The Definition of Points
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From: Lester Zick on 19 Mar 2007 17:58 On Mon, 19 Mar 2007 10:42:43 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On 18 Mar 2007 11:12:39 -0700, "VK" <schools_ring(a)yahoo.com> wrote: >> >>> On Mar 18, 8:33 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >>>> Oh I don't actually disagree; I just can't tell exactly what all these >>>> qualifications amount to and mean. You've got "abstraction" and >>>> "perception" and "equivalence" and all sorts of terms mixed up in here >>>> that make me suspect none of us including you knows exactly what >>>> you're talking about in mechanically exhaustive terms. >>> If anyone of rivals (mathematics, philosophy, religion) would knew one >>> day "in mechanically exhaustive terms" what is a "thing without sides" >>> or say what is "infinity" - wow, the rest would come begging to clean >>> their shoos :-) >> >> Personally I don't agree. I see the issue of points with or without >> sides as almost frivolous as I've never known anyone who thought >> points had sides. >> > >You've met Ross, and I'm not adverse to the concept of points of various >dimensions with zero measure, depending on their spatial context. :) But zero is zero, Tony. I've speculated on the existence of "points" with infinitesimal dimensions. Just never on the existence of actual points with non zero dimensions. >>> <snip> >>>> Well maybe that would be true if your initial predicates had any >>>> specific and exhaustive value. But lots of things may be true of >>>> points without being essential to their definition. I don't understand >>>> what "ti en einai of infinity" is supposed to mean nor a "reversed >>>> infinity". >>> That was not a question which one of definition is correct, neither >>> "in mechanically exhaustive terms" nor even by some intuitive feeling; >>> well probably neither one. I was asking: do you believe that there is >>> one and only one correct definition of the point (a point on a line) >>> implied by the very nature of this entity? >> >> I think probably so. However my interest as I pointed out early on was >> more directed at whether lines are made up of points or not if points >> are in fact defined by the intersection of lines. >> > >Can't lines be defined mutually as the set of intersections with other >lines? Maybe, though that doesn't identify a root concept. More to the point though, Tony, it identifies a circular concept. The same problem with points defined as intersections of lines which in turn constitute lines. Just doesn't work in mechanically exhaustive terms. > I would say >that the point is undoubtedly the atom of space, indivisible while every >line or segment can be divided at any given internal point. In that >sense, the point is more elementary than the line. Elementary in a certain sense, yes. But constituents of lines, no. > The relevant >question, as I see it, is whether useful mathematics can be developed by >only looking at measureless points, or whether the concept of the line >is more central to what really flowers in science and math. A line >connects two points, and a point identifies the intersection between two >lines. Is one more "important" than the other? No. But lines occupy a similar station of relevance with respect to surfaces. Geometric figures are all boundaries. They aren't material artifacts or constituents of one another. What is the constituent of a shadow? >>> The fact that maybe no one can bring it in some mechanically >>> exhaustive terms right in this second does not change anything in the >>> question. >> >> No of course not. However the issue I'm really interested in doesn't >> require a mechanically exhaustive or any other kind of definition for >> points apart from what is mentioned directly above. >> > >Do you think ALL points are "intersections of lines"? I think so. But more to the point in this context is whether points are constituents of lines and the intersection of lines represent points. That's the specific circular issue I'm trying to address here. > I am not sure this >is so, especially when you consider a 1-D space like the number line, >where there are no other lines to intersect with. There are certainly >still some infinite number of points. But here, Tony, we just go back to the same old merry go round. Do geometric figures just represent boundaries or are they some kind of material substance with material constituents? >>> After all there is a number of unresolved problems not >>> because they don't have any solution but simply because they are not >>> solved yet due to different obstacles. >>> But as long as we arrived to such entities as "point", "line", >>> "infinite set", "natural number", "real number", "irrational number" >>> etc. - as long that: do you believe that each of them there is one and >>> only one proper mechanically exhaustive definition to find - coming >>>from the very nature of these entities? >> >> Once again probably so. I just haven't spent a lot of time on those >> issues as yet - if I ever do. >> > >Oh, do! Well, Tony, in the beginning I set myself three more or less physical objectives: mechanical elucidation of Michelson-Morley, analytical origin of Planck's constant and related quantum effects, and Hubble's constant. And so far the pickings have been mighty slim. I only got into mathematical issues because mathematikers turn out to be a bunch of silver tongued cloaked empirics on such issues as transcendental numbers and curves in addition to SOAP operas. So the outlook is a little grim at the moment. Apart from Bob's one time agreement on the non existence of a real number line I really haven't had any success. >>> So once found we may expect >>> them universally correct, so even for some civilization from another >>> star they will be necessary either the same or wrong (so the said >>> civilization did not find the proper definition yet)? >> >> Sure. The truth of what I'm after is universal in scope and not just a >> particular or local truth in the sense it is demonstrably so. >> >> ~v~~ > >I have some ideas concerning universal truth, but you might not find >them quite tautologically regressive enough. Or, you might. Well, Tony, the demonstration of universal truth is my idea. It's not really open to debate or alternatives. So unless you have something specific you'd like to ask about or suggest is wrong with my approach or defective in my arguments of what is necessarily universally true and why, tautological mechanics in general, or the mechanical basis for Boolean logic, I'd have to say the issue is pretty much just what it is and where it stands at the moment. This isn't a guessing game any more. ~v~~
From: Lester Zick on 19 Mar 2007 18:06 On Mon, 19 Mar 2007 09:04:41 +0100, "SucMucPaProlij" <mrjohnpauldike2006(a)hotmail.com> wrote: >"Lester Zick" <dontbother(a)nowhere.net> wrote in message >news:29erv29qotk1c65v9mruh7rdjl9biqmf0q(a)4ax.com... >> On Sun, 18 Mar 2007 18:07:13 +0100, "�u�Mu�PaProlij" >> <mrjohnpauldike2006(a)hotmail.com> wrote: >> >>>I have one question regarding sets but I can't find the answer. Maybe someone >>>can help me. >>> >>> >>> >>>I wonder if sets theory is self describing. >>> >>>Can you describe sets theory as a set? >> >> Are you talking about a set of all points or what? >> > >no, "set" as "any set" Well that's a much easier issue to address. Just draw up a list of predicates and apply tautological logic. Self description of the set then depends on whether one can determine the ultimate truth applicable to predicates in general. That in turns depends on whether "not not" or the "contradiction of contradiction" is self contradictory and whether "not" or "contradiction" is thus true of all predicates and necessarily so because tautological alternatives are self contradictory and hence false. In which case predicate sets constitute reiterative application of the formative principle for predicates in general of "not" or "contradiction" in mechanical terms. ~v~~
From: Lester Zick on 19 Mar 2007 18:17 On 19 Mar 2007 00:59:15 -0700, "Hero" <Hero.van.Jindelt(a)gmx.de> wrote: > Lester Zick wrote: >Hero wrote: >> >Lester Zick wrote: >> >> Hero wrote: >> >> > Lester Zick wrote: >> >> >> Hero wrote: >> >> >> >> >PS. I just wonder, if a point relates to the word "pointing"? >> >> >> >> I'm convinced the phrase "pointing out" is definitely related to >> >> >> "point". You can easily enough "point out" an irrational on a straight >> >> >> line using rac construction but you can't "point out" a transcendental >> >> >> on a straight line at all. >> >> >> >Using only rac construction ( ruler and compass) results in a >> >> >geometric handicap. Already before Euclid Hippias of Elis did his >> >> >quadratrix with other tools. >> >> >> Well to the best of my knowledge rac construction is the only >> >> mechanically exhaustive method of construction that actually specifies >> >> or defines some point. >> >> >> >Actually a transcendental, as well as an rational, is a mutual >> >> >relation to a one, a measure. A point can live an egocentric life, a >> >> >real number ( not natural number) arises out of a minimum of three >> >> >points. >> >> >> Not sure what this comment is in aid of. Transcendentals are defined >> >> on curves not straight lines. >> >> >The quadratrix is defined with two moving straight lines, one with >> >constant velocity, the other with constant change of angle, look here: >> >http://de.wikipedia.org/wiki/Quadratrix >> >> >And having just a line, one can not point at a point and tell, this >> >point is transcendental. Mark one point as a zero and another one as >> >One, so You have a measure. Now a wheel with radius 1, that is this >> >measure, placed with a contact point onto the zero and rolled along >> >the line exact one revolution will end up with a contact point on the >> >line and measure out a distance, which is in relation to the distance >> >between zero and one transcendental. >> >> Well sure, Hero, this is pretty much what I imagined. The difficulty >> is one of dynamic measures. Rac construction is static not dynamic. It >> requires motion to set up but none to measure. Your wheel of diameter >> one will roll out to an approximation of pi but since the measure is >> dynamic it will be affected by dynamic factors such as friction, >> temperature fluctuation, stretching, contraction, and so on. >> > >Your rac construction (of two distances in rational or algebraic >relation) is exact, a "mechanically exhaustive method of construction" >- in Plato's paradise. In Plato's hell a ruler is allowed to move with >constant speed. >Which gives us still another definition of point, that of a puncture. >The puncture of a compass-tip into a solid or through a surface. > >NB1: When You do a "mechanically exhaustive method of construction" of >a circle with a compass, the distance between the tips of the compass, >the radius of the circle is of course transcendental, when You regard >the length of the circle-perimeter as one [unit]. So now all Your rac- >constructions give trascendental length. Two different rooms in >Plato's space. >NB2: Euclid was not totally a Platonist, he defines solids like cones >with a dynamic construction by means of rotation. Well this is true, Hero. Which is the primary reason rac construction doesn't allow dynamics in actual measurements. However I'm of the opinion that if we can decipher what is actually happening to the point of a compass in dynamic terms of constant velocity and constant transverse acceleration we can nonetheless determine the mechanical nature and definition of a circle and other curvilinear forms exactly. However this still woudn't allow combination of dynamic and static measures. We couldn't just "roll out" a circular form on a straight line to "point out" pi this way. ~v~~
From: Lester Zick on 19 Mar 2007 18:59 On Mon, 19 Mar 2007 15:42:04 -0400, Bob Kolker <nowhere(a)nowhere.com> wrote: >Lester Zick wrote: >> They are if they're associated with points and points define line >> segments. > >And what if they aren't? The integers are the integers regardless of how >they are interpreted. So you and David don't associate integers with points? Then how do you "model" geometry and define circles using SOAP operas and how do you come up with a "real number line" which isn't real?A miracle I'd say. ~v~~
From: Tony Orlow on 19 Mar 2007 19:04
PD wrote: > On Mar 19, 10:48 am, Tony Orlow <t...(a)lightlink.com> wrote: >> PD wrote: >>> On Mar 18, 6:08 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >>>> On 18 Mar 2007 10:36:04 -0700, "PD" <TheDraperFam...(a)gmail.com> wrote: >>>>>> All of a sudden you want to talk about original posts? I mean like the >>>>>> original post where in response to your specific questions I spell out >>>>>> the combined vector analysis pertinent to Michelson-Morley and you >>>>>> just ignore it but subsequently pretend there is no combined vector >>>>>> analysis relevant to Michelson-Morley? >>>>> Actually, no, I didn't ignore it. Others could see my posts, but you >>>>> (and to all evidence) you alone said you could not. Then you claimed >>>>> that I was "channeling" through someone else, who plainly could see my >>>>> posts and was responding to them. You, of course, assumed that the >>>>> problem was not yours, and that whatever was happening was by my >>>>> choice or design. >>>> Well if not by design a rather peculiar lacuna in any event since you >>>> subsequently asked me to repeat my analysis of Michelson-Morley. >>> No, I asked you to do what you *claim* to do about your analysis of M- >>> M. >>> What you did in your "analysis" of M-M was propose (guess) a >>> polarization dependency of the speed of light, which you supposed >>> accounted for the null result. >>> But what you *claim* to do to establish truth of a proposal is to >>> catalog all alternatives and to demonstrate that they are false. This >>> you simply have not done in any explicit manner. If you have all those >>> in your notes somewhere in your bottom drawer, do please draw them out >>> and explicate them. >> Of course, PD, you know it's impossible to enumerate all possible >> alternative explanations for a phenomenon, and that's why science works >> the way it does. > > Agreed. Lester thinks not. Read that previous sentence any way you > want. > >> It seems to me Lester wants to find a formula for >> truth, rather than a process to detect falsehoods. > > Agreed. Lester is apparently uncomfortable with the lack of certitude > afforded by science, and though he claims to have a path to the > certitude he craves, he finds it much easier to spend his time issuing > polemics and diatribes than in getting anything done. > >> I don't see his >> vision in that respect, but I do agree with his disagreement regarding >> sets of points as full descriptions of geometric and physical objects, >> as far as he understands it himself. Right, Lester? >> > > No one says a set of points IS in fact the constitution of physical > object. > Whether it is rightly the constitution of a mentally formed object > (such as a geometric object), that seems to be an issue of arbitration > and convention, not of truth. Is the concept of "blue" a correct one? > > PD > The truth of the "convention" of considering higher geometric objects to be "sets" of points is ascertained by the conclusions one can draw from that consideration, which are rather limited. "blue" is not a statement with a truth value of any sort, without a context or parameter. blue(sky) may or may not be true. TO |