Galileo's Paradox
in [Math]
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From: Tony Orlow on 3 Dec 2006 00:28 Lester Zick wrote: > Tony, let me see if I can provide an alternative line of reasoning to > support my analysis. > Okely Dokums! > Over the past couple of years in addition to tautological analysis > I've also provided analysis of angular mechanics in corrected form. > And in that analysis I do make use of arithmetic combinations of > finites and infinitesimals. In particular I take finites such as the > radius of circles, r, and combine them with infinitesimal changes in > radius, dr, showing that for any finite multiple of dr, such as ndr, > the combination can change only infinitesimally such that r+ndr=r and > r remains finitely constant. I don't know if you followed that > discusion but the mechanics involved are identical to what you > suggest. > Yes, I thought it was encouraging to see the notion of a mixture there, though it didn't seem like it followed necessarily. It was more like, there could be an infinitesimal change, that wouldn't be detected. In any case, do go on... ;) > Now the problem for you and your idea of combining finites and > infinitesimals arithmetically is that you can't combine finites and > infinitesimals directly. Oh, then no dr/dt for you tonight, young man. And after you brushed your teeth already... In other words there is no way to say r+dr>r Except you just did it. > as you're trying to suggest because finites and infinitesimals don't > lie together on a common line with the same metric. Same line, different scale. > > In the case of angular mechanics this is also true. However I provide > a common metric for them by definitely integrating a finite velocity, > dr/dt, between 0 and dt which provides a finite dr of infinitesimal > magnitude. Uh, what? A finite dr of infinitesimal magnitude? What makes it finite? In other words you can't provide an arithmetic sum for > finites and infintesimals directly without first providing a common > finite metric for them through definite integration of some kind. > Yeah. That's what IFR's about. The line, Man. That's the common metric. _______________________________________________________________________ > This is how we can know arithmetic combinations of finites of finite > magnitude and finites of infinitesimal magnitude. Mathematically > modern mathematikers incorrectly analyze the same problem in the > reciprocal terms of n/dr instead of ndr and wind up with various kinds > of 00 they like to pretend follow the finites on a common real number > line. However this makes the proper analysis of angular mechanics > impossible unless one takes r to be an infinite and ndr to be finite. > > In any event I hope this clears up my perspective on analysis of the > arithmetic combination of finites and infinitesimals. Actually I got lost at the end there. Infinitesimals are things that, if you multiply them together, they disappear. *poof* <snip diggy dig> 01oo
From: Tony Orlow on 3 Dec 2006 00:45 Virgil wrote: > In article <4572510c(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > >> Virgil wrote: >>> In article <45704f2b(a)news2.lightlink.com>, >>> Tony Orlow <tony(a)lightlink.com> wrote: >>> >>>> Eckard Blumschein wrote: >>>>> On 11/29/2006 6:37 PM, Bob Kolker wrote: >>>>>> Tony Orlow wrote: >>>>>>> It has the same cardinality perhaps, but where one set contains all the >>>>>>> elements of another, plus more, it can rightfully be considered a >>>>>>> larger >>>>>>> set. >>>>>> Not necessarily so, if it is an infinite set. >>>>>> >>>>>> Bob Kolker >>>> What, is it not necessarily so that it CAN rightfully be considered a >>>> larger set, with some justification? It doesn't have a right to be >>>> considered that way? Why? Because it contradicts theoretical >>>> transfinitology? >>> Depends on one's standard of "size". >>> >>> Two solids of the same surface area can have differing volumes because >>> different qualities of the sets of points that form them are being >>> measured. >>> >> Absolutely true. I agree. >> >> A formula relating the surface area s to volume v of a given scalable 3D >> figure would boil down to a s=y^(2/3), given any linear unit of measure. > > So is TO claiming that all sets are "scalable figures", each of which > can be scaled to every other set using some ingeneous formula. I'm not the one claiming that everything mathematical can be captured as a "set", remember? >> >>> Sets can have the same cardinality but different 'subsettedness' because >>> different qualities are being measured. >>> >> True. > >>>> You do? Do you mean that the addition of elements not already in a set >>>> doesn't add to the size of the set in any sense? >>> In the subsettedness sense yes, in the cardinality sense, not >>> necessarily. In the sense of well-ordered subsettedness, not necessarily. >>> >>> TO seems to want all measures to give the same results, regardless of >>> what is being measured. >> Well, Virgilium, what I want, and I don't really think this is >> unreasonable or even unrealistic, is to have mathematics become a single >> cohesive system of knowledge, with respect to facts and rules, with >> respect to measure and the real world, such that there exists no >> contradiction within this "entire" "system". I guess that makes it sort >> of a science, and I apologize for how distasteful that may seem to you. :) > > What TO wants, TO has repeatedly shown that he not have the capacity to > get, at least in mathematics. Nor has he shown that anyone else has the > capacity to get those things, nor even that those things are worth > striving for. Dude, you're really bumming me out. Total downer, man. You need to, like, step off and chill, seriously, man. That was way uncalled for. We're gonna have to talk, like, later. Totally later, dude. Later. Whew. ;)
From: Virgil on 3 Dec 2006 03:33 In article <45725d9e(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > cbrown(a)cbrownsystems.com wrote: > > Tony Orlow wrote: > > > > <snip> > > > >> Anyway, ala Leibniz, each object IS the set of properties which it > >> possesses, so any two objects with the exact same set of properties are > >> the same object. > > > > But this begs the question: what do we mean, exactly, by a SET of > > properties? What exactly are we trying to say when we say "This set of > > properties is the same as this other set of properties"? > > > > Cheers - Chas > > > > Well, what we really mean is that there is a set of universal > properties, each of which is a set of values, and that each object is > defined by a set of values, one from each set of property values, such > that any two distinct objects differ in at least one property value. Was > that specific enough? No! Just more gobbledegook. You define "set of properties in terms" of a whole bunch of other undefined terms, so you are n better off. The only way to get off the round is to have primitive terms and axioms which tell you how these primitive terms are to be allowed to work.
From: Virgil on 3 Dec 2006 03:40 In article <45726460(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > > > What TO wants, TO has repeatedly shown that he not have the capacity to > > get, at least in mathematics. > > Dude, you're really bumming me out. Total downer, man. You need to, > like, step off and chill, seriously, man. That was way uncalled for. > We're gonna have to talk, like, later. Totally later, dude. Later. Whew. ;) Which flimflam proves my point.
From: Lester Zick on 3 Dec 2006 13:26
On Sat, 02 Dec 2006 13:26:13 -0500, Tony Orlow <tony(a)lightlink.com> wrote: [. . .] > >01oo > >(btw, do you like my Zickesque signature? It's like when I sign >responses to MoeBlee as "ToeKnee", though I'm starting to like TOEknee, >better, what with the Theory Of Everything reference and all. >Mathematical truth, tautologically determined or otherwise, IS the basis >for all reality. You'll see that eventually, Herr Lester. :)) Oh I see it right now, Tony, but there is no other epistemology of truth possible mechanically than finite tautological regression to self contradictory alternatives. By the way I noticed your signatures and thought that was what you were up to. But I was confused by changes from one to the other so I thought I'd let you settle on one signature before commenting. I like the effort to develop a kind of symbolic trademark for your posts. I get the TOE reference but the other looks a little confusing. I can't really construe it as anything more than the numerals "01" and infinity so I'm not really sure what it's supposed to mean. You might consider something like "1-00" if that's what you're after. Personally if I had to go in that direction I might use something like "0-0-0" as a kind of hyper infinity. Stumbling on these things takes a lot more effort than most people might think. 1% inspiration, 99% perspiration as Edison used to say. But at least you're making an effort. (I'll comment on the rest of your post later) ~v~~ |