Can the Value of Pi be Changing?

Originally posted by ProfEmeritus

Pi is an irrational, transcendental number, and as such CANNOT be expressed as a fraction of any two integers(thus irrational), and CANNOT be expressed as a finite number of algebraic expressions of any kind. At last count, Pi has been calculated to over ONE TRILLION decimal places, but anything that you can write as a value, will only be an APPROXIMATION, due to the very definition of a transcendental number.

Only if you insist on using decimals. As others pointed out, you have no such problem if you simply use the proportional fractions, as people have done for well over 3,000 years.

What if the beginning of pi is the big bang, and the numbers that follow are the history of everything and someway related to it ( not sure how )....
Maybe there is a hell of a lot more to pi then we know. Could we predict things based off this new understanding of pi if it were reached?

It is never ending and so is life. It is like a spiral that never ends, just like life....Hmmmmmmm

reply to post by LucidDreamer85


Phi (golden spiral, etc.) is more fun for this sort of thing.

Originally posted by Razmear23
Pi is infinitely long due only to our base 10 numbering system.
If you were to figure Pi in binary you would get 11.001001
I don't have an app handy to test how long Pi would be in base 2 (binary) or base 8 (oct) or base 16 (hex), but I would guess that the result would no longer be infinitely long.

Irrational numbers never terminate in any natural number base. The binary and octal expansions of pi are infinitely long, as in decimal or what have you.




[edit on 13-3-2009 by nscopheacriaaclters]

reply to post by Johnmike


I never really researched the golden spiral. Looking into it now.

But it's kinda funny because when I try to imagine what a dimension truly is this is what I think of:

1st dimension: a point with no length/width/depth, I always tend to think of a point as a circle

2nd dimension: a plane. a plane with two points connected could be a circle (or a line).

3rd dimension: a sphere with length/width/depth

4rth dimension: a sphere in motion (time). I imagine a sphere spiraling upward leaving a trail in it's wake. The spiral may even be representative of a golden spiral.

I'm not a scientist so I don't know if my current line of thinking is true. Nonetheless my thinking goes further.

5th dimension: the sphere entire timeline can be seen all at once, every place it has been from it's inception to it's end.

6+ dimension: other spheres yet the same sphere but with other destinies, dimensions and timelines.

Obsidience

Can the value of pi be changing?

It's not a matter whether it can; it DOES.

The poof is simple: Start with value pi(a) = 3.14. Then attach the next digit to make some computation more precise: pi(b) = 3.141. Since pi(b) - pi(a) = 0.001, pi(b) doesn't equal pi(a) and therefore the value of pi is not constant. As an irrational number, there is no end to the number of digits in the fractional part of pi and that means pi goes through infinitely many stages of its change.

Pi doesn't change.

pi(a) isn't pi, it's an approximation of pi, as is pi(b) and any other attempt you have to represent it in decimal form.

Originally posted by science lol
Pi doesn't change.

pi(a) isn't pi, it's an approximation of pi, as is pi(b) and any other attempt you have to represent it in decimal form.

If both pi=3.14 and pi=3.141 are approximations of pi, can you write down pi in a form, which is not an approximation? It would be a good thing to do, coz given two different approximations pi(a) and pi(b), the comparison pi(a) doesn't equal pi(b) cannot be changed, coz pi(a) - p(b) doesn't equal 0.



[edit on 3/18/2009 by stander]

Yes you can write pi in a form that is not an approximation, like pi = 2 arcsin(0). In decimal form you would need an infinite sheet of paper. Not practical.

Originally posted by nablator
Yes you can write pi in a form that is not an approximation, like pi = 2 arcsin(1). In decimal form you would need an infinite sheet of paper. Not practical.

equation fixed

[edit on 18-3-2009 by science lol]

It is my belief that pi IS ever changing, though it's change is not perceivable to us, as it is changing in correlation with the changes that the entire universe is undergoing. So where the absolute representation of pi in any given situation could be different, because everything is changing in a perfectly relativistic way, said changes cannot be observed.


ie: though pi right now is 3.14159.... 10 seconds ago, it was 3.14159... but the current 3.14159 is not equal to the former 3.14159, as due to the universe expanding at near the speed of light, the absolute value of 3.14159 is incredibly different now than it was 10 seconds ago.

Very interesting thread...

I like the multidimensional approach, and I agree to its useage for the explination of PI.

Yes, Pi is the ratio between the Diameter and the circumference.

But what do these two things mean?

Diameter... and Circumference.


Firstly, Diameter is a One dimensional measurement.

Whereas Circumferance is a Two dimensional measurement.

The diameter is a straight line measurement, and Circumference is NOT.

So, then... what IS the circumference?

Well, it is one of two things.

A function of a straight line measurement in CURVED space, OR a temporal measurement around a fixed point.

This is why PI CANNOT be a rational whole number... because it is an incorrect representation of mathematics.

Secondly... Circles do not exist in reality, or nature.


We have approximations of circles, and we have ORBITAL circles, that are merely a point that orbits anouther in roughly a fixed (closed) path.

This sort of goes back to gravitational "Space-Time" theory, that states that a planet is acually traveling in a STRAIGHT line through CURVED space.

The circles that we measure, are not really TRUE geometric shapes, they are merely ABSTRACTIONS of an IDEALIZED geometric shape.



I think an interesting mathematical question to shed some light on this is, at what axis along an oval (symetrical elipse) does th measurement of the Diameter achieve Pi?

(I would assume 45 degrees off the major axis)


But, that is just my two cents.

As far as the original question "Can the Value of Pi change?"

Yes, I believe it can, given the unfolding of dimensions.

And I think that an interesting presumption would be, in the instant before the "Big Bang" that Pi = 1

And all of the sudden, that symetry broke, and the value of PI has been resetteling ever since.

It is an interesting hypothesis... allow me to explain.

Imagine a Spherical universe, in which space time is wrapped in on itself, in such a way, that if you traveled in one direction, you always came back to your original starting point.

A closed-Space universe.

Now, imagine that this "Universe" is the scale of a Planck Length (Really Really small)

So, no matter how small you drew the circle, the diameter would ALWAYS be the same size, because it would ALWAYS wrap around the "universe" (Which is what your "Circle" would do.)

Therefore, the Diameter = Circumferance....

So... Pi = 1

(Just some mental gymnastics)

-Edrick

Originally posted by nablator
Yes you can write pi in a form that is not an approximation, like pi = 2 arcsin(0). In decimal form you would need an infinite sheet of paper. Not practical.

I believe that the correct trig version of pi is 4 arctan (1). Your formula 2 arcsin (0) returns 0.

I also believe that the simplest exact formula is pi = circumference / diameter. The crux of the problem with any of the exact formulas is that you cannot use them to find out whether there are changes to pi. You need to write pi in its approximate form to compare the digits. Since the number of the digits 'n' in the fractional part of pi aproaches infinity, for each pi(n) you come up with, I come up with pi[n+1] and the value of both approximations of pi won't be the same. The value of number pi is constantly changing, as the number of its digits is approaching infinity. But as long as the value of the digit increment doesn't stray away from the value given by the exact formula, then pi(n) = pi(n). But you never find out if its so, coz infinity won't let you do that.

Suppose that the universe is a perfect sphere. In order to compute the circumference to the precision of the size of one proton, you need to use pi 39 digits long. There is really no way to "test" the value of pi beyond 15 digits or so.

So, then... what IS the circumference?

Well, it is one of two things.

A function of a straight line measurement in CURVED space, OR a temporal measurement around a fixed point.

Edrick,

Great post and this is exactly the point I'm trying to get across. It's very simple for someone that has "read the books" to say that pi is a constant of the relation between the circumference and diameter of a circle. But does education equate to understanding? Because understanding is what I'm after here. What the heck is a circle? What is circumference and diameter? And why do we have this "constant" defining the rules of a "perfect" circle?

I love the analogy you make about objects always moving in straight lines in curved space. I never thought about it that way but it makes total sense now.

The last bit about a spherical universe and time wrapping in on itself is something that I'm going to try to get a grasp of for the next few weeks (maybe months/years). But I feel it's relevance as I've read of similar theories before.

The incite has been much appreciated, I hope to hear more from you in the future!

Obsidience

Originally posted by Edrick
Secondly... Circles do not exist in reality, or nature.

So don't triangles, squares, rectangles, or any other geometric shapes that you see on the pages of geometry books. That's because we and the nature live in 3D space and those shapes live in 2D space. But that means we can't see these shapes on a piece of paper. If we could, we would be able to see things that live in the 4D space. 3 + 1 and 3 - 1 is the same dimensional shift. So how come that we can see the circles and triangles drawn on a piece of paper?

You can't answer the question by looking at the shapes; you need to be present when they are created. After you have drawn plenty of these shapes and want add many more, you need to sharpen your pencil. After many hours of continuous drawing, you notice that the business part of your pencil -- the lead -- is getting shorter. Where is it disappearing into? Into the fourth dimension?

That's hardly so. You can see that the lead transformed itself and added one dimension to the 2D -- a dimension called "thickness." Suppose that there are very precise scales that you use to weight the piece of paper before and after the lead from your pencil is gone. You find that the paper with all the shapes drawn on it weighs more; the increment is the weight of the lead.

Now take an eraser and erase the additional dimension. By doing so everything goes back to 2D and the shapes are -- gone? No they are not gone; you just can't see them, coz you are a physically a part of a 3D space and can't see what is going on in 4D or 2D.

Hello again.
OK here goes nothing.

A point, can contain within it an indeterminate amount of other points. It is impossible to find a point. A point is merely a representation. Below subatomic, the rules break down as far as we know. If there were to be a representation of a point, numerous versions could exist simultaneously in numerous areas. Perhaps numerous dimensions. This is why pi cannot be calculated. Indeterminacy applies to the micro universe as well as the macro universe as well. If a point cannot be found, how can it be calculated.
Our best guess is to determine the furthest extent before we give up and settle on a value. There will however always be a distortion to any mathematical formulas arising from this calculation. The distortion may be so tiny, that it more or less doesn't effect the overall out come of the solution.
The answer to the original question, "is pi changing?" is yes and no.

This answer also implicates something rather philosophical in it's own right.
The duality of the universe.
Yes and no.
Light and dark.
Macro and micro
Yin and Yang
etc...

How come everyone passes over the Lucas numbers? They are very important too, as in the construction of the solar system.

Pi as it is derived is a rule. A rule is absolute, but the expression thereof may fluctuate. If you change the rule, then the universe will alter accordingly. Like wagging a dog by its tail. It would be easier to find a universe where the rule is different. It also would be a fundamentally different universe, a 1.5 D for starters.

And I submit that binary numbers are natural. Sure, man discovered binary, all the way back to Tesla. But they have always been the building blocks of reality, starting with the subatomic particles. Analog is merely a highly evolved smooth progression of binary.

So anyway, pi is a rule, and rules are absolute. You cannot break them, only respect them. Accept it and move on.

Pi as it is derived is a rule. A rule is absolute

I think you've misunderstood. I'm pretty much saying that nothing is absolute. As our universe expands and cools - the very laws of physics change with it.

That being said, I don't know if we can perceive the change. It's kind of like orbiting near a black hole. Your perception of time doesn't really change but to others you are almost frozen in time.

Take care,

Obsidience

reply to post by obsidience

Pi is a number. It is a number just like any other number. Granted, it is a special kind of a number called an 'irrational' number, but fundamentally it is a number like any other.

Number

A number is a mathematical object used in counting and measuring. A notational symbol which represents a number is called a numeral, but in common usage the word number is used for both the abstract object and the symbol, as well as for the word for the number. In addition to their use in counting and measuring, numerals are often used for labels (telephone numbers), for ordering (serial numbers), and for codes (ISBNs). In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers.

Source : Wikipedia

A number is merely an 'abstraction' or 'representation' of 'something else.'

This 'something else' can be 'quantity,' 'dimension,' 'temperature,' 'hardness,' etc, etc ...

This 'idea' of 'number' makes possible things like 'counting' and 'calculating,' etc, etc ...

So, to ask -

Can the Value of Pi be Changing?

is 'equivalent' to asking -

Can the value of 1 be changing?

My apologies, but the matter is actually no more 'mysterious' than that.

The simple answer is that -

No, the value of Pi can not be changing, just as the value of 1 cannot be changing.

That being said, I think it's it is fair to say further that people have the 'intuition' that 'something' is changing ...

When the 'scientists' first began developing the field of 'physics' maybe a few hundred years ago, certain 'assumptions' were made ...

One 'catagory' of assumptions these 'pioneers' of physics made was in the area of 'fundamental physical constants.' These are 'quantities' such as 'the gravitational constant,' the 'permitivity of free space in a vacuum,' 'the speed of light,' 'planks constant,' etc, etc ...

Currently in the field of physics there is quite a lively debate going on as to whether or not some of these 'fundamental constants' are actually 'constant' or not ...

Some people think, for instance, that the 'gravitational constant' is not 'constant' at all, to give only one example of many.

This is what I think the OP is really trying to address -

Something in the physical universe is changing - what is it ?

Just my 'two-cents' ...

Hope this helps.

reply to post by obsidience


Well dear sir, if you can provide some evidence of the physical constants changing I would be inclined to consider your position with more care.

In the meantime, just as the notion of a Creator/Sustainer being absolute, the value of physical constants will remain absolute. The variables are in the details.