Essays on the real line? Are there any essays on real numbers (in general?).
Specifically I want to learn more about:


*

*The history of (the system of) numbers;

*their philosophical significance through history;

*any good essays on their use in physics and the problems of modeling a 'physical' line.
Cheers.
I left this vague as google only supplied Dedekind theory of numbers which was quite interesting but not really what I was hoping for.

The following books should cover your interests. Not all are strictly about real numbers, but are concerned with modeling the "physical continuum" or providing different foundations for analysis. A good starting point might be the entry Continuity and Infinitesimals in the Stanford Encyclopedia of Philosophy by J. L. Bell, who has lots of related articles on his homepage.
John L. Bell, The Continuous and the Infinitesimal in Mathematics and Philosophy
Philip Ehrlich, Real Numbers, Generalizations of the Reals, and Theories of Continua 
Oliver, Deiser, Reelle Zahlen: Das klassische Kontinuum und die natürlichen Folgen (German)
Richard Dedekind, Essays on the Theory of Numbers
Hermann Weyl, The Continuum: A Critical Examination of the Foundation of Analysis 
