Random Number Questions

[PopeBeanieModerator]

Firstly, context matters, just as context colors one’s view of “infinity”. Even the definition of a “random sample” of manufactured products from an assembly line can vary depending on product, just because different manufacturing situations call for different priorities and are based on documented history and experience. “Noise” is random, yes, but hey… by definition! I.e. even noise is ultimately caused by previous events that could probably (…oops, I threw in a constructed-by-humans-weasel-word there) ultimately be traced back to the causes of those events.

Like infinity, the question is, to what extent does one seek a supposedly “final” answer before deciding when possible outcomes are random or infinite. Yeah, infinite monkeys could type out War and Peace eventually, but the problem is that it’d take an infinite number of universes created and destroyed before War and Peace actually occurred, and what if no human was even there to see it at the right time and place?! I.e., the hypothetical possibility of the event occurring is practically meaningless, other than in a fantasy that will never even matter.

As a naive, armchair-amateur-sorta-scientific-pseudo-scientist, I suspect that even quantum level randomness may one day be discovered to be non-random, or if it’s not, it’s only because there wasn’t enough infinite time in our particular universe to figure it out.

OMG, did someone mention free will again?! Jeez, how predictable!

[MattParticipant]

1) Is ANYTHING truly random? Or does randomness mean nothing more (or less) than unpredictability?

Does it matter? What matters to me (typically in cryptography) is that the entropy source is unpredictable. So for all intents and purposes, unpredictable is “random enough”.

2) My friend declares he’s invented a random number generator.

2a) Is a random number generator an oxymoron?

See answer to question 1 above. If the random number generator sources it’s entropy from an unpredictable source, it’s output will be unpredictable, and thus we consider it to be random.

2b) The machine generates a series of 9’s and has been doing nothing but 9’s for days. After how many 9’s can it be concluded that something is wrong with his machine?

You can’t tell whether a random number generator is truly random by looking solely at it’s output. The only way to know if those 9s are truly random is track them back to the entropy source. If the entropy source is suitably random, the machine is inevitably random.

Remember, to believe that what came before in a random series has any influence on future random outcomes is called The Gambler’s Fallacy.

I think I’ve avoided this issue with my answer, correct?

Given a truly random system, is a continual series of one number an impossible outcome?

No, just unlikely.

and given that mathematically infinite series are not just possible but inevitable, surely an ongoing series of 9’s is one such possible series, is it not?

Yes, but that doesn’t mean that the series is or is not random. The fact that we have only seen 9s being output would be fairly suspect.

 

EDIT: In response to some of the other comments regarding using signal noise as an entropy source: In computers, when generating a “strong” random number we typically use a multitude of entropy sources… things like the length of time between key strokes, movements of the mouse, CPU timings, network timings, and other such unpredictable sources.

• This reply was modified 6 years, 7 months ago by  Matt. Reason: Add extra detail about entropy sources in computers

[_Robert_Participant]

Unseen wrote:

_Robert_ wrote:

Thermal noise and background radio signal noise are very much random signals.

What does that mean? How can anyone know that? Or are we back to “as far as we’ll ever know…”?

It means that if you have a wide-band receiver that is very sensitive you will receive background radiation which is very random, especially if you filter out all periodic signals. Sample (digitize) this and you have a random source of numbers. Remember when the TV stations went off air and you got snow…that is very much a random signal.

Simply beyond our current ability to predict the next number. However, even with these types of signals, you can still make general predictions about their frequency content, etc.

• This reply was modified 6 years, 7 months ago by  _Robert_.

[UnseenParticipant]

_Robert_ wrote:

…if you have a wide-band receiver that is very sensitive you will receive background radiation which is very random, especially if you filter out all periodic signals. Sample (digitize) this and you have a random source of numbers. Remember when the TV stations went off air and you got snow…that is very much a random signal.

You didn’t answer my question: How do we know that the noise is random? Or does is it random in terms of mimick the “randomness” of a random number generator?

• This reply was modified 6 years, 7 months ago by  Unseen.
• This reply was modified 6 years, 7 months ago by  Unseen.

[Reg the Fronkey FarmerModerator]

The “background radiation” signal originates from about 380K years after the Big Bang. It is called the CBMR or very short length radio wave. It was discovered by accident by Bell Labs in the sixties. The Television reference is from back in the days of analogue when the stations went of the air and your aerial then picked up the signal. A small percentage of the static “snow” on the screen is from the afterglow of the Big Bang.

We have no way to influence this so if we were to convert these microwaves to somehow generate a number or if we were to count the “snowflakes” on a screen at a specific time we would get a random number?

Note: If my use of the word “snowflake” above triggered an emotional reaction in some people then take a few deep breaths.

[_Robert_Participant]

Unseen wrote:

_Robert_ wrote:

…if you have a wide-band receiver that is very sensitive you will receive background radiation which is very random, especially if you filter out all periodic signals. Sample (digitize) this and you have a random source of numbers. Remember when the TV stations went off air and you got snow…that is very much a random signal.

You didn’t answer my question: How do we know that the noise is random? Or does is it random in terms of mimick the “randomness” of a random number generator?

You have it backwards. A random number generator is algorithmic in nature, so there is a process or equation involved. It is predictable if you know the process.  It emulates noise, and usually that is enough to be useful. True noise has no predictor available that leads to statistically meaningful results.

[StregaModerator]

@drbob the moderators are me, Reg and Pope.  You were welcome at TA and also welcome here.   I expect we will get around to updating the rules at some stage.   The most basic rule is , “don’t be a dick”. The one you might bump into occasionally is , “don’t preach your gospel here”.   Guided by those, you should be ok!

[NoelParticipant]

This thread is way over my pay grade but, (who said that anything before the word “But” is superfluous?), I can now see that when playing chess on my Kasparov electronic chess board the moves are not random depending on the time I allot. The board will be given a set time to make a move (that time is set by me in the form of “what level do you want to play” where level 1 the board has very little time to check each move and pick the best one or levels 2 through 10 where it has a ton of time to pick the best move.)

From what I’m reading here nothing is ever truly random. Events need a beginning and that start, push, shove, bang, what ever… sets things in motion and removes the randomness?

Reading is fundemental…LOL

[DrBobParticipant]

Unseen wrote:

I should last a little longer.

Glad to hear it, mate.  You had me concerned for a moment there.  Take care of yourself, and have fun at the new job.

Bob

 

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