
Re: NonEuclidean Arithmetic
Posted:
Sep 8, 2012 6:55 PM


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 multitude.
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