In Signs of Meaning in the Universe (about which I will have more to say in coming days), Jesper Hoffmeyer devotes a chapter to the idea of repetition. He says:
Life itself exemplifies Nature's tendency to acquire habits. With the emergence of an arrangement of matter and energy as unique as that found in a living cell, so too a new and intricate pattern was established in the world–a pattern that could be repeated ad infinitum. And repetition is of course the epitome of habituation: the key to predictability, law and order.
(p. 28)
I can disavow infinity and repetition in the same breath, but I'll confine my remarks to the problem of repetition. It would seem that the idea that repetition isn't truly possible–an idea that I've entertained without adopting–needs to be defended, lest it be confused with an expression of abject nihilism or rabid anti-intellectualism. Therefore I will now take up the position that repetition is at best a virtuality of questionable virtue– indeed it might be bad to think–and I will face up to the cosmic implications of thinking a universe without repetition. In the end I may not fully come around to the view that repetition is impossible, but I hope to resolve, in my mind at least, whether or not it is wise to leave open the question of its possibility.
If I don't accept the idea that repetition is possible am I necessarily acquiescing to a universe without laws, a permanent state of disorder and chaos? This would be the implication of Hoffmeyer's statement, but I don't know that it's true. Let's take for example a simple natural phenomenon, the orbit of a planetary body around a star. I believe I can question the possibility of repetition while believing that laws of gravitation and Kepler's laws of planetary motion still apply.
The eccentricity of Earth's orbit is not constant, but changes over time (see this graph). In fact the eccentricities of all of the planets in the Solar System vary due to mutual gravitational perturbations. We can imagine a perfect solar system of exactly one planet that does not vary in its eccentricity, just as we can imagine a universe where matter is evenly distributed; however, that's not a suitable description of the solar system we live in, and the probability of finding such a system may be exceedingly low (for all I know, which in the case of astronomy is only what I read online). Suffice it so say that in the case of Earth's orbit around the Sun, no orbital period is exactly the same as the next. In orbiting the Sun, the Earth never exactly repeats itself.
Do I need to say that gravity doesn't repeat itself every time the Earth orbits the Sun? That might seem to be a strawman, but I hope it opens up onto an illuminating point. The event of gravitation happened once and is still ongoing. If we accept the idea of heat death, which is based on the Second Law of Thermodynamics, then we must conclude that gravitation is far more likely to cease to be (after 10150 years) than it is to repeat itself. We could say the same thing about time, though it may turn out that time and gravitation are not coextensive, raising the question then of whether they are discrete cosmic events rather than being aspects of the same event, namely, the existence of the universe. If we accept that gravitation is an event–I do realize this sounds odd, although as I see it it's not altogether unreasonable–what do we call the occurrences that take place within its reach; how do we describe the relation between cosmic events of long duration and occurrences of shorter duration like astrogenesis or biogenesis? If we call them all events equally, are we using "event" in different senses? If this is the case, the sense of a relationship between gravitation and astrogenesis would be lost; it would require some other kind of explanation. Alternatively, in calling all cosmic occurrences "events" we might in effect be saying that an event can be subdivided, that there are events within events. Is the relationship between the subdivisions of an event, which are also events, and the event as a whole a relationship of parts to the whole?
Philosophy has already sketched out a position called mereological nihilism which isn't a proper nihilism, but rather a denial of the existence of part/whole relations. Short of fully endorsing merelogical nihilism, I'd like to suggest that part/whole relations are in question when we examine the relation between an single orbital period and the whole business of planets orbiting a star. The Earth may be considered a part of the Solar System; if its orbital period is therefore also part of the solar system, is that because it is part of Earth's orbit, because it is part of the Earth, or, rather, is its relationship to the whole of the Solar System simply not that of a part to a whole? If the relationship between orbital periods themselves does appear to have a meristic character, must we then accept repetition as a fact of the cosmos?
Imagine if you will having a very large interplanetary hammer and being able to summon enough force to knock the Earth out of its orbit. Its orbital period would come to an end coterminously with the demise of its orbit. It would seem to be physically impossible to decouple the Earth's orbital period from its orbit around the Sun. If we maintain that the Earth's orbital period is part of its orbit, then we must allow for some kind of relation of identity between a part and its whole. I'm not sure that this sort of mereological relation is kosher.
If we take a common sense view that the Earth's orbit around the Sun is neither one big event nor a series of discrete events (orbital periods) but rather a recurring event, we must then allow for some fuzziness in our concept of recurrence, because the orbital period is not just related to the orbit of a single planet, but to all the planets that perturb its orbit. The Earth's orbital period belongs to a larger whole of the Solar System, and in this System there is never exactly a repetition of orbits. The meristic character of the orbital period is deceptive if we believe it only relates to the orbit of a single planet. There may in fact be no true repetition in the universe.
Labels: astronomy, heat death, Hoffmeyer, mereology, repetition
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