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Re: Non-Euclidean Arithmetic
Posted:
Sep 8, 2012 6:55 PM
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On Sat, Sep 8, 2012 at 2:31 PM, Jonathan Crabtree
<sendtojonathan@yahoo.com.au> wrote:
> A note to all.
>
> Please keep replies relevant to the topic.
>
> My post is about arithmetic and defining operations.
>
I think when it comes to defining operators, the most interesting
languages are the ones that let you override a small vocabulary of
existing operators, as this allows a decoupling of specific glyphs
from internal logic. If I hand you a different character in place of
":", you should be able to write the same algorithms in this new
notation. A first test of the shallowness of a concept is if it dies
when the notation is taken away. Like calculus would survive minus
its famous Riemann Sum symbol, just as lambda calculus and functional
programming languages don't really hinge on using the Greek letter
lambda.
But then it does come down to style, trademark / hallmark or, shall we
say branding. Leibnitz and Newton were fighting over the "branding"
of calculus, as it clearly had a future, but they had different
notations and nomenclatures. Newton's was all about 'fluxions' with
little dots over the "functions" (as we call them today) whereas
Leibnitz notation ended up being the better known.
In that sense I'd say what you're doing is politics. You're trying to
insert new notation into the game, much as I do lobbying on behalf of
"dot notation" (not universal but widely used, to indicate something
belongs in or is a member of, used to specify the behaviors and
properties of "objects"). Getting dot notation into everyday STEM
curricula has been an uphill battle, but I'd say today many of not
most scientists are familiar with it, thanks to their need for
computing and reliance on modern languages such as Python and others.
> Philosophy is down the hall and politics is in building B.
>
Which hallway is Politics? Never mind, I'll just follow your voice.
Kirby
> Thank you.
>
> ########
>
> I have defined multiplication for the rationals as mk = the combination of m either added to or subtracted from zero k times ie multiplication is the combination of a multiplicand either added to or subtracted from zero as many times as there are unities in the multiplier.
>
> My definition of mathematical scaling is 'a change of magnitude created by making the multiplier the unit of measure.
>
> Multiplication involves many nstances of the same object in units or parts and relates to multi-tude.
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