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Comment by amarte | Hacker News Reader

Interesting title, and I will have to dip into the book when I have some spare time, but statements like "the world is built on probability" always sound strange to me. Is it that chance and randomness are fundamental aspects of our world, or is it that our knowledge of the world is inherently limited, and the laws of probability that people have expressed over time are useful descriptive tools that help us choose or dismiss certain outcomes based on the knowledge we do have? If the latter is true, I would not say the world is "built" on probability, but that the way we perceive the world can be built on probability.

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I think there is often a lack of distinction between situations where uncertainty is due randomness in the natural process, versus situations where uncertainty is due to your incomplete state of knowledge.

For example, a coin flip is physically deterministic but you can't take advantage of that in a normal coin flip situation. But if you have a chunk of radioactive material and two particle detectors held nearby, I don't know of any way even theoretically to determine which will trigger first -- that would be physically nondeterministic (unless I'm wrong, but other situation could be i.e. famously quantum experiments).

Then, most of the situation that are physically nondeterministic are things that we experience is a way that is aggregated over a large number of events: i.e. you aren't seeing individual particle emissions, you are just eventually getting radiation poisoning. It takes special equipment to experience the probabilistic nature of nuclear radiation, brownian motion, etc.

So there are really lots of natural processess that are probabilistic but you only experience them in aggregate which conceals it, but then you have incomplete knowledge about the world which re-introduces the uncertainty.

I've been reading a book on the philosophy of statistics, and what is interesting is that the statistical community has been, historically, completely divided on that question.

The only thing they agree on is the equations. Once you ask the question of "and what situation are we facing in the real world" consensus starts to break down.

Interestingly, the core of probability - the "Random Variable" is almost completely unobservable in the world of science. Everything in classical mechanics turned out to be deterministic. The parts that were grappled with statistics were probably not random effects, but unpredictable deterministic effects. For example, the measurement errors could be treated as random variables, but ultimately were not expected to be random in cause.

Compare this to geometry and algebra, where I would argue it is easier to find a 'real' example right from the get go. Opinions, obviously, vary.

Quantum mechanics has a lot of random variables.

Cipher text can look a lot like randomness to the uninformed observer. If a deterministic system produces results, but the observer cannot model the underlying process from the results, are those results now random?

Now might be a good time to brush up on https://en.wikipedia.org/wiki/Bell's_theorem

> "Bell's theorem rules out local hidden variables as a viable explanation of quantum mechanics (though it still leaves the door open for non-local hidden variables, such as De Broglie–Bohm theory, etc)"

> though it still leaves the door open for non-local hidden variables, such as De Broglie–Bohm theory

Though non-local hidden variable theories need to be reconciled with special relativity lest it be possible to transmit information faster than light.

Enter the implicate (folded) order of the holoverse ("holographic universe"), which Bohm (among others) developed and supported.

See the non-local, higher-ordering properties of true holograms and eg. this mixed fluid experiment: https://www.youtube.com/watch?v=UpJ-kGII074

More on all this in Michael Talbot's amazing book "Holographic Universe": https://wikischool.org/book/holographic_universe

Yeah, but there is an important subtlety. Quantum mechanics has a bunch of things that can be /modeled extremely well/ by random variables. But it might still turn out that that they are deterministic in some complicated way.

Then we would be back in a universe where we have an extremely useful concept in the humble random variable, and no examples of anything that is fundamentally random. If I start with a random variable, I couldn't reasonably approximate it with a real phenomenon, because the phenomenon would be deterministic.

Compare that to a line - I can define a line between the center of mass of my two hands. We can quibble all day about whether that is a well defined definition (I suppose it isn't), but if I wanted to approximate a real line with two points in space I could.

I contend this is an interesting an important difference between subjects like geometry and subjects like statistics. The underpinnings of statistic are _extremely_ philosophical.

Book name?

Statistical Thought - A Perspective and History (Shoutir Chatterjee). I'm really enjoying it, quite approachable at an undergraduate level of mathematics.

Quantum mechanics. Thermodynamics. Fluid dynamics. Signal processing. Information theory.

All are statistical in nature. Nature is built on probability.

Nature/the world is what is being described. QM, thermo, fluid dynamics, signal processing, information theory, probability, etc.. are descriptions which have been devised to depict and communicate nature/the world. We never say that da Vinci's painting of Mona Lisa is so good that the historic woman who was Mona Lisa was paint.

They're more than descriptions because (most of them) make testable predictions about the world. Doesn't mean they're correct, of course, but making predictions is really important.

In my view, dealing with genuinely random phenomena is rare. More common is that our knowledge is limited.

I have my own "take" on math. Of course we enjoy math as an end unto itself. But when we use it for practical purposes, we choose math tools that we expect to work for the problems that we're trying to solve. In the case of probability and statistics, those tools are useful for situations where we know something about a set, but not everything. There are other situations where we use calculus, algebra, and so forth.

Incomplete knowledge corresponds to a lot of problems and situations in our world, and so prob & stats are useful for modeling those situations. But it doesn't require the world to be fundamentally probabilistic.

"...dealing with genuinely random phenomena is rare. More common is that our knowledge is limited."

Quantum mechanics is the best thing we have to an exactly correct physical theory, and it is tied completely up with probability. So probability in the form of "genuinely random" is very fundamental.

As you go up from that level, our knowledge is limited at every turn, so it's hard to separate the one from the other ("genuinely random" vs. limited knowledge).

For example, you may have a large-scale physical system governed by differential equations, but the boundary conditions are not exactly known or knowable, or the governing equations are not closed (i.e., they depend on other things outside the system).

I recently reread the classic book “Permutation City” by Greg Egan which hinges on the ability to believe that consciousness can be said to exist within a completely deterministic (no true entropy) system.

The book itself is amazing but I’ve been sitting with this idea for awhile now and am becoming increasingly convinced that what we call consciousness might require entropy for us to recognize it as such ... in a way — if we believe that consciousness requires probability, then might we subsequently lose the ability to believe in any state of existence where probability played no role ...?

"Is it that chance and randomness are fundamental aspects of our world, or is it that our knowledge of the world is inherently limited [..]"

Both. The latter is obviously true, and quantum physics tell us that the former is also true.

And the author knows (this in the book):

"Elements of quantum mechanics are also involved, and this allows the author to demonstrate how probabilistic laws are basic to microscopic phenomena."

> and quantum physics tell us that the former is also true.

True is a dangerous word to use in science, since our understanding can always change. What QM tells us is that our best understanding of the world at the micro physical is based on probability. Whether this is actually true of the world is open to interpretation.

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