He famously said that: "Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin."
I wonder if he knew about the Collatz Conjecture when he said that.
On his Wikipedia page, I read:
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At times he could be ignorant of the standard mathematical literature, finding it easier to rederive basic information he needed rather than chase references.
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So it's possible, even likely, he did not know about it.
The Collatz Conjecture definitely involves a deterministic process, and I say it produces random numbers.
Here is my informal proof of that: given any number, there is no algorithm for determining how many iterations it will take the Collatz Conjecture process to reach 1. There is also no algorithm or equation you could use to find the maximum value of the iterations. Small changes in the initial value produce drastically different results, which is a hallmark of chaos theory.
In this way, the process is akin to rolling dice. The overall and final results can be calculated beforehand, but the specific and intermediate results are unknowable.
If something is deterministic but unpredictable, it is effectively random.
