Survival

[Guest Doron Shadmi]

Survival

 

 

Most books that teach the language of Mathematics, ignore our cognition’s abilities to understand and define the fundamental concepts of this language.

 

Language is a tool that gives the cognition its ability to examine the object, the subject and the value of object/subject relations.

 

For billions of years, living things have been learning how to deal with internal and external challenges occurring in their ways, and as the phenomena of life becomes more and more complex, it needs better tools of communication that will give it the ability to save and develop life from the single gene to the existence of civilizations.

 

The language in its both inherited and purchased sides is the most significant environment of life phenomena, and through it life can flourish from generation to generation.

 

Any language is examined first of all by its ability to connect between at least two opposite properties: the simple and the complex.

 

This ability is the clearest signature of reality in the global memory of life, and this memory is the guarantee to their existence.

 

Because of this insight, we as living things have to take extra care when we are using a powerful language like Mathematics, because it has the straightest influence on our own survival.

 

An imprecise use of this powerful language (when the meaning of “precise” is not just technical formal precision but the ways of using its products to support and develop life) can quickly bring us to a dead-end.

 

Our abilities to avoid it are connected with our abilities to understand the deep relations between language, reality and the cognition that involved with them.

 

Through this participation, we can tune our life and lead them away from a dead-end.

 

The first hints to an imprecise use of this powerful language can be found when we are loosing our abilities to distinguish between the simple and the trivial and between the complex and the complicated.

 

The opposite of the trivial is the complicated, when by saying “trivial” we mean a non-deep reference between the cognition and the thing(s) it is referred to.

 

For example: our belief that our models are equivalent to reality, which leads us to the trivial conclusion that what holds in our models also holds in reality.

 

The indistinguishability between the complex and the complicated appears when the cognition tries to force its trivial conclusions on the reality, but then it become aware to the complexity of the reality and concluding that reality is complicated.

 

A question that should be asked by any civilization that is using a powerful language like Mathematics is: can we find signs of using Math in an incorrect way?

 

I think that a very brief look on our civilization gives us too many signs of complicated paths that lead us to nowhere.

 

If we want to avoid these obstacles, I think we have to include feedback (cybernetic) methods which reflecting the influence of a powerful language like Mathematics language on our life.

 

By this approach we get at least two main advantages:

 

a) Quality control based on tuned dynamic balance of the influence of Math language on our cognition, which supports our cognition's abilities to deal with abstract and non-abstract non-trivial complexity of the real life.

 

b) An improved ability to create deep and versatile relations between opposites, which give us better and more valuable conditions for flourishing life.

 

So the first step to this goal is to reexamine fundamental concepts .

 

Let us start by checking our ability to count.

 

The eye does not see itself until it is aware to its own limitations, and then it can be included as an explored element.

 

Now please change "eye" by "cognition" and read the above again.

 

The above point of view leaded me to ask myself what are the minimal conditions that give us the ability to identify and count things?

 

For example, let's examine this situation:

 

On the table there is a finite unknown quantity of identical beads > 1

and we have:

 

A) To find their sum.

 

B) To be able to identify each bead.

 

Limitation: we are not allowed to use our memory after we count a bead.

 

By trying to find the total quantity of the beads (representing the discreteness concept) without using our memory (representing the continuum concept) we find ourselves stuck in 1, so we need an association between continuum and discreteness if we want to be able to find the bead's sum.

 

Let's cancel our limitation, so now we know how many beads we have, for example, value 3.

 

Now we try to identify each bead, but they are identical, so we will identify each of them by its place on the table.

 

But this is an unstable solution, because if someone takes the beads, put them between his hands, shakes them and put them back on the table, we have lost track of the beads identity.

 

Each identical bead can be the bead that was identified by us before it was mixed with the other beads.

 

We shall represent this situation by:

 

((a XOR b XOR c),(a XOR b XOR c),(a XOR b XOR c))

 

By notating a bead as 'c' we get:

 

((a XOR b),(a XOR b),c)

 

and by notating a bead as 'b' we get:

 

(a,b,c)

 

We satisfy condition B but through this process we define a universe, which exists between continuum and discreteness concepts, and can be systematically explored and be used to make Math.

 

It means that what is called Natural number is at least a structural/quantitative information form.

 

Standard Math axioms that define the Natural numbers ignore our cognition's abilities to define them, and the result is a quantitative-only information form where cardinality (quantity) and ordinality (order) are both well-defined.

 

By this attitude, Standard Math is not aware of several structural/quantitative information forms that exist within any given quantity > 1, and uses only the wall-defined information forms that have no redundancy and no uncertainty.

 

By using Organic Mathematics ( http://www.geocities.com/complementarytheory/ONN1.pdf), any number is first of all an information form that can be understood only by cognition/object interactions.

 

From this point of view, redundancy and uncertainty cannot be ignored and they are taken as "first-order" (fundamental) properties of Math language, which is a paradigm shift of the Natural numbers concept that open for us a gateway to non-trivial complexity.

 

 

About non-trivial complexity:

 

Let us examine the balance concept.

 

For example: we have two pyramids, pyramid A and pyramid V.

 

Pyramid A stands on one its surfaces, and in this case we have a trivial balance problem.

 

Pyramid V stands on one its angular points, and in this case we have a non-trivial balance problem.

 

The skills of a self aware non-trivial complex system can be measured by its ability to use any balance degree that can be found between A and V polar states, in such ways that at least do not reduce the non-trivial complexity of itself and its environment, in the long range.

 

 

About Included-Middle reasoning:

 

Some analogy:

 

Let us say that the property of being a glue depends on some mixing between material A and material B.

 

A and B are not defined (exist) by each other, but when they are mixed together in a particular way, we get the property of a glue.

 

The most comprehensive principle of this point of view is based on the middle domain that can be found between at least two opposites, when the property of the middle domain is a new thing that cannot be found in each separate opposite.

 

And this is exactly the main principle of Included-middle logical reasoning, which define most of the time new products, which are the outcome of at least two opposites.

 

In other words, any non-trivial abstract/non-abstract product is first of all based on constructive associations between opposites as their first-order products, and then the rest of the middle domain elements, are some n>1 order products.

 

For further information about Included-Middle logical reasoning, please open http://www.geocities.com/complementarytheory/CompLogic.pdf , thank you.

 

 

 

What do you think ?

 

 

Doron