Thus spake Robert Holmes circa 10/01/2008 12:44 PM: > Hmmm.... not sure about that Glen. Seems to me that your "formalism" can be > pretty freely applied. So give me a specific example - when I'm coding > Python what is the specific formalism that I am using? Please feel free to > use equations.
It is pretty free because it's a turing complete formal system. Here are the general categories of the alphabet: None, NotImplemented, Ellipsis, Numbers, Sequences, Set types, Mappings, Callable types, Modules, Classes, Class instances, Files, Internal types And here are some of the inferential operators for deducing one statement from previous statements: +, -, /, *, %, <<, >>, lambda, if, for, while, try, etc. It would take quite a bit of space to outline the entire formal system. Feel free to consult: http://docs.python.org/ref/ref.html > Or does your formalism just mean "something with a syntax"? In which case > French is math as well, as is English, as is music as is (continue ad > nauseam)... Excellent point. However, neither English nor French have a strict syntax. For example, I can say something like "You an apple, have." and you will understand what I'm saying. That's why we found Yoda to be such a cute character in those movies... well, that and because he's ugly, short, and green... and can kick ass with a light saber. No syntax error arises when I speak such "incorrect" sentences. That's because English is a language for describing reality/thoughts. Mathematics, too, is a language. And one can formulate incorrect sentences in math, too. Similarly, a good math teacher can even read the correct implication from an incorrectly stated mathematical sentence (math teachers do this all the time to determine how to teach their ailing students). However, in any _particular_ formalism (formulated mathematically), an incorrect sentence will be undoubtably incoherent. That's different from a _false_ sentence. E.g. "1 + 1 = 3" is a false sentence. But "1/inf" is an incoherent sentence (statement of existence) -- i.e. it is undefined. Is it coincidence that an incorrect Python sentence immediately halts the whole process, too? No, it's not a coincidence. It's because Python is a formalism and every statement is either parsable or not. There is no middle ground.... like tripping when winding up a pitch or putting the verb at the end of an English sentence. Python is a formal system and correct programs written in Python are valid mathematical transformations (deductions) from initial to final conditions. -- glen e. p. ropella, 971-219-3846, http://tempusdictum.com ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
