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.