This complementary Blog to the Chinese Challenge Blog is presenting studies to a mathematical theory of Diamonds. Diamond theory is studying for the first time, tabular categories as an interaction of categories and saltatories.
The idea behind this patchwork of conceptual interventions is to show the possibility of a “buffer-free” modeling of the crossbar architecture for memristive systems on the base of a purely difference-theoretical approach.
It is considered that on a nano-electronic level, principles of interpretation appears as mechanisms of complementarity.
The most basic conceptual approach to such a complementarity is introduced as an interchangeability of operators and operands of an operation.
Therefore, the architecture of crossbars gets an interpretation as complementarity between crossbar functionality and “buffering” translation functionality. That is, the same matter functions as operator and at once as operand – and vice versa.
Hence, the construction of an additional devise for translations between crossbars is conceptionally an inheritance of the old paradigm of (mirco)electronic computation, and probably or hopefully, superfluous.
The exercise is concertized by a an example of the cnceptual architecture of a multi-crossbar arithmetic processor in the sense of Blaise Laurent Mouttet’s patent.
Nevertheless, a new challenge arises, how to realize on a nano-technological level functional interchangeability of any complexity and complication?
This blog entry gives a first, albeit short critical reflection on the concepts of memristive systems and the history of similar movements. This entry is more or less a collection and compilation of theoretical and propagandistic citations about the future of memristive technology as it can be found in online publications and videos.
My own focus is on a possible interplay between memory and computing functions, at once, at the same place and time. A new kind of complementarity between computation and memory on a single chip without retarding buffering conditions, is contemplated.
The first time I had the honor to participate in a similar inauguration was in 1988 at the first annual meeting of the INNS (International Neural Networks Society) in Boston, organized by Harold Szu from DARPA.
It was an enormously powerful event during an Indian Summer week, perfectly organized and for that reason didn’t offer much space for improvised critical and meta-theoretical reflections. As a contemplative contrast I visited the Boston Computer Museum.
I had the chance to talk to Harold Szu in Boston, and recieved a friendly encouragement to continue with my work in Germany. But my approach was obviously far too strange to be included into the powerful new movement of neural network designs. Nevertheless I got some funding in Germany to continue my project of a “Theory of Living Systems”, at my former Institut für Theoretische Biowissenschaften, within and beyond the neural network paradigm.
Neither was Bernard Widrow given enough time at this mega-event to report from his historical results from the time of the very first neuro-technological “boom” in the 60s, his invention of the “memistor – resistor with memory”. Sounds familiar?
The movement was interested in the future only and missed to learn from the past. Approaches like Second-Order Cybernetics and autopoiesis had been totally unknown to the enthusiasts of the new neural network community, and Artificial Intelligence had just become obsolete (Minsky’s decree, the Mansfield Amendment (1969), AI-winter).
The success of the new artificial neural networks, from neuro-cybernetics to neuro-aesthetics, nevertheless, was and still is enormous and has changed our life radically – in peace and war.
LEON 0. CHUA, Memristor-The Missing Circuit Element
"This paper presents the logical and scientific basis for the existence of a new two-terminal circuit element called the memristor (contraction for memory resistor) which has every right to be as basic as the three classical circuit elements already in existence, namely, the resistor, inductor, and capacitor. Although the existence of a memristor in the form of a physical device without internal power supply has not yet been discovered, its laboratory realization in the form of active circuits will be presented in Section II.”