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Hi, again. Random Numbers.


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Am I correct in saying that all existing random number generators work at projecting the next number with no regard to what has been generated previously?

I have an idea for a generator that is wholly unpredictable, non-repeatable, and that implies "randomness" does not exist in reality.  Some very smart people have tried to disabuse me of the idea but none seemed to understand it.  Perhaps I can say it in a more understandable way now.  

 

Edited by cladking
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  • cladking changed the title to Hi, again. Random Numbers.

All methods I've seen make your first statement completely reverse.

They are: number -> do the math -> next number -> do the math -> next number ...

So if you know the current number, and the math, you know what the next number will be. The very first number is called the "seed" and (if unspecified) might be taken from something randomish, like milliseconds since the computer was turned on; back in 8-bit days I saw computers use the refresh register on the Z-80 to give a sort of randomish seed to start with.

In other words, take two separate computers with the same language/library version (e.g. two TRS-80's, or two modern Windows PC's with the same version of C#, ...), start their random number generator with the same seed, and you will get the same sequence of outputs.

If you have a truely random number generator (not relying on some external input), that would be quite impressive.

Edited by pzkpfw
typo
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4 hours ago, cladking said:

Am I correct in saying that all existing random number generators work at projecting the next number with no regard to what has been generated previously?

Most pseudo random number generators maintain an internal state that is many more bits than the output, so the next number is not a function of the prior number returned, but it is very much a function of that internal state and they all will repeat the same numbers after a very long period.

There are true random number generators, but they typically require something more than just software, say a radioactive source or something, which is an example of the external input of which pzkpfw spoke . Radioactive decay is unpredictable, and an example of randomness existing in reality under some interpretations of reality.

 

4 hours ago, cladking said:

I have an idea for a generator that is wholly unpredictable, non-repeatable, and that implies "randomness" does not exist in reality. 

First of all, unpredictable doesn't necessarily imply true randomness. The completely deterministic methods I describe above are essentially unpredictable from a black box point of view.

Given a counterfactual interpretation of reality, if you have a non-repeating generator, that would seem to imply true randomness. Maybe not if it works from some kind of infinite internal state. The nuclear decay thing is entirely unpredictable, but is also entirely deterministic under several interpretations of quantum mechanics. I'd be hard pressed actually to find an interpretation with actual randomness (God playing dice, and Einstein put it). A metaphysical implementation of Copenhagen interpretation perhaps.

 

You put this topic under Computer-Science, which implies an implementation of a non-deterministic function using only completely deterministic software. I don't think so.

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  • 2 weeks later...
On 11/6/2022 at 4:56 PM, Halc said:

Most pseudo random number generators maintain an internal state that is many more bits than the output, so the next number is not a function of the prior number returned, but it is very much a function of that internal state and they all will repeat the same numbers after a very long period.

There are true random number generators, but they typically require something more than just software, say a radioactive source or something, which is an example of the external input of which pzkpfw spoke . Radioactive decay is unpredictable, and an example of randomness existing in reality under some interpretations of reality.

 

First of all, unpredictable doesn't necessarily imply true randomness. The completely deterministic methods I describe above are essentially unpredictable from a black box point of view.

Given a counterfactual interpretation of reality, if you have a non-repeating generator, that would seem to imply true randomness. Maybe not if it works from some kind of infinite internal state. The nuclear decay thing is entirely unpredictable, but is also entirely deterministic under several interpretations of quantum mechanics. I'd be hard pressed actually to find an interpretation with actual randomness (God playing dice, and Einstein put it). A metaphysical implementation of Copenhagen interpretation perhaps.

 

You put this topic under Computer-Science, which implies an implementation of a non-deterministic function using only completely deterministic software. I don't think so.

Thanks for the replies.  

They are very helpful and this one in more understandable to me.  

Apparently, a truly random number generator has little value anyway.  

Let me tell you what I'm thinking.   If my logic is correct then in a large sampling 0's and 1's we would expect half of them to be stand alones, ie-a different number on either side.  25% would be in groups of two, 12.5% in groups of three, 6.25% in groups of four, etc.  On this basis a computer could be programmed to churn out the "right" number in order to make this true.  Of course this could be quickly solved by another computer and duplicated.  But, in reality these %ages would fluctuate chaotically and this could also be programmed into the generator.  

 

To me the implication seems to be that "randomness" doesn't exist in reality and is always only being approximated by nature.  Observation often suggests this "approximation" can be quite poor.  

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On 11/6/2022 at 1:30 PM, pzkpfw said:

 

They are: number -> do the math -> next number -> do the math -> next number ...

So if you know the current number, and the math, you know what the next number will be. The very first number is called the "seed" and (if unspecified) might be taken from something randomish, like milliseconds since the computer was turned on; back in 8-bit days I saw computers use the refresh register on the Z-80 to give a sort of randomish seed to start with.

 

I was not aware of this.  Thanks for the input.  

 

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23 hours ago, cladking said:

If my logic is correct then in a large sampling 0's and 1's we would expect half of them to be stand alones, ie-a different number on either side.  25% would be in groups of two, 12.5% in groups of three, 6.25% in groups of four, etc. 

Yes, but this is true of any simple deterministic pseudo-random number generator as much as anything more real. No special coding is needed to ensure this and said chaotic fluctuations, etc.

 

23 hours ago, cladking said:

To me the implication seems to be that "randomness" doesn't exist in reality and is always only being approximated by nature.

It very much does exist in nature. Quantum mechanics has clearly show that reality is fundamentally probabilistic. It's just that computer architecture doesn't leverage this by design, so true randomness isn't available to the normal code set of a computer, which is instead designed to be entirely deterministic.

So you want a device that generates true random output? Make something that measures the spin of a sample electron. It's 50/50 which way the measurement will go. There is fundamentally no way to predict the outcome. I suppose such a quantum amplifier wouldn't be too hard to put on a chip, and if such a chip were in a computer, it would have access to true random numbers. But as you say, there's very little actual value to that, so it's not been a priority to manufacture such a thing.

Edited by Halc
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On 11/7/2022 at 5:56 AM, Halc said:

Most pseudo random number generators maintain an internal state that is many more bits than the output, so the next number is not a function of the prior number returned, but it is very much a function of that internal state and they all will repeat the same numbers after a very long period.

There are true random number generators, but they typically require something more than just software, say a radioactive source or something, which is an example of the external input of which pzkpfw spoke . Radioactive decay is unpredictable, and an example of randomness existing in reality under some interpretations of reality.

 

First of all, unpredictable doesn't necessarily imply true randomness. The completely deterministic methods I describe above are essentially unpredictable from a black box point of view.

Given a counterfactual interpretation of reality, if you have a non-repeating generator, that would seem to imply true randomness. Maybe not if it works from some kind of infinite internal state. The nuclear decay thing is entirely unpredictable, but is also entirely deterministic under several interpretations of quantum mechanics. I'd be hard pressed actually to find an interpretation with actual randomness (God playing dice, and Einstein put it). A metaphysical implementation of Copenhagen interpretation perhaps.

 

You put this topic under Computer-Science, which implies an implementation of a non-deterministic function using only completely deterministic software. I don't think so.

"First of all, unpredictable doesn't necessarily imply true randomness. The completely deterministic methods I describe above are essentially unpredictable from a black box point of view"

I totally agree with this statement.

We can surely make a number appear to be random simply by making the input to the "random" generator as complex as possible. One simple example would be to use a white noise generator, such as the output of a white light, as the input. We would not be able to predict the output generated, because of complexity, not true randomness. If we had the technology to decode the complexity, we could predict the output with great accuracy.

Unlike some people in this thread, who think there is nothing useful about being able to generate a true random number, I think it would be a great scientific breakthrough to be able to do this. We might even be able to predict the future if we could understand how to decode extreme complexity. However, I am not sure that would be a good thing. Maybe we are better off not knowing the future and believing in non-predeterminism. Once we can generate a true random number, we will lose our illusion of a non-prederterministic existence, and along with that, we will lose our illusion of free will.

Maybe some things are better off just left alone? 

Unfortunately, some mathematical scientists just will not rest until they crack this nut open, and release pandora's box on all of us.

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10 hours ago, OceanBreeze said:

Unlike some people in this thread, who think there is nothing useful about being able to generate a true random number, I think it would be a great scientific breakthrough to be able to do this.

What breakthrough? It's pretty trivial to do. A random bit can be generated by measuring the spin of say an electron. They've been able to do that since over a century ago, long before there was electronic computing. The future fundamentally cannot be predicted, even given say a completely deterministic interpretation of quantum mechanics.

 

10 hours ago, OceanBreeze said:

we will lose our illusion of a non-prederterministic existence

How is the word 'predeterministic' distinct from 'deterministic'? It sound to me like the non-word 'irregardless'.

 

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On 11/23/2022 at 9:04 AM, Halc said:

What breakthrough? It's pretty trivial to do. A random bit can be generated by measuring the spin of say an electron. They've been able to do that since over a century ago, long before there was electronic computing. The future fundamentally cannot be predicted, even given say a completely deterministic interpretation of quantum mechanics.

 

 

 

 

One rule around here is to provide your sources. You say they have been able to generate a (true) random bit for over a century. So provide your source.

I will provide my source that says this"

"Science presupposes causal determinism, meaning it presupposes that any state is completely determined by preceding states. This kind of a system is incompatible with true randomness, which Yohan John herein defines as "the absence of structure or pattern" because the absence of structure or pattern implies that a given state is unaffected by a preceding state, not to mention completely determined by a preceding state.

Even if you could allow a fraction of true randomness within a deterministic system - in the hopes of some sort of compromise - the effects could branch out in unpredictable ways (as discussed below) and the ultimate goal of tracing all effects to their causes would be impossible - resulting in an non-deterministic system. Essentially science would be doomed to a paradox if it admitted to having truly random components."

As a scientist, I tend to agree with what science has to say about this. It may be wrong, but you would have to prove that! True randomness cannot be proven scientifically because it would be paradoxical in a deterministic universe.

 

Quote

How is the word 'predeterministic' distinct from 'deterministic'? It sound to me like the non-word 'irregardless'.

Regardless of what you may think, "predeterminism" and by extension, "predeterministic" are actual words with distinct meanings. Try doing a bit of research before commenting; just a suggestion.

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8 hours ago, OceanBreeze said:

One rule around here is to provide your sources.

This place has rules? I see so little evidence of say moderation. The spammers run rampant on this site, driving away members looking for actual discussions.

Nevertheless, I have no specific reference. Wiki says that radioactivity was discovered somewhere around the turn of the century, and from that you have a source of say free electrons at random intervals. From that you just need to count them, and the least significant bit of that count becomes a random bit. That anybody actually did this (implemented a binary counter say) is quite questionable since there was at the time no call for binary numbers or random ones. Such a device (something that generated one random bit) was a critical component of Schrodinger's cat thought experiment, something not actually built, but one that utilized an instrument that existed at the time.

An actual use case for a true binary random number generator probably didn't occur until say the 70's, a guess. It could be argued that except for philosophical purposes, there is still no need for such a generator today.

8 hours ago, OceanBreeze said:

I will provide my source that says this"

"Science presupposes causal determinism, meaning it presupposes that any state is completely determined by preceding states."

Illustrating why one shouldn't get one's facts from quora, a site with no mechaism to filter correct answers from wrong ones. This poster (who is apparently just some student who in turn does not cite his sources) is very wrong. Science has tried to demonstrate said determinism, but simply cannot. There are some valid interpretations of quantum theory that are deterministic, and some that are not. The chart here lists them. First column indicates which ones are deterministic. If the non-deterministic ones cannot be falsified, then science has not demonstrated determinism. If it presupposes this determinism, it would wrongly cast out valid interpretations that have not been falsified.

Science presupposes as few things as possible. Methodological naturalism is one of them. That presupposition got science out of the dark ages.

Determinism and predictability are different things, as correctly pointed out by your quora guy. For instance, MWI is entirely deterministic, but also entirely unpredictable even given full knowledge of a state of a system. Radioactive decay is one of those 'uncaused' things, so it makes an excellent random number generator.

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Hi Halc, 

First, I would like to answer your questions about moderation on this site, and your question about rules.
Just for your information, Yes this site does have some rules, although only very few, and Yes again, there is moderation, but it is mainly meant to keep the spammers down to a minimum. Most members prefer that the site is lightly moderated, instead of the heavy-handed moderation you may see elsewhere. As for spammers, you, and other members here, can be a great help in keeping the spammers in check by using the Report Function, rather than just complaining about them in the forum.


As for the rules, as I already said, if you are going to state something as a fact, as you did, you are asked to provide your source. This not only preserves your own credibility, but also gives others a chance to research your fact, and maybe learn something new.
As things stand, you did not/could not provide a source, so your “fact” was not a fact at all. As the saying goes, you are entitled to your own opinions, but not your own facts.


Of course, you are free to state your opinion on anything, and as long as you make it clear it is just your opinion, there is no need to provide a source. It is understood that you are the source of your own opinion. That does not mean you will not be challenged to defend said opinion, only that providing a source is optional. Likewise, you are free to disagree with opinions expressed by others, but you cannot demand they provide a source, although it is always best if everyone can cite a source as the basis for their opinion.


If and when you do disagree with anything posted here you need to do better than just attack them or their source, as you attacked Quora. It would be much better if you can provide a counter argument, rather than a personal or impersonal attack.


That is about it as far as rules go. I think they are logical and quite mild and easy to follow, compared to some other sites which are much stricter. You will find that the moderation here is fairly laid back, with very few warnings or suspensions given, with the exception of spammers.
OK, enough about rules and moderation!


Returning to the subject of generating a “true” random number, the source I quoted hardly comes across as a “student” unless perhaps someone who is pursuing an advanced degree. He makes perfect sense in stating that it would be a paradox for a universe that is scientifically deterministic, to contain anything that is truly random. We know the universe is scientifically deterministic since we can trace events back to about 380,000 years post-big bang, by looking at the cosmic microwave background radiation. With the new James Webb telescope, we should be able to look back as far as perhaps 100 million years after the big bang, easily finding examples of the first galaxies theorized to have taken shape about 400 million years into the universe's existence. Source: https://www.popularmechanics.com/space/deep-space/a9632/how-close-to-the-big-bang-can-we-see-16105099/

This all goes to show that cause and effect are fundamental principles of the universe we know. 


On the other hand, there is no possible "scientific proof of randomness" of anything. It is fundamentally impossible to scientifically prove that something is "fundamentally random". 


The fact is, atoms still must follow physical laws. It is my opinion that I reject anything in this universe, as being truly random, including radioactive decay, and such is only an assumption and not a scientific fact. If I were to accept true randomness as a fact, that would be an abandonment of science, because science is the study of the reason things are the way they are in nature, and everything in nature points to cause and effect. A truly random event would basically destroy our science of cause and effect because we have run into something that just happens for absolutely no reason at all.


Consider an electron's motion around a nucleus. Is it a truly random event? According to the Copenhagen interpretation of the wave function, we can only consider the probabilities about whether an electron is at a specific location or not. However even these probabilities obey a deterministic law, known as the Schrodinger equation, which is a fact.


 I will state my opinion: Anything can be classified as random until an explanation is found that determines that event. In closing, again in my opinion, an inability to predict is not the same as proof of randomness.

 

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20 hours ago, OceanBreeze said:

As for the rules, as I already said, if you are going to state something as a fact, as you did, you are asked to provide your source.

OK, then my assertion that randomness has been observed for at least a century is apparently mere opinion, as is alternatively that quantum theory, as unintuitive and non-classical as it is, was actually proposed a century ago without any actual evidence at the time. The evidence perhaps only was observed far more recently, verifying what was until then pure conjecture.

As for the quora thing, I did not base my denial of the quote on the reputation of the site nor on the qualifications of the author. I based it on a reference to quantum interpretations list which explicitly list several valid interpretations that deny determinism. So the claim that "Science presupposes causal determinism, meaning it presupposes that any state is completely determined by preceding states." has been shown to be incorrect.

20 hours ago, OceanBreeze said:

He makes perfect sense in stating that it would be a paradox for a universe that is scientifically deterministic, to contain anything that is truly random.

MWI is a good example of an interpretation that is scientifically deterministic that nevertheless generates true random numbers, all without paradox.

20 hours ago, OceanBreeze said:

We know the universe is scientifically deterministic since we can trace events back to about 380,000 years post-big bang, by looking at the cosmic microwave background radiation. With the new James Webb telescope, we should be able to look back as far as perhaps 100 million years after the big bang, easily finding examples of the first galaxies theorized to have taken shape about 400 million years into the universe's existence.

Not to discredit the statement, but I'd like to point out that some sites will not accept pop articles as evidence. The writers often get facts wrong. I'm not disagreeing with the article, but since the CMB (noticed over 50 years ago, no link to back claim) is 'further back' than the 100 million years that JWST is observing, so JWST doesn't seem to be looking any closer to the big bang than has already been observed.

Your linked article does not make the claim that our ability to look back to the CMB is in any way evidence that our universe is scientifically deterministic. Perhaps the term needs definition, since I don't know the distinction between that and just 'deterministic'. It has been laboratory quantum experiments, not telescopes, that give evidence one way or the other on this debate. They have, BTW, done interesting quantum experiments with telescopes.

 

20 hours ago, OceanBreeze said:

On the other hand, there is no possible "scientific proof of randomness" of anything.

Agree, but a weak statement since in general there's very little scientific proof of almost anything. Science is in the business of making good predictions, not of proving things. So to reword, "there's no conclusive evidence of randomness or lack of it".

20 hours ago, OceanBreeze said:

It is my opinion that I reject anything in this universe, as being truly random, including radioactive decay, and such is only an assumption and not a scientific fact.

OK. I can say that your opinion narrows down the number of QM interpretations that you will accept. Notably, Copenhagen is unacceptable.

20 hours ago, OceanBreeze said:

Consider an electron's motion around a nucleus. Is it a truly random event?

It has not been demonstrated that there is such a thing as an electron's motion around a nucleus. The phrase is a counterfactual one, and counterfactuality is another column on the list of valid interpretations. Most do not assume the principle of counterfactual definiteness, so if you do, your list of interpretations drops to Bohmian mechanics and a few more obscure ones. The former has some effect occurring before their cause, something else which you seem to find distasteful since you're big on linear causality. But Bell proved that you can't have both classical causality (cause before effect) and counterfactuality (a system being in a specific state even unobserved). You seem to have very classical opinions, but it has been shown that physics cannot be described by classical laws.

20 hours ago, OceanBreeze said:

According to the Copenhagen interpretation of the wave function, we can only consider the probabilities about whether an electron is at a specific location or not.

Per the link I gave in the prior post, no. According to the Copenhagen, we can only consider the probabilities about where an electron will be measured, not about where it is between measurements. I can't think of an interpretation that would suggests it having an actual location expressed as a probability. Bohmian mechanics says it has a location, and the wavefunction probability is just an expression resulting from our lack of knowledge of that one location, not that it might in fact be elsewhere.

20 hours ago, OceanBreeze said:

In closing, again in my opinion, an inability to predict is not the same as proof of randomness.

That seems to not be in need of being opinion. It's pretty trivial to prove that statement.

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Halc said "It has not been demonstrated that there is such a thing as an electron's motion around a nucleus"

Link: Researchers coaxed an electron to orbit an atomic nucleus like a tiny planet.

I don't see any point in continuing this discussion, so I am dropping out, but the thread remains open for others to  waste their time on.

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