Notes

Chapter 12: The Principle of Computational Equivalence

Section 9: Implications for Mathematics and Its Foundations


Properties [of logical primitives]

Page 813 lists theorems satisfied by each function. {0, 1, 6, 7, 8, 9, 14, 15} are commutative (orderless) so that f[a,b]==f[b,a], while {0, 6, 8, 9, 10, 12, 14, 15} are associative (flat), so that f[a,f[b,c]]==f[f[a,b],c]. (Compare page 886.)


From Stephen Wolfram: A New Kind of Science [citation]