Bruno, It's been a long holiday weekend here in the US, Bruno, thank you for your reply, and your patience for my responce.
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 commentary. 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 mathematics. 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 > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to email@example.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---