Formal symbol manipulation transforms and recombines words, numbers, or logical statements according to explicit rules. Symbols compress thoughts into packets that are easier to remember, inspect, and revise. section 1.2.1
Seeing multiplication as structure
A 6×8 grid can be viewed as six columns of eight dots or eight rows of six dots. Reversing the symbol order preserves the same 48 dots, making the commutative property more than a memorized manipulation rule. section 1.2.1
In natural-language processing, the technique connects writing, logical statements, and programming-language compilation. It represents thought symbolically, then reshapes that representation for communication or reasoning. section 1.2.1
