## Mathematical Theory of Understandability

**Mathematical Theory of Understandability**

**Michael Leyton**

**Abstract:** Creative advances proceed by the generation of increased levels of *understanding*. Therefore, one cannot understand creativity, unless one *understands understanding*. In one of my books, *A Generative Theory of Shape *(Springer-Verlag, 550 pages), I elaborate a mathematical theory of understanding – what it is, and how it can be produced. The central problem handled in the book is what I call the *conversion of complexity into understandability*. This leads to an extensive reformulation of computer-aided design, human and machine vision, the structure of software, robotics, and the laws of physics. There is no more important problem, for modern industry, than the conversion of complexity into understandability, as can be seen in all phases of the product life-cycle. The reason is that the modern world is dependent on large-scale engineering-systems integration. An example of one of the major obstacles to integration is the interoperability problem. Current studies estimate that the costs to industry of inadequate interoperability are enormous – in the billions of dollars. The interoperability problem, like all problems of integration, is, in fact, a crisis in understanding. Whether one deals with upgrading large legacy systems of software, or the transfer of a CAD model from one design program to another along the manufacturing supply chain, or the multi-disciplinary nature of engineering systems in an aerospace mission, one is dealing with the problem of understandability. And it is exactly the failure to handle this through the only solution possible – a rigorous theory of understandability – that is destroying industry's capacity to fulfill its goals. It is to solve this crisis, that I developed a mathematical theory of understandability. In this talk, I will give a very brief introduction to how this approach works, and is able to solve problems.

Michael Leyton Bio