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MathGroup Archive 2004

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Re: random numbers?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46143] Re: random numbers?
  • From: junk4 at microserf.org.uk (C Rose)
  • Date: Sat, 7 Feb 2004 23:35:59 -0500 (EST)
  • References: <bvvo26$j8l$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi

Your question is not silly at all! I am not an expert in randomness,
but I can probably give a reasonable overview.

Random number are very useful. Random numbers are used in cryptography
(for generating keys), in computer-based scientific experiments (the
application for which I use them) and more trivial things, like
computer games (e.g. a simple betting game based on simulating
throwing a fair die). The 'quality' of the random numbers you require
depends upon the application. In a computer game, we'd probably be
happy with numbers that appear to be random, but might actually be
numbers drawn from a predefined pattern which would eventually repeat.
In scientific experiments, we may be happy with the predefined
sequence, but we'd probably prefer to have much more confidence in the
quality of the randomness (again, the application determines the
required quality). In military-grade cryptography, such simple
approaches could result in messages being decrypted by the 'enemy',
and this could have devastating consequences.

Most computer languages provide random number generators which are
better termed "pseudo-random": this emphasises that the numbers are
not really random, but appear to be. They are typically generated by
an algorithm, and are therefore largely deterministic.

It is possible (though difficult), to generate 'really' random
numbers. Usually, these are not produced via an algorithm, but by
measuring a physical phenomenon that is known to be governed by a
random process. For example, we might time the interval between
emissions of quanta of radiation from a radioactive source (which
follows a Poisson distribution). Such methods are not provided on a
typical computer! There are services on the internet that will provide
you with random numbers generated from such sources. (But if you are
into cryptography, how do you establish that you are not receiving
these from the 'enemy'!)

I have already mentioned the Poisson distribution. This raises the
question of what you mean by randomness. Really, what is meant is that
the source of the random numbers follows a particular distribution
(i.e. uniform distribution, Normal distribution, Poisson distribution,
etc.). Once you have defined the distribution from which you want to
sample, and have a method for generating number that follow that
distribution, you need to be able to compare the two, to verify that
your source is random enough. Here, one can use statistical tests.

I'm not a Mathematica user, but you'll almost certainly find a
pseudo-random number generator that can draw from a number of
distributions. These random numbers will probably be of a high
quality, but they will not be truly random.

Here are some links you may find interesting:

www.random.org/
en.wikipedia.org/wiki/Random
documents.wolfram.com/v5/Built-inFunctions/MathematicalFunctions/RandomNumbers/Random.html


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