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A deterministic process is one you can predict. If I implement a random number generator on a computer (to satisfy the pedants, let’s say it’s a linear congruent one with fixed random seed), I can predict the entire sequence of numbers it spits out if I know the seed and number of numbers pulled off the generator before.

A nondeterministic process is one you cannot. We don’t really know of such a process, because we’re finite creatures yet the potential number of patterns an infinite sequence could follow, yet appear random over finite lengths, is infinite. Let me hand you a sequence of numbers:

05820974944592307816406286208998628034825342117067

98214808651328230664709384460955058223172535940812

84811174502841027019385211055596446229489549303819

64428810975665933446128475648233786783165271201909

14564856692346034861045432664821339360726024914127

37245870066063155881748815209209628292540917153643

67892590360011330530548820466521384146951941511609

43305727036575959195309218611738193261179310511854

80744623799627495673518857527248912279381830119491

29833673362440656643086021394946395224737190702179

86094370277053921717629317675238467481846766940513 …

It goes on indefinitely. You throw every test for randomness you know of at it, and every one passes. You declare it to be random, at which point I reveal it’s actually the digits of π after the first 50. As there are an infinite number of offsets within π I could pick, that alone gives me an infinite amount of infinite sequences.

So there’s no way to prove a process is nondeterministic. We can, however, say that a process is nondeterministic according to our best knowledge, rescuing the concept from Ockham’s Razor by invoking relativism.

But even if we grant nondeterminism exists in the absolute sense, we can still muddy the waters. Suppose I have a process that generates events at nondeterministic times; given an arbitrary amount of information, no-one can predict the precise moment the next event occurs.

However, this process is one-way, with a certain probability of happening at any given time. And as it’s rather inconvenient to carry around one copy of this process at a time, I instead cart around several trillion trillion. Now, however, you can describe my process with a high degree of accuracy. Not only can you give me a good estimate of how many events I’ll see over a given timeframe, you can put precise error bars on that estimate.

Is it nondeterministic, if you can partly determine the outcome? Or is it deterministic, if you partly can’t?

Marvin Edwards

said:A deterministic universe is necessary for predictability, but it only offers the theoretical possibility of predictability. It is not uncommon that we fail to determine the causes sufficiently to determine what determines the effect. 🙂

hjhornbeck

said:In general, I agree. The universe does not owe us an explanation, let alone an explanation we can understand. In this specific case, though, the universe seems to deliberately muck up our determinism/non-determinism divide. Take the Bell Inequalities, and variations thereof.

Emphasis mine. One approach to kick away the non-deterministic parts of QM was to propose “hidden variables,” things we couldn’t measure or weren’t part of our theories. That would mean any appearance of non-determinism was just a side-effect of ignorance.

So far, however, we’ve found no evidence for hidden variables and plenty against them. The non-determinacy in Quantum Mechanics appears to be truly non-deterministic, and not the result of ignorance. And as Quantum Mechanics is currently tied with General Relativity for the best known explanation of the universe, we’re forced to believe that, at its lowest level, the universe is a mishmash of determinism and non-determinism.

Marvin Edwards

said:No way I’m going to attempt to understand the Bell’s Theorem article. I’m satisfied to accept the -ism on the end and take my determinism on faith. I would therefore believe that any truly nondeterministic effects (uncaused) will eventually reveal their causes.

hjhornbeck

said:I’m very cool with that, given all the things we incorrectly thought were non-deterministic. I’d still recommend studying up on Quantum Mechanics, though, if only because of the way theories progress. Each former successful theory we’ve had been an approximation of the next. You can derive Newtonian gravity from General Relativity if you assume everything moves much slower than light, and you can derive Aristotelian gravity from Newtonian if you fix Earth as your reference frame. This derives from the fact that all theories are constrained by prior observations.

Those non-deterministic bits of QM are critical to the theory, and have held up over trillions of observations. Even if it’s completely deterministic at the core, the theory that replaces QM will have to appear to be non-deterministic to the same degree as QM.

Marvin Edwards

said:Thanks. The resolution of the paradox works even with a perfectly deterministic universe, so I get to skip all the QM stuff. Apparently free will was an inevitable result of the evolution of those species with the intelligence to imagine, plan, and choose.

The concept of free will, as it actually operates day to day, actually requires a deterministic universe to be in any way meaningful. Without reliable cause and effect, the will can never implement its intent. There is no rational meaning of the word “free” which does not presume a deterministic universe.