Thing is, the output of an equation that takes one iteration's output as input for the next round, etc. is 100% deterministic: The same equation, with same initial input, produces the same output every time.
Would not a coin flip with the exact same initial parameters (height, force, deterministic air currents, and striking surface) have the same result?
Only if measures are taken to maintain precise control of these variables; in practical terms, a human tossing a coin will produce an unpredictable result every time due to variations in muscle tension, the path the coin takes, etc.
Yes, but those parameters can be expressed with a single vector encoding force and direction. The POINT is the number of states of a single 64-bit word, for example, is nearly the number of atoms in the known universe.
Only physical sources can generate real entropy in this sense: Decaying isotopes, noise from a leaky diode, tumbling dice, snapshots of variable hardware states in a computer (least significant n. digits of CPU temperature, fan speed, keystroke intervals, etc.) do qualify as entropy;
That's part of the question, are those things deterministic, albeit at several more orders maginitiudes than our computers?
Again, the outputs of these processes can not be predicted unless their inputs are under precise control, which in practical situations they are not.
Right, but this is analogous to SEEDING your starting variable -- you only have 1.8E19th choices, LOL. Practically speaking, double that and you're golden. After than you just have to communicate your seed value (somehow), like the least significant bit of each pixel in a random image uploaded to the web.
A big factor here is that the random number generators used to make cryptographic keys are under the control of the user (or had better be!), and the user will act to assure that the variables driving the generator are not monitored to produce predetermined outputs.
I ask this semi-rhetorically, because in my cosmology, the universe must have some non-determinism in order for life to appear.
This far, physics describes a Universe where the balance of Order and Chaos is ideal for creating life.
Ah, that's only the ecosystem of the Earth. Science, to my knowledge has not expanded this balance to include the heavens.
Almost as if somebody set that up on purpose. To put a stop to that kind of "superstitious" speculation, some physicists propose that a vast, unlimited number of distinct universes must exist, each with its own physical laws, where only a few have conditions supporting the development of life.
The confusion here is in the word "universe". The word already encodes an idea of WHAT IS. Namely, a three dimensional void with a continuous single vector of time. But see, that order is already presumptive. (This is why I say "in MY cosmology")..
But if so, there must be a larger cosmic context in which all these universes happen, and the same speculation arises - how did this massively parallel trial and error process get started? Which jumps us up to yet another "higher" context, etc. ad infinitum.
Verily, 'tis a mindfucker.
LOLz, funny, but there are answers. Keep probing... Marxos