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. On Tue, Jan 8, 2013 at 10:16 PM, David Clark <[email protected]>wrote: > My point was that the formula looks like Math but isn’t.**** > > ** ** > > My syntax isn’t just another way of writing Math but a different way that > only looks something like Math. My reasons for only using 3 levels of > precedence in a full condition has nothing to do with some higher order > axiom. Like I already said, some programming languages have up to 20 > levels of precedence but I wanted to spare programmers having to remember > them all. Not Math, just plain old real world simplicity.**** > > ** ** > > Math is based on axioms while the language I have created has other CS > concepts that are quite different. I limit how long variable names can be > because I don’t like typing all those characters. To make sure I can reuse > the names of functions that I like, I made all function and variable names > relative to their Object Container or function. Just plain old CS > practicality.**** > > ** ** > > David Clark**** > > ** ** > > *From:* Aaron Hosford [mailto:[email protected]] > *Sent:* January-08-13 2:04 PM > > *To:* AGI > *Subject:* Re: [agi] Why Logic & Maths Have Sweet FA to do with Real > world reasoning**** > > ** ** > > But I could describe the way that expression is interpreted in strictly > mathematical terms. (Though I would hate to waste my time on such a useless > endeavor.) You've just described a different way of writing down the same > meaning. There is nothing intrinsically special about the way standard > mathematical notation is used. It was an accident of history. I could just > as well write it out in reverse polish notation.**** > > ** ** > > y 5 2 + b * :=**** > > ** ** > > This is still math, just a different dialect. We can invent new dialects > all day. This dynamic extensibility is one of the wonderful things about > math as opposed to ordinary language; if math in its current form doesn't > do what I need it to do, I can just expand it in the direction I need it to > go. So long as the end result is unambiguous and I've communicated how it > works effectively to others, I'm good. The integral sign is a classic > example of this process in use. It's just a fancy S (for "sum") made up to > simplify the expression of a complex construct for which the existing tools > of the time were inadequate. **** > *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
