I think this is more about how we use the term "mathematical" differently than anything. When I call something mathematical, I mean it can be expressed mathematically, or it is amenable to mathematical analysis. I think a lot of people use the term this way. I'm a bit surprised to find that other people use it differently, to mean that it is literally part of math and/or is expressed in mathematical notation. This difference in usage could potentially explain a lot of disagreement and misunderstanding on this list, not just in this particular conversation.
On Wed, Jan 9, 2013 at 7:43 AM, David Clark <[email protected]>wrote: > 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> > <https://www.listbox.com/member/archive/rss/303/23050605-2da819ff> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <http://www.listbox.com> > ------------------------------------------- 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
