Randomn Numbers

[Jadzia]

I thought this was interesting when I read it this morning.

http://www.nature.com/news/2010/100414/full/news.2010.181.html

When it comes to unpredictable strings of numbers, some are more random than others. Until now there has been no way to confirm 'true' randomness, leaving encryption techniques that rely on random strings vulnerable. But physicists have now generated the first string of verifiably random numbers — a feat that could help to shore up security.

I've often felt that randomness is a strange and subtle phenomenon, because so many things in life we say are random, when it is more correct to say they are deterministic yet chaotic processes, such as the tumbling of a dice. And when you think about that for a short time, you realise that a dice is not random, and neither is the lottery. They are both chaotic though.

So could this machine they've built be one of the first injections of truely random numbers into our world, and is that anything special in the grand scheme of things?

Now is choice is really distinguishable from randomness? Are they different things at all, when it comes down to it?

Wouldn't it be good if we could somehow test human choice, to see if we are capable of true randomness also? Do we have free-will? Or are we deterministic?

 

[sojourner]

Isn't "proving" something is random inherently disproving said randomness? Think about it.

 

[Jadzia]

It is said that one can't analyze a given sequence of numbers and deduce that they have been randomly generated.

There is always the possibility that our sequence was generated by a sufficiently complex deterministic process that we're blind to. In fact, Issac Newton's divided differences shows how one can replicate any finite number sequence through a single polynomial interpolator.

In the article above (which I don't fully understand because it's complicated QM), they appear to be looking at the generator rather than the number sequences. The generator appears to be reliant on quantum uncertainty (eg, entanglement of photons going through two different paths), and then showing that the output is not classical because they can statistically estimate the level of correlation between entangled particles, and see it is beyond what is possible in classical mechanics.

So it's not proving that the output is random, but it is proving that it is non classical. We infer that it is randomness insofar as quantum uncertainty is uncertain.

...or something like that

 

[Robert Maxwell]

I think it's safe to say even "quantum uncertainty" isn't truly random, it's just too complex for us to figure out so far. If we ever find a way around the uncertainty principle, look out.

 

[PurpleBuddha]

I think it's safe to say even "quantum uncertainty" isn't truly random, it's just too complex for us to figure out so far. If we ever find a way around the uncertainty principle, look out.

My gut wants to agree with you, but why do you think it is safe to say such a thing? I would think to confidently make that claim as you have, you would need to have something pretty compelling to back it up. And perhaps you do. If so, please share, because I am in a learning mood.

 

[Jadzia]

I think it's safe to say even "quantum uncertainty" isn't truly random

If you believe that there is no randomness, then is it your opinion that free will doesn't exist either?

Because I believe that randomness and free will do exist, and that they are in fact the same thing. I don't think that classical processes can be responsible for either.

 

[Robert Maxwell]

I think it's safe to say even "quantum uncertainty" isn't truly random, it's just too complex for us to figure out so far. If we ever find a way around the uncertainty principle, look out.

My gut wants to agree with you, but why do you think it is safe to say such a thing? I would think to confidently make that claim as you have, you would need to have something pretty compelling to back it up. And perhaps you do. If so, please share, because I am in a learning mood.

What reason is there to believe it is random? We see plenty of determinism in nature. The only reason science works at all is because it is predictable and consistent. Quantum physics is a relatively new field and our understanding of it is still quite limited.

How can you truly test whether the universe is random or not? Say we started over from scratch and reset the universe to the Big Bang. Would it unfold the same way it did this time? If so, then there is no genuine randomness in the universe--however, there is no way to test that unless we have a spare copy of our universe somewhere.

I would say any randomness in the universe is more pseudorandom rather than truly random: it is based on the original "seed", the original state of the universe. In short, I am not convinced that particles behave randomly (or more accurately, probabalistically) at the quantum level, but that we have failed to find a means of accurately predicting their behavior.

I think it's safe to say even "quantum uncertainty" isn't truly random

If you believe that there is no randomness, then is it your opinion that free will doesn't exist either?

Because I believe that randomness and free will do exist, and that they are in fact the same thing. I don't think that classical processes can be responsible for either.

You have free will to the extent that you can consider your options, decide on one, and execute it. However, all else being equal, you will make the same choice every time assuming the surrounding universe remains unchanged. Decisions are made on the basis of the information at hand--if the information you have is identical each time you encounter the same decision point, you will always make the same decision.

Taking a very simple example, suppose we have two universes that are, at this moment, identical. They have evolved along identical paths. You exist in both. This morning, you are driving to work and encounter a piece of debris in the road. Is there any reason to believe you would veer left around it in one universe, and veer right in the other? You are the exact same person in both universes, with the same upbringing, same history, same personality, with the same information available at the decision point: you must swerve to avoid the obstacle, so which way will you go? It makes very little sense at all that you should make a different decision in the other universe.

From our own point-of-view, we do have free will: we're the ones making the decisions about our lives. However, if you step back and look at all the things that make you who you are, it is not hard to imagine that the decisions you make are really the result of everything that came before. You cannot make a different decision at the same decision point unless something else was in different in your past. And if something else was different, what was it? How far back do you have to go to find a divergence point, if there is no true randomness in the universe?

What I find curious is that people would equate free will ("I can make my own decisions") with being arbitrary ("given the same situation, I might make a different decision"). All things being equal, I do not see how anyone could make a different decision than they did the first, second, or nth time.

 

[Jadzia]

I have a thought experiment for you.

If you believe in the big bang, then you believe that the universe expanded from an infinitely dense point.

A point is isotropic, so the universe that expanded from that would have been perfectly symmetric.

Every point would be exactly the same as every other point, so there is no opportunity for that universe to break symmetry and condense it's uniform energy into particles.

There are two ways out:

(1) The universe didn't expand from an infinitely dense point.
(2) Randomness is what allowed the universe to break its initial symmetry.

 

[Chaos Descending]

I'm under the impression that current scientific opinion is that the universe didn't expand from a perfectly isotropic point. It's possible, of course, that I simply didn't understand what I was taught, though.

 

[Robert Maxwell]

I have a thought experiment for you.

If you believe in the big bang, then you believe that the universe expanded from an infinitely dense point.

A point is isotropic, so the universe that expanded from that would have been perfectly symmetric.

Every point would be exactly the same as every other point, so there is no opportunity for that universe to break symmetry and condense it's uniform energy into particles.

There are two ways out:

(1) The universe didn't expand from an infinitely dense point.
(2) Randomness is what allowed the universe to break its initial symmetry.

Why is randomness required to explain the differentiation of matter following the Big Bang? You have what is essentially an explosion, which is chaotic to be sure, but not random. The interactions of particles during that explosion allowed fusion into heavier elements--differentiation. Over time, these interactions continued until matter accreted into galaxies, stars, and planets. I do not argue that it is not a long and chaotic process, however I think given sufficient time, intelligence, and brain capacity, it would be possible for a thinking being to predict the current state of the universe knowing nothing other than the initial state of the matter immediately preceding the Big Bang, assuming also that they knew the nature and mechanics of the Big Bang itself down to the particle level. Obviously, no human will ever achieve that, and since the universe is continually evolving, we cannot develop a comprehensive model to predict its behavior. We can predict behavior at a localized level under controlled conditions, but we can't, for instance, accurately predict weather activity far in advance--or even at a moment's notice, in many occasions.

I do not think this is evidence of randomness emergent from quantum properties, but rather a lack of information on our part. Whether this information is actually attainable (that is, we can find a way around the uncertainty principle) remains to be seen.

Quantum behavior is only considered random because we currently find it unpredictable with absolute certainty. That is not the same as it being genuinely random, meaning it is arbitrary and there is no mechanism controlling outcomes.

 

[Lindley]

No, I see what Jadzia is getting at there. In order for chaos to be sufficient to explain all that heterogeneous development, you need to assume some nonuniformity in the starting conditions. Otherwise, no matter how much matter expanded, it would remain of uniform density. In order for two particles to cluster, they must move in opposite relative directions (towards each other), but that wouldn't happen if the distribution of mass around them were identical.

If you assume that at some point the universe was point-like, then you can't assume any nonuniformity, which means randomness is the only way things could start to cluster and differentiate.

Hmm. If the universe was a point of infinite density, then it would somewhat resemble a black hole. Except that it wouldn't occupy space since space wouldn't yet exist.....still, the fact that matter could ever escape from such a situation is curious. It begs the question of what would happen if you somehow accelerated the expansion of space in and around a black hole, rather than trying to overcome its gravity directly.

 

[Jadzia]

I've got another thought experiment, which is a little more interesting.

Imagine two particles (red and blue) that are positioned like this:

The experiment is completely symmetric along the horizontal axis.

The closer the particles are together, the higher their energy state. (imagine that the particles are both positively charged) As they are now, they are in a relatively high energy state.

Should one particle move across to the adjacent/free corner, so that the particles are in diagonally opposite corners, that would be the lowest energy state, and is the preferred arrangement. Should both particles move to the adjacent/free corner, then that would be worse than the situation they are in they are now.

Now since the experiment is symmetric, and if we assume deterministic, then both particles must make the same decision. If they choose to communicate, they will both be asking the same questions or giving the same commands, and at the same time. So either both move simultaneously or both stay still.

Logically, they would both choose to stay still, unable to break symmetry they would be unable to find the low energy state.

But this is game theory isn't it? It's very reminiscent of the prisoner's dilemma.


There is an optimal strategy to winning this game. And that is for each particle to make a random choice: 50% chance I stay still, 50% chance I move to the adjacent/free corner.

I find this quite startling, that in some problems, randomness can be a more successful strategy than if decisions are made logically.

 

[Robert Maxwell]

In a deterministic universe, all that matters is the initial momentum of the particles. Since particles are always moving, neither one will stay put. Given a 2D space, they would move along their initial vectors, interacting if they're close enough to do so.

What makes the lower energy state the "preferred" arrangement? I don't think I understand the premise of your argument.

The Big Bang works just fine even if the initial mass is undifferentiated, because we don't know the nature of the Bang itself. It would have imbued momentum into every particle involved, and depending on whether it was perfectly centered or its energy evenly distributed, it is conceivable that the particles interacted as a consequence of that.

Particles coming together, fusing into heavier elements, accreting into stars and planets--I see no reason why you need randomness to explain this. It comes off to me as an easy out. There are too many particles in the universe for us to predict the behavior of all of them, so we don't even try, and call it random.

What if the uncertainty principle only reveals physical limitations in our ability to observe quantum phenomena, and we're mistaking that for randomness since we can only deal in probabilities at that level?

 

[Jadzia]

In a deterministic universe, all that matters is the initial momentum of the particles.

Before that... how do the particles form in the first place if the expanding energy field is completely uniform? Why should a particle form here and not there? If here and there are identical, then particles must form in both places or neither.

Since everywhere is the same as here and there, then particles must form everywhere simultaneously (which is meaningless) or nowhere at all (which is what would happen)... unless there is a random factor at work.

Particles coming together, fusing into heavier elements, accreting into stars and planets--I see no reason why you need randomness to explain this.

Once there is non-uniformity, randomness is not needed. Chaos will turn a small non-uniformity into a greater one. So planets and galaxies do not need randomness. Non-uniform matter will swirl together and coagulate according to deterministic laws.

What makes the lower energy state the "preferred" arrangement? I don't think I understand the premise of your argument.

Sorry I forget to add that.. imagine that they are both electrically charged particles, so there is a potential energy associated with their proximity.

 

[Robert Maxwell]

In a deterministic universe, all that matters is the initial momentum of the particles.

Before that... how do the particles form in the first place if the expanding energy field is completely uniform? Why should a particle form here and not there? If here and there are identical, then particles would form nowhere at all... unless there is a random factor at work.

But now you're talking about particle generation! I do not claim to know how that happened, only that we had a bunch of particles to start with, and they went "boom!" and gave rise to the universe we have now.

Particles coming together, fusing into heavier elements, accreting into stars and planets--I see no reason why you need randomness to explain this.

Once there is non-uniformity, randomness is not needed. Chaos will turn a small non-uniformity into a greater one. So planets and galaxies do not need randomness. Non-uniform matter will swirl together and coagulate according to deterministic laws.

I agree there.

What makes the lower energy state the "preferred" arrangement? I don't think I understand the premise of your argument.

Sorry I forget to add that.. imagine that the particles repel each other, so there is a potential energy associated with their proximity.

You could've just said they had opposite charges.

 

[ProtoAvatar]

Robert Maxwell

If you want to equate quantum mechanics with classical mechanics via some 'hidden variables' you'll have to do more than just negate Heisenberg's uncertainty; you'll have to do away with superposition (a particle being in ALL its possible states simultaneosly until it's measured), entanglement, virtual particles and a few other "minor phenomena".
All of this while respecting the experimental evidence.

Until now, you just made the claim and failed to back it up at all. Well, let's see your proofs.

 

[Lindley]

I find this quite startling, that in some problems, randomness can be a more successful strategy than if decisions are made logically.

That's a well-known principle of computer science algorithms, actually.

 

[Defiant]

Wheeler delayed-choice pretty much establishes there is an absolute limit to what we can know about the position and momentum of a particle. Heisenberg wins absolutely.

It's clear that the closer you try to measure p, x becomes completely unpredictable.

You can measure randomness by the actual measurement of entropy. In information theory there is a mathematical definition for entropy. Read this paper:
http://cybersolutions.mantech.com/library/Sliding%20Window%20Measurement%20for%20File%20Type%20Identification.pdf

You can see that information entropy (as the article that started this thread was really about) can be reduced to a measurement of the compressability (through an algorithm such as NZW). Repetitive strings will eventually make sudden decreases in entropy - a signal.

I have recently been wondering if these sorts of information entropy analysis tools could be applied to DNA to determine if the "junk" is really "junk," or if there are definite signals within the extra stuff. The test of removing "junk" DNA and checking to see if the organism works the same is a bit like the old experiment which led to the (mis)conception that people only needed 10% of their brains - the experiment involved chickens and whether or not they still ran around after you scrape out bits of their brains.

As for free will, I found a fascinating bit in Andrew Glassner's "Principles of Digital Image Sythesis" back when I designed graphics systems for IBM. A retinal cell, which is just a neuron with a photo-sensitive dendrite in essence, can be studied by itself (removed from a retina). According to Glassner, a neuron exposed to a single photon of the same energy will release 0 to 3 pulses along the axon - and no one knows why. Glassner doesn't really go into the point (the mechanism behind it is not relevant to human vision, which is what he was exploring), but I find it very instructive.

There is some quantum-mechanical effect at work in neurons. When you can take the same neuron, expose it to the same single photon, and have it have 4 different possible responses there's some randomness there. Of course, you can argue that they overlooked some other initial condition, but ultimately every test of QM has shown that these types of oddity are not simply a lack of measurement of all of the initial conditions, but rather a complete inability to ever know all of the initial condiitions.

I suggest that even if you went back in time to run the exact same QM experiment a second time (measure P instead of X) you would not break through the Bell inequality problem. QM places firm limits on knowledge - which means randomness and disorder will always rule at the very small scale (and work their way into the very large scale).

I wrote a thought experiment on this some time back here:
http://schrodingersgrandfather.blogspot.com/2009_10_01_archive.html

You can't beat Heisenberg...

 

[Jadzia]

I often wonder if the synapses between neurons add some quantum mechanical effect. Synapses seem like strange and suspect things to me, if it is as we're told just binary logic from one brain cell to the next. If the neurotransmitters are too much or too few, the brain doesn't work right. This suggests to me that a signal can be transmitted with too much certainty, or too little certainty, which wouldn't be simple binary logic.

So perhaps the synapse allows a signal to be both transmitted and not transmitted, causing a neuron input to be both triggered and not triggered.

 

[Asbo Zaprudder]

Re: Random Numbers

I often wonder if the synapses between neurons add some quantum mechanical effect. Synapses seem like strange and suspect things to me, if it is as we're told just binary logic from one brain cell to the next. If the neurotransmitters are too much or too few, the brain doesn't work right. This suggests to me that a signal can be transmitted with too much certainty, or too little certainty, which wouldn't be simple binary logic.

So perhaps the synapse allows a signal to be both transmitted and not transmitted, causing a neuron input to be both triggered and not triggered.

This is an active research field, see for example,
Mind, Matter and Quantum Mechanics by Henry Stapp, and:

http://www.qedcorp.com/pcr/pcr/mmqguide.html
http://www.dontveter.com/caipfaq/systems.html

Personally, I believe that Penrose may be on the right track in his hypothesis that microtubules play a role in creating consciousness. I don't agree, however, that this precludes the possibility of creating an AI -- it just makes it more technologically difficult.