So tonight I was working my way through this book on the philosophy of science that I borrowed and want to return soon. There's a bit about Parmenides that gave me pause for thought. According to this interpretation, the universe is full of unchanging stuff, and our perceptions of change are nothing more than rearrangements of it. In other words, combinatorics is what makes the world go 'round.

I have to admit, the idea apeals to me. So imagine for a moment this world:

The 'stuff' of existence is nothing but arrangements. It doesn't make sense to ask arrangements of what because there probably isn't any stuff. Just arrangements. Wait, it gets stranger. There are all kinds of these arrangements. Let's call them frames. There is no space or time, but the frames can be related logically to one another purely by classification. That is, there is an identity relation (that one is the same as that other one), and other more complicated kinds of relations. Let's hypothesize that some of these relations have interesting properties. In particular, some have properties that we could call 'cause and effect'.

For example, let's take a zero-dimensional frame {1}. Suppose that a frame has a causal relationship to an effect frame if the latter is the same or double the first. In this case {1} -> {1} or {1} -> {2}. There are two possible outcomes for the 'cause'. Note that this is not a deterministic cause and effect. Don't get hung up on that.

Let's call a sequence of cause and effect frames like {1} -> {1} -> {2} -> {4} -> {4} a world history.

Have you ever noticed how tightly linked the notion of time is to the notion of cause and effect? Suppose we have it all backwards and the latter is the cause of the former? That is, the causal link between these frames creates a literal timeline.

But wait a minute--where's "now"? In this model, all moments in time are the same. There's no priviledged one that we can say is special. That's really okay. Each one is its own little "now".

If you lived in such a world history, you'd experience life just the way you do now (perhaps with one small caveat, as we'll see). But your view of the universe would be very narrow. You wouldn't notice that the 'you' that exists this instant is no different from the 'you' that exists five minutes in the past or future. Each was fulfilling its part in the causal chain. So all of the 'yous' that have ever existed or will ever exist simultaneously experience time moving forward.

Because of all the branching of world histories, the you that exists right now and the me that exists right now will go our separate ways down different world lines. We'll never notice this because at every instant "our" histories will have the same causes and effects, but the continual branching would assure that most versions of you and most versions of me diverge.

In this version of reality, one wouldn't be too surprised to find ways of looking at the world that were ambiguous--that is we find places where cause and effect begin to break down. This can happen only in such a way that it never really violates the relationship, but it can be ambiguous, as in quantum behavior.

Finally, the way I constructed the one-dimensional world wouldn't work because multiple histories collide. That is, {1} -> {2} -> {2} ends up in the same place as {1} -> {1} -> {2}. Could it be that the dimension of the frame has something to do with the possibility of constructing a causal relationship? There are differences in random walks in one, two, ... dimensions, for example. Perhaps there's something special about three-D frames? Alternatively, is it possible that we can find examples in our own world where different histories arrive at the same frame? So you and I could legitimately disagree about who won the Super Bowl and we'd both be right, from our own perspective.

If all else fails, one could invoke the anthropic principle and claim that without causes there would be no time, and therefore we wouldn't be here to worry about it.


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