To create a real random number,

[shaxper]

let

random number = q * r
where q = an irrational number, r = a rational number

Create q and r via any statistical technique to choose two primes, p1, p2

r = p2
q = pi * p2
where pi = 3.14... out (p1) places

real random number = q * r = pi * p2

[mfgoode]

Originally Posted by shaxper

let

random number = q * r
where q = an irrational number, r = a rational number

Create q and r via any statistical technique to choose two primes, p1, p2

r = p2
q = pi * p2
where pi = 3.14... out (p1) places

real random number = q * r = pi * p2

Maybe shaxper you could win.
I reproduce a probem in The Sunday Times of India today from 'MINDSPORT'
Editor Mukul Sharma

" I wish to decode a set of 100 pseudo-random numbers of two digits 01 to 99 which have been placed in a sequence. Could your column provide some help? A reward of Rs.10,000 (rupees ten thousand will paid to the winner)
Please guide me as to how I could get the the series decoded."
G.B. Goya Sr Mgr, BHEL,
gbgoyal@bhelhwr.co.in

Mally
P.S. I am in no way responsibe for the reward promised.

[ColdFury]

Would these numbers be uniformally distributed?

I don't think this method would work too well on a computer since you cannot truely represent an irrational method on a computer.

Besides, if you can generate random primes, can't you generate random numbers already?

[shaxper]

Hey Makul,

Thanks for the encouragement. :)

BTW, further thought on the problem suggested that both numbers (q,r) should be irrational. Here's a better scheme, based on the same concept.


----------------------------------------------------------

To create a "random number," let

a, b = irrational numbers, constants (like pi, e, c, or sqrt(2))

Create, via two different statistical techniques, two "random" primes, p1, p2

q1 = p1 * a
q2 = p2 * b
where a = constant out to (p1) places, b = constant out to (p2) places

For example, let

a = 3.14, pi out to 2 places
b = 1.414, sqrt(2) out to 3 places

then

q1 * q2 = (p1 * a) * (p2 * b) = (2 * 3.14) * (3 * 1.414) = 26.63976

It seems to me that finding the two primes (2,3) in the number 26.63976 would be very difficult if you didn't know the two schemes for creating p1 and p2 along with the two irrational constants. (And even more difficult if you invert the second constant so that a > 1, b < 1.)

Any thoughts anybody?

>Would these numbers be uniformally distributed?

No. I don't think there is such a thing as truly random, i.e. no order at all. Therefore, the next best thing is creating a number that hides the order.

>I don't think this method would work too well on a computer
>since you cannot truely represent an irrational method on a
>computer.

Actually, that's the beauty of this scheme because the irrational number is represented out to a finite number (p1, p2) of digits.

>Besides, if you can generate random primes, can't you
>generate random numbers already?

There's no such thing as random, so the primes you generate aren't "really" random and, therefore, neither would the numbers that this scheme generates. But, hopefully -- and this is where my knowledge falls short -- this scheme hides the order better then currently existing statistical techniques.

cheers,
jad

[cheesehead]

I recommend Art of Computer Programming, Volume 2: Seminumerical Algorithms by Donald E, Knuth -- Chapter 3 covers random and pseudorandom numbers.

This book and its companion volumes 1 and 3 are worth getting for one's library.

From http://www-cs-faculty.stanford.edu/~knuth/taocp.html:
"At the end of 1999, these books were named among the best twelve scientific monographs of the century by American Scientist, along with: Dirac on quantum mechanics, Einstein on relativity, Mandelbrot on fractals, Pauling on the chemical bond, Russell and Whitehead on foundations of mathematics, von Neumann and Morgenstern on game theory, Wiener on cybernetics, Woodward and Hoffmann on orbital symmetry, Feynman on quantum electrodynamics, Smith on the search for structure, and Einstein's collected papers."

Note: The series was originally titled "The Art of Computer Programming", so it's often referred-to by the acronym TAOCP.

[toferc]

Originally Posted by cheesehead

Note: The series was originally titled "The Art of Computer Programming", so it's often referred-to by the acronym TAOCP.

The cover of the book still has the "The", as does the Library of Congress listing...

</pedant>

Oh, and shaxper... every number you ever do any computing with will be rational.

[Fusion_power]

Re the statement There's no such thing as random, so the primes you generate aren't "really" random and, therefore, neither would the numbers that this scheme generates. But, hopefully -- and this is where my knowledge falls short -- this scheme hides the order better then currently existing statistical techniques.

I will agree that methods we have today generate only pseudo-random numbers. However, I'd suspect that there must be a way to generate truly random numbers based on the Heisenberg Uncertainty Principle.

Thoughts anyone?

Fusion

[ET_]

Originally Posted by Fusion_power

t methods we have today generate only pseudo-random numbers. However, I'd suspect that there must be a way to generate truly random numbers based on the Heisenberg Uncertainty Principle.

Thoughts anyone?

Fusion

Hmmm... you could generate truly random numbers, but their randomness would stop as soon as you choose and use them

Luigi

[jinydu]

Actually, using quantum uncertainty to generate random numbers should be quite simple.

Get a radioactive nucleus with a half-life of x seconds. Wait for x seconds. If it decays, write 1. If it doesn't decay, write 0. Repeat.

[mfgoode]

Originally Posted by shaxper

let

random number = q * r
where q = an irrational number, r = a rational number

Create q and r via any statistical technique to choose two primes, p1, p2

r = p2
q = pi * p2
where pi = 3.14... out (p1) places

real random number = q * r = pi * p2

Could you kindly explain the result you arrived at in the last line?
Mally

[mfgoode]

[QUOTE=cheesehead]I recommend Art of Computer Programming, Volume 2: Seminumerical Algorithms by Donald E, Knuth -- Chapter 3 covers random and pseudorandom numbers.

This book and its companion volumes 1 and 3 are worth getting for one's library.Un Quote]

Thank you for recmmending these books of TAOCP.
As India prints these books brand new under licence but for resticted sale to India, Bangla Desh & Ceylon(Sri Lanka) I was able to order all 3 volumes for as little as under $20. Not bad Eh?
I have a few of the other books related to math and physics as mentioned by American Scientist in my possesion and these 3 vols will be a welcome addition.
Mally