As is probably obvious, this is based on the essay "The Universe as a Mathematical Function." I'll start with a few preliminaries:
First, I’m randomly curious: what brought about the idea of a universe function?
Second, I give notice now: what follows is rather unpolished. I tried to smooth things out a bit, but honestly it was enough of a challenge for me to rough-cut some of these ideas, let alone trying to work them into a more polished state and order.
And as a third preliminary (though getting closer to the point): I’ve got to admit that through much of this essay, I was rather out of my league. I think this could be traced in part (though I'm sure not fully) to the fact that it dealt with a math concept. Math was a longstanding nemesis of mine. We did finally come to something of a peace treaty, but there’s never been friendship between us. As you may be able to surmise from the personification there, literature has always been my more natural ally. Ironically in light of that, however, I did get through quite a bit of math in high school – up through calculus (at least the beginnings), so I can appreciate the idea of a function as an image (again with the literary-mindedness) if not as… well, a mathematical function.
But to begin working out what we’re actually dealing with in this image – since it has now been at least five years since I’ve had to do any serious work with functions – am I correct in remembering that the domain in a function F(x) would be “x”? It seems fairly straightforward, even to me, that “x” would be the input, but again, it’s been a while, and as stated, math is not one of my strengths.
Given all that, what I think (assuming there was no misunderstanding involved) I was able to take away was something of a help in understanding possible interactions between free will and time.
Basically… hmm. Some setting for the problem I see this relating to might help. It hails back to a college philosophy class that dealt with various arguments posed to either prove or disprove the existence of God. I think it was in a discussion with the professor that he suggested that foreknowledge on God’s part implied a deterministic universe (if it is knowable, then it must already be determined). And a deterministic universe would preclude free will. I would tend to ground God’s foreknowledge in His being outside of time, but I think the reply to this was somewhere along the lines of, “If there’s an ‘outside’ to time, then the timeline (so to speak) must already all be in existence from the start, which means everything is already determined.” (It occurs to me now that I could conceive of a sense in which “determined” and “deterministic” were not the same things… but just as "nondeterminism" and "ignorance of determinism," though different, would be indistinguishable from within time and the universe, so I think might these). The subject came up when we were discussing the problem of evil as an argument against God’s existence, since my answer to this argument depends in large part on free will.
So back around to the function, free will, and foreknowledge. I think the function, as an image, gives me slightly more ability to conceive of an “outside” to time that doesn’t necessarily imply determinism than does, say, the above-mentioned idea of a “timeline.” (Even if functions, now that I think about it, often did result in lines on a graph. Meh
.) I think I can picture willful components within a function – components not entirely determined by the function, but rather by their own choice – while at the same time seeing that for one outside the function, the answer, so to speak, is still the answer and was all along. I’m not sure how much this image would aid me in a resumption of the above-mentioned discussion with my professor (which probably indicates the limits of how well I understand it), or what he might answer to it. I suppose he might respond that he was not sure what I meant by willful function components. And come to mention it, I’m not entirely sure I do. What, conceptually, would such a thing be?
On second thought, I’m going to have to put that question on hold, because in trying to work it out, I think I landed on something relevant, but entirely different. This would be the matter of cause and effect, which I believe you said you didn’t get into very deeply. I’m curious as to what part cause and effect play in the universe function. Because if I consider how a function works… you have one static or constant set of mathematical operations, in which a variable “x” plays at least one, and often several, roles. Of course in this case, “x” is time. But then what is functioning as the static or constant set of operations? I could, perhaps, guess the laws of physics, but I can’t think of any other possibilities. And if it’s just the laws of physics… I’m uncertain whether I could consider this complete or not. If I think of the creation of the universe (the creation of the function) as a combination of the setting-in-place of the laws of physics (the establishment of the constant operations) and the creation of “stuff” (matter, creatures, etc.) for those laws to work on, maybe I can begin to see it… if the relationship between the output for one given time and the output for the next moment in time were established. This is something on which I’m unclear where the universe function model is concerned. It sorta seems to leave each moment in time disconnected from and unrelated to the last… to the extent where I can’t see how the one could relate to the other in any sort of causal fashion. I believe you said you wanted to leave things open to people to conceive of a continuous or a discrete sequence where time was concerned. However… I don’t see how this could work in a universe where the “output” or “state of things” at any given moment is dependent in part on the output/state of things of the moment prior. I don’t see how any function, if it remains the same function, could also be partially influenced by the results of prior inputs in a progressing sequence. Is there/could there be any kind of operation that would, in essence, say, “insert the results from the last step in the sequence here”? Would something along the lines of f(x-1) as an operation within the function "f" represent that connection? Or does that work into something of a mathematical infinite regress, since if the function itself appears as an operation within the function, the same would happen each time?
See, I told you, I'm dealing with math that's out of my league. But in short, I’m not sure how a function with time as the variable could work as a reflection of the universe as a whole unless there was some way, within the function, of also expressing the impact of the point in time prior to whatever given time you're working with.
And after all that, I’m not sure I have enough steam left to try and return to the question that came before it – that of what a willful function component would be. Maybe I’ll have to either pose it as a question, or leave it for a later time.
*Looks at the above. Looks at the clock.* Yeah, I think that’s enough for the moment. There were other thoughts, but I’m sorta finding holes in them, and I should probably limit the amount of mental wandering I inflict with any one post, anyway.
I guess I’ll end with my two main questions:
Does any of that make sense?
Any thoughts?
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