The Definition of Points
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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
From: Hero on 19 Mar 2007 19:13
Lester Zick wrote: > ...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. So You wouldn't accept the ropes and strings of the first geo-meters in egypt? Are You flexible enough to accept Origami-math for exact transcendentals? And another question: is the trace, left by a movement, not part of static geometry? It is an invariant of dynamic geometry. With friendly greetings Hero |