Can Deterministic Computers Truly Generate Chaos?

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Discussion Overview

The discussion centers on whether deterministic computers can generate chaos or true randomness. Participants explore the implications of chaos theory, the nature of randomness, and the limitations of computer-generated outputs in relation to these concepts.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants argue that a deterministic computer can create chaos if it models equations sensitive to initial conditions, leading to unpredictable outcomes despite deterministic inputs.
  • Others assert that any randomness generated by a computer is pseudorandom, as it can be replicated by an algorithm, and true randomness requires external inputs.
  • A participant mentions that chaos theory is fundamentally deterministic and distinct from true randomness, emphasizing that chaotic systems can yield unpredictable results from deterministic processes.
  • There is a suggestion that true randomness may only be achievable through external environmental factors, such as electronic noise or human input, rather than solely through computer algorithms.
  • Some participants discuss the use of chaotic algorithms in modeling chaotic systems, indicating that computers can simulate chaos but may not generate true randomness independently.
  • One participant highlights the distinction between randomness generated by a computer alone versus randomness derived from external sources, suggesting that practical applications often rely on the latter.

Areas of Agreement / Disagreement

Participants express differing views on the ability of computers to generate chaos and true randomness. While some agree that computers can simulate chaotic behavior, there is no consensus on whether they can produce true randomness without external inputs.

Contextual Notes

Participants note the limitations of deterministic systems in representing instantaneous chaos and the challenges in defining true randomness, indicating that definitions may vary significantly across discussions.

MathematicalPhysicist
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can a computer (determnistic) create chaos (disorder)? if it can be done how can it be done?
 
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I think so, if say the equation it's modeling is very sensitive to input parameters. If a change in a varible of say one part in a billion causes a large change in output, then the equation is chaotic, but every time you input the EXACT same input as a previous time, you will get the same anwser, so it is deterministic too.
 
No.

Any random data generated by a computer is known as pseudorandom, data that has the characteristics of random data but that was created (and can be exactly recreated by) an algorithm.

The computer could sample information from the environment (CPU temperature or fan speed would be fairly easy to get) and that would be truly random. For it to be useable you’d probably need to process it a bit first though.
 
nevermind

I've changed my mind, I agree with MisterBig, it's impossible for a computer to have random output without random input. True randomness is impossible to recreate. I don't know how I explicitly stated that a computer will come up with the same anwser in a "chaotic" equation if the inputs are EXACTLY the same without seeing the flaw in my logic.
 
One complication here is the use of the word "Chaos".

The mathematical theory of chaos (taking it's name from Yorke's paper "Period Three Implies Chaos") is deterministic, not random.

In a sense it's the opposite of the "Central Limit Theorem".

We've all seen the demonstration where if you drop a large number of marbles (or shot) onto a grid so that each one goes left or right a number of times and then the "pile" comes right up to a pre-drawn curve. In other words, a sequence of purely random events can give a pre-determined result.

"Chaos" (again, technical, mathematical meaning) refers to a purely deterministic process that is so sensitive to "initial conditions" that it is impossible to predict the results.

Simple example: given xn, double it. If the result is larger than 1, drop the integer part: xn+1= (2 xn) modulo 1.

One can show that two intial values arbitrarily close together can rapidly give completely unrelated values.
 
that's what I was saying

That's what I meant, but I now question how chaotic something really is if it is repeatable. Now I've contradicted myself ... asprin! ... asprin! ...
 
Any basic inquiry into what chaos theory is would teach you that, as HallsOfIvy pointed out, chaos is entirely a study of deterministic systems. It has nothing to do with "true randomness," which is an entirely different topic.

- Warren
 
then let's rephrase the question can computer create randomness?
 
Actually, it wouldn't hurt to define 'chaos' or 'randomness'. I personally don't think 'true randomness' is possible unless acausal is involved, in principle.

Of course computer can create chaos. See http://www.isp.nwu.edu/~rocky/Pendulum/QuintuplePendulum.html
It can compute trajectory that is chaotic. But there's no way to determine what caused it given trajectory alone.

How do you define 'randomness'? There are many definitions. For eg. infinite period before repitition begins. Its enough to calculate Pi infinitely to produce randomness. For eg. maximum information density. Then generate white noise.
 
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  • #10
Most people in the "biz" call chaos theory, "Nonlinear Dynamics" these days. It's a little more accurate and doesn't have the who baggage where people think chaos = random.
 
  • #11
And the answer to "can a computer generate true random numbers?" is quite unequivocally NO.

- Warren
 
  • #12
They actually manufacture electronic noise generator circuits that you can hook up to a computer to generate random bit patterns, so that you will have true random input. Not a very common piece of computer hardware though.
 
  • #13
The discrete nature of an electronic digital computer precludes in general its representing instantaneous chaos. A quantum computer, being linear, cannot fully reproduce fractal patterns. Careless superfast computer architecture can induce, on small-scale, nonlinear resonances analogous to those on the grid of the Great Blackout in 1960's New York.
 
  • #14
of course a computer can generate chaos, I remebr well in my first year of university that we inpute chaotic algorithms into the computers in the lab to model chaotic systems.

Modern day computers cannot generate true randomness, though I beleivethere is a device (maybe it's still in the developmental stage) which uses the probabiltistic nature of QM to generate truly random numbers,
 
  • #15
When you seek for true randomness in computers, you need to ask if what you mean is randomness generated by computer alone, or with help of external environment. Thats crucial distinction, as for practical purposes, 'true' randomness is needed and taken from environment. But computer alone cannot generate 'true' randomness.

To get truly random numbers, many comps are using human keyboard input as initial conditions in chaotic algorithm. Like every time you type something, comp measures time between keystrokes and randomness depends on that heavily. Thats about simplest way to get randomness form environment.

In addition, thermal conditions affect frequency of operation abit, and if computer has 2 independent clocks, minute differences between them are independent on environment alone. The only task is to amplify these tiny changes by chaotic algorithm into randomness.
 
  • #16
Computers and Random Numbers

The answer to the question, can computers create random numbers? Of course depends on the inputs to create the numbers. If no input(ie a pseudo random number generator) then no*. If the input is random then yes. Intel therefore have created the Intel Random Number Generator on their chips to create what should be truly random numbers.
http://apps.intel.com/scripts-util/download.asp?url=/design/security/rng/techbrief.pdf&title=The+Intel+Random+Number+Generator&fullpg=3&site=Developer
Very useful if you are encrypting data.
Some encryption products like PGP get inputs from keyboard and mouse use. These provide non-deterministic input to help create random numbers.

Duncan


* If you define random numbers as being non-deterministic.
 
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