By Steven Roman
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Closely related to this claim is the question whether it is possible for an algorithm to understand itself. Can the brain understand itself, either as a computer or in any other machine terms? This leads to the question of the internal vs. external observation of a system. In other words, does self-measurement lead to a different interpretation of the system than measurement obtained by an external observer? The state of a system as seen from within is very different from the state measured by an outside observer.
And if it not, as repeatedly emphasized by Einstein, we still have a first approximation whereby quantum uncertainty on one hand and the incompleteness of logic on the other join together in circular causation. It is in this sense that we suggested before that Gtidel's theorems can be interpreted as a kind of quantum-mechanical statements [Ref 88]. Provided quantum mechanics is incomplete without logic in the same way as logic is incomplete 42 without quantum mechanics, can we understand the intelligent brain by joining these two incompletenesses of Wigner and Gtidel together?
The purpose of this foundational section is to show that by exploring matrix theory it is possible to take the complexities of human thought and reduce them to intelligible and workable simplicities. We begin with the formulation of the key theorem which provided the main motivation for the development of matrix logic. Matrix theorem THE IMPLICATION INFERENCE IS THE MATRIX PRODUCT To gain insight into the matrix theorem, we treat thinking as of forming connections between some logical elements a, b, c, ....