It's been a long holiday weekend here in the US, Bruno,
thank you for your reply, and your patience for my

Fromconventional math, everything you said was 
correct, put to me by a co-list friend as .. should I 
offer you a financial reimbursement for your answer:

            "1m$ that is: 0m$"  
:-) .

Well, I'm not sending you 1m$, but I will continue

Consider for a moment, the possibility that the entire
used ediface of mathematics is an analog of Abbott's
"Flatland".  That though we may think we are 'calculating'
in a completely identified domain, that the 'environment'
of mathematics is extensive in new ways, and that there 
are new/different operators needed to access the extended 

Consider G.Cantor.  Suppose I said that not only are
Aleph>0 regions of math calculations, but that addional
functions make all of those infinities - calculation
accessible.  That 'normal math' still applies .. but if
and only if .. notated as referencing each frame-of-reference
Aleph n.  That to segue (equationally transduce) from any 
Aleph to any Aleph requires additional notations marks, in 
order to keep separate what Aleph the immediate notation
referneces, or, mores into or out of.

You remarked that it is absurd to :

> "From (-5)^2 = 5^2 you will not infer that 5 = (-5), right?" 

Actually, what I suggest does -relate- to this question.

We make such presumption about positive or absolute value
numeration that when we do back-functioning we overlook
relations and information that might be inconvenient or
cumbersome to treat.  Such as differentiating an
already integrated operation.  That pesky throw-away
scalar transform value of (+C) is unceremoniously
thrown out because we assume is to be a non-consequential
shift- or spatial-translation factor that needn't
be considered in mathematical generalization.

When we take a square-root, we ignore the minus signs
option.  When we look at quantum equations, we keep the
positive set and ignore the negative set .. which in and
of itself is contrary to quantum-math philosophy .. where
all variables are included, even if anti-thetical. [M and not-M
are concurrent rather than computationally mutually exclusive.]

A closing thought for this morning (possible discussion
of particulars being left for another day):

--from an off-list letter, same list-subject 

Dear __ ,

I am broaching a substantially new logic.

      "1m$ that is: 0m$"

-is- a patent absurdity in current math.

The version that I came up with essentially
restructures the analysis of mathematics
as comparisons of dimensions.  I did one analysis 
around the pythagorean theorem that results
in a statement  b=b^2 for any and all numbers, b.
[with the autonomous inclusion of new +/- markers
that arrive everytime a dimension is added to
or calculated to.]  

What is missing in math notation are markers that
help a person to remember they may be co-navigating
several different dimensional fields at the same time,
where the left side of an equation is in 'm' dimensions
and the right in 'other than m' dimensions, yet
the equation is valid.  The trouble persists if the
notations presume that native dimensionality on both 
sides is identical.  

In -that- presumption, the numbers have to match conventional
math concepts and no such thing as " b=b^2 for any and all
numbers, b" is allowed or even sensible.

It is like trying to have perfect translation
among human languages.  Not possible.  It's only
when we convert languages into the larger 
information network of memes, that 'equal translation' 
makes sense.  That's what I'm doing.  Identifying 
a core realm of 'information' (albeit, mathematical
notions, concepts, information) that can transduce
as real and valid 'equalities' across the equals sign.

When the realm of dimensions is recognized as the
larger realm of mathematical memes.

If a person doesn't do that shift of 
consciousness/sensibilities, they'll never 'get it'.

 ... but I see a shining country of mathematics that
no one else seems to recognize .. yet.   Jamie"

Bruno, I know you are still going to treat this line of
thought/conversation as sophomoric. A natural reaction.
I can assure you it is 'of significance' however.

Best Regards,
Jamie Rose



Bruno Marchal wrote:
> Le 26-mai-06, à 02:50, James N Rose a écrit :

> > An example at the core of it is a most simplistic
> > definition/equation.
> >
> >                 1^1 = 1^0
> >
> > [one to the exponent one  equals  one to the exponent zero]
> >
> > To all mathematicians, this is a toss-out absurdity, with
> > no 'real meaning'.  n^0 is a convenience tool at best ;
> n^0 = 1, because 1= (n^m)/(n^m) = n^(m-m) = n^0.
> Or better n^0 = the number of functions from the empty
> set (cardinal 0) to the set with cardinal n. This 
> justifies also 0^0 = 1 (there is one (empty)
> function from the empty set to the empty set).
> > along with  'n/0 is 'undefined''.   We note the consistent/valid
> > notation, but walk away from any active utility or application.
> >
> > My thesis is that doing so was a missed opportunity.
> >
> > To be hyper-consistent, the equation set-up
> >
> >                 1^1 = 1^0
> >
> > indicates that there -must- be some valid states/conditions
> > (not just 'interpretation') when 0 and 1 are 'equal' in some
> > real meaning/use of the word "equal".
> Why? It is usual that a function (like y = 1^x) can have
> the same value for different argument. From (-5)^2 = 5^2
> you will not infer that 5 = (-5), right?  From
> sinus(x) = sinus(pi - x) you will not deduce that x = pi - x,
> right?
> >  If they can be substituted
> > in the above equation, without changing a resultant of
> > calculations (they are embedded in), then they must somewhere
> > somehow in fact be identical in some way or condition.
> You talk like if all functions are bijections (one to one function).
> >
> > The entire ediface of physics is hamstrung because of this,
> > because mathematical definitions and language compounded
> > the error by applying - actually DIS-applying - a related
> > concept .. the notion of 'extent' .. also known as 'dimension'.
> >
> > Physics and mathematics transform and wholly open up when
> > we throw away the old concept of 'dimensionless' and instead
> > reformulate -everything- as 'dimensional'.  Including zero;
> > including numbers unassociated with variables.
> >
> > As much as you are brilliant and mathematically inventive,
> > your statement  "some plain falsity (like p & ~p, or 0 = 1)"
> > shows you haven't quite awoken to everything yet.  I hope
> > I'm in the process of stirring you from your slumber.
> I am using the name 0, 1, ... for the usual numbers. 1 is different
> from 0 for the same reason that 1 cup of coffee is different from 0 cup
> of coffee, or that 1 joke is different from 0 joke ...
> Bruno

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