A UNIFYING THEORY OF THE TOTALITY AND THE ALL
Posted: Fri Dec 09, 2011 9:23 pm
Consider the properties of operations and the set they act on:
The natural numbers are said to be closed under the operation of addition.
This simply means that if you add two natural numbers together you get another natural number.
The natural numbers are not closed under the operation of division.
I.e. you cant divide any arbitraly obtained natural number by any other and still get a natural number.
e.g. the natural number 2 divided by the natural number 3 yeilds the number 2/3 which is not in the set of natural numbers.
Now take these examples and imagine using these concepts when discussing the totality.
I beleive that we could have a set of all things (or every-thing) that is closed when using certain operations (of which i will speak later on).
Any two things when subjected to the operation will yeild another thing.
A thing being an artifact or being "constrained" by the axiom of identity.
Now what would the case be if we found an operation that was not closed in the the set of things.
We would have opened the door to the "rest" of reality.
"Things" that are not things (dont submit to the axiom of identity), imaginary things.
This would imply that the totality (imaginary and "real" things) is not the same concept as the set of all things (everything).
Two questions remain: what are the operations and how do we perform them and what is the nature of imaginary things.
Since i beleive that the axiom of identity is co-intwined with the concept of dimentionality that reffers to both traditional dimensions such as space as well as cardinal comparisons such as temperature and speed, the concept of cardinality does not apply in this realm.
Imaginary things are acardinal and so merge whith each other in a way that they dont.
Or rather using the word "they" already means that we have not understood what "they" (theres that word again) are about. (i spotted an "are" there too).
On the question of operations i am not clear though i know that the operation must have the quality of being beautiful or in other words have some aspects of symmetry. I find if i meet an equation that i havent seen before , it either strikes me as beautiful or it is wrong.
Of course that not exactly the "scientific method".
Could a quantum physicist on this site help me out by showing how mathematics (and its operatoins) describe matter and how ,matter (things) interact mathematicaly or in such a way that we can use the concept of operation in their interactions.
We also might need a broader generelisation of the higgs mechanism (which gives mass to particles) to cater for this.
Problems:
These concepts lead to the idea that perhaps there is an operation that the totality (imaginary and real things) do not have closure and so there is other "things" that are neither imaginary nor real. Ofcourse leading to an infinite regress , though i have read that all complex numbers are closed under *any* operation so theres no other numbers more allencompassing than complex ones .Though i found that *dicey* it could also apply here.
How are the real and imaginary seperated and doesnt separation imply cardinality even to acardinal (imaginary) things?
The framework on which these different "thing" realms could be "real" even though things attached to them arent.
One last problem is that language fails us when we come to explain these things and i may have gotten confused with the different tenses (not only temporal ones) of the words i used.
What do you think?
The natural numbers are said to be closed under the operation of addition.
This simply means that if you add two natural numbers together you get another natural number.
The natural numbers are not closed under the operation of division.
I.e. you cant divide any arbitraly obtained natural number by any other and still get a natural number.
e.g. the natural number 2 divided by the natural number 3 yeilds the number 2/3 which is not in the set of natural numbers.
Now take these examples and imagine using these concepts when discussing the totality.
I beleive that we could have a set of all things (or every-thing) that is closed when using certain operations (of which i will speak later on).
Any two things when subjected to the operation will yeild another thing.
A thing being an artifact or being "constrained" by the axiom of identity.
Now what would the case be if we found an operation that was not closed in the the set of things.
We would have opened the door to the "rest" of reality.
"Things" that are not things (dont submit to the axiom of identity), imaginary things.
This would imply that the totality (imaginary and "real" things) is not the same concept as the set of all things (everything).
Two questions remain: what are the operations and how do we perform them and what is the nature of imaginary things.
Since i beleive that the axiom of identity is co-intwined with the concept of dimentionality that reffers to both traditional dimensions such as space as well as cardinal comparisons such as temperature and speed, the concept of cardinality does not apply in this realm.
Imaginary things are acardinal and so merge whith each other in a way that they dont.
Or rather using the word "they" already means that we have not understood what "they" (theres that word again) are about. (i spotted an "are" there too).
On the question of operations i am not clear though i know that the operation must have the quality of being beautiful or in other words have some aspects of symmetry. I find if i meet an equation that i havent seen before , it either strikes me as beautiful or it is wrong.
Of course that not exactly the "scientific method".
Could a quantum physicist on this site help me out by showing how mathematics (and its operatoins) describe matter and how ,matter (things) interact mathematicaly or in such a way that we can use the concept of operation in their interactions.
We also might need a broader generelisation of the higgs mechanism (which gives mass to particles) to cater for this.
Problems:
These concepts lead to the idea that perhaps there is an operation that the totality (imaginary and real things) do not have closure and so there is other "things" that are neither imaginary nor real. Ofcourse leading to an infinite regress , though i have read that all complex numbers are closed under *any* operation so theres no other numbers more allencompassing than complex ones .Though i found that *dicey* it could also apply here.
How are the real and imaginary seperated and doesnt separation imply cardinality even to acardinal (imaginary) things?
The framework on which these different "thing" realms could be "real" even though things attached to them arent.
One last problem is that language fails us when we come to explain these things and i may have gotten confused with the different tenses (not only temporal ones) of the words i used.
What do you think?