A Mathematical Model of Consciousness

Consciousness is a major force driving the development of quantum leaps in science. Although it is elusive and fundamentally impossible to define directly, it can be directly experienced and indirectly expressed, for example, through language that articulates the level of consciousness of a person and a researcher. It is actually mathematics, which is considered the height of objectivity, wherein lies the key to the development of a new logic that will express consciousness in a scientific manner and lay the foundation for an enhanced language.

In the context of consciousness, we have developed new numbers called ‘Soft Numbers’ of the following form: a0∔b1. These numbers are analogous to, but different from, the complex numbers a+bi, whereby i=-1. Complex numbers were also new, once, but they eventually facilitated the development of electrical theory.

Regular mathematics usually avoids paradoxical situations in which one thing and its opposite exist simultaneously. However, in the history of mathematics, several famous paradoxes were created, such as Zeno’s paradox of Achilles and the tortoise, the liar’s paradox, Russel’s paradox and others. For years, mathematicians have attempted to cope with these paradoxes and in fact to eliminate them, and to this day there is a constant fear of discovering a paradox that will totally collapse the structure of knowledge of mathematics.  

On the other hand, the existence of consciousness is specifically related to the possibility of a space in which paradoxical situations can exist simultaneously. Thus, the theory we developed has made possible a Möbius strip that is, at one and the same time, both local with opposites (two sides) and globally unified (one side).

Researchers of consciousness are completely unafraid of paradoxes and contrasts; in fact quite the opposite. It is the positive tension generated between different situations that creates an alert consciousness and expands it. For years, and especially in the 20th century, many researchers (mathematicians, philosophers, etc.) were interested in mathematical paradoxes. In the first half of the 20th century, many efforts were made to formally (axiomatically) establish mathematics in order to solve them. We offer a unique solution. Our approach is that the language of mathematics can be richer if it fundamentally includes paradoxes (i.e., the simultaneous existence and non-existence of time and space), and therefore it is not necessary to ‘solve’ them. One of our points of departure in the development of Soft Logic is optic phenomena that demonstrate the possibility of choosing among several different situations and deciding what one sees. A fruitful example that we will use is the Necker cube, which is a drawing on a plane that appears as a 3-dimensional cube. Observers can choose one of two ways to decide which are the three sides closest to them, and of course both answers are correct

In the new system of coordinates, this phenomenon can be described mathematically as well. The solution we offer begins with the construction of a new system of numbers.

The new system of coordinates of Soft Logic enables distinguishing between –0 and +0, which facilitates the development of a new math of consciousness. The new language is based on two coordinates:  the one axis of real numbers, which are in fact multiples of the number one; this axis expresses the world of reality. Another axis is the zero axis of numbers, which are multiples and quotients of zero, expressing the world of inner consciousness. 

The bending of the Soft Coordinates system shows that Soft Numbers are a simple mathematical model of the Möbius strip.

In conclusion, the study of mathematics is one of the important keys to a scientific understanding of the concept of consciousness and a foundation for research in this field. Through the application of Soft Logic, we aspire to research and develop the mathematics of consciousness in the Laboratory for Consciousness Research and Soft Logic. In addition, we aim to gain an in-depth understanding of the concept of non-locality in physics and develop technological applications such as autonomous vehicles, medical imaging, data mining, brain research, and new forms of computation.

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