Stephen Wolfram

MARCH 7, 2022

One can view a symbolic expression such as f[g[x][y, h[z]], w] as a hierarchical or tree structure , in which at every level some particular “head” (like f ) is “applied to” one or more arguments. and at t steps gives a total number of rules equal to: &#10005. which we can read as “there exists something a for which equals a ”.

Mathematics 120

Mathematics Physics Computer Algebra 120

Stephen Wolfram

FEBRUARY 3, 2023

Sometimes textbooks will gloss over everything; sometimes they’ll give some kind of “common-sense-but-outside-of-physics argument”. Once one has the idea of “equilibrium”, one can then start to think of its properties as purely being functions of certain parameters—and this opens up all sorts of calculus-based mathematical opportunities.

Computer 92

Computer Energy Physics Construction 92

Stephen Wolfram

NOVEMBER 10, 2021

For integers, the obvious notion of equivalence is numerical equality. Then (by the assumed properties of equality) it follows that. But what about other models of computation—like cellular automata or register machines or lambda calculus? Some correspond to theoretical computer science.

Physics 122

Physics Mathematics Computer Construction 122