Thank you for pointing out my mistake about Turing versus von Neumann. Although I know most of the history of microcomputers because I worked on them since 1975, I am a little rusty on the details for computers in general.
Just because something can be represented in Mathematical terms doesn't make them Mathematical! I appreciate you agreeing "that CS is not merely mathematics" but I press this point mostly because I want people to understand that creating large complicated computer systems will require much more than just a Mathematical approach. David Clark From: Aaron Hosford [mailto:[email protected]] Sent: January-08-13 11:19 PM To: AGI Subject: Re: [agi] Why Logic & Maths Have Sweet FA to do with Real world reasoning Sorry, it was von Neumann, not Turing, although I believe their work was closely related and/or interdependent. Turing machines are used to study computational complexity in mathematical terms, but they are very unwieldy to implement in real hardware. The von Neumann architecture is the great grandfather of modern digital computers. http://en.wikipedia.org/wiki/Von_Neumann_architecture (Both Turing and von Neumann were mathematicians, BTW.) You are right that in programming languages, variables typically behave somewhat differently from how they do in mathematical statements. This is because variables in programming languages actually correspond to subscripted variables in mathematics, with the timestep of execution being the subscript. Thus, x := y would be represented in standard mathematical notation as x_(t + 1) = y_t, and the fact that y is not assigned to at the same moment in time would be represented as y_(t + 1) = y_t. (I hope my ASCII version of the notation is clear.) All data structures, and even entire computers plus operating systems, running programs, and files on disk, can be represented in mathematical notation. (Attempting to do so is not advisable.) The fact that we use these things for non-mathematical, practical purposes doesn't make them non-mathematical; it simply makes our use of them non-mathematical. But, having said all this, once again I'll come back around to say, you are correct that CS is not merely mathematics. I would compare this to saying a house is nothing more than a pile of bricks and other building materials. And doing CS requires skills completely different from those required to do mathematics. ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
