xiv Preface
The Astronomer is, again, a useful metaphor. The celestial globe,
the focal point of the painting, boldly places it into a cosmological
perspective. The Astronomer is reaching out to the Universe—but,
according to the widely held attribution of the painting, he is Ver-
meer’s neighbor and friend Antonij van Leeuwenhoek, the inventor
of the microscope and the discoverer of the microcosm, a beauti-
ful world of tiny creatures which no one had ever seen before. Van
Leeuwenhoek also discovered the cellular structure of living organ-
isms, the basis of the unity of life.
Microstructure of nerve fibers: a drawing by Antonij van Leeuwen-
hoek, circa 1718. Public domain.
The next principal feature of the book is that I center my dis-
cussion of mathematics as a whole—in all its astonishing unity—
around the thesis, due to Davis and Hersh [21], that mathematics
the study of mental objects with reproducible properties.
In this book, the Davis–Hersh thesis works at three levels.
First, it allows us to place mathematics in the wider context of
the evolution of human culture. Chapter 11 of the book is a brief
diversion into memetics, an emerging interdisciplinary area of re-
search concerned with the mechanisms of the evolution of human
culture. The term meme, an analogue of “gene”, was made popu-
lar by Richard Dawkins [167] and was introduced into mainstream
philosophy and cultural studies by Daniel Dennett [25]. It refers to
elementary units of cultural transmission. I discuss the nature and
role of “mathematical” memes in detail sufficient, I hope, for mak-
ing the claim that mathematical memes play a crucial role in many
meme complexes of human culture: they increase the precision of
reproduction of the complex, thus giving it an evolutionary advan-
tage. Remarkably, the memes may remain invisible, unnoticed for
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