"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."
Writing software is not merely mathematics. But, if an AGI would write Java or C# it would be extremely mathematical IMO since we "cheat" a lot due to the limitations we have in easily expressing ourselves using mathematics. So we throw in a lot of loops and other kludges and shortcuts. When I say an AGI here I mean a sufficiently intelligent AGI or as another example one could imagine a super advanced alien race writing code in Java. I assume this based on guestimation of energy expenditure. An increase in mathematical sophistication implementation results in less bit flips needed to run the app to achieve goals. so an increased intelligence would be able to inject more efficiency, modularity and dynamism. Mathematics contains and allows for that. Code "kludges" due to our intelligence limitations make up for it using more bit flipping and memory moving intensive source code basically. This is a general assumption on my part that I feel confident in. John From: Aaron Hosford [mailto:[email protected]] 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 | <https://www.listbox.com/member/archive/303/=now> Archives <https://www.listbox.com/member/archive/rss/303/23050605-2da819ff> Error! Filename not specified.| <https://www.listbox.com/member/?&;> Modify Your Subscription <http://www.listbox.com> Error! Filename not specified. AGI | <https://www.listbox.com/member/archive/303/=now> Archives <https://www.listbox.com/member/archive/rss/303/248029-3b178a58> Image removed by sender.| <https://www.listbox.com/member/?&;> Modify Your Subscription <http://www.listbox.com> Image removed by sender. ------------------------------------------- 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
<<~WRD016.jpg>>
