There are many path-breaking areas of research at the nexus of meaning and matter. I am particularly interested in the following areas, with the specifics described below.
Table of Contents
The problems of quantum physics are legend, but the solution to these problems is still not known. My angle to research in quantum theory is that quanta are not things, but symbols. Symbols have semantic properties that make them behave like concepts, rather than things. The paradoxes of quantum theory vis-a-vis classical physics are problems in understanding how concepts behave differently than classical particles.
I believe that current quantum theory requires a new mathematical formulation that derives the physical aspects of quanta from their semantic aspects. This new semantic theory will come from attempts to incorporate meanings within mathematics.
There is no area in science where the problems of meaning can be stated more succinctly and demonstrated more clearly than mathematics. The history of mathematical development is replete with paradoxes such as Godel’s Incompleteness, the Burali-Forti Paradox, Zeno’s Paradox, Tarski’s Undecidability, etc. These paradoxes arise through a curious mingling of everyday concepts and numbers. Mathematics uses many notions about numbers, but is unable to distinguish between them.
I believe that mathematics requires a new theory of numbers where numbers are known as types rather than quantities (types in everyday language denote concepts rather than quantities; numbers should also be treated as types – i.e. concepts). Attempts to include types in mathematics have led to paradoxes because types are derived from quantities, based on the idea that the world is primarily objects from which we construct meanings. The inverse proposition – that the world is meanings from which objects are created – is free from paradoxes, and represents a different foundation for mathematics.
The Nature Of Chemical Law
The central dogma in modern chemistry is that it can be reduced to the study of atoms, which are described using quantum theory. Since quantum equations cannot be accurately solved for any molecule that has more than a couple of subatomic particles, the dogma has hindered the development of a theory of reactions. Chemists use a wide variety of intuitions in chemical understanding but hardly any predictive laws exist.
I believe that chemistry deals with structures which have additional properties when atoms are treated as symbols of meaning. Structural meanings cannot be reduced to the properties described by quantum theory, and chemical reactions are governed by laws unknown so far. These laws will be understood through a study of semantic structures, in analogy to grammar, which creates new meanings using structures.
Evolutionary theory in biology claims that the diversity of species comes from DNA mutation and its replication. However, DNA replication does not have a sound theory behind it. Ordinary chemical molecules like water and salt do not replicate. What causes the DNA to replicate, and what type of phenomena does replication denote? Additionally, what properties in molecules make them descriptions of other molecules? Matter, in the classical sense, is at best a structure, and not a description of other objects. The DNA molecule, however, is a description of much of the body’s organization. Like the table of contents references the chapters in a book, the DNA too describes the body succinctly. New properties in matter are required to understand how a material object can be an abstract representation of something more detailed.
I believe that DNA replication represents a new class of intentional phenomena in which one molecule is a description of another molecule. Biologists freely talk about information in biology in the sense that the DNA encodes meaning, but the representational properties of meaning have no explanation. DNA replication and transcription correspond to a new type of property in matter where one object describes another object.
The failure of artificial intelligence (AI) to elicit intelligent tasks such as language comprehension (leave alone creativity, problem solving and metaphorical thinking) has led most scientists to recognize that computers cannot deal with meaning. Why? Because a token in the computer has physical properties but no meaning; the programmer supplies that meaning during designing, writing and testing programs. In what way is the human mind able to design, write and test programs that a computer cannot? How does a human mind fix problems in a computer program when Turing’s Halting problem proves that it is impossible to write a program that will detect the program’s problems?
Advances in semantic computing depend on advances in mathematics and physics where a symbol can denote types besides quantities. Computing theory has an important role in delineating the necessary types for different classes of problems. In other words, semantic computing is about finding the elementary symbols and operations (i.e. language) using which any arbitrary semantic program can be written, compiled, and executed.