20041202, 00:45  #34 
Aug 2002
2^{6}·5 Posts 
There's an algorithm to compute the value of PI to any desired precision. Therefore it's determined and predictable and cannot be random.
A property of randomness is that there's no algorithm that can reproduce the sequence. 
20041204, 12:46  #35 
Aug 2002
Portland, OR USA
112_{16} Posts 
Another cross reference that may be causing confusion is the debate whether "in the digits of pi base ten, the digits 09 are randomly distributed".
The particulars of that debate cannot be used in this one. Quite the opposite: such a debate couldn't even be framed unless the digits in question were determined and predictable. Last fiddled with by Maybeso on 20041204 at 12:46 
20041205, 04:21  #36  
Nov 2004
2×7 Posts 
I've been thinking about this issue for a few days, bugged by the feeling that with Jindyu's defintion, pi could be considered 100% order. But I think it's impossible. I don't think anything in this universe is 0% or 100% order.
Quote:
I'll concede that in irrational space pi may be determined in the sense that it's constant (only one possible outcome), but, now, I'll argue that to determine something means to bring it into rational space. And in so doing, pi becomes part random. But instead of defending my position by reinterpreting 'undetermined', which you guys disagree with, I'll hide behind definition number 2. In the process of determining pi, there is more then one possible outcome: 3, 3.1, 3.14, 3.141, etc. each of which is, in real and rational number space, a different outcome. Which is the basis of my real random number scheme: it is the determination of one of the two pseudorandom number generating schemes and/or one of the two irrational numbers that creates a truly random number. 100% random? No, there's no such thing as 0% order. Well, maybe in irrational space. Last fiddled with by shaxper on 20041205 at 04:26 

20041205, 05:04  #37 
Aug 2003
Snicker, AL
7·137 Posts 
A property of randomness is that there's no algorithm that can reproduce the sequence.
I would have to expand this a bit by saying that a random event cannot be predicted. Conversely, that which can be predicted cannot be random. This entire thread seems to be focusing into a disagreement over the old and proven wrong position that "if all possible variables are known, the end may be predicted from the beginning". In other words, if all possible interactions are known, then the universe's destiny is predictable from the big bang. I would then point to the uncertainty principle and show a single event that is unpredictable and therefore the entire argument falls apart. By definition, Pi is not random. It is precisely defined but cannot be represented in a decimal expansion. Fusion 
20041205, 17:02  #38  
Dec 2003
Hopefully Near M48
2×3×293 Posts 
Quote:
Quote:
[algorithm to compute pi] [end at 1 million digits] That computation would have only one possible outcome: The value of pi to a million digits. I don't really understand what you mean by Rational Space and Irrational Space. Could you explain that more please? Last fiddled with by jinydu on 20041205 at 17:03 

20041205, 18:12  #39  
Banned
"Luigi"
Aug 2002
Team Italia
12DB_{16} Posts 
Quote:
Luigi 

20041206, 16:50  #40 
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}·3^{3}·19 Posts 
To create a real random number
[QUOTE=Fusion_power]A property of randomness is that there's no algorithm that can reproduce the sequence.
I would have to expand this a bit by saying that a random event cannot be predicted. Conversely, that which can be predicted cannot be random. This entire thread seems to be focusing into a disagreement over the old and proven wrong position that "if all possible variables are known, the end may be predicted from the beginning". In other words, if all possible interactions are known, then the universe's destiny is predictable from the big bang. I would then point to the uncertainty principle and show a single event that is unpredictable and therefore the entire argument falls apart. By definition, Pi is not random. It is precisely defined but cannot be represented in a decimal expansion.] / Unquote I perfectly agree with your definition. Its the only one that makes any sense of mathematical randomness. Please refer to Xyzz's new Thread 'Measuring randomness' and the website given for other related 'randomness's'. It is very instructive and educational. To the last line I would like to add ' in a finite length of time ' But Pi is a complete concept and equal to 'Aleph null' in Cantors theory of transfinite cardinals. Mally Jinydu : Quote/ Actually, I've been trying to argue that pi is a mathematical constant whose existence and value can be derived deductively from mathematical axioms. Thus, its existence and value is independent of anything that happens in the physical universe. We can conceive of a universe with no stars, but a universe without pi is unthinkable. Thus, in some sense, pi goes beyond this universe./ Unquote. Very true. Pi does not even require a universe to exist. It is an abstract concept in the MIND OF THE CREATOR . Kronecker was against the irrational, leave alone the transcendental numbers. His famous dictum in response to Cantors theory of the transfinite cardinal numbers was ' God only made the whole numbers. The rest is the work of man (menshenwerk). However Cantor proved him very wrong and his theories (Cantors) were accepted by the math fraternity but many years after his bitter controversy with Kronecker. Mally 
20041209, 10:54  #41  
Nov 2004
2×7 Posts 
Quote:
Quote:
Quote:
Quote:
Quote:
The difference between the two is how they describe infinity. Personally, I think Cantor was wrong. There are not different "levels" of infinity, but different kinds of infinity. In rational space, we conceive of infinity as the numbers increasing without ending. In irrational space, in fractals, we conceive of infinity as magnification, i.e., we can expand (magnify) a fractal at any point without ending. The distinction between "levels" and "kinds" is an important one because there are an infinite number of spaces that, I suspect, require different conceptions of infinity. We can easily (now) rationalize irrational space (with fractals), but can we rationalize all the other spaces? For example, I think sound (music) is another space. Can music be rationalized, e.g., can we turn music into numbers so that the patterns (order) becomes conceivable? I think in time we will, but then there will be another space and another space and...maybe those are different levels, but it implies a hierarchy that I don't think exists. It just happens to be the chronological order in which we "discover" these other kinds of infinity. Maybe someday we'll discover that these different spaces have an order but I can't, at this time, predict it when that day will occur. Quote:


20041209, 16:51  #42  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2·5,477 Posts 
Quote:
Imagine a country where northsouth distances are measured in miles and eastwest distances are measured in kilometers. Now take a rod and place it eastwest. Measure it, and find that it is x kilometers long. Take the rod and turn horizontally through 90 degrees. You find it measures y miles long. Careful measurements made over many years shows that there is a proportionality constant, which scientists call "d" and which has units of kilometers per mile. Every single measurement of a fixed rods, with ever increasing accuracy and sensitivity, shows that d is completely independent of the length of the rod, of the location in the country, of its temperature, the material that it is made of, everything. It is a fundamental constant of the universe. Eventually some scientist got tired of the complications caused to their equations by the presence of d and made a radical proposal. They agreed to measure all distances in kilometres and defined d=1. Now all the equations became much simpler and no one had to worry about d any more. Of course, all the engineers, schoolkids, travellers and so forth continued to use the traditional measurements and when anyone wanted to use the equations to calculate something which was actually useful, they had to remember to put an appropriate power of d back in the final result  but you can't please all of the people all of the time. Now move to our fourdimensional space time, where we measure northsouth in metres, eastwest in metres, updown in metres and pastfuture in seconds. According to the view of classical relativity, there is nothing mysterious about the value of the speed of light in empty space being exactly the same for all observers no matter how, where or when they measure it. The quantity "c" has exactly the same nature as the quantity "d" in my mythical country. It is used solely to convert from measurements made in one direction to measurements made in another directlion. So, of course, when manipulating the equations of relativity, special and general, it is much easier to define c=1 and to measure pastfuture in metres too. Paul 

20041210, 01:16  #43  
20422_{8} Posts 
Quote:


20041210, 07:03  #44  
Dec 2003
Hopefully Near M48
2×3×293 Posts 
Quote:
Similarly, the validity of the argument: "It is raining. Therefore the ground is wet." does not depend on whether its actually raining. The same can not be said about physical constants, such as the speed of light (measured in meters per second). That value cannot be calculated from any known physical theory, at least not without some experimental measurements. This is essentially what seperates mathematical constants from physical ones. In addition, a universe with different physical laws is conceivable. To a very good approximation, gravitational field strength varies according to an inverse square law. But there is no logical reason why there can't be a universe where gravity follows an inverse cube law. In short, what separates physical laws from the value of pi is that physical laws make claims about the way this universe is, whereas the value of pi doesn't (at least, not without physical laws); instead it makes claims about the way a universe would be if the axioms of mathematics were satisfied. Quote:
Quote:
In what you call "rational space", you say that infinity is conceived of as numbers increasing without end. But in fact, there are other ways to use numbers to think of infinity. Another way is to think of "infinity" in terms of limits, what something approaches as a variable gets arbitrarily close to a certain variable. The notion of limits is central to the entire (mathematical) theory of calculus. In addition, pictures and music aren't really seperate from numbers. You seem to imply that fractals are the prime example of pictures. However, if you study Chaos Theory, you would know that fractals are mathematical objects that cannot be described without numbers. For a more detailed description of this, see http://pirate.shu.edu/~wachsmut/Workshops/Camden/. One example of generating fractals is to use Newton's Method on a cubic equation in the complex plane. If you color each point according to what root it converges to, and all three roots are distinct, you get a fractal. For more information, see http://mathworld.wolfram.com/NewtonsMethod.html. I am even more mystified by your claim that music is another seperate space. Yet you have not explained how music has its own conception of infinity, which seems to be your definition of a "space". Furthermore, there is already a way to turn music into numbers so that the pattern becomes conceivable. The mathematical theory of osciallations has already been applied to the study of sound waves, and plenty of regularities in music have already been found. Furthermore, there is already a device that can convert music into numbers, at least to a good enough approximation that most people don't notice: its called a DVD recorder/player. Finally, you claimed in an earlier post that to determine something is to bring it into rational space. First of all, this is inconsistent with your claim that nothing is 100% determined, since by this definition, anything in rational space would be completely determined. Furthermore, you haven't explained why determinism is only possible in rational space. 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Finding multiples of a real number that are close to a whole number  mickfrancis  Math  16  20170301 07:17 
Using quarternions instead of Gaussian primes when factoring a real number?  Stargate38  Factoring  4  20120410 04:20 
Odds that a Random Prime is a Number?  R.D. Silverman  Homework Help  60  20101013 10:31 
About random number (random seed) in Msieve  Greenk12  Factoring  1  20081115 13:56 
Largest number in the real universe  danjmi  Science & Technology  17  20040926 20:25 