Axiomatic Permanence
Science works by assuming permanence. When a single obseration is made, it is assumed that the system remains stable and unchanging. Upon further observation, when change is noted, the nature of that change is assumed to be constant. When the nature of that change is itself modified, we must assume another, deeper permanence. Consider a ball: at first glance, we might guess the ball always sits there. Until we tilt the surface and it starts moving — at which point we might assume its movement is constant with respect to the incline of the plane. Until we see that it moves faster over time, and we discover acceleration. In a sense, we assume our present knowledge is constant until we are required to take the derivative: from position, to velocity, to acceleration. But the example doesn't stop here — if we travel high enough above the Earth, we'll note a difference in the acceleration. The question is: how deep does this rabbit hole go?
4 comments:
It's my experience that the depth of the rabbit hole is, for all practical purposes, infinite... you can always remove another layer of abstraction. At least in the physical world, possibly elsewhere.
Funny how we start at the maximum abstraction and work our way down, yet in man-made things at least (Computer Science is the immediate example to me, heh), we are taught bottom up, only learning the abstractions at the end (if ever).
It seems to me that we think and learn best going top to bottom (which is probably why I found history and sciences so easy to follow -- you build up a rough image, and progressively fill in the details), so why are things like math and computers taught bottom to top?
Is it because the abstractions don't exist yet?
Perhaps it's the difference between recursion and induction?
This was more of an afterthought on "God in the Gaps". If you look at the recursive progress of science, it makes the problem more like "God in the Leaves". As a Christian, it wouldn't make sense to say "the rabbit hole is infinite", because God has to be the constant (Colossians 1:15-18).
I don't think it's so much "removing another layer of abstraction"; it's more like creating layers of abstraction. We always assume that the deepest layer we have is concrete, until we discover otherwise.
As for why things are taught different ways... It's probably related to the difference between systems we construct and systems we observe. Math and computer science are primarily tools we've developed, while science and history are primarily things we observe and describe. Writing is a tool, so it's taught bottom up (words, sentences, paragraphs, essays, etc.). But it can also be taught analytically, top down (reading books, analyzing the themes, characters, style, vocabulary, etc.)
"As a Christian, it wouldn't make sense to say 'the rabbit hole is infinite', because God has to be the constant."
Agreed, with reservations. Note that I was speaking from a practical perspective, however. Show me a way to measure God, and I'll show you that it's not God you're measuring.
(You'll see here the reservations. God is unmeasurable, so far as I understand it (it could be my understanding is flawed... much like you can measure a sphere in two dimensions but not grasp it's fullness, it's possible that God could, in fact, be measured but not fully comprehended? I'm not sure if the dimensions analogy fits here though. Anyway, back to before the digression...). If you can get to the point you're measuring Him... it's not Him, it's something else. So either: my assumption is wrong and God can, in fact, be measured; you hit a brick wall, and there is no God; there are sufficiently many layers such that it's impossible to measure past a certain layer or that layer can not be acheived within the timeframe man has; or else God does not directly control physical laws.)
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"We always assume that the deepest layer we have is concrete, until we discover otherwise."
But that's what I'm curious if that's the best approach. Since many things continue to have more layers beneath the surface, should we not assume it is so by default?
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As for the last part, that's the dichotomy I was thinking myself. But I am still left wondering what the fundamental difference between observing and constructing is... since after something is constructed, it is observed, and everything which is observed had to be constructed at some point.
So why treat the two separately, when they are parts of a whole? I wonder if it's easier to grasp? More convenient to think about?
It's like, I keep thinking this: cases are ugly. Generalizations are more elegant and simple. However, this leads me into confusion, as the world I see around me is elegant, but seems to have so many cases in it. So where does the fault lie, with my understanding that cases are always inelegant, or with my observation that the world is elegant?
Or perhaps, we've (as Computer Scientists, and Mathematicians) just built the wrong abstractions, and my mind has solidified around them, when I'm really missing the whole point.
"Show me a way to measure God, and I'll show you that it's not God you're measuring." This is why I called the approach "God in the leaves": if you accept the description of science I gave, it puts God as the last immeasurable constant (until we measure it, then He becomes the next immeasurable constant). Also, see the No True Scotsman fallacy.
"Since many things continue to have more layers beneath the surface, should we not assume it is so by default?" We can assume this, but it doesn't give our theories any more utility. Which is why the assumption is part of the attitude rather than any specific theory.
"Or perhaps, we've... just built the wrong abstractions, and my mind has solidified around them, when I'm really missing the whole point." I think this is all it is, not that cases are elegant, or the world is inelegant, or some combination of the two, or neither. It's that we assume one perspective and are then surprised when the picture seems incomplete (i.e., there is a subtle assumption of the objectivity of our single perspective). See the note on Anekantavada here (section 3) (note: Anekantavada is not relativism, it does not deny an absolute truth).
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