But obviously, human experience includes, among other things, the framing of purposes, impressions of beauty, and the deliberation of intractable problems, phenomena that it would be absurd to try to explain by way of mathematical statements
The Gordon hypothesis is that complex mathematical statements
are less likely to be operational relative to other economic statements: We offer evidence on this proposition.
So, Hawking's claim is that physical theories are like Godel's mathematical statements
in being self referencing, since both we and our physical theories are part of the universe we wish to describe.
This interchange of ideas among five philosophers of mathematics includes a discussion of non-realism as supported by Hugly and Sayward, in which they reject the assumption that mathematical statements
purport to refer to objects, bring up the issues surrounding the debate over pure and empirical arithmetic.
Unlike the problem Brush Up, both girls found the problem A Good Sport demanding and difficult to understand because it required two mathematical statements
to be manipulated simultaneously.
Finally, the pair melded the mathematical statements
into a program to run on an extremely fast, massively parallel computer.
The new model, a series of mathematical statements
describing the motions of periodic comets through the solar system, explains how streams of material from discrete active areas on a comet's crust can create the observed nongravitational shifts.