Let me propose an analogy. Let's say you were very bored one day. Searching for a way to while your time away, you find a pair of dice lying around, so you decide to just roll them over and over. With each roll, you come up with various numbers between the numbers 2 and 12. There is never any order or sequence to the numbers you get – they are just random numbers. Now let's say that, after a while, you roll the dice at one point and you get a 2, you roll again and get a 3, then a 4, then 5, 6, 7, 8 all the way to 12 in perfect consecutive sequence. You find this very strange, as they are just a normal, un-rigged pair of dice, and you lack the precise muscle control to deliberately make the dice fall in this manner. Nevertheless, you keep rolling. As you roll again, the pattern starts again: 2, 3, 4, 5, 6, and so on. This continues to happen for roll after roll. You even obtain a different pair of dice but the same pattern still keeps happening. At a certain point, you will probably say to yourself "This is impossible!" or "How is this happening?"
But why are you surprised by this event? It is probably because you understand the rolling of a normal pair of dice to be an activity that operates within the realm of chance. Chance is understood to be devoid of structure and pattern. Thus for a meaningful pattern to unfold immaculately through the random rolling of dice should be virtually impossible. But why? How can we impose restrictions or rules on chance? How can we dictate what chance can or cannot do?
Here’s an additional thing to consider: Is this event just a strange coincidence or are the dice generating this pattern for some particular reason? Where exactly do we draw the line between a coincidence and a reason? Is there a line at all?
One might think of the roll of dice to be something that conforms to laws of statistics. But strictly speaking, there are no statistical "laws" in the sense of something that explains what necessarily will occur. Statistics does not produce laws; rather, it produces models. The purpose of these models is to attempt to predict the unpredictable and understand the inscrutable. Statistics is not something that can stipulate what can or cannot happen; it can only map out the way things tend to happen given a large number of instances.
How long, would you say, can this strange dice behavior last? Technically speaking, nothing in probability is impossible. The pattern could go on forever. But our everyday experience with random behavior seems to tell us that this will not happen. We know intuitively that, although randomness has no strict rules, there is still a certain regimen that we expect randomness to follow. The dice will generally yield a pattern-less progression in which there is no meaningful relationship between successive numbers. There may be occasional instances where you may roll a series of consecutive numbers (or even a series of the same number or a repeating sequence of different numbers), but you would expect such instances to be rare and short-lived. But exactly how many times are the dice “allowed” to yield consecutive numbers before they must return to their normal regimen of unpredictability? Exactly how much repetition is allowed before "random" is no longer random? How do we precisely measure the "pull" of randomness and the "pull" of structure?
With this analogy in mind, consider the idea that maybe randomness and structure are not mutually exclusive or distinctly separate things, but are intermingled somehow. My belief is that the universe in which we live is a mysterious harmony and unity between randomness and structure, chance and purpose, between what could be and what is meant to be.
I describe the relationship between order and chaos as a tension, like a game of tug-of-war. Regarding the dice-rolling analogy, the "pull" that causes the dice to want to produce random results is the pull of chaos, and the "pull" that causes the dice to want to produce an ordered sequence is the pull of order. — mysterio448
This can be demonstrated by many examples. For example, take snowflakes. Snowflakes are beautiful, ornate, symmetrical designs that materialize out of random activity in clouds. Another example is gemstones, which are orderly-shaped minerals that materialize from random geological processes. The sphericity of stars, planets and moons is a product of the force of order emerging from the chaos of mindless astronomical activity. — mysterio448
There are more sequences like this in the decimal of pi. One might think that such sequences are merely "accidents," statistically inevitable instances of randomness stumbling upon structure. — mysterio448
Murphy's law is essentially the opposite of the randomness paradox. — mysterio448
But I think where you run into problems is imagining the situation as two kinds of "pulls" as that puts you back into a reductionist metaphysics of causal forces. You have a literal antagonism of one thing against another thing rather than a complementary pair of things, each of which is essential to the other in a way that justifies talk of a resulting unity or synergy. — apokrisis
And does your dice story fly when there is no reason to expect a "pull" in terms of order at all. The point of a die is to design out the possibility of a correlation between outcomes. The goal is to make a "machine" that maximises our uncertainty by creating a symmetry among the alternatives. — apokrisis
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