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Re: Non-Euclidean Arithmetic
Posted:
Sep 11, 2012 9:50 PM
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On Tue, Sep 11, 2012 at 3:52 PM, Paul Tanner <upprho@gmail.com> 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".
For your stance to appear heroic, you must keep "repeated addition"
from meaning anything close to "changing a length".
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.
You've made it your business to hobble one of the memes to prove the
superiority of the other.
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.
Where we agree is "multiplication" is neither one thing nor the other,
neither repeated addition nor scaling, or rather, it is all these
things and more.
You can multiply modulo N, you can concatenate, you can compose
functions and permutations, you can rotate polyhedrons (matrix
multiplication, or
quaternions).
All of these operations may be presented as "multiplication" of one
kind or another.
> And this ""non-computable" is just daft" remark causes me to again
> reiterate everything in my post in this thread
>
> http://mathforum.org/kb/message.jspa?messageID=7887042
>
Yes, you tend to regurgitate on cue, a known technique in the NFL
(National Forensic League).
As debaters go, you definitely know some of the tricks. That's good.
People should be good at rhetoric, in order to defend their points of
view.
> and especially what I said here:
>
> "The crux of all this is that those who think that "multiplication is
> repeated addition" is just fine for R seem to treat the irrationals as
> not all that important, just a side curiosity, just "those numbers
> over there" that "don't really count" for what is really important
> (which seems to be finite computation for those who think this way
> about multiplication), and all that. But again, it's the irrationals
Whereas somehow your favored "scaling" meme is starkly precise about
the difference?
You can always tell when scaling whether irrationals were involved?
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.
When it comes to absolute distance from 0, and changing that, based on
a binary operation, you've given us no reason to treat Q and (R-Q) any
differently, from the point of view of the scaling model.
Sure, we can both turn to the audience and recite what we know about
those differences, but they're not intrinsic to the scaling model.
As evidence: the ancient Greeks used scaling for a long time before
they formalized any position on incommensurability and non-rational
length measures.
The so-called "real numbers" are a relatively recent cultural
invention, and multiplication was going on a long time before they
were promulgated.
That goes to my point that models of multiplication that sometimes
obscure differences between species of number are not thereby "bad" or
"misleading". They come from a time when different games were played.
And different games are played even today.
You've accepted scaling all along.
Just without explaining how taking 1/pi of a pie (a slice) is not
adding that amount to my plate and subtracting it from the pie. And
if I take 4/pi slices of pie, I'll need more pie than one. That's
repeated addition. You can do it with a calculator and explain that
there's rounding in the real world.
Kirby
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