Thursday, January 09, 2014


Without a Beginning but with an End

My problem with the semantics of "infinity" may be that I'm trying to apply its etymology too literally. It seems to me that "finite" means limited, having an end, bounded. Therefore, "infinite" should mean unlimited, endless, unbounded. So, I tell myself, "infinity" may be a good name for the size of a set like the natural numbers which increases--goes on--without end, but there should be another word for things that have no known beginning--they've just always been--but can come to an end. We tend to say that such things, the negative numbers for instance, which end at zero, are also infinitely many. Yet, when time and time-ordering is involved, might there not be an appropriate conceptual distinction to make?
This conceptual distinction is evident in a case I noted recently (writing on breaking of records): the difference between "first" (and sometimes "second", "third", and beyond) which is forever, and "last" which might not be forever. Beginnings of new states can be thought of as endings of prior states. Must we suppose that before being broken, for instance, something must be made?
The difficulty, our difficulty, may be that it is even harder for us to conceive of beginninglessness than endlessness, whence our lack of a word for it and our beginningless search for origins. "Beginningless" being "from time immemorial". Perhaps some things were in stable states--pure, or whole, or something else which can end-- not just since some moment no longer remembered, but since forever in the past (the concept I cannot find a word for).

Why It Matters

Precedent and tradition are strong arguments in human society. Property ownership and territorial sovereignty have been justified by arguments of descendanceline of descent from Adam and Eve, the original "owners" (or at least custodians) of the earth. Property ownership and territorial sovereignty are the way they are because that is the way they were meant (by the creator) to be, goes the argument, and it is not mankind's to challenge. Social Contract theory proposes various resolutions that do not require perpetuation of an original situation if it can be improved upon. But some may prefer to avoid re-negotiation of just power by claiming original rights and authority. Lack of an origin necessarily undermines such claims.
Evolution as a process does not necessarily mean there was no origin, but it may make some origins too fuzzy and too uncertain to be credible bases for claims to ownership and authority. Is it sacrilegious and subversive to ask "which came first, the chicken or the egg?" No? Well, how about "which came first, the human or the deity?" And if there was no beginning, what state of affairs can remain unchallenged as necessarily "right" simply because it has been so since time immemorial?
Writer Ta-Nehisi Coates recently made a personal observation about belief in the non-teleological nature of things. He wrote, in part
I don't have any gospel of my own. Postwar, and the early pages of Bloodlands, have revealed a truth to me: I am an atheist. (I have recently realized this.) I don't believe the arc of the universe bends towards justice. I don't even believe in an arc. I believe in chaos. I believe powerful people who think they can make Utopia out of chaos should be watched closely. I don't know that it all ends badly. But I think it probably does.

I suspect this sort of nihilism follows from a lack of a creation event, and is not necessarily excluded by a creation event either (is it?). God could play dice with the world, or might have done so initially. If that is where the concept of "beginninglessness" would lead, is it any wonder that society lacks it?

By The Way

An author called "Skullsinthestars" has published a nice four-part series of notes on infinity, beginning with "Infinity is weird: how big is infinity?". The second part ("What's bigger than big?") considers the infinity of numbers in the [0,1] interval. This serves as a reminder that caution is required when thinking of infinity as "limitless" or "unbounded": there can be infinitely many pieces of something if it can be split without limit.
That reminds me of an old joke I heard long ago, about the difference between a mathematician and an engineer. It involves a couple of heterosexual guys, but I suppose it works with a couple of heterosexual gals as well; I don't know about other cases. The story goes, that given a set-up with an attractive (and nekkid) potential mate a certain distance away and a rule allowing one to advance half the remaining distance to the target each unit of time, the mathematician stays put whereas the engineer advances. The mathematician explains that he (or she) would never fully reach the desired party so there is no point advancing. The engineer admits that this is true, but figures he (or she) will get close enough for a good approximation before too long.

To Consider

A teleological universe might also be without a beginning but with an End, but why would it?

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