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Musings

"Full many a gem of purest ray serene
The dark unfathomed caves of ocean bear;
Full many a flower is born to blush unseen,
And waste its sweetness on the desert air."

      From, "Elegy Written in a Country Churchyard", by Thomas Gray

If a tree falls in the forest, with no-one there to hear it, does it make a sound?          (? Anon.?)

Evolution

Darwin posited random biological change selected for preservation by circumstance. Neo-Darwinism believes it has found the "mechanism" for this in DNA. There are a number of puzzles, not the least of them how, in detail, a micro-molecular difference translates into macro-molecular form. I gather that proteins are eventually synthesised, different in ways depending on differences in the DNA. Well and good. How do these proteins then assemble into functional forms? Is it like crystallisation? We are told that crystals have a macro-form reflecting micro-form, and perhaps they do, but I have not seen anything of that micro-form specific to stopping or promoting crystal growth, and I have often seen crystals whose forms are only approximately regular - having dished or bulging facets, for example. The crystals you finally get seem as much formed out of their environments as from internal order. I do not know in detail what the structures of the atoms that go to form a crystal are, but it seems they must be similar, and also "fit" one to another, if growth is to occur. It seems to be an equilibrium between the formed and the unformed, between solid and solute. They have different orderings.

If a new cell is in some sense a duplicate of the old, as the components of a crystal lattice seem to be, what are the two cells together? In other words, what determines the latticework, especially its limits?

I hear that cancers are cells failing to die. This suggests that in the normal way of things there is a dynamic equilibrium between life and death, and that the form of an organism is at the boundary of the two. What sets it? Genes? How? How exactly?

For another example, if, as one hears said, the newly-advantaged individual is better-placed by the advantage to mate, it does not mean that other individuals not so favoured cease to mate: they are not all "elbowed aside", surely, especially if they live at a significant distance from the changed one. I suspect that the majority mostly do. It is difficult to see how a change in one individual is going to make much difference to a species, as the odds in favour of old-style mating must be greater than those in favour of the new style, simply because the new individual is just one in all of the old, of which there are no doubt very many, and one-in-so-many is how probability is defined.

Assume that a "favourable" change occurs (for no particular reason—i.e., at random) in an individual organism. Is one event such as this enough to make the change "take" in the species? It strikes me that a whole set of circumstances, besides the change itself, would need to be "just right" for this one individual for the change to propagate to descendants, and then would need to be equally "just right" for each of those descendants, one at a time (as only individuals mate, not species). Furthermore, advantages accrue to individuals, via individuals, not to species, via species.

The change may have been random—but so, to a significant extent, are the natural circumstances into which the alteration is introduced. If the circumstances are random with respect to individuals (that is, are unpredictably different for each), it is hard to imagine that genetic change and extra-genetic circumstance would sufficiently often agree (at random, mark!) to establish the alteration as a non-random (constant) feature, meaning, in effect, that change has stopped. This because there are, equally available, far more non-agreeing states than agreeing (cf Entropy). Well, one successful mating (i.e., one having similarly-advantaged offspring) is always one more potentially agreeing state, so we have two, not one, in however many of the other, so the odds no doubt improve.

I seem to be thinking about something with the character of a "trigger" event. One might think of supercooled liquids, that do not freeze until triggered by something small, and having nothing to do with temperature. Avalanches might come to mind: they tend not to happen until something small (a shout, perhaps) sets them off. Snow in one stable distribution changes to the same snow in another, quickly. Earthquakes. Tectonic plates slip catastrophically from one stable state to another. A minor bump might trigger one. In all such cases we have systems poised to go, and "poise" refers to components arranged in a simple way that is certainly not random (if it were, it would not be simple). Are random mutation and natural selection of this kind?

For sexual reproduction, an individual has a gender, one of two. Does the favourable change propagate automatically to the other gender, such that the advantage of the one becomes the advantage of the other? Does it need to? Assume the original advantage occurred in a male. Do then only males inherit the advantage? If not, why not? If not, then the change must be genderless, in the sense that it cannot matter which gender suffered it, despite the fact the actual transmission is very much a matter of gender! Are there such genderless changes?

So, how may advantage be properly defined? With respect to what? Well, clearly with respect to the status quo, for a start—those things not expected to change much, the "secular" variables, changing so slowly that they can be thought of as constant, such as the shape of a mountain. Or climate as opposed to weather. Or the shape of an arm as opposed to the shapes of the uses to which that arm is put. In short, with respect to the things not subject to evolution.

More later. Maybe.

Idea versus Actuality

The world does not approximate to itself, though ideas about the world  certainly do approximate to the world.

A glove approximates a hand, but a glove does not approximate a glove, and a hand does not approximate a hand..

While it would appear that some relationships between mathematical elements pertain to aspects of the world, to the exclusion of all other relationships, all relationships must be true simultaneously, and are not subject to change. The question then is, "Why is this?"  And, "Do redundant relationships nevertheless play a role?"

We write down some equation, intended to describe some perceived situation, such as the passage of electric charge through a conductor, precisely.  The equation, in this example Ohm's "Law", has a limited number of terms and corresponding operators.  It therefore selects a subset of all such simultaneously true.  We in such cases are the agents responsible for the selections and suppressions: is there a similar selection in whatever brings about the real situation that the equation is intended to describe?  In other words, is selection a part of non-approximate reality, and if so, what agents are responsible for it?

If an object, such as a hand, is to appear (that is, to be distinguishable at all, and recognisable, and discrete), there must be an "equilibrium of selections" (to phrase it loosely - and provisionally), belonging to that object.  I suppose it might be visualised somewhat like a region as in a Venn diagram, as a thing within a thing, having a boundary.   But what agent sets that boundary?

Boundaries, then.

Boundaries may arise from a limiting process: we spill a cup of coffee, and see a stain spread.  The  stain develops a boundary (so Time is a feature), defined in large measure, we suppose, by the amount of coffee available, and by the terrain encountered locally by it during its spread.  So we think about initial and subsequent conditions, and these conditions are presumably the agents we seek.  They, we believe,  make the selections that set the stain boundary, and alone determine its limits.  Is this correct? If correct, is this complete?

A hand exposed to heat is changed by it.  It acquires a new boundary, another selection is made, a fresh equilibrium is found, new limits, and another equation must be written to describe it. Well and good. But what wrote the original, pre-burn specification?

I am saying that the boundaries of buds, if not hands, are at least in part set by an outworking of the laws of incidence - that these laws make some of the selections.  But a bud is "stuff", and stuff has its own regulations (selections). We must have some kind of synthesis.  I am wondering whether or not that synthesis applies to the coffee-stain, too.

When I contemplate a pure line, I comprehend it as a "whole thing".  That is, it is not decomposable, since it is a quality, as a colour is a quality.  It  is an element of consciousness not unlike a perception, but it cannot be a sense perception.  It is taken to be a representative element of Space (though it may not in fact be that), but since it is just extension, it is continuous by its very nature - this is its quality: it cannot extend unless it is continuous. In a quite real way, extension, continuity and straightness are all one and the same thing. Each of these words is bedevilled by verbal, actioning nuances having no relevance to pure geometry. Action is not a geometric quality.

Simplicity is another quality belonging to the psyche, rather than to the world.  I do not suppose that the world "knows" that it is sometimes simple, and sometimes complex, nor do I suppose that its actions are in any way modified in the light of such knowledge.  Like infinity to pure geometry, simplicity is undefined, except perhaps by us.

How does an interval measure itself?

It cannot compare itself to another interval, since that would be a case of two intervals, measuring each other, which is not the case that we seek, namely that of of one interval, measuring itself.

This implies that all measurements must be comparisons of at least two intervals — and this in turn surely means that, in both principle and practical fact, an interval cannot measure itself.  Thus, intervals are not intrinsically (i.e., in and of themselves) absolute.