Russell, You are absolutely right. BioDynamic's Big Dog learned to walk over uneven ground using evolutionary neural networks. So are ANN's math? Well, yes (my answer) and no. Actually, it depends on your concept of math - which I sense is rather rigidly defined within this discussion. ANN's can solve non-analytic equations, which are beyond differential equations.
http://www.youtube.com/watch?v=W1czBcnX1Ww Ken > -----Original Message----- > From: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] On Behalf Of Russell Standish > Sent: Wednesday, October 01, 2008 3:50 PM > To: [EMAIL PROTECTED]; The Friday Morning Applied > Complexity Coffee Group > Subject: Re: [FRIAM] Is programming a mathematical formalism > > Actually a robot would probably do it the same way we do - > trial and error with some kind of feedback loop. Solving > differential equations tends not to work too well in > controlling robots. > > But is the feedback loop used by the robot maths? The > computer code is, the formal structure of the loop is, a > model of something using it is. The execution of the code, > however, is not maths, AFAICS. > > Cheers > > On Wed, Oct 01, 2008 at 11:56:20AM -0700, Russ Abbott wrote: > > Is catching/throwing a ball math? A robot would do these > things using math. > > But we don't, and we don't prove the result. We just check out the > > result against reality. So why call it math? Or if you > wouldn't call > > it math, how does it differ from writing a program, which also > > produces a result/product/effect. We may not treat that result as a > > mathematical object. As with catching/throwing a ball, we > often just > > check it out against the reality of its use. > > > > -- Russ > > > > > > On Wed, Oct 1, 2008 at 11:48 AM, glen e. p. ropella > > <[EMAIL PROTECTED]>wrote: > > > > > Thus spake Robert Holmes circa 10/01/2008 11:29 AM: > > > > Is programming a mathematical formalism? No. I know > that when I'm > > > cranking > > > > out Python scripts I am not doing any math. > > > > > > Just to be clear, programming is the _act_ of > constructing a program. > > > As an act, it is not a formalism. However, the program > produced is > > > a construct within a particular formalism. To boot, that > formalism > > > is a mathematical formalism. > > > > > > So, when you are programming, you are doing mathematics, > even if you > > > don't realize it. The same is true of the child counting on her > > > fingers. She's doing mathematics even though she may not > realize it. > > > The same is true of the plumbing contractor when she > _figures_ out > > > how to lay pipe in a house. She's doing math, even > though she may > > > not realize it. > > > > > > Programming is (a form of) mathematics. > > > > > > But I don't want to give the impression that _everything_ > is math. > > > When we construct an actual/physical object, the object is not > > > (necessarily) a construct within a particular formalism. > So, when > > > we build something, say, a chair, we may or may not be > doing math. > > > If we did all the figuring prior to the construction, then the > > > construction phase isn't mathematics. If, however, we use the > > > various pieces to measure the other pieces and figure things out > > > during the construction process, then we're doing math. > > > > > > So, actions (and sensing) are not math. Of course, Guenther will > > > probably pop back in and say that _if_ the entire universe is a > > > mathematical formalism and all things in the universe are > constructs > > > in that formalism, then all actions and sensing are math, > as well. > > > But aside from that pathological ontological conclusion [grin], > > > there are non-math things. > > > > > > I would also posit that general thought (not calculation or > > > "figuring") may be non-mathematical. But I can't defend > that position very well. > > > > > > -- > > > 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 > > > > > > ============================================================ > > 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 > > -- > > -------------------------------------------------------------- > -------------- > A/Prof Russell Standish Phone 0425 253119 (mobile) > Mathematics > UNSW SYDNEY 2052 [EMAIL PROTECTED] > Australia http://www.hpcoders.com.au > -------------------------------------------------------------- > -------------- > > ============================================================ > 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 ============================================================ 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
