“Every sufficiently complex deterministicity is indistinguishable from stochasticity”. Can you Please explain this in layman analogies?

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I have encountered this sentence in some form or another in several sciences journals-articles or sometimes in the social media bio of random strangers. I get a gut idea of what it is, but I’d like this explained in detailed words, so that I might also be able to explain this to someone, if prompted.

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If the event in question is complex enough in its nature, then there is an analytical point where it is impossible to determine whether it the event sprung from causation or by pure chance.

Think of rolling a ball across the table. This is fairly deterministic (at least in the abstract).

Now think of rolling a ball into another ball on that table. It’s still deterministic, but a bit more complex.

Now think of rolling a million balls into a million other balls and all the collisions that result. While technically there is some sort of cause-effect relationship that you might be to (theoretically) trace, realistically you can only describe the entire system statistically.

deterministicity means something along the lines of “an event which happens because of a reason”.

Stochasticity means something that is random.

Using these layman terms it becomes something like this

“Every sufficiently complex event which happens due to a cause is indistinguishable from an event which happens randomly”.

**Terms:**

_deterministic_ = the outcome is fully determined by the starting conditions. Randomness is not involved. If you repeat the experiment from the same starting conditions, you will get the same result. In theory, you can predict everything that will follow just by looking at the initial situation and computing how it will go on from there.

_stochastic_ = something random is going on. You can still say what is more likely and what is less likely, but not how a system will actually evolve.

**An example of the meaning of the sentence is:** a die roll. It may well all work in a fully deterministic way. Thay die _had_ to come out 5, because it had to follow the laws of physics. There is no randomness in any of the laws involved (motion, gravity, collisions with the table…). It’s all deterministic and nothing else but a 5 had to come up. But because the system is already fairly complex, for all practical purposes it is _as if_ the 5 came out randomly.

A Thing happens. What happens next?

If you can figure out exactly what happens next, then it’s *deterministic*. A game of Candyland is deterministic: draw card, go where it says. That’s it. The end.

If you can make multiple predictions about what happens, but you have no way to know for sure, then it’s *stochastic*. A game of Monopoly is stochastic: if someone lands on an unowned property then they *might* buy it…depending on what it is, and how much money they have, and whether or not anyone else at the table can talk them into it or out of it, etc.

This is saying: “If A Thing happens, and what happens next can be exactly determined but it’s *really really hard* to do so, then it *seems* like it’s unpredictable”.

In fact, if you can only observe an outcome of an experiment and have no knowledge of the internal mechanics of it, then more strict statement is true: **any deterministic behavior is indistinguishable from stochastic behavior**.

Suppose you roll a dice 100 times and every time it yields 6. Is it deterministic? Probably yes, but also it can be an abnormal dice which yields anything else 1 time in 100000 throws. But it is still random. For such a dice this outcome is perfectly normal.

Anyway, in real world all that you get is a probability that in a given experiment we observe a stochastic behavior or a deterministic one. For the above experiment, if you know that the dice is normal, it is still possible that you observe results of a random experiment, but the probability of it is very low.

Incidentally, this phrase is a play on a different one of longer standing: “Any sufficiently advanced technology is indistinguishable from magic.”

This is also known as Arthur C. Clarke’s 3rd law. He was a science fiction writer. The new phrase is similar in a number of respects to what Clarke said, but phrased in a more scientific fashion.

[Here](https://www.youtube.com/watch?v=ls_66dIM9-4) is a YouTube video of a computer simulation of shining a laser through three rows of reflective round pegs. [Long version](https://www.youtube.com/watch?v=_s4NLA8aAgw).

The geometry of angles and positions means any change in the laser angle gets amplified every time it bounces off a peg. So with multiple bounces, you get to a point where variations of like the 10th decimal place in the laser’s initial angle cause its path and the point it exits to be completely different, jumping all over the place.