Re: Theory versus idea

Posted by eaglesondouglas on November 22, 2003 at 11:45:31:

In Reply to: Theory versus idea posted by davidmac on September 21, 2003 at 04:25:04:

A theory as the idea given a relation appears a valid theory. A mathematical relation is only a single kind.

A topology used to derive a mathematical relation and hence used to cause the theory's definition is an abstracted topology.

And here the abstracted differential is the relation allowing this transformation of topology to any mathematical relation.

So, given a hamiltionian matrix geometry, state its
topology??

Applying the abstracted topology identiy is the
solution? Hamilton never realized the necessity to
place his matrix in a unique mathematical theory? A solution is surely possible.

A topology as the resolved abstract Hamiltonian is
considered only its integral. Except in physical theory
the concept of measure, as units, is left to foundational
definition.

Making the abstracted unit as the means of all topology differention. A solution appears as the cause of the
differential itself. I used Hamiltion's odd means of derivative solution as the hint.

A rather analytic solution to any differential was his
odd method. And it is of course using the abstract unit as its derivation from the abstract topology of the Hamiltionian.

No functions, only relations of a consistent mathematical
foundation are the outcome of the solution.

No theory need correspond to anything but the abstract physical theory in this independently defined mathematics.

So, just take the necessary unit and abstract it one time.
Take the eigen of the Hamiltonian!! A single applied transofrmation appeared once more. Abstract the eignvalue unit in relation to its eigenfunction unit, once more!!

And the appearance of the relation, of any mathematical relation to any geometric relation is once more the same
solution.

|*H| = 1 first

A = abstracted unit

|A||H|= 1 second

Making the first topology represent by the matrix, |H|
the integral of the eigenfunction identity matrix.

Implying the |A| matrix to be a necessary unit matrix for any measure given to the geometry.

And so the fundamental matrix |a| for any |A| is
the transformation of the second hamiltonina to cause
its integral.

|a|
___ = 1
|A|

Causing the dilemma of the ratio of units in foundational
theory of mathematics.

And so the abstract unit is to cause its own relation
to its own difference. A paradox resolved.

A theory of mathematical measure. All topology is implied to have the geometry unitless, for the reason of the dilemma resolved.

So just think about the transformation of the abstracted
|A| to this theory to imply the relation |a| as identity.

Causing the differential to have a integral in the same
relation always.

No dilemma. A differential is caused in relation to its necessity to exist.

SO, |a| = |A| is the identity to transform the two Hamiltonians.

|*H||a| = |A||H|

Making the use of the topology as the abstracted unit the solution to the entire theory's still existing dilemma.
Remove the matrix theory's need for the solution of |a|.

Cause this topology to always exist as the abstract unitless solution. And to normalize to the topology is
the means to always have the capacity to solve the differential in relation to its topology.

A theory is stated.

Douglas Eagleson
Gaithersburg, MD USA

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