15 Some More Mathematical Concepts of Space, Dimension, Outside, and Inside

Foreword. My aim in this chapter is to introduce some further mathematical concepts which I believe will be helpful if we are to try to think further about the internal world.¹ Now, I am aware that many psychoanalysts are inclined to discount the value of mathematical notions for the study of the internal world. They seem to feel that there is no correspondence between psychical objects and mathematical abstractions. I believe that such views are based on a misconception of mathematics and a rather too simple-minded idea about the concepts regularly used by psychoanalysts.

Such critics often think of mathematics in terms of arithmetic. I must confess that if this were true I would be inclined to agree with them. In fact, arithmetical calculations do not have much of a part to play in our understanding of the internal world. The notions of outside, inside, and dimension, however, are matters for detailed study in mathematics and these concepts are quite clearly central to psychoanalytic thinking. Psychoanalytic conceptions about inside and outside are mostly taken without much thought from the more or less naive notions which are ordinarily employed in our everyday understanding of the physical world. Clear definitions and considerations of the spatial notions employed in psychoanalysis are absent. Because ordinary spatial notions can be expressed in mathematical ways, it seems likely that the formal consideration of exactly these concepts by mathematicians might be useful.

To understand what I have in mind the reader must allow me to present