Paradigm shift : a simple example.

Hi posters !
Many a time, I use this expression : "paradigm shift".
I would like to show you a simple example of what it is.

I think that like everybody, you have been told that the circumference of a circle is 2xPIxR. That is, the diameter of the circle multiplied by 3.14159....

Well follow me on this image :

[atsimg]http://files.abovetopsecret.com/images/member/75f08944af82.jpg[/atsimg]

On Fig#1, you see a circle, and a square in it.
Obviously, the circumference of the circle is longer than the perimeter of the square !

So, like in Fig#2, let us divide each side of the square so the figure ACB fits more to the circle than the side AB.
Obviously, the length of ACB is longer than the length of AB : are we approaching the length of the circumference ?

You see in Fig3 that we continue this process : ADC is longer than AC.

So, each time we divide a segment, the resulting length is longer than the original length.

If we repeat that many many times, the resulting length will be ever longer than the original length.

That means that the circumference of the circle is INFINITE !

This is one of the examples given by MANDELBROT, a mathematician, who invented and promoted the FRACTALS.

He gave as an other example this question : what is the length of the coasts of Britany ?
As you guess it, the answer is : INFINiTE.

You may figure the logic of such an answer if you search the surface of a sponge, or a very porous stone.
Same answer : INFINITE !

Paradigm shift is like the shock you're feeling there.

Considering the certain things under an other angle.

Example of "certainty" : "one may never travel between galaxies, because C (the speed of light) is the limit speed of everything"

But here, explaining the paradigm shift is less trivial ...

However, when you think about it, there is no such thing as a continuos circle.

Zoom in close enough to the circle you drew, you will eventally see individual pixels. Zoom in close enough to the finest circle you can think off and you will eventually see atoms. When that happens, the smallest segment you will be able to add will merely be the distance between atoms.

Think of an imaginary continuos circle, and then you have an infinite circunference, but then again the infinite length would be true for any shape, even a straight line. If you were able to zoom in on that line and never find any discontinuity, then you could claim the line is infinite since its apparent length would be dependent on how far you zoom in and you could hypothetically zoom forever.

reply to post by daniel_g


Exactly.

Euclide's geomaetry has to be abandonned by us if we want a quantum leap in our knowledge.

By the way, the limit is NOT the distance between two atoms.

The notion of distance is obsolete.

Not to rain on your parade, but all you've done is restate Zemo's dichotomy paradox viewed through the context of a Mandelbrot fractal. However, you have misinterpreted this to mean that the circumference of a circle is infinite, it isn't, however a fractal of infinite surface area can exist within the circumference of a circle in theory, because it keeps repeating in infinitely smaller scales.

All in all, I would say that using bad science to create an inapt metaphor to describe a "paradigm shift" is, although a good attempt, an ultimately unsuccessful one.



[edit on 13-11-2009 by Doglord]

reply to post by Doglord


Hi Doglord,
Just coming back from a journey in Guatemala.
Very, very interesting one.
But far from the topic.

Thanks for the link on Zeno's paradoxes.

Here are some extracts of this very same link :

Another proposed solution is to question the assumption inherent in Zeno's paradox, which is that between any two different points in space (or time), there is always another point. Without this assumption there are only a finite number of distances between two points, hence the infinite sequence of events is avoided, and the paradox resolved.

So, it seems that there are indeed some conditions for the mathematics to be "good"...

Zeno is often said to have argued that the sum of an infinite number of terms must itself be infinite - that both the distance and the time to be travelled are infinite.
However, Zeno's problem was not with finding the sum of an infinite sequence, but rather with finishing an infinite number of tasks: how can one ever get from A to B, if an infinite number of events can be identified that need to precede the arrival at B, and one cannot reach even the beginning of a "last event"?
Philosophers claim that calculus does not address that question, and hence a solution to Zeno's paradoxes must be found elsewhere

Haha ! Is there really a problem between Philosophy and Mathematics ?

According to quantum theory, it can never be possible to measure distances with any greater accuracy than one Planck length (about 1.616252 × 10−35 metres), nor times less than one Planck time (about 5.391 24 × 10−44 seconds) apart. As of 2004, the shortest time difference capable of actually being measured was about 10−16 seconds

Extraordinary.

Can you figure out that
- there is a "distance" that can't be divided ?
- there is a "duration" that can't be divided ?

Not to "rain" on your post, but fractals are the most mindblowing part of modern geometry.
I don't think that nowadays, someone could call them "bad science".
Just read Mandelbrot, it's full of such "misinterpretations"...

Well mathematical goemetry aside. Just spotting and identifying an anomally... I have been aligned with another site which some may know.(THE PARADIGM SHIFT) for over a year now because of their crusade against the NWO /Illuminati . but it appears now they have flipped and gone all christian fundamental . Now I do understand this to be a true P/shift within a P/shift But any views that are at odds with their doctrine now are being deleted /blocked and ignored. People leaving and being aghast in droves. Does anyone have any ideas what transpires with this once admirable group..???
ps.. this is reply 1 of day 1 on here, so .... quell the itchy triggers chaps.