The Definition of Points
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From: Bob Kolker on 17 Mar 2007 09:40 SucMucPaProlij wrote: > > Mathematikers do claim that math has nothing to do with reality but if it is > true you can't use math to prove it because math has nothing to do with reality. > It means that there is little possibility that math has some connections with > real world. Mathematics has an instrumental connection with the world. It makes physics possible. Isaac Newton first had to invent calculus to develop a physical theory of dynamic motion. Without mathematics there is no physics. Bob Kolker
From: SucMucPaProlij on 17 Mar 2007 10:22 "Bob Kolker" <nowhere(a)nowhere.com> wrote in message news:5629arF26ac36U1(a)mid.individual.net... > SucMucPaProlij wrote: >> >> I don't want you to expect too much because this is not mathematical proof, >> it is philosophical proof (or discussion). This is just the way how I explain >> things to myself. > > If it ain't mathematics and it ain't physics, it is bullshit. Philsophy, by > and large, is academic style bullshit. > Isaak Newton: Philosophiae Naturalis Principia Mathematica or "academic style bullshit" Think first, reply latter, Bob!
From: SucMucPaProlij on 17 Mar 2007 10:31 >> >> Mathematikers do claim that math has nothing to do with reality but if it is >> true you can't use math to prove it because math has nothing to do with >> reality. It means that there is little possibility that math has some >> connections with real world. > > Mathematics has an instrumental connection with the world. It makes physics > possible. Isaac Newton first had to invent calculus to develop a physical > theory of dynamic motion. > > Without mathematics there is no physics. > And I agree but can you tell me does point exist? How do you explain it? You don't have to lecture me about Newton. Newton is not subject of this discussion. And you don't have to reply if you don't understand my question.
From: SucMucPaProlij on 17 Mar 2007 10:46 "Bob Kolker" <nowhere(a)nowhere.com> wrote in message news:5629arF26ac36U1(a)mid.individual.net... > SucMucPaProlij wrote: >> >> I don't want you to expect too much because this is not mathematical proof, >> it is philosophical proof (or discussion). This is just the way how I explain >> things to myself. > > If it ain't mathematics and it ain't physics, it is bullshit. Philsophy, by > and large, is academic style bullshit. > Reality check: If I say "This is math" does it make it math just because I say so? If I say "This is physics" does it make it physics just because I say so? If I say "This is philosophy" does it make it philosophy just because I say so? How can you tell if something is math, physics or philosophy if you never saw this thing I talk about? Introduce yourself with Shakespeare!
From: Tony Orlow on 17 Mar 2007 11:42
Lester Zick wrote: > The Definition of Points > ~v~~ > > In the swansong of modern math lines are composed of points. But then > we must ask how points are defined? However I seem to recollect > intersections of lines determine points. But if so then we are left to > consider the rather peculiar proposition that lines are composed of > the intersection of lines. Now I don't claim the foregoing definitions > are circular. Only that the ratio of definitional logic to conclusions > is a transcendental somewhere in the neighborhood of 3.14159 . . . > > ~v~~ Hi Lester - How's it going? Yes, the relationship between points and lines is rather codependent, isn't it? I looked at some of the responses, and indeed, one can define points as tuples of coordinates, but of course, that all depends on defining a set of dimensions as a space to begin with, each dimension constituting an infinite line along which that coordinate is defined. In language, both points and lines are taken as primitives, since their properties are not rooted in symbols and strings, but geometry. So, we may be left with the question as to what the primitives of geometry really are, sets of points, or sequences of lines. That's the conundrum right, that differences and differences between differences are lines, and not points? :) Well, here's a thought I had that I think relates to your derivative perspective. I was considering the number line and geometrical representation of basic arithmetic operations, and in considering whether addition or subtraction was more basic, I noticed something interesting. In order to represent a-b, all we need to know is the locations of a and b. In order to represent a+b, we need to know the location of 0 as well, form a vector from 0 to a or b, and apply it to b or a, respectively, to find the sum point. So, in that respect, the difference between the two is more basic than the sum, since it requires less information. That sits well with your differences between differences. The specification of a given point on this line is the same as the difference between that point and 0. A number is a vector from the origin, a difference, not just a point. The elements of the tuple specifying the point represent offsets from the origin, in specific directions, defined by lines. Have a nice day. 01oo |