be conceptually indivisible.
Cassius I'll dive into God and the Atom after the new year, hopefully I won't drown! I'll post as I come up for air 
I have read several books by Stenger-- I enjoyed them all. But I haven't read that one, Godfrey, and I'm looking forward to hearing about it.
My intuition about indivisibility is that without it, it might be easier to propose a "god of the gaps"-- a supernatural force whose effects are hiding out in the unmapped territory. If matter were infinitely divisible, we could never describe the behavior of any particle without considering the possible influences of unknown sub-particles, which we could never be finished dividing. It would feed straight into Skepticism, wouldn't it? Intrinsic unknowability of nature?
But Idk if I'm right about that. Someone who is better at physics might give a different answer.
one of Zeno's paradoxes. This suggests that there are, supposedly, an infinite amount of steps to complete any distance, that it's hopelessly impossible because it can neither begin nor end. From this, the argument concludes that motion is an illusion.
Yes exactly thank you Oscar! Do you also have a short explanation of the problem with Zeno's argument ( other than walking across the room, which I gather is the standard and good! response?
My intuition about indivisibility is that without it, it might be easier to propose a "god of the gaps"-- a supernatural force whose effects are hiding out in the unmapped territory.
Elayne, I've never heard the phrase "god of the gaps", but that's exactly why I'm interested in this topic. Many of the terms thrown around from modern physics can lead the uninformed layman such as myself to consider such an idea. To address that I'm attempting to get more informed, and from what I gather Stenger's book takes that on pretty directly. We'll see!
Oscar, that's a cool video-- I remember my dad teaching me that when I was in 4th grade, but I hadn't thought of it in relationship to this issue of indivisibility. Nice!
It's also a great example of how using our senses, including through their extensions of instruments, gives us primary evidence about reality that is not found in abstract theories. Abstraction is helpful, definitely, but it can't give us accurate information unless real evidence is used. Planck was wise to start from the evidence!
Godfrey, I couldn't recall who came up with that term, so I had to look it up. Cassius will be excited to find out Nietzsche was involved! I think it's very useful-- and the wild thing is that you could put anything you wanted in that gap. You could say everything we don't know is explained by witches, magical unicorns, Zeus, universal consciousness, or an as yet undiscovered type of herb. So you can have one gap person debating another gap person-- "the gap is filled by leprechauns"-- "no, it's by elves"-- and nobody can base an argument on any kind of data.
It has also meant that their gods have gotten squeezed into an ever smaller space. If they want their gods, that seems like a strategic error, lol.
Regarding "The God of the Gaps", Neil Degrasse Tyson expresses it well;
If that's how you want to invoke your evidence for God, then God is an ever-receding pocket of scientific ignorance that's getting smaller and smaller and smaller as time moves on.
And to put Elayne's point more concretely, we can look to an argument made in DRN. Lucretius makes explicit the analogy that compounds of atoms are a kind of coded information, just as latin letters come together to form words. But in order for this to work out, there must be a finite library or alphabet of atomic 'letters'. If they could be infinitely divided, no such set would be possible. In this instance, infinity really does lead to zero.
Analogies are always flawed. It is certainly the Epicurean position that there are a finite number of kinds of atoms, but an infinite quantity of each kind.
The idea of an infinite alphabet is one I can't really wrap my head around. And of course, for an alphabet and a language to carry meaning implies a subject capable of interpreting meaning. Atoms and their compounded objects don't require a subject.
