4 ms·
Writing things on paper is just a term rewriting system [0] which is just another universal computational system. [0] https://en.wikipedia.org/wiki/Abstract_re
by konjin 6y ago
Writing things on paper is just a term rewriting system [0] which is just another universal computational system.
[0] https://en.wikipedia.org/wiki/Abstract_rewriting_system https://en.wikipedia.org/wiki/Abstract_rewriting_system
- 082349872349872 6y agoTuring was explicitly trying to abstract from the sort of symbol manipulation mathematicians of his time did with pen and paper. Presumably his angelic counterparts have no need of an infinite tape of finite symbols, and can use a single square with an infinite repertoire of symbols instead.
- konjin 6y agoTuring was interested in mechanical manipulation. The church turning thesis showed that he neededn't have bothered since lambda calculus, a term rewriting system, is equivalent to a Turing machine and dozens of other methods of effective computation. You can pick which ever is the most aesthetically pleasing.