randomness in math?

[Guest sinexec]

I came to thinking whether there is such thing as randomness in math. So far, from my studies of math I can only see strictly defined patterns with definite outcomes. For example, take the pseudo random number generation in computer science. Those numbers are nothing but the outcome of many factors taken into the equation.

So, the question is if math is supposed to explain (or come from) the nature, wouldn't this contradict the thermodynamics law of tendency to strive to randomness? Or, if there is nothing random about math, is it fair to say that there is no such thing as occurance by a pure chance in nature?

[bloodhound]

there is such thing as chaos in certain iterations. I am not sure if that qualifies as random. maybe someone else here can elaborate

[Z-space]

Math is completely determinant. Chaos is also determinant but it is not predictable. The only thing that is neither determinant nor predictable is noise. Noise does display certain spectral properties that allows us to classify it, ie white noise, 1/f noise, etc. Noise is ubiquitous, especially in biological systems.

 

IMO, noise functions as a buffer to circumvent the all-out propagation of chaos.

 

As far as "randomness in nature", IMO randomness is likely manifest through noise.

[Aeschylus]

Not all maths is completely deterministic, sattistics is obviously not deterministic. Chaos theory is a just an branch of maths that is detreministic.

 

Noise just means unwanted informatioon in a signal and can be completely dedteriministic. If there's anythg random in nature it's quantum physics.

[NSX]

So' date=' the question is if math is supposed to explain (or come from) the nature, wouldn't this contradict the thermodynamics law of tendency to strive to randomness? Or, if there is nothing random about math, is it fair to say that there is no such thing as occurance by a pure chance in nature?[/quote']

 

Thermodynamics is Physics though right?

 

Physics isn't just Math, and vice-versa.

[Guest sinexec]

Math is completely determinant. Chaos is also determinant but it is not predictable. The only thing that is neither determinant nor predictable is noise. Noise does display certain spectral properties that allows us to classify it' date=' ie white noise, 1/f noise, etc. Noise is ubiquitous, especially in biological systems.

 

IMO, noise functions as a buffer to circumvent the all-out propagation of chaos.

 

As far as "randomness in nature", IMO randomness is likely manifest through noise.[/quote']

In my opinion noise is determinant as well (correct me if I am wrong). As Aeschylus pointed out, noise can be chaotic and your statement itself suggests that chaos is determinant.

 

 

Not all maths is completely deterministic' date=' sattistics is obviously not deterministic.

Noise just means unwanted informatioon in a signal and can be completely dedteriministic. If there's anythg random in nature it's quantum physics.

[/quote']

This seems to revolve back to the question posed here, since statistics is used to describe the occurances of events and the question is whether those events are, in fact, chaotic (predetermined) or random.

Can you elaborate on the randomness in quantum physics?

[Z-space]

sinexec: Noise and chaos are 2 very different things. Noise can not be chaotic. Noise is not determinant.

 

The best way to differentiate noise from chaos is determine the Lyapunov exponent for the function. In practice, this is of limited applicability because usually the function is not known.

[Aeschylus]

sinexec: Noise and chaos are 2 very different things. Noise can not be chaotic. Noise is not determinant.

 

The best way to differentiate noise from chaos is determine the Lyapunov exponent for the function. In practice' date=' this is of limited applicability because usually the function is not known.[/quote']

 

No noise just means unwanted information in a signal it can be completly deterministic and not even chaotic. Noise can either be patterned or random.

[Z-space]

Aeschylus: You are talking about a noisy signal. If you want to talk about a noisy signal, then I absolutely agree with you that a noisy signal can be either completely deterministic or chaotic. The pattern in noise that you mention was also mentioned in my preceeding post (#3 in this thread).

 

In the post #7 in this thread, I am talking about pure noise (ie, no signal mixed in with the noise). Pure noise is a different thing altogether from a noisy signal, and its mathematical properties are also different.

[Aeschylus]

Aeschylus: You are talking about a noisy signal. If you want to talk about a noisy signal' date=' then I absolutely agree with you that a noisy signal can be either completely deterministic or chaotic. The pattern in noise that you mention was also mentioned in my preceeding post (#3 in this thread).

 

In the post #7 in this thread, I am talking about pure noise (ie, no signal mixed in with the noise). Pure noise is a different thing altogether from a noisy signal, and its mathematical properties are also different.[/quote']

 

I've took noice to do with coding, etc. Are you talking about something like a noise sphere??

[Guest sinexec]

Z-space: What exactly are you reffering to as pure noise. What would be the source of that noise?

 

Coming back to a topic of a discussion, can anyone elaborate on the randomness in quantum physics mentioned by Aeschylus earlier?

[Aeschylus]

Z-space: What exactly are you reffering to as pure noise. What would be the source of that noise?

 

Coming back to a topic of a discussion' date=' can anyone elaborate on the randomness in quantum physics mentioned by Aeschylus earlier?[/quote']

 

The collapse of the wavefucntion from a state of superpostion into a single eigenstate is inhererntly random.

[YT2095]

Z-space: What exactly are you reffering to as pure noise. What would be the source of that noise?

a fair question as it REALY does depend on the noise source, ie/ digital shift registers can make pseudo white noise, it`s not a random patern and does re-occur after many thousand steps.

however exploiting breakdown voltage of a P/N junction is pure random as it relies entirely upon part of Eisenbergs uncertainty principal as the electrons cross the depletion zone of this junction. THAT maybe said to be "Pure Random"

[MandrakeRoot]

Do you mean in mathematics or applied math ?

There is a big difference you know.

In math i would say no there is no randomness as every "random variable" is just a measurable function. In statistics or probability theory, properties of these functions are used to show that some estimator or something else converges to what we would like to have.

 

In applied math the situations of the practice are modelled by random variables and this turns out to be very usefull.

So in fact it depends of what you call "random" in "the real life" i guess as to whether or not randomness really exists in "nature" or if it is just a usefull model ?

 

Mandrake