A new point of view on Math language

[Doron Shadmi]

You can find this point of view here:

http://www.geocities.com/complementarytheory/CATpage.html


I'll be glad to get your remarks and insights.


Doron

[Hurkyl]

FYI the links at the bottom are invisible on my browser. (Opera 6.05)

[jammieg]

I'm no mathematician, but it seems like the fundamental idea here is that we humans tend to see the world in relation to other things, that is we define the degree of something based on what we know of something else when there is no absolute wrong or right and I'm guessing that this tendency for a discreet world view is a part of math?

[Doron Shadmi]

Hi Jammieg,

In Math there is no right or wrong.

All we can know is if some system is consistent or inconsistent.

An inconsistent system is not "wrong" but not interesting,
because through inconsistent system you can prove anything
without any limitations.

My fundamental idea is that if we use some concept in our system,
first of all we have to find and define its relations with its
opposite concept, otherwise our system is closed on itself under
one concept, and we lost our ability to explore this fundamental
concept.

In this case we can build an inconsistent system without even
knowing this.

I think that our abilities to find and define opposite concepts,
and the verity of the relations (if exist) between them, Is one of the most powerful tools that was developed through the evolution process.

Another thing is that no one (including mathematicians) wants
to change its familiar concepts or terms, but I think that if we
(again) learn from the evolution process, we find that in addition
to the variety concept (different axiomatic systems)
we have the mutation concept (changing familiar concepts or tems).



In my work I show two levels of complementary concepts by using
the set idea:

Power 0 = The simplest level of some set's content

Emptiness = Esim (sim for simplicity) = {} = 0 (without power symbol)

Continuum = Csim = {__} = 0^0

Discreteness = Dsim = {...} = Infinity many elements^0



Complementary Level A:

Content does not exit = {} = 0 <--> Content exists = ({__}~={...}) = 1
and level A is phase transition between 0(=on content) to 1(=content).


Complementary Level B:

{__} <--> {...}



By defining the relations between the above concepts, we find that the structure concept has more interesting information than the quantity concept because:

0^0 = infi^0 = 1 = content exists

and we can't distinguish between the contents by the quantity concept.


But it can be done by the structure concept because:

{__}~={...}

and we can learn that the structure concept has more information than the quantity concept.

[Doron Shadmi]

Dear Hurkyl,

Please use Windows Explorer-like browser.

My pdf file is bigger than the limitations of this forum, sorry.

(if it doesn't help please look at the private message that I
sent to you)