##
Real Computation

`Standard' models of computation—Turing machines,
Random Access Machines (RAMs), and even parallel
variants like the PRAM—all
operate on discrete objects: bits, Booleans,
integers; at most, rational numbers (fractions)
are considered in the form of numerator/denominator
pairs of integers. These are the entities to be read, stored, processed, and output.
A large amount of scientific computation, however,
evolves around continuum rather than discrete problems. Fields like fluid dynamics, computational material science, and space mission design are just
a few of them. In fact, most of applied
mathematics amounts to solving various classes of
ordinary or partial differential equations over the reals. This raises the need for a formal model to describe and analyze the prospects
and limits of computations over $\mathbb{R}$.
Leaving aside continuous-time (so-called analog, as opposed to clocked) computers,
most models are either of an algebraic nature
(such as the real-RAM aka Blum-Shub-Smale Machine) or produce approximations (like in Domain Theory,
interval arithmetic, Recursive Analysis and Weihrauch's TTE);
some even both (Hotz' analytic machines).