ABSTRACT

Mappings have still to be viewed phenomenologically more broadly, but this much can be said, that if mappings present themselves in any geometric context whatsoever, they are fi rst of all mappings of restricted parts of space, which can be indicated or fi lled by bodies. (Freudenthal, 1983, p. 231)

Many philosophers consider contact and tact as the condition for human forms of knowing to emerge. Whereas we can do without the other senses-beautifully exemplifi ed in the life story of Helen Keller or of Meschcheryakov’s students who became university professors despite their deaf-blind nature-we could not ever do without touch. The other senses come to be coordinated with and enabled when we are with contact, and in contact. Yet, perhaps because we experience the world as one given to all of our senses simultaneously, we tend to be unaware that the senses are not inherently coordinated and that what we “see”—i.e., perceive and understand-is not necessarily what we know when we can merely touch. There is a mapping that we learn when we are in contact with, as Freudenthal writes in the introductory quote, “restricted parts of space, which can be indicated or fi lled by bodies.” Although I understand the nature of phenomenological investigations differently from Freudenthal, I too use this term to denote my investigations into the problem of mathematics and its relation to the fl esh.