If I follow this correctly, choices are both deterministic and non-illusory.
The traditional line of thinking is something along the lines of "if my choices are determined by something else, they are illusion, and therefore do not matter." If the choices were illusory, then—if I have correctly understood—removal from the system would not have an effect on the system. Which is to say, 'past' leads to 'choice'—I'm unsure if 'present' is more correct in this case—leads to 'future' is indistinguishable from 'past' leads to 'future'
However, this is something akin to saying '1 + 1 = 2' is indistinguishable from '1 = 2'. Both the '+ 1' and 'choice' are integral to '2' and 'future', respectively. Furthermore, the reverse—'2 = 1 + 1' and 'future is outcome of choice that is determined by past'—also needs the middle to work correctly.
So—to relate this to terms more intuitive—the past determines the choices we are presented with and the options we take, but the future is the direct outcome of the choice, not the past. Our choices are non-illusory because they have effect. Our choices are more deterministic than we would like to think. After all, I know I like to think that I'm the only determinator in my choices, but that would ignore my thoughts on the current situation, the outcomes of similar choices made in the past, and what has happened to me recently.
Now, I wonder what happens if we have—instead of a function f(n-1) = n, where n is a node along a chain of causality—a function f(n) = n - d, where d is some distance along the chain. Put another way, what if a choice were to somehow effect what we consider the past—or, if n is negative, the future—and this discontinuous function affected the chain in such a way as to affect node n? After all, if 'past', 'present' and 'future' are only the way we interpret causality, what prevents a chain from looping back on itself as one of many inputs.
In asking the question, I may have answered it myself. I was thinking timefully, in that adding a new node would affect an old node, where instead there are no 'new' or 'old' nodes. The nodes 'are'.
Perhaps any node which appears to affect the chain is an illusion, and instead is merely another chain of causality that is similar to the chain being considered. The present doesn't change the past, it links to something that looks like the past.
Eliezer:
Although the I chose bits that were part of the whole, I think they are useful to consider how parts inform the whole, and use the parts-to-whole relation to—at least crudely—model the outer-to-inner relation.
HA:
What I was attempting to say is that the human mind appears to me to be a chaotic system. While it may be entirely deterministic, the outcome can be radically changed by small inputs.
The usage of the word 'illusion' as I am interpreting it is akin to "since all things are made up of a small amount of atoms and a large amount of space, the sensation of solidity is an illusion." This, I suppose, is true, but it leaves out a rather large bit about the fundamental forces. Saying choice is an illusion appears to me to leave out the rather large bit of the workings of the brain.