Mathematics as Sign addresses both aspects--mental and linguistic--of this machine. The opening essay. "Toward a Semiotics of Mathematicw" (long acknowledged as a seminal contribution to its field), sets out Roman's underlying model. According to this model, "doing" mathematics constitutes a kind of waking dream or thought experiment in which a proxy of the self is propelled around imagined worlds that are conjured into intersubjective beingthrough sings.
Other essays explore the staus of these signs and the nature of mathematical objects, how mathematical ideograms and diagrams differ from each other and from written words, the probable fate of the real number continuum and calcus in the digital era,the manner in which Platonic and Aristotelean metaphysics are enshrined in the contemporary mathematical infinitude of endless counting, and the possibilityh of creating a new conception of the sequence of whole numbers based on what the author calls non-Euclidean counting.
1. Toward a Semiotics of Mathematics
2. Making Marks on Paper
3. How Ideal Are the Reals?
4. God Tricks: or, Numbers from the Bottom Up?
5. Counting on Non-Euclidean Fingers