I Do you have an example of a truly random phenomenon?

[Baluncore]

− so far, no competent math or science guy or gal to whom I've described the notion has to me decried the idea as in any way not ok.

An XOR is a product detector, so you will have built a correlation receiver that will detect cross channel interference. Where can I find Cosmic Microwave Background free from interference? Would it not be better to throw out the dishes and just terminate the antenna leads in hot resistors with Johnson noise?

What are the “SETI filters”? Presumably you take raw data and remove signals, effectively maximising entropy of the data set. The result will not have recognisable patterns, but it will contain patterns you did not consider in the filters. In effect, you are reading the tea leaves.

That ignores the fact that real random noise contains short sequences of recognisable patterns. If you remove those patterns you have coloured the data, and the result is guaranteed NOT random.

For all we know, extraterrestrials maximise channel utilisation and correct all errors by communicating efficiently in what we see as random noise.

 

[sysprog]

@Baluncore, I recognize that XOR gates can be employed (e.g.) in phase detectors, but I had in mind single gate modulo-2 binary addition of two different signal sets for purpose of co-masking to produce a 3rd signal set that I supposed would not exhibit regularities that were present in either of the two original signal sets. Do you think that this notion is in error?

 

[Baluncore]

... for purpose of co-masking to produce a 3rd signal that I supposed would not exhibit regularities that were present in either of the two original signal sets. Do you think that this notion is in error?

Yes.
Fundamentally it is a product detector that will lift any common signal out of the noise. It will also place harmonics of both signals into the resulting noise floor.

Wide-band radio astronomy receivers, that digitise the signal with a comparator to one bit, are gain independent, and use XOR gates to correlate signals in shift registers with changing lags. Spread spectrum systems use XOR gates to modulate and demodulate the signals. They also use them as correlators in the PLL to lock the spreading code clock rate.

An XOR gate is not different to a broad-band frequency mixer. Where A, B and Z are the probabilities of boolean signals being high, the XOR statistics arithmetic is as follows;
Z = A*(1-B) + (1-A)*B
That is the same as a frequency mixer.

XOR and XNOR are really the same. Note that if you have a “Random” bit stream, and pass it through an inverter, it becomes NOT “Random”. You must watch out for these word games.

 

[sysprog]

XOR and XNOR are really the same.

I'm confident that you well know that XOR means one or the other is true, but not both, whereas XNOR (IFF) means either both are true, or neither is true $-$ they're similar; in that one is the inverse of the other, but they're not what I would call "really the same".

Note that if you have a “Random” bit stream, and pass it through an inverter, it becomes NOT “Random”.

How would changing all the 1s to 0s and all the 0s to 1s make a bit stream less random?

You must watch out for these word games.

Yes.

 

[sophiecentaur]

How would changing all the 1s to 0s and all the 0s to 1s make a bit stream less random?

+1. Modulation (which is what's happening, basically) can't alter randomness.

 

[Baluncore]

I'm confident that you well know that XOR means one or the other is true, but not both, whereas XNOR (IFF) means either both are true, or neither is true − they're similar; in that one is the inverse of the other, but they're not what I would call "really the same".

NOT(XOR) = NXOR = XNOR; which is just another word game.
Randomness is independent of signal polarity.
The power spectrum is independent of signal polarity.
Minimising entropy is independent of signal polarity.
The vast majority of signals are independent of polarity.
Does a telephone conversation sound different if the twisted pair has the mate and colour swapped ?

 

[gmax137]

Does a telephone conversation sound different if the twisted pair has the mate and colour swapped ?

Rhetorical question?

 

[sbrothy]

To quote an answer from a more knowledgeable person than myself on the topic, given to me from a question I posed as, "Can you generate a random number from a machine?"

Not sure that's all relevant, or that I can support the assertion, but that is the mostly complete answer. He seemed to be aware of something similar vis a vis white noise generators for randomness.

I want to also reiterate that I believe radioactive decay is considered stochastic (random?) at the individual atomic level. From the wikipedia on radioactive decay, we can see there are some applied methods that work from the premise that radioactive decay is random:from: https://en.wikipedia.org/wiki/Radioactive_decay

I seem to remember some programs using noise from GPUs (how the audio [EDIT: Yeh ok, bad word] was captured I can't seem to remember...) to seed random number generators. Theoretically at least, one could use the noise from a *NIX HDD shredding data and base your numbers on that.

I admittedly didn't read your entire thread though. If I know you guys just superficially you probably already descended into some black hole entropy theory or something, where, as normally you couldn't get out, I wouldn't be able to get in in the first place. :)

Regards.

Stumbled across this, admittedly a little dated, reference:

Quantum Random Number Generators

Although I think skimmed enough to understand that quantum randomness wasn't really the subject.

 

[sysprog]

Rhetorical question?

Presumably ;-)

 

[Art G]

What if all information CANNOT be known? For example, pi. Then a truly random number would be the decimal value that is just past the knowable value of pi.

 

[Nugatory]

the decimal value that is just past the knowable value of pi.

There is no such thing as "just past the knowable value of pi". The problem is that for any rational number greater than $\pi$ there exists another smaller rational number also greater than $\pi$ (thus even closer to $\pi$).

 

[sysprog]

There is no such thing as "just past the knowable value of pi". The problem is that for any rational number greater than $\pi$ there exists another smaller rational number also greater than $\pi$ (thus even closer to $\pi$).

Can we generalize this a bit more? e.g. 'for any real number that is greater than another real number $x$, there exists another lesser real number that is also greater than $x$ (wherefore such a lesser exceeding (greater than) $x$ real number is closer to $x$)' $\dots$

 

[gentzen]

What if all information CANNOT be known? For example, pi. Then a truly random number would be the decimal value that is just past the knowable value of pi.

For pi, all information actually can be known. But let us evaluate your conclusion instead for Chaitin's constant. In that case, all information cannot be known. Does that mean that its digits are truly random numbers? It is known that they actually pass any mathematical test for being uniformly distributed and independent (just as good as truly random numbers). So it will be hard to refute your claim mathematically.

But can you give positive arguments for your claim, and explain why we should accept those digits as truly random numbers?

 

[sophiecentaur]

For example, pi.

For pi, all information actually can be known.

Two different 'experimenters' can calculate the nth digit in pi and they will get the same answer. There's nothing random about that. I can't imagine that 'nearly random' is a very meaningful term. But Mathematicians may say otherwise - as they do about the various levels of Infinity.

 

[bland]

Wouldn't a high coin toss in a turbulent air flow effectively be truly random for all practical purposes?

 

[Dale]

Wouldn't a high coin toss in a turbulent air flow effectively be truly random for all practical purposes?

Yes, but put the word “truly” in there and suddenly nothing qualifies. That isn’t unique to randomness.

 

[bland]

@Dale,

OK, I got led to an apparently 'related thread', and this quote by @Vanadium 50 ...

1. What is the difference between "random" and "truly random"? (And truly truly random, and truly truly truly random, etc.)
2. What measurement would convince you that one or the other is correct?

Well not sure if I'm being asked the same question in a different way, but what I meant, by 'truly' was a randomness without any qualification for example a radioactive decay event. As opposed to some other not 'in principle' randomness but just as good for all practical purposes.

So regarding the thread topic, I am asking the question would a coin toss into a chaotic turbulent air flow be considered as random as which path a photon would take on a 50/50 semi reflecting mirror. Or would it be considered solvable 'in principle' like the way an ordinary coin toss is said to be not random if you knew everything there was to know, blah blah and so forth.

This is a question.

 

[Nik_2213]

Bit faults in RAM due to 'cosmic rays' and back-ground radiation as an example of 'random detections' ?

With proviso that cosmic ray flux is modulated by solar cycle, while Radon flux may vary with atmospheric pressure and water table height...

 

[Automaticsteam]

I mean that if we had all of the data we could have on the phenomena, then even theoretically it will still be random.

The primary random order of the universe.

 

[wrobel]

"

Do you have an example of a truly random phenomenon?​

"

do you have an example of a truly right triangle?

 

[Automaticsteam]

I mean that if we had all of the data we could have on the phenomena, then even theortically it will still be random.

I have real trouble with the format of this discussion board. Nonetheless, on the grandest scale the universe is random, random as the expansion and creation of new synapses and thought paths in the brain with new, especially original thought. At the inception of a seemingly intentional thought, was the thought to carry out, or even conceive of the intent, random? Is photon distribution in the Slit Experiment, random? So in the random but contained expansion of the universe, there is order universally in universal randomness. Yin & Yang, I reckon. Like it's getting to the philosophy of science/physics.

Mu

 

[George Keeling]

I have real trouble with the format of this discussion board.

I love the format of this 'discussion board'. It's briliiant.

 

[berkeman]

Like it's getting to the philosophy of science/physics.

And in a random act of kindness, this long thread is now done. Thanks everybody for your contributions.