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Comment by 6gvONxR4sf7o | Hacker News Reader

Even more so, randomness as people usually use it exists independently of "true physical randomness." If I flip a typical coin in a typical manner, then regardless of whether quantum mechanics is truly random, a sufficiently detailed measurement fed into a sufficiently powerful computer can predict it essentially perfectly. It's a long way of saying a coin flip is close enough to deterministic in practice.

But there's something going on there that I can't predict, and we need a language to talk about it. That language is the same whether "true physical randomness" exists or not. Calling a coin flip "50-50" is just as valid in a deterministic universe as it is in a random one. Probability is a language more than a theory.

Too many people get hung up on "true" randomness, when that's probably not relevant to the the situation they're describing.

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Yes!

You’re talking about something different from algorithmic randomness, which would be a property of (infinite...) sequences. When I throw a coin in the air and say “heads or tails”, you have to make a prediction as to where it will land based on the information you have. Not someone else’s information— _your_ information. If you feel like you have as good a chance of winning as losing, you’ll tell us you think it’s a fair — a “random” — coin toss.

You’re talking about betting behavior. It’s not a wild tangent the way some would think — from this we get the structure of probability theory, we get derived preferences, we get the entire mechanics of Bayesian inference that underlies all systems which learn.

From studying this math — the math of the coin flip with a dollar on the table, the math of the universe — we learn that there _cannot be_ “chances” or “odds” out there in the world that we can see if we look hard enough— what we see if we look closely enough will be the structure of our perception, which is a perception itself constituted by subjective probabilities.

We learn that belief states must be subjective, must be local. There can’t be a fact of the matter in any way that makes sense to anyone. And yet we also can prove that we cannot truly reserve judgment, that we cannot be true skeptics— unless we are also not anything recognizable as scientists.

So, yes, absolutely. In the consensus reality we all agree to occupy, how you decide to answer the question “heads or tails” matters — in the deepest possible sense — just as much as anything else. And folks can get _so_ wrapped up in the idea of what an imaginary computer might do, they forget to notice what they are doing with every waking moment.

If you want to get really crazy about it, you can talk about betting about what the 999999999th digit of pi is. It's not random, it's not even really unknown, but I sure don't know the answer without a bunch of extra work.

this isn't true. given a chaotic system with enough degrees of freedom (even a deterministic) there is no computer powerful enough.

In classical computing maybe. And with phase space analysis millions or even tens of millions of events can be visualized for emergent attractors that would indicate an underlying pattern.

No. Chaotic systems mean that if you integrate the time horizon out, there'll be a time after which your measurement precision isn't precise enough, and you'll get an unpredictable bifurcation. For a typical you-or-me coin flip, the necessary precision for a hypothetically powerful computer to predict with say 99.99% accuracy is probably well above the quantum-weirdness level of accuracy. And that 99.99% accuracy (or even 90% accuracy) is different from the 50% without the measurement and computer that necessitates a 50% theory or 50% language of coin flipping.

>No. Chaotic systems mean that if you integrate the time horizon out, there'll be a time after which your measurement precision isn't precise enough, and you'll get an unpredictable bifurcation.

how is that substantively different from what i said?

>99.99% accuracy is probably well above the quantum-weirdness level of accuracy.

what is quantum-weirdness scale and what is well above? hbar is 34 zeros out.

You said it's untrue that you can predict a typical coin flip because it's a chaotic system. I laid out the limitations of chaotic systems and argued they don't apply to a typical coin flip. Are you arguing about predicting "essentially perfectly?" I use that to mean predicting with a couple nines of accuracy.

By quantum weirdness scale, I mean that the accuracy (epsilon) of a necessary measurement includes accurate position and momentum measurements. If epsilon is too small, we might not be able to hypothetically measure both to the necessary precision. I'm guessing that the necessary epsilon for essentially perfect prediction is large enough that you can hypothetically measure both to within that precision.

If you like, you can work out the maximum number of degrees of freedom that could theoretically be involved in something you could call a fair coin toss.

Hint: it’s a free body under rotation on a parabolic trajectory. You won’t end up needing Tony Stark hardware for this one.

Bonus factoid before bed: coins flipped by humans empirically have a small (~51%) bias toward heads. Supposedly folks tend to start with heads up more often, and the coin tends to flip over 0 times more often than you’d think, and that adds up to a bias you can measure in an afternoon.

Well this is where the law of large numbers comes into play. Flipping a coin half a dozen times is likely several points away from 50:50; randomness isn't an emergent property of a coin flip dataset until hundreds or perhaps thousands of flips later assuming a precise coin flip mechanism and fair coin. So randomness at least within this context is a function of time.

That's not what I was trying to get at. For even a single coin flip, we still need a language to talk about the situation when you and I can't predict it. If I flipped a hypothetical coin that poofs out of existence after a single flip (or more generally single-time events like elections or poker games) the usual probability language applies. No law of large numbers necessary.

Perhaps that language is time. Literally no research has been done into the analysis of precise time series observer effect data.

You mean "unpredictable"?

Exactly, yes. We have a language of mathematical unpredictability that applies to many things independently of whether the universe is deterministic. Fundamental unpredictability is irrelevant to practical unpredictability, but when you replace the word "unpredictable" with the word "random" people get weird about it. It's the same damned mathematical theory. Fundamental randomness is irrelevant to practical randomness.

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