3.141592653589 blah blah blah.
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Mosheh Thezion
Registered Senior Member
Light said:
PI HAS everything to do with dimensions... being based on 90 degrees.
you do see that much dont you?
-MT
Mosheh Thezion
Registered Senior Member
IF YOU CAN make the realization that Pi... has everything to do with dimensions....
then.. if the universe.. formed as a progression of dimensional motions..
i.e.. 1d... 2d... 3d... 4d... and so on...
then indeed.. Pi.... signifies... or represents... the most fundamental quality of the formation of all space....
but... how and why... and exactly.. what the nature of that energy is... is still mysterious...
do you get it?
-MT
then.. if the universe.. formed as a progression of dimensional motions..
i.e.. 1d... 2d... 3d... 4d... and so on...
then indeed.. Pi.... signifies... or represents... the most fundamental quality of the formation of all space....
but... how and why... and exactly.. what the nature of that energy is... is still mysterious...
do you get it?
-MT
Pete, really... you're probably the only one on this page with a valid point... Blue UK, what bar did you win the free drink at, just i know to NEVER go there... i might have to poor one on someone if i have to listen to them yammer out the 100 dp of Pi, especially in a bar.. and even more so that theyve wasted minutes if not hours on something so terrible...
PS.. pi's got nothing to do with energy guys.. its just a ratio of circ to diam. its not given to us by aliens, it doesnt explain crop circles, and it sure doesnt signify "the fundamental quality of the energy applied to make the universe as we know it" whatever the hell that means anyway... i'm pretty sure you got that line from someone who's better at sounding much smarter than you.. and probably has some other good one liners to back it up... sure sounds like something they would have said in the movie Pi tho...
if theres any fundamental shape or number, it'd probably be the spiral and golden ratio, and if youre going to talk yin yang, chi type energy crap, then PETE - remind them where this conversation belongs... ive got a few ideas.. but i'll keep them to myself :bugeye:
PS.. pi's got nothing to do with energy guys.. its just a ratio of circ to diam. its not given to us by aliens, it doesnt explain crop circles, and it sure doesnt signify "the fundamental quality of the energy applied to make the universe as we know it" whatever the hell that means anyway... i'm pretty sure you got that line from someone who's better at sounding much smarter than you.. and probably has some other good one liners to back it up... sure sounds like something they would have said in the movie Pi tho...
if theres any fundamental shape or number, it'd probably be the spiral and golden ratio, and if youre going to talk yin yang, chi type energy crap, then PETE - remind them where this conversation belongs... ive got a few ideas.. but i'll keep them to myself :bugeye:
Mosheh Thezion said:
seriously... MT, lots of words, no meaning... the only thing mysterious here is exactly how much hot air is packed into this flatus of a concept of yours...
My own personal theory is that the universe was formed for the one simple fact that a few billion years later on a single spec of a planet, life would evolve into man and create those little carmel candy cubes that you can find in the grocery store. And that THESE candies represent the universe in their shape and changing form, and that each of these represents a dimension, ie 1d 2d nd wrapped in plastic and piled into a bin together and that if you unwrap these, ie destroy the Universes dimensional boundary, the smushing of two of these candies together actually represents the convergence of two dimensions and opens up possibilities of time travel... which is why i think they give me a stomach ache when i eat too many... dimensions converging in my stomach gives me gas, or perhaps opens a portal to a dimension that contains higher atmospheric pressure than that of my internals and thus seeps its atmospheric gasses of methane, nitrogen, etc, into my bowels... This also serves as an explanation on where half baked ideas are born... maybe even yours... do you know anyone that eats these candies?
in any case, i would venture to say that MY argument holds WAY more water than yours... hey maybe pi can predict the lotto?
Sarkus said:If the bet was to recite pi to 100dp - how the @#!& would anyone know if it was right or not!!
I was wondering about that, myself. :bugeye:
I remember from a History of Math class that a mathematician in the 1700's spent his entire life calculating Pi out to 200 decimal places. A few years after he died, someone discovered a mistake in about the 50th place. All the rest was GIGO. Sad.
Sarkus said:If the bet was to recite pi to 100dp - how the @#!& would anyone know if it was right or not!!
A lot of people point this out! But if I can give the same number out twice in a row that's enough for most people.
The barman (a student) brought the topic of pi up in conversation and proudly recited 20 or so d.p. When I came out with 100, he must have recognised the first 20 and so believed me.
The guy who taught me how to memorise pi knew it to some insane level of precision (but I couldn't be arsed after 100).
schizoid1984
Registered Senior Member
MT: are you talking about pi as it relates to polar functions?, in which an angle theta is the input to any sort of various geometric function.... such as cardiod, butterfly curve, flowers, and even the golden spiral? For instance, if you place p=e^(x/5) in your graphing calculator you will receive a spiral (make sure you're in polar coordinates). This is also known as a logarithmic spiral. The irrational numbers of pi, e, and phi are all related in this one equation. I would agree that pi and universal energy are related since the 'x' variable is directly related to angles on a unit circle. The reason i use spirals to illustrate this is because they're a great source of cosmic energy.
Hey did anyone see that black and white movie called Pi?
.Hey did anyone see that black and white movie called Pi?
Your link did not respond in several tries, will try more later. Do they give any results relating to my question. I.e. given all the Pi sting in base 10 that is now known, what is the probably that it is not normal?shmoe said:
That changing base can change a infinitely long, but normal, string of numbers into a non-normal one surprises me, but I will take your word over my intuition.
There are a lot (well, infinite in fact
) of different bases possible. Suppose that an infinite string in base 10 is known to be "non-normal," for example, to be extreme, the fraction 1/9 = 0.1111111111111111...11111111111111.... etcis it possible that some one (or more) of the infinite set of possible bases can "normalize" a string which is non-normal in base 10?
Also I was wondering if it is possible to construct (not actually do it of course, but specify how to do it) an infinite string that is certainly "normal."
Again I will give my opinion, before you tell me the answer: I think not possible, because if it were, it would seem to me that you could have a perfect random number generator and I do not think that is possible.
But in either or both of these beliefs, I could be wrong again. I.e. (1) I may be known that it is impossible for even a guaranteed normal string to be used ,or adapted to be used, as a perfect random number generator or, (2) it may be possible, in principle, to make a perfect random number.
generator.
PS some of these things are so interesting, I now wish I had read at least one number theory math book while in college.
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Billy T said:
It is possible, although difficult, to construct numbers that are normal in a particular base. I don't think that any of the known constructions are absolutely normal (that is, normal in any base). See here:
http://mathworld.wolfram.com/NormalNumber.html
In particular:
"As stated by Kac (1959), 'As is often the case, it is much easier to prove that an overwhelming majority of objects possess a certain property than to exhibit even one such object....It is quite difficult to exhibit a 'normal' number!'
[...]
While Borel (1909) proved the normality of almost all numbers with respect to Lebesgue measure, with the exception of a number of special classed of constants (e.g., Stoneham 1973, Korobov 1990, Bailey and Crandall 2003), the only numbers known to be normal (in certain bases) are artificially constructed ones such as the Champernowne constant and the Copeland-Erdos constant. In particular, the binary Champernowne constant"
I don't know much about using constructions of normal numbers as random number generators, so I won't comment on that part of your question...
Billy T said:
Hmm, funny, it's working for me. Here's an older one (less digits) http://oldweb.cecm.sfu.ca/personal/jborwein/Kanada_50b.html
Try searching for Kanada and pi if this one doesn't work. Kanada is often at the lead in calculating many digits.
For the 1.2 trillion digits they give
119999636735, 120000035569, 120000620567, 119999716885, 120000114112, 119999710206, 119999941333, 119999740505, 120000830484 ,119999653604
as the number of 0's, 1's, 2's, etc, all pretty evenly distributed, and this gives a chi-squared of 13.13. I have no recollection of what a 'good' value for a chi squared test is, but the data looks pretty darn evenly distributed to me. I believe for a normal number we'd expect in n digits that you'd be no more than sqrt(n) away from the expected values. In this case, sqrt(n) is a little more than 1000000, and the actual distributions are certainly within this distance of 120 billion. There's more to normality than just single digit distributions though, you need to look at 2 digits, 3 digits, etc, all must be uniformly distrubuted in the sense of the asymptotic limit.
The Champernowne constant is 0.12345678910111213141516...., just the naturals in order, this is normal in base ten. see http://mathworld.wolfram.com/ChampernowneConstant.html I'm quite certain it's not normal in all bases, but I can't recall if there's a proof for an explicit one. Of course you can do the same construction in any base.
Rational numbers are all not normal. In any base they will eventually repeat (possibly 0's).
There's an article somewhere online about using the digits of pi as a random number generator, I don't recall all the details and can't seem to find it right now*. No naturally occuring numbers have been proven to be normal, they are all 'artificial', that is constructed for the purpose of explicitly demonstrating a normal number. I would have my doubts that these artificial ones are terribly useful for this purpose, since there's definite structure in how the digits are laid out. Normal isn't demanding random so much as it's demanding a uniform distribution, which is how random should look in an asymptotic sense.
* press release about an attempt to use pi to generate random numbers http://www.sciencedaily.com/releases/2005/04/050427094258.htm
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Thanks for all, but especially the above. - I had only the single digit concept.shmoe said:
I suspect that if I "interdigitate" two of the normal Champernowne constants (0.12345678910111213141516....), the result is no longer normal. I.e. the "pairwise correlation" is at least initially much too strong, but perhaps that "washes out in the long run."
11223344556677889900111111221133114411551166....
What do you think?
Now suspose that do not begin the interdicitation until some integer number, N. Is it still not normal, (Here, I am assuming the N = O case was not normal.) for all N not 0? for example if N = 5 the series would be:
123451627384950....
but now the "fifth cousins" are too correlated, I think, and in general the Nth cousins will also always be "too correlated." I think N = the base, in his case 10, is nothing special.
What do you think about this?
If, however, N is an often changing shift to right by N for insertion of next interdigitation, and always equal to the next number of the Champernowne series to be interdigitated, Then I am inclined to think that "normality" is preserved in this "dual, random spaced / offset" Champernowne construct.)
What do you think about this?
Is it any use to you to have someone, like me, ignorant but not too dumb, ask you questions? I have found that to be very useful in physics.
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Billy T said:
No problem. The condition for just single digits makes a number what's called "simply normal", full on normalness needs all finite sequences.
Billy T said:
The first one is not normal, you'll never see the 3 digit sequence 101 for example. It will be simply normal though. Any 3 digit sequence in this number will be xxy or xyy.
If you shift by 2 before 'interdigiating': 0.121324354657... any 5 digit sequence will be wxyzx or wxywz if that makes sense, the 2nd and 5th or the 1st and 4th digits must match, so you'll never see 01234 for example.
Shifiting by 5 should have missing 11 digit sequences, and so on for any fixed shift.
Billy T said:
How is this N changing? This may have an effect, I'm not really sure.
Billy T said:
Yea, there's so rarely any math on this board that I find interesting. This gives me a reason to think about stuff I don't, well think about usually.
I thought I had specified that well but will try again with different words, which I hope will be more explicit. (This attempt, plus a re-read of my original text should do it.)shmoe said:
Let me give the two series short names, A & B. If I may be a little crude, A is the female one and B the male, in sense that pieces of B will be inserted into A. (Never did appreciate math as much as now, thanks again.)
Imagine that when a piece of B is inserted, it is always cut off (ouch
) from the front of B's string. If something of B is sticking out in front, or as you math guys more accurately say: B's front part has "a positive value," (hehehe) then there will always be at least one item of A between the last insert of B and the next insert of B, and in fact this is the case if .|. is the next insert from B, which is always the first element, just "exposed" (I never knew math could be so pornographic ) by the most recent "cut off" of B. If, however, the next element of B to be inserted is a 3, then there will be 3 female items between the 3 (when inserted in A) and the previous insert from B.As I stated before, I am inclined to guess this does restore "full normality." - Wonderful what a string of "random spaced insertions" into the female can do for you.
- I can't believe I said that.Perhaps I should drop this line of questioning before being arrested as the "Dirty Old Man" I am.
What do you think? (About "full normality," not my DOM status.)
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