On Tue, Sep 11, 2012 at 9:50 PM, kirby urner <email@example.com> wrote: > On Tue, Sep 11, 2012 at 3:52 PM, Paul Tanner <firstname.lastname@example.org> wrote: > >> Nonsense. >> >> You are just trying to resurrect the attempt to rescue repeated >> addition with this "roughly" talk I debunked in my post in this thread >> >> http://mathforum.org/kb/message.jspa?messageID=7884356 >> >> in which I said: >> >> "That you have to introduce a "roughly" part demonstrates the truth of >> what I'm saying when both factors are irrationals. >> > > I see that you're an adamant segregationist, eager to side with Devlin > and uphold the superiority of "scaling" over "repeated addition".
Well, it is much more general. It is the the only one that holds up universally and unchanged though all the reals and more generally on any set on which there is order that gives absolute value or magnitude.
> > For your stance to appear heroic, you must keep "repeated addition" > from meaning anything close to "changing a length".
Not so. It can mean that all it wants.
> > Taking 1/pi of a pie (of possibly irrational volume), pi times, cannot > be confused with adding 1/pi to itself a little more than 3 times to > get a whole pie.
Back to speaking of repeated addition to get "roughly" the output of the binary function to try to salvage the claim that repeated addition is as general as scaling even though it's not.
Again: It cannot model two non-computable reals in any way.
But scaling does quite easily. In my recent post in this thread
I give the model, a geometric construction that gives point (product) ab on the real number line given including any two points (reals) a and b including any two non-computable ones.
> > You've made it your business to hobble one of the memes to prove the > superiority of the other. >
No, just showing that one is in fact more general than the other. The "superior" term is yours.
> > It's not enough for "scaling" to stand on its own, you must denigrate > "repeated addition" by repeating repeatedly a watered down > presentation of what it means. >
Again, no, just pointing out the fact that it has to be redefined again and and again to the point it cannot apply at all.
> I consider it a tad hypocritical to be offering "scaling" as a > unifying heuristic, demeaning "repeated addition" (quite > unnecessarily) in the process, and then not showing how multiplying a > sphere by pi is any different from multiplying it by P, where P may or > may not be irrational. >
But that's why scaling is so universal - it's the same either way.
Again: See the geometric construction.
> > The so-called "real numbers" are a relatively recent cultural > invention, and multiplication was going on a long time before they > were promulgated. >
They just didn't understand the continuum even though they were using it, and so it is not recent.
Just because you don't give it a name or know its nature does not mean that it therefore does not exist.