[snip]

    The question; "what is it that moves?" seems an obvious and a valid one but it also seems that Spinoza does not concern himself at all with it and simply says that it is self-evident when he writes:

========= E2: P13, LEMMA. 1:
    Bodies are distinguished from one another in respect of motion and rest, quickness and slowness, and not in respect of substance.

Proof.--The first part of this proposition is, I take it, self-evident. That bodies are not distinguished in respect of substance, is plain both from E1P5 and E1P8 It is brought out still more clearly from E1P15N.
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    This of course does not satisfy my imagination of bodies as something separate from motion and rest but nonetheless this is what he is saying. So, what can I do? I can continue to study Spinoza's writings and try to connect the ideas by following carefully his reasoning. He says that by Intellect or Understanding he knows motion and rest to be immediately produced by God. That is, motion and rest are Modes of the Attribute of Extension which follow (not in time) immediately, nothing in between -no body first, then motion and rest, etc. I believe it might help to look again at Spinoza's 2nd and 3rd "Properties of the Understanding" in the TEI paying close attention to what he says about how the Understanding forms determinate ideas of bodies from other ideas and keep in mind that he is talking here about the ideas of bodies perceived by means of a cause:

========= TEI-P108(87):
...

II. That it perceives certain things, or forms some ideas absolutely, some ideas from others. Thus it forms the idea of quantity [extension] absolutely, without reference to any other thoughts; but ideas of motion it only forms after taking into consideration the idea of quantity [extension].

III. Those ideas which the understanding forms absolutely express infinity; determinate ideas are derived from other ideas. Thus in the idea of quantity [extension], perceived by means of a cause, the quantity [extension] is determined, as when a body is perceived to be formed by the motion of a plane, a plane by the motion of a line, or, again, a line by the motion of a point. All these are perceptions which do not serve toward understanding quantity [extension], but only toward determining it. This is proved by the fact that we conceive them as formed as it were by motion, yet this motion is not perceived unless the quantity [extension] be perceived also; we can even prolong the motion so as to form an infinite line, which we certainly could not do unless we had an idea of infinite quantity [extension]....
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    But even if it is not yet clear to us what Spinoza means here why are we concerned about answering the question "what is it that moves?" If we read the whole Ethics nothing regarding minds or bodies is based on anything other than the simple idea of motion and rest of simple bodies or bodies compounded of simple bodies. He also says that the idea which we have of motion and rest must be adequate (See E2: PROP. 37-39.) At the end of his little collection of lemmas (that is, auxiliary propositions used in the demonstration of another proposition) on bodies following Prop. 13 in Part 2 he writes:

========= E2: P13, LEMMA. 7, Note:
...If we further conceive a third kind of individuals composed of individuals of this second kind, we shall find that they may be affected in a still greater number of ways without changing their actuality. We may easily proceed thus to infinity, and conceive the whole of nature as one individual, whose parts, that is, all bodies, vary in infinite ways, without any change in the individual as a whole.

I should feel bound to explain and demonstrate this point at more length, if I were writing a special treatise on body. But I have already said that such is not my object, I have only touched on the question, because it enables me to prove easily that which I have in view.
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    So he says that for the purpose he has in view, and remember he said in the preface that the purpose of this whole part is "...to lead us, as it were by the hand, to the knowledge of the human mind and its highest blessedness", we need have no other knowledge of bodies than that simple bodies involve motion and rest and may be compounded with other simple bodies. But to make it even more clear that knowledge of bodies need involve nothing more we might look at what he says a short time later about a possible mechanism of memory (which today may seem quite naive):

========= E2: PROP. 17, Corollary:
    The mind is able to regard as present external bodies, by which the human body has once been affected, even though they be no longer in existence or present.

Proof: --When external bodies determine the fluid parts of the human body, so that they often impinge on the softer parts, they change the surface of the last named (E2POST5); hence (E2P13Ab2) they are refracted therefrom in a different manner from that which they followed before such change; and, further, when afterwards they impinge on the new surfaces....[etc.]
=========

he then notes:

========= E2: PROP. 17 Corollary, Note:
--We thus see how it comes about, as is often the case, that we regard as present things which are not. It is possible that the same result may be brought about by other causes; but I think it suffices for me here to have indicated one possible explanation, just as well as if I had pointed out the true cause....
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    So he says that he does not actually know how the human body works and specifically how memory works even though memory, from the viewpoint of the mind, plays a large part in what follows and he further says the actual physical mechanism does not matter for his purposes so does it matter if we know what the hypothetical bodies involved in his description might be?

    I doubt the above will satisfy you so I'm going to continue this with something from my own Imagination, not from my Understanding. You are probably familiar with all of the things referred to below. [My descriptions of the various concepts are probably not quite accurate.] When I was younger I heard about atoms and how they would look like little solar systems if we could see them. In this model the electrons and protons and neutrons were little indivisible simple bodies and all these simple bodies, the atoms themselves, and all matter made by compounding them are in motion or rest within something which seemed very clear to me namely space and time. This space and time, I began to read and hear later, were perhaps really one and inseparable namely something called "space-time" and mass was said to cause this space-time to warp (or was it that mass is the warping of space-time?)

    Still later I heard or read the term "quark" and that parts of atoms and some of the myriad other "particles" that were believed to be fundamental really weren't so simple after all but were composed of something else. Quarks were believed to exist in three different types which, if I recall correctly, could not be separated from each other but did move within a small space relative to each other. More quarks were later hypothesized. Now I'm hearing that no, quarks are not fundamental, they and EVERYTHING else are made up of extremely tiny one dimensional "strings", either closed in a loop or open with two ends. Maybe, they say, these strings might even stretch out into thin membranes of great extent but the one thing that characterizes all strings is that they vibrate and hence resonate in different modes and the theory is that all things in the physical universe (that is what modern science refers to as the universe) which seem to be different --like quarks, electrons, photons, etc. --are really just, fundamentally, various vibrations of little "strings." It seems to me that if "strings", whatever THEY are only differ by their modes of vibration or resonances then even modern physics places motion and rest in a fundamental position.

    Anyway, the above area of physics seems to me like a Zen Koan. There is no correct "answer" to a koan but the effort to find an answer may lead to the discovery of something entirely different from anything our Imagination was urging us toward when we started. In all this searching, and despite all these ways of organizing and changing our theories about bodies, whatever bodies or motion and rest are, still, according to Spinoza, the Eternal part of the mind is not subject to the vicissitudes of life involving the motion and rest of the body. Helping us to attain direct knowledge of this Eternal part of our Mind is what Spinoza tells us he has written the Ethics for, not to explain the nature of the physical world or abstract physics involving measure, number, or time.