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Comment by edko | Hacker News Reader

"Even Dr. Steven Novella, host of the Skeptics Guide to the Universe podcast, has said on the air that the digits of pi are random. They are not. First of all, they are 100% predictable by calculating pi."

Does this mean that randomness is just our inability to "predict"? If we could see the future just as clearly as we see the present and the past, would there be randomness?

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I find it's often more useful to replace the "random" property of an object with the "incapable of predicting" property of the observer/consumer/receiver/attacker/whatever.

This is basically the approach taken by information theory: one of Shannon's many insights is that the content of a message doesn't matter for communicating it; only how well the receiver can predict it. If there are two possible messages, it doesn't matter if they're "yes"/"no" or "invade Portugal"/"bring me a sandwich", the information being communicated is the same (1 bit).

In this way, something is "random" if it's maximally unpredictable, i.e. if it can't be compressed. If we pick a Universal Turing Machine as the receiver, we get the characterisation of randomness given by Kolmogorov complexity.

From https://en.wikipedia.org/wiki/Kolmogorov_complexity#Kolmogor... :

Kolmogorov randomness defines a string (usually of bits) as being random if and only if it is shorter than any computer program that can produce that string. To make this precise, a universal computer (or universal Turing machine) must be specified, so that "program" means a program for this universal machine. A random string in this sense is "incompressible" in that it is impossible to "compress" the string into a program whose length is shorter than the length of the string itself. A counting argument is used to show that, for any universal computer, there is at least one algorithmically random string of each length. Whether any particular string is random, however, depends on the specific universal computer that is chosen.

Yes, one way to grapple with the concept of "random" is to define it as "unpredictable", but that does imply that the randomness of an event is contingent on the observer.

According to Information Theory, the measure of the information content of a message is its unpredictability.

This seems to imply that randomness is information. (This is also supported by Kolmogorov, randomness is less compressible, therefore must contain more information.)

An interesting question is, where does this information "come from"?

And yes, if the omniscient God can predict everything He is an observer to Whom nothing is random.

Now, is He trapped in a static Universe, or can He effectively "stir the pot", and bring "new" information/randomness into existence? But at this point the discussion moves from mathematics to philosophy and right into theology, so ... um... yeah...

Numbers, eh? What a trip.

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I just realized this comment is basically just rehashing what chriswarbo said... :-/

Is God powerful enough to create information that even He could not predict? I think these paradoxes actually hi-light that there's something wrong with the idea of an omniscient agent, at least as we conceptualize it.

Let's put quantum mechanics aside and suppose we live in a universe that is 100% deterministic. In that universe, we still can't predict chaotic and overly complex things very well, like rolling a die or shuffling a deck of cards, even though in principle it would be possible if we had incredible computer models and incredible knowledge about the state of the universe beforehand. That's the kind of randomness that we're talking about when we talk about predictability. It turns out most kinds of randomness most everyone deals with is that kind of randomness. Even in the our universe with all its quantum weirdness, we could in principle predict perfectly predict most die rolls with good enough measurements and computers. It turned out that's what we meant by randomness all along. It isn't tied to physics or philosophy. Most of the things we call random, aren't truly "random" in the strictly physical sense, so we realized that we ought to have a theory that is agnostic to physics and philosophy. It turns out that the predictability version of randomness does a great job at both, so we don't have to talk about that other stuff when we apply it.

I agree with all of this, but the question of true randomness has, of course, the greatest importance to it.

Randomness is a statistical quality and isn't necessarily tied to physical phenomena. It just depends on to what you apply the statistics.

I had similar thoughts but was too embarrassed to ask as I am not a mathematician.

Basically is randomness a human idea/concept or does it really exist? This is sort of along the lines of whether or not Math really exists (mathematical structures) or is just a human way of modeling the universe (Mario Livio and few others have written some novels on this).

I don't know the answer but it seems to have a habit of getting philosophical rather quickly.

VSauce: What is Random? https://www.youtube.com/watch?v=9rIy0xY99a0

It gets a lot easier if you restrict yourself to a definition of random that puts some restrictions on the entity that needs to predict the events. If you for example say that you can only spent a polynomial amount of time looking at the first k bits to predict the k+1-th bit, then you have a rigorous definition where you can prove that such randomness exists (at least using standard complexity theoretic assumptions).

The definition of randomness is that which is statistically unpredictable. There would still be randomness if we could remember the future because we don't have perfect information about the past, and the universe is inherently random at the quantum level.

Not necessarily. Perhaps we live in a many-worlds universe, with no collapse.

Consciousness depends on decoherence (collapsing into one possible universe), which happens randomly (there's no way to predict which states you observe).

Our subjective experience feels like being in one Everett branch, sure. But if you really were in a superposition, what would you expect to experience differently?

I don't know if subjective experience is possible while self-coherent. You need to entangle with only one of your states to have any experience.

I don't understand your claim.

Interacting with something in a superposition creates entanglement. In practice most of you is in contact with most of the rest of you, so any superposition quickly spreads to your whole body and more generally the wider universe. At that point we can call it "decoherence" but there's no collapse. Just your wavefunction becomes cleanly separable into distinct pieces. But the subjective experience of being in either component would feel, well, normal.

Yes, it's normal so long as you are in one component or the other. I don't think that you can experience a superposition of being coherent among both components—of existing in both worlds. I think that we're always unconscious in a Schrodinger state.

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