Paradoxes?

[Jeff P]

Hello

 

I'm an artist working on an illustrative project which revolves around the theme of a paradox. Using the Mobius Loop as its central iconic symbol, the message I'm trying to convey will be that of "the beginning is also the end "

 

In this illustration I'd like to incorporate symbols/formulas of both religion and science. The snake eating it's own tail is a terrific spiritual symbol. However, is there such a scientific problem / formula in mathematics, physics or biology etc. which deals with this theme of a paradox. ie: that the beginning of the equation is also the same as the end?.. or perhaps a problem which turns back onto itself, creating a never ending loop?

 

Any ideas?

 

Thanks for any help

 

Jef

[Cap'n Refsmmat]

This isn't science-y, but you could throw in one of these:

 

[npts2020]

I don't know if this is helpful but it brings to my mind cycles like the food chain, birth/death, nitrogen cycle in ecological systems etc.

[the tree]

Take a look at the examples section of the Wikipedia article on Strange Loops, I think that Shepard tones are the most concrete example although Russel's paradox is the most entirely maths orientated. All the Gödel stuff is a bit well, complicated.

 

In a more physical setting, observer dependency has some interesting implications for our ideas of cause and effect a la the Schrödinger's cat analogy.

[Jeff P]

Thanks for the feedback

 

 

I've been reading the Goedel, Escher, Bach, book. Quite the hefty read!

 

I guess I was inquiring if there was an existing, well known mathematical formula (or at least well known among mathematicians) that would fit my paradox quarry.

 

 

Perhaps i'll have to modify my layout.

 

 

Thanks again

 

Jeff

[Kyrisch]

[math] A = !A[/math] is a pretty standard logical paradox (A equals not-A).

[Tom Mattson]

Paradoxes of self-reference are notorious in logic.

 

"This sentence is false."

 

Another one is

 

"The sentence below is true.

The sentence above is false."

[Kyle]

You could mention a lot of stuff with complex numbers if you wanted.

 

Like the roots of complex numbers circle around the complex plane, arriving back where they started:

 

And e^(i theta) equals e^(i [theta + 2 k pi]) for k being an integer.

 

Also anything involving sin or cos. Adding 2pi just brings you right back to where you were.

[Tom Mattson]

Those aren't paradoxes though...

[the tree]

No, but they answer the question asked in the OP.

[Jeff P]

Thanks!

 

You could mention a lot of stuff with complex numbers if you wanted.

 

Like the roots of complex numbers circle around the complex plane, arriving back where they started:

 

And e^(i theta) equals e^(i [theta + 2 k pi]) for k being an integer.

 

 

That image is the sort of thing I’m looking for, It'll make a great background… thanks

 

 

Also anything involving sin or cos. Adding 2pi just brings you right back to where you were.

 

 

Could you give me an example?

 

 

 

[math] A = !A[/math] is a pretty standard logical paradox (A equals not-A).

 

Thank you Kyrisch

 

Is this a true formula? I really like the simplicity.

 

 

 

Thanks’ again for all the help…

 

Of course you could have easily given examples of complete gibberish..lol. Being the math scholar that I am (which I’m not, btw) I wouldn’t know the difference.

Still, I’m attempting to incorporate at least a sense of accuracy , and even interplay on some of the formulas.

 

 

 

Hmm.. a thought occurred to me.

Is there a copyright held for a mathematical formula ?

 

 

 

Jeff

[Kyle]

Could you give me an example?

 

Sine and cosine are important for almost any part of mathematics and physics. They are cyclical in at least two ways:

 

First, as you can see they repeat. Choose any position on the graph. If you add or subtract 2pi to that x-value, you will arrive at the same place. For instance at x=0 you have sine at 0 and cosine at 1. At 2pi you have the same situation. This goes on forever.

 

Secondly, when you differentiate sine and cosine you get repetition.

The derivative of sine is cosine.

The derivative of cosine is -sine.

The derivative of -sine is -cosine.

The derivative of -cosine is sine.

 

And so on...

 

A similar "end is the beginning" situation occurs with e^x

The derivative of e^x is e^x, and so on...

[Kyrisch]

Thank you Kyrisch

 

Is this a true formula? I really like the simplicity.

 

It's not really a formula, it's what is called a falsum, or a logical statement that always evaluates as false. It is the opposite of a tautology, which is a logical statement that always evaluates as true, and the negation of a tautology is always a contradiction, or paradox.

 

Another sense of the word paradox is a statement that can neither be evaluated as true or false, such as (as I know has been cited already) "this statement is false".

 

An awesome form of this is the set of all non-inclusive sets (which cannot logically exist). If a set is inclusive if it includes itself (on such set would be the set of all sets), then the set of all non-inclusive sets would either exclude itself (therefore becoming non-inclusive and thereby fulfilling the parameter) or include itself (and thereby become inclusive, failing the parameter).

[Mr Skeptic]

Which came first: the chicken or the egg?

Also, if you liked the Möbius strip, you may also like the Klein Bottle

In mathematics, the Klein bottle is a certain non-orientable surface, i.e., a surface (a two-dimensional manifold) with no distinct "inner" and "outer" sides. Other related non-orientable objects include the Möbius strip and the real projective plane. Whereas a Möbius strip is a two dimensional surface with boundary, a Klein bottle has no boundary. (For comparison, a sphere is an orientable surface with no boundary.)

Edited March 10, 2009 by Mr Skeptic

[Jeff P]

Thanks, once again for the information.

 

..I have some elements to start with!

 

 

Jeff

[YT2095]

Which came first: the chicken or the egg?

 

the Egg.

any 1`st year biology students knows that Reptiles (which lay eggs) existed long before chickens.

[Sisyphus]

the Egg.

any 1`st year biology students knows that Reptiles (which lay eggs) existed long before chickens.

 

Clearly. It even works if you specify chicken egg. The line designating the first animal that could be genetically called a "chicken" as opposed to its almost-chicken ancestors is going to be arbitrary, but wherever you put it, that animal was an egg before it was a full grown chicken.

 

Really, it's only paradoxical if you don't know about evolution.

[Gasparri]

Hello

 

I'm an artist working on an illustrative project which revolves around the theme of a paradox. Using the Mobius Loop as its central iconic symbol, the message I'm trying to convey will be that of "the beginning is also the end "

 

Feel free to artistify my mobius junk...

 

http://www.youtube.com/results?search_query=patp2+mobius&search_type=&aq=f