Randomness

[exchemist]

I would say an event is random if there is no way to predict the outcome of that specific event given previous events.

I am more than willing to have the *probabilities* and *averages* be predictable. Hence, a coin flip *could* be random.

If it is simply very difficult to predict, but possible, I would consider it chaotic rather than random. Either way could have predictable averages, though.

Ah OK. So if I had restricted myself to the lack of predictability of individual events, that would have been OK, would it?

And what about the other aspect of randomness, in which we do not consider events separated in time but a spatial distribution? I presume a lack of any order would mean it is random. I'm thinking here of something like the difference between a glass and a crystalline solid for instance - though arguably the arrangement of a glass is not truly random, as there will be a limited range of interatomic distances and so forth. Perhaps the motion of smoke particles in Brownian motion is a better example.

 

[Polymath257]

Ah OK. So if I had restricted myself to the lack of predictability of individual events, that would have been OK, would it?

And what about the other aspect of randomness, in which we do not consider events separated in time but a spatial distribution? I presume a lack of any order would mean it is random. I'm thinking here of something like the difference between a glass and a crystalline solid for instance - though arguably the arrangement of a glass is not truly random, as there will be a limited range of interatomic distances and so forth. Perhaps the motion of smoke particles in Brownian motion is a better example.

The concept certainly generalizes. For example, if you didn't know one particular molecule in a crystal, you could predict where it would be. For a glass, or even more so for a Brownian motion, even such predictability is lacking. But, yet, averages (density, etc) are still available.

So, something is random if, knowing everything else in the system, it is still impossible to predict that variable.

 

[ecco]

Put a bunch of hydrogen atoms in a box with a bunch of oxygen atoms and some will combine to create molecules of water.

• Which specific atoms bind to each other is random (unpredictable).
• The manner in which they bind to each other is completely known and not at all random.
• The fact that they bind to each other is not an accident.

 

[Bob the Unbeliever]

Properly speaking, the 'random numbers' generated by computers are called 'pseudo-random' for exactly this reason. It is very, very difficult to produce high quality pseudo-random numbers. Most fail badly with simple statistical tests.

Yep. I was part of a 17 year project in computing, and we required random numbers for some of our calculations.

We were using compiled BASIC (with a numerical library to take full advantage of the numerical co-processor...yes, that's how old this was. 1981. )

The BASIC library had a RND function-- but was absolutely repeatable, if you didn't re-seed the RND function. The description explained how to re-seed the calculation. Obviously, it was simply a complex mathematical equation, and selected a section of the answer for the "random number".

My favorite solution to this? I build it into the start-up library that initialized all the shared data files the programs used (they would run each other, to create a seamless whole, but each was independent in a way. Data/variable values were shared via binary files).

Intel computers used an interesting clock: the number of miliseconds counting forward, from 1978. At least that is what my memory recalls. It may have been earlier? Some year in the 1970's, for sure. That was ZERO for the CPU. The number increased with each clock-tick. These ran at 4.77 kiloherz, if memory serves. So you knew the correct "time" by reading this upwards-counting register.

Since this number was always different, every time the CPU was initialized? Even if you did not set the clock to the current time, the odds of getting the exact same number was pretty slim... so I'd pull the time of day, and using that, I'd query the raw data from the time-register-- the time of day selected which section of the raw number I'd use (if I remember, it was a 16 digit long integer) Then, I'd feed that into the RND function as a new seed.

A Kludge? Absolutely! But not terrible as Random Numbers go, due to using miliseconds, even if then computer booted at 8 am every day, and the time wasn't set, there'd be a minor variation of the milisecond value from day to day...

 

[Revoltingest]

In the book, the main character kind of lost her non-belief after having experienced her travels to far and distant lands-- and back again.

She, being something of a celebrity (post-trip) had both leisure time and funding, to dabble in Interesting Questions: She queried a very powerful computer system to look for non-random patterns in the endlessly long chain of the number Pi.

in the book, at least, the computer found patterns, using various different BASE (i.e. base 10, base 16, etc) and the pattern was always a BMP picture of a circle.

BMP is a photographic format that is not compressed, and it is therefore possible to figure out what the picture is from the string of numbers, using logic (and perhaps a bit of trial-and-error not unlike assembling a jigsaw puzzle).

In the book Sagan (the author) expressed this "easter egg", (c.f. video gaming) as a kind of Cosmic Joke from the Creator of the Universe-- at least the main character did.

Many critics of the book found that ironic, that Sagan being an out-and-out atheist in a time where such things were Dangerous to one's livelihood, would write such a thing in his novel.

Me? I saw it as a kind of message to theists: THIS would be one possible piece of evidence in support of Deism. In direct contrast to bronze age books purporting to be "evidence".

I rather liked the whole thing myself, and I agree with Sagan: it would take such a piece of Evidence to be realistically convincing that the universe had at least a nominal "designer".

Sagan explored wide ranging ideas.
For him to imagine something which would
go against atheism makes perfect sense.

 

[Bob the Unbeliever]

I am old enough to have had a debate with a friend on whether analog or digital computers would be more useful.....the answer was probably already there when I had that discussion, but I didn't know it.

In theory, Analog Computer would have the potential to store many-many times the raw information that a Digigal one ever could.

Think: You could get a whole music album (roughly 40-45 minutes of uncompressed information) onto a fairly short cassette tape. But, to store the same length in digital form? (if uncompressed), you'd need about 300-400 megabytes of digital memory. The information density of analog is always many times that of digital.

But. And it's a BIG but: What is the quality of retrieval between the two formats?

With digital, if you include strong error correction? You can expect 100% perfection, every time, until the media is destroyed.

With analog? How do you tell if the information has degraded? How do you separate the noise from data?

Analog works very well, if the media is high quality: Using an actual violin, and a master musician, you can get prefect recall of the information (a piece of sheet music). Or not-- is there noise in the room? Is the violin slightly out of tune? Etc.

Analog also works, if the information has a high tolerance of "sloppy", i.e. audio music-- humans are very good at filtering noise.

Bottom line: Digital is much-much easier to differentiate nose from information.

For example: if you store the information as electrical pulses? Say, you define ZERO as negative 5 volts, and ONE as positive 5 volts, and further define each value as plus or minus 4 volts? Any value between +1v and +9v, is a ONE, and any value between -1v and -9v is a ZERO and all other values are noise: discard.

To increase the reliability? You can add in commands to re-send corrupted data, as needed. This is exactly how the very chaotic internet functions: It has many error-correcting engines built right in. Multiple ID values is one (adding redundancy), the ability to request a re-send of corrupted data is another. Tags which indicate a mathematical formalization of the data packet (as good are corrupt), to trigger a re-send, etc.

How would you do this using Analog? Not easy: just ask Dolby Labs.

 

[JoshuaTree]

The concept certainly generalizes. For example, if you didn't know one particular molecule in a crystal, you could predict where it would be. For a glass, or even more so for a Brownian motion, even such predictability is lacking. But, yet, averages (density, etc) are still available.

So, something is random if, knowing everything else in the system, it is still impossible to predict that variable.

Black holes?

 

[Bob the Unbeliever]

Sagan explored wide ranging ideas.
For him to imagine something which would
go against atheism makes perfect sense.

Indeed. Sagan was quite fond of posing "what if" scenarios even on his TV show.

 

[Revoltingest]

Indeed. Sagan was quite fond of posing "what if" scenarios even on his TV show.

Wasn't he on The Big Bang Theory?

 

[Bob the Unbeliever]

Black holes?

If the modern models of black holes are accurate?

The atoms within the singularity, experience a full stoppage of time-- that is, time within the event horizon, does not flow forward with respect to the rest of the universe.

So, in a way, it ought to be theoretically possible to discover the position and state of every single particle within a given black hole.

How to cross the event horizon with your information intact, is left as an exercise for the student. Perhaps you could piggy-back on the emission of infra-red radiation that all black holes emit? (C.f. Professor Hawking's lecture on the subject of leaking black holes)

 

[Bob the Unbeliever]

Wasn't he on The Big Bang Theory?

Sagan? I don't remember. Stephen Hawking was.

Okay: Big Bang Theory, TV show, began in 2007.

Sagan died back in 1996. As far as I know, he did not travel into the future...

So definitively, no.

 

[Bob the Unbeliever]

... Perhaps the motion of smoke particles in Brownian motion is a better example.

Or the water molecules in a really hot cuppa tea.

Into which you could insert a finite improbability generator...

... in an effort to create an infinite improbability generator (which assumes that such a generator being constructed is not infinitely improbable).

Heart Of Gold, anyone?

 

[Polymath257]

Yep. I was part of a 17 year project in computing, and we required random numbers for some of our calculations.

We were using compiled BASIC (with a numerical library to take full advantage of the numerical co-processor...yes, that's how old this was. 1981. )

The BASIC library had a RND function-- but was absolutely repeatable, if you didn't re-seed the RND function. The description explained how to re-seed the calculation. Obviously, it was simply a complex mathematical equation, and selected a section of the answer for the "random number".

My favorite solution to this? I build it into the start-up library that initialized all the shared data files the programs used (they would run each other, to create a seamless whole, but each was independent in a way. Data/variable values were shared via binary files).

Intel computers used an interesting clock: the number of miliseconds counting forward, from 1978. At least that is what my memory recalls. It may have been earlier? Some year in the 1970's, for sure. That was ZERO for the CPU. The number increased with each clock-tick. These ran at 4.77 kiloherz, if memory serves. So you knew the correct "time" by reading this upwards-counting register.

Since this number was always different, every time the CPU was initialized? Even if you did not set the clock to the current time, the odds of getting the exact same number was pretty slim... so I'd pull the time of day, and using that, I'd query the raw data from the time-register-- the time of day selected which section of the raw number I'd use (if I remember, it was a 16 digit long integer) Then, I'd feed that into the RND function as a new seed.

A Kludge? Absolutely! But not terrible as Random Numbers go, due to using miliseconds, even if then computer booted at 8 am every day, and the time wasn't set, there'd be a minor variation of the milisecond value from day to day...

The problem is that even if initialized well, the algorithm itself is pretty poor at giving good random numbers. If you map the results in a high enough dimensional space, you see clear gaps. And I'm not talking high dimension...something like 6.

 

[Revoltingest]

Sagan? I don't remember. Stephen Hawking was.

Okay: Big Bang Theory, TV show, began in 2007.

Sagan died back in 1996. As far as I know, he did not travel into the future...

So definitively, no.

I should warn people when I'm joking.
Maybe it's cuz I have a cold, & am tired from lack of sleep.
Yes...that's it....I'll blame my incompetence on that.

 

[Polymath257]

Black holes?

Depends on the nature of quantum gravity. For big ones, not so much.

 

[Polymath257]

Or the water molecules in a really hot cuppa tea.

Into which you could insert a finite improbability generator...

... in an effort to create an infinite improbability generator (which assumes that such a generator being constructed is not infinitely improbable).

Heart Of Gold, anyone?

Just throw yourself at the ground....and miss.

 

[JoshuaTree]

If the modern models of black holes are accurate?

The atoms within the singularity, experience a full stoppage of time-- that is, time within the event horizon, does not flow forward with respect to the rest of the universe.

So, in a way, it ought to be theoretically possible to discover the position and state of every single particle within a given black hole.

How to cross the event horizon with your information intact, is left as an exercise for the student. Perhaps you could piggy-back on the emission of infra-red radiation that all black holes emit? (C.f. Professor Hawking's lecture on the subject of leaking black holes)

Reading about black hole entropy... pulls cork...

 

[Bob the Unbeliever]

The problem is that even if initialized well, the algorithm itself is pretty poor at giving good random numbers. If you map the results in a high enough dimensional space, you see clear gaps. And I'm not talking high dimension...something like 6.

Oh, absolutely agree! It was, at best, a Kludge.

I remember back in the 8th grade (math club) we were tasked to create a quality random number generator, with a very limited budget. Preferably electronic.

Several of us worked through some of the mechanics of using actual dice coded with magnetic "signature" as to which value landed down (on a magnetic sensor). A mechanical "jumper" would bounce the dice in it's enclosure. Of course-- we could not be certain of a perfectly even balance on the dice, especially as we had seeded it with tiny magnets....

The winner? A simple frequency counter (using NIXIE tubes to display the number), connected to a tunable FM receiver ... and the human element: A capture button.

You struck the button-- the audio frequency of the inter-station HISS was captured for an instant (well-- a very brief interval) and displayed via the NIXIE tubes on the frequency counter.

It worked pretty well, until too many FM stations were brought on line in the city, and you couldn't find sufficient quality non-content hiss...

 

[JoshuaTree]

Oh, absolutely agree! It was, at best, a Kludge.

I remember back in the 8th grade (math club) we were tasked to create a quality random number generator, with a very limited budget. Preferably electronic.

Several of us worked through some of the mechanics of using actual dice coded with magnetic "signature" as to which value landed down (on a magnetic sensor). A mechanical "jumper" would bounce the dice in it's enclosure. Of course-- we could not be certain of a perfectly even balance on the dice, especially as we had seeded it with tiny magnets....

The winner? A simple frequency counter (using NIXIE tubes to display the number), connected to a tunable FM receiver ... and the human element: A capture button.

You struck the button-- the audio frequency of the inter-station HISS was captured for an instant (well-- a very brief interval) and displayed via the NIXIE tubes on the frequency counter.

It worked pretty well, until too many FM stations were brought on line in the city, and you couldn't find sufficient quality non-content hiss...

You were in math club before FM???

 

[shunyadragon]

The concept of randomness comes up pretty frequently in our discussions. In particular, I have seen frequent complaints concerning the development of order out of 'randomness'. This shows up in discussion of evolution (mutations being random), quantum mechanics (quantum events being random), and cosmology (matter interacting randomly).

Often, randomness is conflated with 'accidental' and contrasted with 'intelligently produced'.

I'd like a discussion/debate about the meaning of randomness, its role in our beliefs, the contrast with causality, the issue of 'accident', and the role of 'intelligence' as opposed to 'randomness'.

Random is probably the most misused word in the English language. True randomness likely does not exist, because of the assumptions of the definition of random, and the fact that is mainly a layman's term. Fractal relationships described by chaos theory describes most variable cause and effect outcome relationships where there are many variables like weather prediction, genetic mutation patterns.

In radiation decay and Quantum Mechanics it is the individual events that are not predictable, and the processes themselves follow predictive pattern. Randomness is just a poor term to describe the relationship of cause and effect outcomes in these cases.

More to follow . . .