Been re-reading some old Arthur C. Clarke stories (largely written before I was born). I did not care very much for most of Clarke’s later stories. Whether the fault was his or mine I cannot say. The notions in Science Fiction writings do not affect me nearly so much now as when I first “discovered” science fiction in the early 1970’s. Clarke was one of my first most-favorite authors (only partly because I went alphabetically through the science fiction section of the local public library). I remember as a teenager finding Clarke’s stories quite exciting.

I find the collection of Clarke’s short stories exactly to my taste, if no longer exciting. Did get a bit of a jolt when I re-read “The Other Tiger”. The notions in that story had struck me as “right”, and become so deeply embedded in my thought, I no longer remembered the source.

Of late I have tended to return to an extension to that same line of thought. The starting notion is that if the universe is infinite, all possible combinations of events must occur. (Yes, I have heard of the Big Bang Theory. The theory may yet be proven wrong. It may be that the universe is effectively infinite … but we will get to that later.)

If all possible combinations occur, there are infinitely many Earths with an infinite number of variations. You might think there could be an infinite number of identical Earths as well … but Nature seems to tend to favor simple solutions, so I suspect that each identical variation occurs exactly once. You could imagine a sort of dimension-of-variations with each possible combination strung out along the dimension as a sort of standing wave. (It would of course not be anything like a single-measure dimension … but again, something to return to later.)

You could imagine that dimension viewed over time as an enormous tree, with branchings each time an event or combination could vary. The tree is quite nearly infinite (or a near-infinite count of near-infinite numbers).

Or is it?

Does it really matter when an isotope decays a hundred light years away? Sometimes yes, but mostly not (a most overwhelming “mostly”). Perhaps that tree is more like a weave. Many past combinations lead to our present, so viewed over time the massive branching out of variations is matched by a massive branching in of past variants that make no difference to our present state or future.

You could view this as computation, where many different combinations of past-values could compute to the present-sum. In fact, when viewed as a computation, the size of an infinite universe - when filtered to all meaningful, unique combinations, suddenly becomes finite! So starting with the assumption of an infinite universe, you end up with the conclusion that the universe is finite. (Perhaps there is hope for the Big Bang Theory after all.)

Does the entire universe branch for each quantum variation? Seems a bit like overkill. If the variation makes no difference to our local sum, might they all exist in our “present”? The further away, the larger variations could be without effecting our local sum.

There is an outside chance we might already have proof. If an astronomer took two pictures at the extreme edge of the visible universe, and the pictures came out different, a good scientist would (quite reasonably!) assume a small error in the aim of the instrument. Those two differing pictures could be views into distinct distant “present” variants. Or perhaps the further out we look, the “fuzzier” images become, as we can see all “present” distant variants that do not change our local sum?

Looked at that way, the “weave” of variants might vary over the dimensions of space that we can perceive.

Of late I have been bothered by the question of granularity. It is easy to assume that a quark popping into existence a hundred light years away does not cause a local branch - but where exactly (a poor word in this context) does the fork occur? How much can the past variants differ, without changing the present sum?

I would prefer to believe the variants could only be very small, or very far away. But … I could be wrong. Could the past variants be nearby and macroscopic?

When you and I remember a past event differently, and it makes no difference to our present, or to our future actions, could it be that we are both right? Discounting the unreliable nature of human memory, could it be that some portion of the time our memories of past events differ because we did each experience (slightly) differing events?

Lacking a test, this is no more than an entertaining speculation. But … the question of granularity bugs me. A lot.

Not long after this notion had occurred to me, I started to notice that some of the music (played from the my collection stored on my iPod) sounded different than I remembered. Now I think it far more likely that this is due to a faulty bit in my memory, or the not-very-good sound system in my car, but … what if my memory is right? Could it be that the proof is all around us, but we have gotten used to discarding those bits that did not fit into our metaphor-of-the-world to which we are accustomed?

There is of course no proof for any of this, so the above is just an entertaining speculation. But … could it be true?