20041126, 13:41  #12  
Nov 2004
2×7 Posts 
Response
Quote:
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 is incorrect at this point] where pi = 3.14... out (p1) places real random number = q * r = pi * p2 But as I said in the followup post, both q & r should be irrationalized (i.e., multiplied by a rational version of an irrational constant). Quote:
Quote:
I can't think of how to prove it, but it seems to me that nothing in the universe is 0%, 50%, or 100% predictable, or in other words, nothing is completely random or completely order. That said, I haven't figured out where constants, such as pi, e, or the speed of light, lie on this continuum. Maybe in the middle? Their exact values are random, but approximate values are order (predictable/known)? I dunno. I've been doing a lot of thinking about pi lately (which spawned this random number creating scheme) and would like to chat about it with somebody. If you're interested, please send me a private message. cheers, jad 

20041126, 18:00  #13 
Dec 2003
Hopefully Near M48
11011011110_{2} Posts 
Well, what does it mean for something to be random? When we say that something is random, we mean that it is:
1) Undetermined 2) There is more than one possible outcome If we use these two properties, then I think we must consider constants like pi as 100% order. Clearly, the decimal expansion of pi is fully determined, since there are algorithms that can approximate it to arbitrary accuracy. Furthermore, no matter how many times you calculate a set number of digits, you will always have the same answer. I think the reason pi appears to be random is that we are looking at it in an "unnatural" way. If you think about it, why should a decimal expansion always be the correct way to look at a number? In the case of pi, I think it is not. I'll leave you with a famous and beautiful equation discovered by Euler: 1 + 1/4 + 1/9 + 1/16 + 1/25 + 1/36 + ... = (pi^2)/6 
20041126, 21:58  #14  
Cranksta Rap Ayatollah
Jul 2003
641 Posts 
Quote:


20041126, 22:55  #15 
Aug 2003
Snicker, AL
7·137 Posts 
There are a couple of interesting arguments presented here. First, I had not seen nor had I previously considered using radioactive decay as a means of generating random numbers but since the very nature of the Heisenberg Uncertainty Principle (HUP) ensures true randomness, it was an obvious conclusion that random numbers could be derived.
To argue that a HUP driven process is not truly random is to argue that the physical processes of our universe are not driven in a truly random fashion. A preponderance of evidence discredits this view. The numbers generated by a computer from an algorithm inherently cannot be truly random. This has been well documented since at least the days of the Commodor 64 when some programmers recommended setting the SID chip to a high frequency and then sampling to create a random number. In effect, the randomness was significantly better than the internal random number generator. Fusion 
20041127, 13:01  #16  
Banned
"Luigi"
Aug 2002
Team Italia
2×2,417 Posts 
A bit offtopic
Quote:
On the other hand, irrationaality and trascendency of numbers may as well be seen as a special case of HUP. And there is more in this untechnical stream of thoughts: the demonstration of Riemann Hypotheis may be compared to the photograph of our perceived fourdimentional universe: once we have a snapshot of it, we are able to fix each and every single event in the past, present and future. But, hey, Superstrings and MTheory made us think that there are better ways to describe our reality than the fourdimentional concept, so there may be a better way to analyze RH as well. Quote:
Luigi 

20041127, 17:50  #17 
Bronze Medalist
Jan 2004
Mumbai,India
100000000100_{2} Posts 
To create a real random number
[QUOTE=jinydu]Well, what does it mean for something to be random? When we say that something is random, we mean that it is:
1) Undetermined 2) There is more than one possible outcome I'll leave you with a famous and beautiful equation discovered by Euler: 1 + 1/4 + 1/9 + 1/16 + 1/25 + 1/36 + ... = (pi^2)/6 [unquote] Yes the eqn is marvellous. The circle (pi) is in conjunction with the square. But you have just scratched the surface. Euler derived many more on the same lines. I recommend the book "Journey through Genius" by William Dunham who devotes a whole chapter on such eqns and gives the derivations of each. There is one eqn Euler could not work out and 200 yrs. of math research has not thrown any light on. Read all about it in the book. There are conjectures made but no proof. Here it is: 1 + 1/(2^3) + 1/(3^3) +1/(4^3) = 1 + 1/8 +1/27 + 1/64 +.......... Mally 
20041127, 18:05  #18  
Dec 2003
Hopefully Near M48
2×3×293 Posts 
Quote:
I have also heard about zeta(3). As far as I know, the only real progress on that problem (aside from brute force computer approximations) occured in 1979, when Apery proved that zeta(3) is irrational. In his honor, zeta(3) is now also known as Apery's constant. Determining zeta(3) is such a simple and elegant problem that I couldn't resist making my own attempt at it, despite the fact that it stumped Euler himself. I posted some of my thoughts at http://www.sosmath.com/CBB/viewtopic...11387&start=30 

20041127, 18:13  #19  
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}·3^{3}·19 Posts 
Quote:
Good work Jindyu. Keep up the good work Mally 

20041128, 08:13  #20  
"Richard B. Woods"
Aug 2002
Wisconsin USA
17014_{8} Posts 
Quote:
BTW, those interested in TAOCP might enjoy Knuth's page about TAOCP at http://wwwcsfaculty.stanford.edu/~knuth/taocp.html (he's actually working on Volume 4!), or even Knuth's home page at http://wwwcsfaculty.stanford.edu/~knuth/index.html. Last fiddled with by cheesehead on 20041128 at 08:20 

20041129, 02:08  #21  
Nov 2004
2×7 Posts 
Quote:
But even with the infinite series you offer by Euler, the exact (100%) number is undetermined since you can't write out (or conceive) of the entire expansion. This isn't an arbitrary distinction. As I said above, I don't think anything in this universe is 0% or 100% order (including 50% was an error) unless you shrink the available outcomes to exclusively 0 or 1. Otherwise, every event has some percentage of order, of predictability (i.e., not 0%) and some percentage of chaos, of unpredictability (i.e., not 100%). 

20041129, 03:14  #22  
Dec 2003
Hopefully Near M48
2×3×293 Posts 
Quote:
1/3 = 0.33333333333333333333333333333333333333333333... Morever, I would argue that the same is true of irrational numbers that do follow a pattern, for instance: 0.1234567891011121314151617181920212223242526272829303132333435... Thus, I would argue that pi is determined. It follows precise patterns and its value will always be the same; it doesn't matter what country you're in, what direction your computer is facing, what month it is, what color your mousepad is, whether or not the sun will rise tomorrow, etc. The value of pi will always be the same. 

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