Re: Re: Creating a Random Function to Select an Irrational

• To: mathgroup at smc.vnet.net
• Subject: [mg102251] Re: [mg102239] Re: Creating a Random Function to Select an Irrational
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Mon, 3 Aug 2009 05:44:31 -0400 (EDT)
• References: <h50sss\$743\$1@smc.vnet.net> <200908021000.GAA01660@smc.vnet.net>

```There is no need  for Wolfram to create any RandomIrrational because
for all effective purposes it already exists. You can generate
generate a random real between 0 and one with an arbitrarily large
number of digits, e.g. try

RandomReal[{0, 1}, WorkingPrecision -> 1000]

This is as good a way of generating irrationals as you can wish for
and they are uniformly distributed. As I and others have pointed out,
your original request makes no sense, as there is no such thing as a
random number, there are only random sequences with a specified
distribution. (Well, there are also numbers with "random digits", but
these are essentially just random sequences of integers (digits)).

Andrzej Kozlowski

On 2 Aug 2009, at 19:00, BenT wrote:

> I want to thank everyone who replied and who I've otherwise replied to
> privately. The problem solutions offered were as interesting, to me,
> as he problem definitions <g>.
>
> The randomness of the irrational set of numbers is not really the
> emphasis, but having a virtural set of infinite length is, for them,
> to be used as "seeds" for the RealDigits' function to convert them to
> any number base from 2 thru 12 (for music scales) of any length (for
> music melodies) for use in algorithmic musical compostion. Hopefully I
> can constrain the results sufficiently with "arbitrary" rules to make
> such melodies as "tonal" (or not) as desirable.
>
> Wolfram Research might consider creating a new function called perhaps
> "RandomIrrational" the uses from none to three parameters, (1) if
> none, it would return an irrational number between 0 and 1 exclusive;
> (2) if one (an integer only greater than 1), then it would return an
> irrational number from 1 to that integer exclusive; and (3) if 2, then
> it would return an irrational number between the two integers
> exclusive, and finally (4) if 3 oarameters are included, it would be
> like number (2) except that it would be specific to the definition
> used to create it (as from those defined on the webpage mentioned.
>

```

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