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Mathmeticians, Computer Scientists, Physics dudes - What is random?


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So I was thinking in the shower this afternoon about random number generation in programming (I do all my best thinking in the shower - your mind wanders)...

... and how random number functions in a wide range of languages aren't actually random. All the memory-resident functions that I know of make calls to a timed register from with the CPU (think it's the CPU, could be something higher level; I'm a high-level programmer, I don't care past the compiler/linker)... point is, it's not really random, it's the last few digits of a clock somewhere.

In fact, the "non-randomness" of computer's random numbers is a big issue. As computation ability and speed of computing increases, that non-randomness can be addressed and taken advantage of (and already has in deeper computing) - it ends up causing deterministic issues in stuff like cryptography, that requires true randomness, for example... I remember reading about the problem of psuedo-randomness. It's enough of an issue that I've heard of encryption techniques that rely on digitized and then serialized photos of a specific instance of the wax in a lava lamp to provide random numbers...

... but that specific instance isn't even random either. It's a function of the inherently Chaotic (i.e. non-random) system of non-linear Fluid Thermodynamics.

So my question is two-fold. One, is there any branch of mathematics, physical systems, or computer systems that is capable of generating true random numbers?

Two, assuming the above is negative, and the fact that mathematics and physics generally define our world (Fractal systems (M-sets, Julia sets, etc) found in nature; Chaos systems in weather, fluid dynamics, bifurication population dynamics, etc).... does this mean that the universe is inherently not random, since true randomness is unnatural?

Taking a step back, I guess what I'm asking is if the absence of true randomness in the universe answers the question of determinism vs. free will.

(postscript: If everything is the predetermined function of an overall system, how can we capitlize on this, a la Asimov's science of Psycho-History?)

Sorry to be so heady on a Friday night. It was just kinda bugging me today.
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You bring up some good ideas. Although the mathematics you talk about are beyond me, I can understand the questions you raise.

Regarding your second question. I don't think that mathematics and physics define our world. Although we can explain some natural phenomena in mathematical terms and concepts, I don't believe nature operates on mathematical priciples. I've always believed that nature is the outcome of some random events in an organized fashion. For example all the chemical reactions in our bodies occur as random chance reactions, but result in organized entities such as molecules, cells, organs, and the body. I think what I'm trying to say is that random events that make up our world, depend on other random events that happened immediately before in time, or adjacent in space. For example, air temperature in a certain location depends on what the temperature was just a second ago, what the temperature of the air is immediatelly next to that location in space. Maybe not a good example, but the idea is that random events in conjunction with other random events somehow emerge as nonrandom.


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Probably the most interesting / heady subject that's been posted here in a while. Will give this some thought before responding.

RE: question 1, 416 is in crypto so might be a good person to ask about that. I think mathematically "perfect randomness" might be eschewed for non-reproducibility. I.E. Even if a producing "randomness" relies upon some ordered system to be generated, if the sequence generated can't be exactly reproduced, it is for practical security purposes random. And the question just becomes what is set as the cut off for acceptable non-reproducibility. That cut off being moved depending on how "necessary" it is to the intended application.


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Deus: I'm afraid the examples you give can be analyzed extensively with mathematics... they're called feedback-return systems, and figure heavily in biological mathematics (see 'The Game of Life' and the Nash Equilibrium). Biology and chemistry are not random, and in fact is the antithesis of randomness - there is a distinct and all-pervasive system of cause and effect. This is why the science of medicine exists.

Deep: you're seeing the forest for the trees. The cryptography reference was an example of our experience with true randomness, not an example of why I'm looking for true randomess. Creating an emulation of randomness by defining 'as good as' limits for 'good enough' randomess is merely academic, and doesn't get to the root cause of my search for true randomness that can be objectively proven. So, from what I know of past and current crypto, a practical cryptologist will not be able to answer my question, because the entire science relies on the 'good enough' randomness. But he may have more information on if true randomness actually exists, which would put me at ease and make question #2 moot and invalid.

Please hurry with your reply, it's actually starting to worry me, the more I think about it.


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I did a lot of work in cryptography and computer simulation work (more academic and less in application than 416, which probably makes me useless, but...). I'll post some shit in here when it isn't 4:15AM and what not.
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Operating systems such as Windows and *nix use a mix of user input events and other types of random events to input entropy to a software random number generator. This generates pretty close to purely random data. But from a security prespective it's comming from events which can be monitored and/or corrupted in memory and that sort of random data can't be used for most applications which require more "deterministic" behaviour.

Many cpu's, especially the variety of system-on-chip integrated cpus available these days, use special hardware entropy genenerators which output truely random data. Think of two people playing catch, throwing a ball back and forth, at light speed, and after a few microseconds in computer land, there is no way to say who has the ball. The randomness comes from the random variations in the physcial components. Things like atm machines and video lottery machines use that sort of thing.

If the universe was, at the most fundemental level, deterministic, it would require a minimum technology of equal size and complexity to simulate it. So scince that's impossible, there is no way ever to make the universe deterministic.

Like the game "The Sims" - it's a simple universe based on rules, but for a sim in the game to determine it's future, it would have to make a computer and another SIM game, like we'd have to make another universe to determine our future.


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I had a huge, like, mega-huge reply for you. Then I realized all that I was doing was relating computers and random number generation to quantum theory, which you probably already know or at least have heard about. It's funny but thinking about things on a quantum level can actually help calm your worries about large-scale behaviour! :) Just think: even you are nothing but the most likely arrangements of your own mass/energy!


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Quantum Mechanics only works on the Quantum scale.... which is why the movie 'What the Bleep Do We Know' is just a recruiting film for the TM crowd, and has no scientific basis.

This was the main issue I had with the determinism vs. free will vignette in Waking Life, when the talking head offered a counter-proposal that Quantum Theory can help us figure out free will.

However... if the universe is deterministic, the quantum computing may allow us to build systems that can reconstruct our complete universe at a smaller scale and help predict what's to come.

But I'm calming down a bit... I'm starting to think maybe I am in control of my life, once again.


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Shug said:
Taking a step back, I guess what I'm asking is if the absence of true randomness in the universe answers the question of determinism vs. free will.


even if purely random events occurred at a non-quantum level, it would not resolve the issue of free will. ie. if objects randomly popped up at random, what effect does that have on free will? if our thoughts were random, would that mean that our will was free?

imho, the whole debate is "barking down the wrong path". we're free whether our thoughts are random or pre-determined. it's our definition of "free will" that's out of whack.
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Trancedental Meditation. The film was funded by a TM cult out of Oregon, who's leader is 'Ramtha', that blond chick with the effed up voice in the movie. All the scientists in that movie are involved in the cult except one (the harvard philo/physics professor), and they editted the 3 hour interview they had with him to further their ideals. In fact, he later claimed that he told them at great length why their version of Quantum Theory wasn't correct, but they disregarded it and cut up his lecture to suit their needs.

And Liquidity, you need to drill down into what I'm asking to see how it relates. If there is a system or series of systems that govern everything in the universe with no random input, then this conceivably robs us of free will. Because regardless of how individualistic and unique you think your thoughts are, what you perceive as "you" is nothing more than an extremely complex combination of electricity, biomechanics, and basic chemistry - all of which are subject to those same systems and rules.


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In a practical sense, randomness is simply something we cannot predetermine. Mathematical algorithms, and therefore, computer programs designed to generate random numbers adhere to this definition and only generate numbers as random as the seed value fed to them. This requirement brought into existence such systems that monitor lava lamps and 'mouse-click-entropy' in order to gather sufficiently unpredictable seed values. The ability to predict or to determine a past state of something like a lava-lamp's pixel signature to a digital webcam is a problem so intractible to humans that barring any weaknesses in the random number generation algorithm itself, the number created may as well be random.

In regards to determinism/free will, the same concept will apply depending on what you believe. If you believe that at some level all things are explicitly causable, and that there are no things (except the prime mover) in the universe that can cause things while being uncaused, then randomness is indeed an illusion and therefore to an oracle free will would be readily dismissable.
On the other hand, if you believe that there are things that can cause without being caused (ie: God), then randomness is a possibility however the randomness is bound by the actions of these uncaused entities who may even choose to act in a completely predictable manner. This still, of course, doesn't bode very well for free will until you consider that we don't have an oracle, would probably be unable to operate one if we did, and probably will never be able to build one due to Heisenberg. Since we, and probably nobody else will be able to measure the cosmic chain of events leading up to you eating that booger you are picking while reading this post the notion that your action is determined is not useful for anything other than a thought exercise and for all intents and purposes your will is free.