The Definition of Points
Lester Zick
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~~
Ross A. Finlayson
You should ask me.
Ross
--
Finlayson Consulting
PD
Interestingly, the dictionary of the English language is also
circular, where the definitions of each and every single word in the
dictionary is composed of other words also defined in the dictionary.
Thus, it is possible to find a circular route from any word defined in
the dictionary, through words in the definition, back to the original
word to be defined.
That being said, perhaps it is in your best interest to find a way to
write a dictionary that eradicates this circularity. That way, when
you use the words "peculiar" and "definitional", we will have a priori
definitions of those terms that are noncircular, and from which the
unambiguous meaning of what you write can be obtained.
PD
Sam Wormley
Point
http://mathworld.wolfram.com/Point.html
A point 0-dimensional mathematical object, which can be specified in
n-dimensional space using n coordinates. Although the notion of a point
is intuitively rather clear, the mathematical machinery used to deal
with points and point-like objects can be surprisingly slippery. This
difficulty was encountered by none other than Euclid himself who, in
his Elements, gave the vague definition of a point as "that which has
no part."
Douglas Eagleson
Points are rather importent things to try to get correct. I am still
looking for some references, easy web kind, to allow topology to
express points.
And if a point was expressable, a function. And so nth topoogy is
possible, but I need a Matlab transform that links a theorm, to the
applied coordinate. And so the basic idea is to allow points where the
size as infinity are expressable.
This solves a symmetry problem. And resolves the question of sets of
rationals to irrationals as true sized, infinities!
So the topology of the point is a theorm I need.
Any ideas?
Thanks Doug
SucMucPaProlij
"PD" <TheDrap...@gmail.com> wrote in message
news:1173810896....@q40g2000cwq.googlegroups.com...
hahahahahahaha good point (or "intersections of lines")
SucMucPaProlij
point is coordinate in (any) space (real or imaginary).
For example (x,y,z) is a point where x,y and z are any numbers.
line is collection of points and is defined with three functions
x = f(t)
y = g(t)
z = h(t)
where t is any real number and f,g and h are any continous functions.
Your definition is good for 10 years old boy to understand what is point and
what is line. (When I was a child, I thought like a child, I reasoned like a
child. When I became a man, I put away childish ways behind me.....)
Randy Poe
The modern axiomization of geometry due to Hilbert leaves
points, lines, and planes undefined. In fact, he famously
said about this construction: "One must be able to say at
all times-instead of points, lines, and planes---tables,
chairs, and beer mugs."
In other words, despite whatever intuition and inherent
meaning we might ascribe to these things has no effect
on the mathematical structure.
No doubt Lester will find this approach lacking and
assert he has a superior axiomization built up from "infinite
epistomological ontologies of finite tautological
regression" or something equally meaningless.
- Randy
Clifford Nelson
"SucMucPaProlij" <mrjohnpau...@hotmail.com> wrote:
Primary means like prime, first. First things first, second things
second, third things third, etc..
Bucky Fuller's kindergarten teacher gave her class semi-dried peas and
toothpicks to build "structures". All of the kids built structures that
had 90 degree angles like squares and cubes except Bucky. He could not
see because he didn't have a pair of glasses yet, and felt that the
triangle and tetrahedron were strong, but the square and cube did not
hold their shape. He got a patent for the structure he made about 60
years later. He thought like a child for about 60 years and started to
write Synergetics. 15 years later the first volume was published.
See:
Cliff Nelson
Dry your tears, there's more fun for your ears,
"Forward Into The Past" 2 PM to 5 PM, Sundays,
California time,
http://www.geocities.com/forwardintothepast/
Don't be a square or a blockhead; see:
http://bfi.org/node/574
http://library.wolfram.com/infocenter/search/?search_results=1;search_per
son_id=607
Jesse F. Hughes
> Interestingly, the dictionary of the English language is also
> circular, where the definitions of each and every single word in the
> dictionary is composed of other words also defined in the dictionary.
> Thus, it is possible to find a circular route from any word defined in
> the dictionary, through words in the definition, back to the original
> word to be defined.
The part following "Thus" is doubtful. It is certainly true for some
words ("is" and "a", for instance). It is almost certainly false
for some other words. I doubt that if we begin with "gregarious" and
check each word in its definition, followed by each word in those
definitions and so on, we will find a definition involving the word
"gregarious".
Here's the start:
gregarious
adj 1: tending to form a group with others of the same kind;
"gregarious bird species"; "man is a gregarious
animal" [ant: ungregarious]
2: seeking and enjoying the company of others; "a gregarious
person who avoids solitude"
(note that the examples and antonym are not part of the definition!)
--
"All intelligent men are cowards. The Chinese are the world's worst
fighters because they are an intelligent race[...] An average Chinese
child knows what the European gray-haired statesmen do not know, that
by fighting one gets killed or maimed." -- Lin Yutang
Douglas Eagleson
wrote:
If you think points are trivial in topology please give me your
reference. Because the Dekind Cut as the rate expresses the infinite
sequence of all. A size as absolute infinite expression was his
abstract size!
Always was it a small little cut of exact size.
So the appearance of the??????
And here we sit.
A bunch of question marks. Abstract the Cut, no big deal?
It is hard for me to accept Dekind's invention in the first place
until you are informed you need assitance. SO it is hard stuff. What
is a Dekind cut?
And if you can answer, then the relation of its cause in geometric
space is apparent. SO a single little theorm I am ignorent of.
Please help.
Lester Zick
Lester Zick
>On Mar 13, 12:52 pm, Lester Zick <dontbot...@nowhere.net> 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~~
>
>Interestingly, the dictionary of the English language is also
>circular, where the definitions of each and every single word in the
>dictionary is composed of other words also defined in the dictionary.
Well see the problem here, PD, is that most dictionaries of language
would be embarrassed to give a circular definition outright. In other
words I should be quite surprized to find a definition of "gregarious"
along the lines of "gregarious is gregarious" or "gregarious means
gregarious people". Mathematikers however are not quite so timid. They
routinely resort to tight loops in their definitions adding very
little of substance anywhere along the line. In this particular case
mathematikers feel quite comfortable defining points as "intersections
of lines making up lines". Quite lame.
Nor does one find dictionary definitions arbitrarily drawn to support
various contentions they can't support logically. The question here is
not whether there are mathematical objects we call points but whether
in fact they compose lines. Obviously mathematikers are too lazy or
stupid to demonstrate that contention so they just define it that way.
>Thus, it is possible to find a circular route from any word defined in
>the dictionary, through words in the definition, back to the original
>word to be defined.
Scarcely the point, sport. Ostensible definitions often wind up being
particular rather than general. It's just unfortunate mathematikers
prove comparably inept.
>That being said, perhaps it is in your best interest to find a way to
>write a dictionary that eradicates this circularity.
Or mathematikers might consider defining their objects in somewhat
more general terms which don't just assume what they should prove.
> That way, when
>you use the words "peculiar" and "definitional", we will have a priori
>definitions of those terms that are noncircular, and from which the
>unambiguous meaning of what you write can be obtained.
Well I've certainly made more progress in that direction with generic
language than mathematikers seem to have made in theirs. Kinda makes
one skeptical whether mathematikers claim that lines are made up of
points is in fact true. I see no evidence to support that claim in the
definition of points. It appears to be nothing but an arbitrary claim.
~v~~
Lester Zick
And it might be an even better point if it weren't used to justify
mathematikers' claims that lines are made up of points.
~v~~
Lester Zick
<je...@phiwumbda.org> wrote:
>"PD" <TheDrap...@gmail.com> writes:
>
>> Interestingly, the dictionary of the English language is also
>> circular, where the definitions of each and every single word in the
>> dictionary is composed of other words also defined in the dictionary.
>> Thus, it is possible to find a circular route from any word defined in
>> the dictionary, through words in the definition, back to the original
>> word to be defined.
>
>The part following "Thus" is doubtful. It is certainly true for some
>words ("is" and "a", for instance). It is almost certainly false
>for some other words. I doubt that if we begin with "gregarious" and
>check each word in its definition, followed by each word in those
>definitions and so on, we will find a definition involving the word
>"gregarious".
>
>Here's the start:
>
>gregarious
> adj 1: tending to form a group with others of the same kind;
> "gregarious bird species"; "man is a gregarious
> animal" [ant: ungregarious]
> 2: seeking and enjoying the company of others; "a gregarious
> person who avoids solitude"
>
>(note that the examples and antonym are not part of the definition!)
An interesting point. One might indeed have to go a long way to
discern the circularity. However my actual contention is that this
variety of circularity is quite often used by mathematikers to conceal
an otherwise orphan contention that lines are constituted of points.
~v~~
Lester Zick
wrote:
Sure, Sam. I understand that there are things we call points which
have no exhaustive definition. However my point is the contention of
mathematikers that lines are made up of points is untenable if lines
are required to define points through their intersection.It's vacuous.
~v~~
Lester Zick
<eagleso...@yahoo.com> wrote:
Well if the intersection of lines defines points it indeed occurs to
me that points must be spherical since lines can double back on
themselves from all different directions. However that suggests as
well that if the contention of mathematkers is true then points
constituting a line must connect through points on each sphere.
~v~~
ŠućMućPaProlij
> toothpicks to build "structures". All of the kids built structures that
> had 90 degree angles like squares and cubes except Bucky. He could not
> see because he didn't have a pair of glasses yet, and felt that the
> triangle and tetrahedron were strong, but the square and cube did not
> hold their shape. He got a patent for the structure he made about 60
> years later. He thought like a child for about 60 years and started to
> write Synergetics. 15 years later the first volume was published.
>
it is nice story but nothing more.
It is one of the stories that fits in "how to become rich and successful" book,
chapter "Change the way you think and all your problems will be solved"
Lester Zick
<eagleso...@yahoo.com> wrote:
I don't see points as having any topology. That's what makes them
points. Nor do I see points as making up lines. That's egregiously
absurd on the face of it. And it is scarcely supportable just because
mathematikers make up a pointless circular line of reasoning.
~v~~
Lester Zick
<mrjohnpau...@hotmail.com> wrote:
>> 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 . . .
>>
>
>point is coordinate in (any) space (real or imaginary).
>For example (x,y,z) is a point where x,y and z are any numbers.
That's nice. And I'm sure we could give any number of other examples
of points. Very enlightening indeed. However the question at hand is
whether points constitute lines and whether or not circular lines of
reasoning support that contention.
>line is collection of points and is defined with three functions
>x = f(t)
>y = g(t)
>z = h(t)
>
>where t is any real number and f,g and h are any continous functions.
>
>Your definition is good for 10 years old boy to understand what is point and
>what is line. (When I was a child, I thought like a child, I reasoned like a
>child. When I became a man, I put away childish ways behind me.....)
Problem is you may have put away childish things such as lines and
points but you're still thinking like a child.
Are points and lines not still mathematical objects and are lines made
up of points just because you got to be eleven?
~v~~
Lester Zick
wrote:
>On Mar 13, 1:52 pm, Lester Zick <dontbot...@nowhere.net> 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 . . .
>>
>
>The modern axiomization of geometry due to Hilbert leaves
>points, lines, and planes undefined.
Probably just as well. I think what we have to consider however is
whether lines are made up of points and the intersection of lines
defined by points defines points. Or whether perhaps Hilbert and
others were a little too preoccupied with problematic axioms and
circular logic to ascertain the actual truth of what he didn't define.
> In fact, he famously
>said about this construction: "One must be able to say at
>all times-instead of points, lines, and planes---tables,
>chairs, and beer mugs."
>
>In other words, despite whatever intuition and inherent
>meaning we might ascribe to these things has no effect
>on the mathematical structure.
>
>No doubt Lester will find this approach lacking and
I mainly find circular regressions pretty much meaningless and unable
to support mathematikers' contention that points constitute lines.
>assert he has a superior axiomization built up from "infinite
>epistomological ontologies of finite tautological
>regression" or something equally meaningless.
Aha, Randy. As usual you lie like a flatfish. Unlike mathematikers I
don't use axioms. It's just that I have an unusual penchant for truth
as opposed to guesses and assumptions typifying mathematikers.
~v~~
Hero
> 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 . . .
>
> The modern axiomization of geometry due to Hilbert leaves
> points, lines, and planes undefined. In fact, he famously
> said about this construction: "One must be able to say at
> all times-instead of points, lines, and planes---tables,
> chairs, and beer mugs."
>
> In other words, despite whatever intuition and inherent
> meaning we might ascribe to these things has no effect
> on the mathematical structure.
>
A mathematical structure, which is the same for points, lines, and
planes as well as for tables, chairs, and beer mugs, seems to me not
very far advanced, there is not even a difference between an object
with a volume and one without.
Take any object of volume, a chair. It's center of gravity is a point.
Rotate the chair, the axis of rotation is a line. Let the axis spin
(precession), so every part of the chair is moving with the exception
of one "thing", which is at rest - a point.
So points really exists, not as matter or stuff, but as an aspect of
things.
Just describe them. This is possible in different ways, f.e: one point
is an invariant in a precessing rotation.
With friendly greetings
Hero
PS. Lester, You claim
> > ...that the ratio of definitional logic to conclusions
> > is a transcendental somewhere in the neighborhood of 3.14159 . . .
So definitional logic behaves like a radius extending to conclusions
like half a circle. Just reverse Your way and search for the center
and You have defined Your starting point. Nice.
NB, why half a perimeter?
SucMucPaProlij
"Lester Zick" <dontb...@nowhere.net> wrote in message
news:2t8ev292sqinpej14...@4ax.com...
hahahahaha
the simple answer is that line is not made of anything. Line is just
abstraction. Properties of line comes from it's definition.
Is line made of points?
If you don't define term "made of" and use it without too much thinking you can
say that:
line is defined with 3 functions:
x = f(t)
y = g(t)
z = h(t)
where (x,y,z) is a point. As you change 't' you get different points and you say
that line is "made of" points, but it is just an expressions that you must fist
understand well before you question it.
Clifford Nelson
"ŠućMućPaProlij" <mrjohnpau...@hotmail.com> wrote:
You missed the point in a discussion about points. The point is that
some things are primary, first, simple. The beginning geometry text
books say that the tetrahedron is advanced "solid" geometry. Bucky
Fuller discovered it when he was four years old because he could not
see. Geometry is taught in a way that psychiatrists would call an
example of, in layman's terms, a "thought disorder". Ditto for
geometry's "points".
If RBF had spelled out the obvious conclusions between the lines,
sections, and chapters in Synergetics, I'll bet he wouldn't have been
able to get his books published at all.
Eric Gisse
Points, lines, etc aren't defined. Only their relations to eachother.
ŠućMućPaProlij
> some things are primary, first, simple. The beginning geometry text
> books say that the tetrahedron is advanced "solid" geometry. Bucky
> Fuller discovered it when he was four years old because he could not
> see. Geometry is taught in a way that psychiatrists would call an
> example of, in layman's terms, a "thought disorder". Ditto for
> geometry's "points".
>
> If RBF had spelled out the obvious conclusions between the lines,
> sections, and chapters in Synergetics, I'll bet he wouldn't have been
> able to get his books published at all.
>
And I am still missing the point. You can't learn all at once. If someone tells
you that line is made of points and point is intersection of two lines you can
accept it if you don't know anything better.
We know better that this and we don't have to accept this definition of point
and line.
The_Man
> The Definition of Points
> ~v~~
>
> In the swansong of modern math lines are composed of points.
This is true if you consider "modern math" to begin with Euclid.
> But then
> we must ask how points are defined?
Yes, you must ask, since you obviously can't READ.
? However I seem to recollect
> intersections of lines determine points.
Did you even pass higvh school geometry? The intersection of two lines
can be the null set (no intersection at all for parallel or skew
lines), it can be a single point, or it can be a whole line. A
fundamental theorem of linear algebra shows that there are THREE
possibilities for the simultaneous solution to two equations in two
unknowns.
> But if so then we are left to
> consider the rather peculiar proposition that lines are composed of
> the intersection of lines.
You can "consider" anything you please, but the only "peculiar" thing
is that you know nothing about even simple high school geometry.
> Now I don't claim the foregoing definitions
> are circular.
Sure you do.
> Only that the ratio of definitional logic
Why talk about logic, when you nothing about it, either?
> to conclusions
> is a transcendental somewhere in the neighborhood of 3.14159 . . .
Who gives a flying fuck if you think lines are made of points, or
not?
You can piss on science and math all you want, but it puts up
buildings and bridges that still stand up, gives us telephones that
work almost all the time, TV sets that we flip on and get 150
channels. You can "doubt" the laws of EM radiation, but we know those
laws are right, 'cause all the shit we build according to those laws
WORKS.
What do YOU produce, Mister Nick Ick? What have YOU accomplished?
>
> ~v~~
Clifford Nelson
"©uæMuæPaProlij" <mrjohnpau...@hotmail.com> wrote:
Bucky Fuller quoted an author who said: science is an attempt to put the
facts of experience in order. Does the tetrahedron create 4 vertexes, 6
edges, and 4 faces, or is it created by them? The axiomatic method of
classical Greek geometry begins with the point. Bucky rejected the
axiomatic method. He said you can't begin with less than the tetrahedron.
 Cliff Nelson
On Feb 19, 2007, at 6:57 AM, David Chako wrote:
"I agree that the axiomatic method is insufficient in and of itself. It
must be informed by experience.
Having said that, it is possible to devise rather generic and abstract
mathematics which can be shown to work in harmony with most, if not all,
relevant experience. As an example, the notion of vector space is one
such abstraction. It is in harmony with Fuller, too.
Now, axiomatic geometry is a whole other matter vis a vis harmony with
Fuller."
- David
--End Quote--
Examples of vector spaces use the Cartesian coordinate idea of 90
degrees between the axes and Bucky Fuller wrote that that 90-degree-ness
has put humanity in a "lethal bind" of scientific illiteracy.
http://mathworld.wolfram.com/VectorSpace.html
Rational coordinate geometry with Synergetics coordinates was part of
his solution. BuckyNumbers are fields over the rational numbers and a
field is a stronger notion than a vector space.
Tom Potter
"Eric Gisse" <jow...@gmail.com> wrote in message
news:1173831482.9...@y66g2000hsf.googlegroups.com...
Euclid's Elements
Definition 1.
A point is that which has no part.
Definition 2.
A line is breadthless length.
Definition 3.
The ends of a line are points.
Definition 4.
A straight line is a line which lies evenly with the points on
itself.
Definition 5.
A surface is that which has length and breadth only.
Etc.
I suggest that the best definition of point
as far as physics is concerned, would be:
"A point is the intersection of orthogonal properties."
In other words,
a physical point is where time, x,y, and z spaces,
charge and impedance are referenced.
--
Tom Potter
*** Time Magazine Person of the Year 2006 ***
http://home.earthlink.net/~tdp/
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Sam Wormley
> Euclid's Elements
>
> Definition 1.
> A point is that which has no part.
>
> Definition 2.
> A line is breadthless length.
>
> Definition 3.
> The ends of a line are points.
>
> Definition 4.
> A straight line is a line which lies evenly with the points on
> itself.
>
> Definition 5.
> A surface is that which has length and breadth only.
>
Hey Potter--That was a useful posting for a change!
ŠućMućPaProlij
> facts of experience in order.
And I agree with this.
>Does the tetrahedron create 4 vertexes, 6
> edges, and 4 faces, or is it created by them? The axiomatic method of
> classical Greek geometry begins with the point. Bucky rejected the
> axiomatic method. He said you can't begin with less than the tetrahedron.
>
I really don't know if you can't begin with less than the tetrahedron but I know
that you must begin somewhere. Beginning is just one point of your journey and
after you choose from where to begin you can go in any direction.
You can start from the point and create tetrahedron or you can analyze
tetrahedron and get to point. At the end you will have both tetrahedron and
point.
OG
What you call 'orphan' is in fact 'abstract', as points necessarily are.
Lester Zick
wrote:
You mean points are abstract from the intersection of lines? Or that
the composition of lines is abstract from points? Curious I must say.
~v~~
Lester Zick
You don't have to accept anything. It might be nice however if you had
some tenable alternative to suggest. Are you suggesting lines are not
made up of points and the intersection of lines does not define a
point? Or are you suggesting we just ignore the problem because modern
mathematikers are too lazy or stupid to resolve it?
~v~~
Lester Zick
Yes but those represent the intersection of lines. What I'm asking is
whether lines are composed of points.
~v~~
Lester Zick
Which is all just swell. So now the question I posed becomes are
abstract lines made up of abstract points?
>Is line made of points?
>If you don't define term "made of" and use it without too much thinking you can
>say that:
Why don't you ask Bob Kolker. He seems to think lines are "made up" of
points, abstract or otherwise. I'm not quite clear about how he thinks
lines are "made up" of points but he nonetheless seems to think they
are.
>line is defined with 3 functions:
>x = f(t)
>y = g(t)
>z = h(t)
>
>where (x,y,z) is a point. As you change 't' you get different points and you say
>that line is "made of" points, but it is just an expressions that you must fist
>understand well before you question it.
Frankly I prefer to question things before I waste time learning them.
~v~~
Lester Zick
Who said anything about half a perimeter, Hero? I believe the ratio pi
is between the full circumference of a circle and its diameter.
~v~~
Lester Zick
So is the relation between points and lines is that lines are made up
of points and is the relation between lines and points that the
intersection of lines defines a point?
~v~~
Lester Zick
Fascinating. But are lines composed of points? The foregoing
definitions are reasonable as far as they go however I see nothing in
them that sheds light on this issue.
~v~~
Lester Zick
wrote:
>Tom Potter wrote:
Certainly useful as far as it goes however not very useful for
elucidating the basic question as to whether points compose lines.
~v~~
Lester Zick
wrote:
>On Mar 13, 12:52 pm, Lester Zick <dontbot...@nowhere.net> wrote:
>> The Definition of Points
>> ~v~~
>>
>> In the swansong of modern math lines are composed of points.
>
>This is true if you consider "modern math" to begin with Euclid.
What is this "truth" thingie whereof you so fondly speak?
>> But then
>> we must ask how points are defined?
>
>Yes, you must ask, since you obviously can't READ.
Only because I learned to write before I learned to read.
>? However I seem to recollect
>> intersections of lines determine points.
>
>Did you even pass higvh school geometry?
Obviously you didn't even pass grade school spelling.
> The intersection of two lines
>can be the null set (no intersection at all for parallel or skew
>lines), it can be a single point, or it can be a whole line. A
>fundamental theorem of linear algebra shows that there are THREE
>possibilities for the simultaneous solution to two equations in two
>unknowns.
Obviously in your case one of the three wasn't learning to spell.
>> But if so then we are left to
>> consider the rather peculiar proposition that lines are composed of
>> the intersection of lines.
>
>You can "consider" anything you please, but the only "peculiar" thing
>is that you know nothing about even simple high school geometry.
Of course not. Just look what it did for you.
>> Now I don't claim the foregoing definitions
>> are circular.
>
>Sure you do.
Oh really? How clever of you to notice, sport.
>> Only that the ratio of definitional logic
>
>Why talk about logic, when you nothing about it, either?
When I what? Are you quite sure you're off baby formula?
>> to conclusions
>> is a transcendental somewhere in the neighborhood of 3.14159 . . .
>
>Who gives a flying fuck if you think lines are made of points, or
>not?
I don't.
>You can piss on science and math all you want, but it puts up
>buildings and bridges that still stand up, gives us telephones that
>work almost all the time, TV sets that we flip on and get 150
>channels. You can "doubt" the laws of EM radiation, but we know those
>laws are right, 'cause all the shit we build according to those laws
>WORKS.
And a lotta shit you also build doesn't.
>What do YOU produce, Mister Nick Ick? What have YOU accomplished?
Just as soon as I learn high school geometry you'll be the first to
know.
~v~~
Eric Gisse
[...]
I was speaking of Hilbert's formulation of Euclidean geometry.
Euclid's formulation is imprecise, and some of his works have errors.
The words "point, line, on, between, and congruence" are undefined and
left to us to determine the meaning within a specific model. The book
"The Geometric Viewpoint - A survey of Geometries" by Thomas Sibley
would be useful for you, among other things.
>
> I suggest that the best definition of point
> as far as physics is concerned, would be:
> "A point is the intersection of orthogonal properties."
A vague and un-needed definition. Geometry does well enough without.
>
> In other words,
> a physical point is where time, x,y, and z spaces,
> charge and impedance are referenced.
But x,y,z is coordinate-dependent, it isn't physical.
Eric Gisse
No, it is more complicated than that.
http://en.wikipedia.org/wiki/Hilbert's_axioms
>
> ~v~~
Bob Cain
> What do YOU produce, Mister Nick Ick? What have YOU accomplished?
He's good at starting vanity threads to demonstrate his self
proclaimed and self appreciated wit.
He's a legend in his own mind.
Bob
--
"Things should be described as simply as possible, but no simpler."
A. Einstein
SucMucPaProlij
> You don't have to accept anything. It might be nice however if you had
> some tenable alternative to suggest. Are you suggesting lines are not
> made up of points and the intersection of lines does not define a
> point? Or are you suggesting we just ignore the problem because modern
> mathematikers are too lazy or stupid to resolve it?
>
I think that you are just playing dumb.
"Line is made of points" is not definition of line and modern mathematikers can
resolve your questions.
Intersection of lines can define a point and we both know it just as we both
know that line is made of points.
If you don't think that line is made of points then how do you explain the fact
that two lines can have common point? If two lines are intersecting in a point
is this point one part of both lines or is it created during intersectioning?
Tom Potter
> On Mar 13, 5:17 pm, "Tom Potter" <tdp1...@gmail.com> wrote:
>
> [...]
>
> I was speaking of Hilbert's formulation of Euclidean geometry.
> Euclid's formulation is imprecise, and some of his works have errors.
>
> The words "point, line, on, between, and congruence" are undefined and
> left to us to determine the meaning within a specific model. The book
> "The Geometric Viewpoint - A survey of Geometries" by Thomas Sibley
> would be useful for you, among other things.
>
>>
>> I suggest that the best definition of point
>> as far as physics is concerned, would be:
>> "A point is the intersection of orthogonal properties."
>
> A vague and un-needed definition. Geometry does well enough without.
>
>> In other words,
>> a physical point is where time, x,y, and z spaces,
>> charge and impedance are referenced.
>
> But x,y,z is coordinate-dependent, it isn't physical.
You can use whatever coordinate system you like ,
and whatever units you want,
but a ***physical point*** is referenced by
time, x,y, and z spaces,charge and impedance.
Leave out an x, y, or z
and you define a line.
Leave out Q,
and you define nothing.
Leave out a t,
and you have a static universe.
Leave out a Z (And a second Q),
and you have no rotation (Action aka angular momentum).
--
Tom Potter
*** Time Magazine Person of the Year 2006 ***
Bob Kolker
>
> Intersection of lines can define a point and we both know it just as we both
> know that line is made of points.
>
> If you don't think that line is made of points then how do you explain the fact
> that two lines can have common point? If two lines are intersecting in a point
> is this point one part of both lines or is it created during intersectioning?
Maybe he thinks there are objects other than points on lines. If so,
they are not ever mentioned in any axiom system for Euclidean Geometry.
Likwise for planar curves. L.Z. rejects the usual definition of a cirlce
as a set of points on a plane a given distance (the radius) from a
specified point (the center). If a circle does not consist of its
points, what else besides points lie on the circle? If there are any
such objects they are never mentioned in the axioms.
Zick'w problem (among several problems he has) is that he simply does
not comprehend what an axiomatic system is. He cannot comprehend the
notion of undefined terms or objects whose only properties are given in
the axioms. For example, whatever a point is, given two distinct points
there is one and only one line (whatever a line is) containing them.
Bob Kolker
SucMucPaProlij
"Bob Kolker" <now...@nowhere.com> wrote in message
news:55qac4F...@mid.individual.net...
> SucMucPaProlij wrote:
>
>>
>> Intersection of lines can define a point and we both know it just as we both
>> know that line is made of points.
>>
>> If you don't think that line is made of points then how do you explain the
>> fact that two lines can have common point? If two lines are intersecting in a
>> point is this point one part of both lines or is it created during
>> intersectioning?
>
> Maybe he thinks there are objects other than points on lines. If so, they are
> not ever mentioned in any axiom system for Euclidean Geometry.
>
One can assume that there are some objects other than points but I don't think
that anyone can prove that this objects are not points becouse you can't tell a
difference between single point that stands alone and some imaginary object that
is on a line. They both have the same simple characteristics (coordinates) and
that is all they have.
> Likwise for planar curves. L.Z. rejects the usual definition of a cirlce as a
> set of points on a plane a given distance (the radius) from a specified point
> (the center). If a circle does not consist of its points, what else besides
> points lie on the circle? If there are any such objects they are never
> mentioned in the axioms.
>
> Zick'w problem (among several problems he has) is that he simply does not
> comprehend what an axiomatic system is. He cannot comprehend the notion of
> undefined terms or objects whose only properties are given in the axioms. For
> example, whatever a point is, given two distinct points there is one and only
> one line (whatever a line is) containing them.
>
well, nobody is perfect...
Wolf
[...]
>
> Only because I learned to write before I learned to read.
Lester, I suggest you present yourself to the nearest experimental
psychologist, and explain how you managed this trick.
Wolf
Hey, Eric, you're actually trying to teach Zick something. IOW, you're
assuming he really wants to know.
But Zick doesn't want to be taught. To be taught would mean admitting
that he doesn't know what he's talking about, or worse, that he cannot
understand what you are explaining. For reasons we had better not
examine to closely, Zick can't tolerate that admission.
--
Wolf
"Don't believe everything you think." (Maxine)
Bob Kolker
>
> One can assume that there are some objects other than points but I don't think
Only if one makes this assumption explicit. This means introducing
objects other than points and lines into the system and it means some
axiom must somehow mention and characterize this additional object or
kind of object.
The idea of an axiom system such as Hilbert's is to -explicitly- mention
those objects which are not defined and characterize them with the
axioms. Thus, given two distinct points there is one and only one line
containing the points. The containment relation expressed in a number of
ways is also undefined. We we say a point is on a line. A line contains
a point or a line passes through a point etc..
Look at hilbert's axiom system in wiki.
Bob Kolker
Eckard Blumschein
On 3/13/2007 6:52 PM, Lester Zick wrote:
>
> In the swansong of modern math lines are composed of points. But then
> we must ask how points are defined?
I hate arbitrary definitions. I would rather like to pinpoint what makes
the notion of a point different from the notion of a number:
If a line is really continuous, then a mobile point can continuously
glide on it. If the line just consists of points corresponding to
rational numbers, then one can only jump from one discrete position to
an other.
A point has no parts, each part of continuum has parts, therefore
continuum cannot be resolved into any finite amount of points.
Real numbers must be understood like fictions.
All this seems to be well-known. When will the battle between frogs and
mices end with a return to Salviati?
PD
wrote:
> On 3/13/2007 6:52 PM, Lester Zick wrote:
>
>
>
> > In the swansong of modern math lines are composed of points. But then
> > we must ask how points are defined?
>
> I hate arbitrary definitions. I would rather like to pinpoint what makes
> the notion of a point different from the notion of a number:
>
> If a line is really continuous, then a mobile point can continuously
> glide on it. If the line just consists of points corresponding to
> rational numbers, then one can only jump from one discrete position to
> an other.
That's an interesting (but old) problem. How would one distinguish
between continuous and discrete? As a proposal, I would suggest means
that there is a finite, nonzero interval (where interval is measurable
somehow) between successive positions, in which there is no
intervening position. Unfortunately, the rational numbers do not
satisfy this definition of discreteness, because between *any* two
rational numbers, there is an intervening rational number. I'd be
interested in your definition of discreteness that the rational
numbers satisfy.
PD
Bob Kolker
> glide on it. If the line just consists of points corresponding to
> rational numbers, then one can only jump from one discrete position to
> an other.
Points don't glide. In fact points don't move. You are still pushing
discrete mathematics? All you will get is a means of totalling up your
grocery bill.
Bob Kolker
VK
> Are points and lines not still mathematical objects
The point is το τί ήν είναι ("to ti en einai") of the infinity.
If you want a definition based on something fresher than Aristotle
then:
The point is nothing which is still something in potention to
become everything.
IMHO the Aristotle-based definition is better, but it's personal.
Now after some thinking you may decide to stay with the crossing lines
and hell on the cross-definition issues ;-) The speach is not a
reflection of entities: it is a reflection - of different levels of
quality - of the mind processes. This way a word doesn't have neither
can decribe an entity. The purpose of the word - when read - to trig a
"mentagram", state of mind, as close as possible to the original one -
which caused the word to be written. This way it is not important how
is the point defined: it is important that all people involved in the
subject would think of appoximately the same entity so not say about
triangles or squares. In this aspect crossing lines definition in math
does the trick pretty well. From the other side some "sizeless thingy"
as the definition would work in math as well - again as long as
everyone involved would think the same entity when reading it.
The_Man
> On 13 Mar 2007 17:46:20 -0700, "The_Man" <me_so_hornee...@yahoo.com>
> wrote:
>
> >On Mar 13, 12:52 pm, Lester Zick <dontbot...@nowhere.net> wrote:
> >> The Definition of Points
> >> ~v~~
>
> >> In the swansong of modern math lines are composed of points.
>
> >This is true if you consider "modern math" to begin with Euclid.
>
> What is this "truth" thingie whereof you so fondly speak?
>
> >> But then
> >> we must ask how points are defined?
>
> >Yes, you must ask, since you obviously can't READ.
>
> Only because I learned to write before I learned to read.
>
> >? However I seem to recollect
> >> intersections of lines determine points.
>
> >Did you even pass higvh school geometry?
>
> Obviously you didn't even pass grade school spelling.
Sorry, typo. If the best rejoinder you have is to notice a typo, you
don't have much.
>
> > The intersection of two lines
> >can be the null set (no intersection at all for parallel or skew
> >lines), it can be a single point, or it can be a whole line. A
> >fundamental theorem of linear algebra shows that there are THREE
> >possibilities for the simultaneous solution to two equations in two
> >unknowns.
>
> Obviously in your case one of the three wasn't learning to spell.
The question wasn't my spelling ability or lack thereof, but YOUR
ideas about lines.
>
> >> But if so then we are left to
> >> consider the rather peculiar proposition that lines are composed of
> >> the intersection of lines.
>
> >You can "consider" anything you please, but the only "peculiar" thing
> >is that you know nothing about even simple high school geometry.
>
> Of course not. Just look what it did for you.
Yes, I can do math, and you can't.
>
> >> Now I don't claim the foregoing definitions
> >> are circular.
>
> >Sure you do.
>
> Oh really? How clever of you to notice, sport.
>
> >> Only that the ratio of definitional logic
>
> >Why talk about logic, when you nothing about it, either?
>
> When I what? Are you quite sure you're off baby formula?
If I'm not off baby formula, what does that say about you? Come back
when you can pass a college math course, and not be self-important to
the hamburger-flipping set because you got your GED 90 years ago.
>
> >> to conclusions
> >> is a transcendental somewhere in the neighborhood of 3.14159 . . .
>
> >Who gives a flying fuck if you think lines are made of points, or
> >not?
>
> I don't.
You don't what?
>
> >You can piss on science and math all you want, but it puts up
> >buildings and bridges that still stand up, gives us telephones that
> >work almost all the time, TV sets that we flip on and get 150
> >channels. You can "doubt" the laws of EM radiation, but we know those
> >laws are right, 'cause all the shit we build according to those laws
> >WORKS.
>
> And a lotta shit you also build doesn't.
Such as? What - your French Fry broiler is on the blink again? That
cash register, where you push the little picture of the food idea, so
that you don't have to know arithmetic - is it broken again? It must
be a FAILURE of Modern Math!
>
> >What do YOU produce, Mister Nick Ick? What have YOU accomplished?
>
> Just as soon as I learn high school geometry you'll be the first to
> know.
Start soon; you obviously aren't gifted.
>
> ~v~~
Lester Zick
<mrjohnpau...@hotmail.com> wrote:
>>
>> You don't have to accept anything. It might be nice however if you had
>> some tenable alternative to suggest. Are you suggesting lines are not
>> made up of points and the intersection of lines does not define a
>> point? Or are you suggesting we just ignore the problem because modern
>> mathematikers are too lazy or stupid to resolve it?
>>
>
>I think that you are just playing dumb.
I can speak as well as anyone and better than most.
>"Line is made of points" is not definition of line and modern mathematikers can
>resolve your questions.
Oookay.
>Intersection of lines can define a point and we both know it
Can define a point or does define a point? And if the former what
exactly defines a point without the intersection of lines?
> just as we both
>know that line is made of points.
Either this comment is facetious or you like to hold all opinions at
once.
>If you don't think that line is made of points then how do you explain the fact
>that two lines can have common point?
Rather easily if their intersection defines the point. But I don't see
that this has any bearing on whether lines are made up of points.
Intersections of lines defining points would still be made up of the
points making up the lines. The reasoning is still circular.
> If two lines are intersecting in a point
>is this point one part of both lines or is it created during intersectioning?
If the point is defined by the intersection what happens to the point
and what defines the point when the lines don't interesect? On the
other hand if the point is not defined by the intersection of lines
how can one assume the line is made up of things which aren't defined?
~v~~
The_Man
> On Tue, 13 Mar 2007 23:40:39 +0100, "SucMucPaProlij"
>
>
>
>
>
>
> >"Lester Zick" <dontbot...@nowhere.net> wrote in message
> >news:2t8ev292sqinpej14...@4ax.com...
> >> On Tue, 13 Mar 2007 20:48:34 +0100, "SucMucPaProlij"
> >> <mrjohnpauldike2...@hotmail.com> wrote:
>
> >>>> 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 . . .
>
> >>>point is coordinate in (any) space (real or imaginary).
> >>>For example (x,y,z) is a point where x,y and z are any numbers.
>
> >> That's nice. And I'm sure we could give any number of other examples
> >> of points. Very enlightening indeed. However the question at hand is
> >> whether points constitute lines and whether or not circular lines of
> >> reasoning support that contention.
O.K. Tell us, Icky-po: What do YOU think lines are made of? What do
YOU think is a "suitable" definition for point, line, plane, etc.. I'm
sure Gauss, Euler, Cantor, Cauchy, Riemann, and Hilbert are rolling
over in their graves with anticipation.
Maybe the crew of my local Burger King will redefine QM next week, and
the Friendly's will unify all the forces of nature in one theory.
Yes -learning things is such a "waste". That's why you know so little.
>
> ~v~~- Hide quoted text -
>
> - Show quoted text -
Lester Zick
wrote:
>SucMucPaProlij wrote:
>
>>
>> Intersection of lines can define a point and we both know it just as we both
>> know that line is made of points.
>>
>> If you don't think that line is made of points then how do you explain the fact
>> that two lines can have common point? If two lines are intersecting in a point
>> is this point one part of both lines or is it created during intersectioning?
>
>Maybe he thinks there are objects other than points on lines. If so,
>they are not ever mentioned in any axiom system for Euclidean Geometry.
Objects other than points on lines, Bob? Show me the points on lines
without intersection with other lines. You're a little confused.Points
aren't on lines. They're at or on the intersection of lines.
>Likwise for planar curves. L.Z. rejects the usual definition of a cirlce
>as a set of points on a plane a given distance (the radius) from a
>specified point (the center).
The hell you say, Bob. What LZ rejects is the conventional practice of
mathematikers in co opting geometric objects while pretending they're
doing SOAP arithmetic definitions without geometry.
> If a circle does not consist of its
>points, what else besides points lie on the circle?
Your logic?
> If there are any
>such objects they are never mentioned in the axioms.
Begging the question is often employed by but rarely mentioned in
axioms.
>Zick'w problem (among several problems he has) is that he simply does
>not comprehend what an axiomatic system is.
Of course I do. It's a series of undemonstrable empirical assumptions
whose truth can only be guessed at and whose falsity is concealed with
implausible definitions which are defined as neither true nor false.
> He cannot comprehend the
>notion of undefined terms or objects whose only properties are given in
>the axioms.
Sure I can. Except when axiomatic assumptions prove false or
definitions prove untrue. Minor problem I admit but there it is.
> For example, whatever a point is, given two distinct points
>there is one and only one line (whatever a line is) containing them.
Well more likely the two distinct points define a straight line
segment which doesn't actually contain the points since the points
define the straight line segment and not vice versa. In other words
distinct points contain the straight line segment.
See, Bob, this is the whole problem with SOAP definitions. Between
every pair of "distinct" points a straight line segment is defined and
not a curve. That's what makes the points distinct to begin with. In
point of fact I'd like to see you show us some "indistinct" points and
tell us exactly what they define.
~v~~
Lester Zick
<mrjohnpau...@hotmail.com> wrote:
>
>"Bob Kolker" <now...@nowhere.com> wrote in message
>news:55qac4F...@mid.individual.net...
>> SucMucPaProlij wrote:
>>
>>>
>>> Intersection of lines can define a point and we both know it just as we both
>>> know that line is made of points.
>>>
>>> If you don't think that line is made of points then how do you explain the
>>> fact that two lines can have common point? If two lines are intersecting in a
>>> point is this point one part of both lines or is it created during
>>> intersectioning?
>>
>> Maybe he thinks there are objects other than points on lines. If so, they are
>> not ever mentioned in any axiom system for Euclidean Geometry.
>>
>
>One can assume that there are some objects other than points but I don't think
>that anyone can prove that this objects are not points becouse you can't tell a
>difference between single point that stands alone and some imaginary object that
>is on a line. They both have the same simple characteristics (coordinates) and
>that is all they have.
The difficulty isn't whether there are objects on lines but whether
lines are composed of them. Certainly points are properties of the
intersection of lines and are not defined on lines in themselves.
>> Likwise for planar curves. L.Z. rejects the usual definition of a cirlce as a
>> set of points on a plane a given distance (the radius) from a specified point
>> (the center). If a circle does not consist of its points, what else besides
>> points lie on the circle? If there are any such objects they are never
>> mentioned in the axioms.
>>
>> Zick'w problem (among several problems he has) is that he simply does not
>> comprehend what an axiomatic system is. He cannot comprehend the notion of
>> undefined terms or objects whose only properties are given in the axioms. For
>> example, whatever a point is, given two distinct points there is one and only
>> one line (whatever a line is) containing them.
>>
>
>well, nobody is perfect...
What never? Well . . . hardly ever.
~v~~
Lester Zick
wrote:
>SucMucPaProlij wrote:>
>>
>> One can assume that there are some objects other than points but I don't think
>
>Only if one makes this assumption explicit. This means introducing
>objects other than points and lines into the system and it means some
>axiom must somehow mention and characterize this additional object or
>kind of object.
Well for that matter why introduce points into the system except as
the intersection of lines? The obvious answer is so that mathematikers
can pretend they're doing arithmetic with SOAP definitions instead of
geometry.
>The idea of an axiom system such as Hilbert's is to -explicitly- mention
>those objects which are not defined and characterize them with the
>axioms. Thus, given two distinct points there is one and only one line
>containing the points. The containment relation expressed in a number of
>ways is also undefined. We we say a point is on a line. A line contains
>a point or a line passes through a point etc..
In other words you can just make the problem go away with erroneous
definitions? Straight line segments don't contain points; points
contain straight line segments. Hell points don't even contain curves.
~v~~
Lester Zick
>On Mar 14, 1:28Â am, Lester Zick <dontbot...@nowhere.net> wrote:
>> Are points and lines not still mathematical objects
>
> The point is ?? ?? ?? ????? ("to ti en einai") of the infinity.
>If you want a definition based on something fresher than Aristotle
>then:
> The point is nothing which is still something in potention to
>become everything.
>IMHO the Aristotle-based definition is better, but it's personal.
I don't want a definition for points fresher or not than Aristotle.
I'm trying to ascertain whether lines are made up of points.
>Now after some thinking you may decide to stay with the crossing lines
>and hell on the cross-definition issues ;-) The speach is not a
>reflection of entities: it is a reflection - of different levels of
>quality - of the mind processes. This way a word doesn't have neither
>can decribe an entity. The purpose of the word - when read - to trig a
>"mentagram", state of mind, as close as possible to the original one -
>which caused the word to be written. This way it is not important how
>is the point defined: it is important that all people involved in the
>subject would think of appoximately the same entity so not say about
>triangles or squares. In this aspect crossing lines definition in math
>does the trick pretty well. From the other side some "sizeless thingy"
>as the definition would work in math as well - again as long as
>everyone involved would think the same entity when reading it.
~v~~
Lester Zick
Well that's certainly a relief. I thought you said "only their
relations to each other". It's certainly good to know that what lines
are made up of is not "only a relation" between points and lines.
~v~~
Lester Zick
wrote:
Only because pedagogy is less your forte than philosophical
ineptitude, Wolf.
~v~~
Hero
> Hero wrote:
> >Randy Poe wrote:
> >> Lester Zick wrote:
>
> >> > The Definition of Points
> >PS. Lester, You claim
> >> > ...that the ratio of definitional logic to conclusions
> >> > is a transcendental somewhere in the neighborhood of 3.14159 . . .
> >like half a circle. Just reverse Your way and search for the center
> >and You have defined Your starting point. Nice.
> >NB, why half a perimeter?
>
> Who said anything about half a perimeter, Hero? I believe the ratio pi
> is between the full circumference of a circle and its diameter.
>
Accepted. By Your own reasoning You've got already three points:
A center, from which definitional logic starts out into two
directions,and two points, where it changes into conclusions. And You
can go in circular way in Your picture from conclusions to conclusions
( NB there is more than one diameter and it can be extended to a
sphere).
Historical, axioms are not the beginning of geometry. You start with
full, complex life, understand here a bit and there, proceed from
simple things to complex ones and than You look for the most simple
and common structure underlying the geometry you have done so far.
F.e. You shrink a sphere to it's infinitesimal minimum, which is
radius ( and diameter ) zero - and like the smile of Cheshire cat -
there You have, what You've looked for.
Have a smile
Hero
Lester Zick
wrote:
>Lester Zick wrote:
I managed it the same way empirics manage their explanations, Wolf:
pure divination.
~v~~
Lester Zick
<arc...@arcanemethods.com> wrote:
>The_Man wrote:
>
>> What do YOU produce, Mister Nick Ick? What have YOU accomplished?
>
>He's good at starting vanity threads to demonstrate his self
>proclaimed and self appreciated wit.
Better to be witty than witless I suppose.
>He's a legend in his own mind.
And in the minds of others too, Stringfellow. You seem to think these
threads are one sided extemporaneous lectures on my part. You also
seemed to think Ken Seto and I would have some kind of monumental
donnybrook. You also pretty much just seem to think when you don't.
~v~~
OG
"Lester Zick" <dontb...@nowhere.net> wrote in message
news:8a2fv212gphd4ndim...@4ax.com...
> On Wed, 14 Mar 2007 02:22:35 -0000, "OG" <ow...@gwynnefamily.org.uk>
> wrote:
>
>>
>>"Lester Zick" <dontb...@nowhere.net> wrote in message
>>news:758ev21t8r8ch5sju...@4ax.com...
>>> On Tue, 13 Mar 2007 16:16:52 -0400, "Jesse F. Hughes"
>>> <je...@phiwumbda.org> wrote:
>>>
>>>>"PD" <TheDrap...@gmail.com> writes:
>>>>
>>>>> Interestingly, the dictionary of the English language is also
>>>>> circular, where the definitions of each and every single word in the
>>>>> dictionary is composed of other words also defined in the dictionary.
>>>>> Thus, it is possible to find a circular route from any word defined in
>>>>> the dictionary, through words in the definition, back to the original
>>>>> word to be defined.
>>>>
>>>>The part following "Thus" is doubtful. It is certainly true for some
>>>>words ("is" and "a", for instance). It is almost certainly false
>>>>for some other words. I doubt that if we begin with "gregarious" and
>>>>check each word in its definition, followed by each word in those
>>>>definitions and so on, we will find a definition involving the word
>>>>"gregarious".
>>>>
>>>>Here's the start:
>>>>
>>>>gregarious
>>>> adj 1: tending to form a group with others of the same kind;
>>>> "gregarious bird species"; "man is a gregarious
>>>> animal" [ant: ungregarious]
>>>> 2: seeking and enjoying the company of others; "a gregarious
>>>> person who avoids solitude"
>>>>
>>>>(note that the examples and antonym are not part of the definition!)
>>>
>>> An interesting point. One might indeed have to go a long way to
>>> discern the circularity. However my actual contention is that this
>>> variety of circularity is quite often used by mathematikers to conceal
>>> an otherwise orphan contention that lines are constituted of points.
>>>
>>
>>What you call 'orphan' is in fact 'abstract', as points necessarily are.
>
> You mean points are abstract from the intersection of lines? Or that
> the composition of lines is abstract from points? Curious I must say.
As you wish.
PD
> On 14 Mar 2007 10:10:55 -0700, "VK" <schools_r...@yahoo.com> wrote:
>
> >On Mar 14, 1:28 am, Lester Zick <dontbot...@nowhere.net> wrote:
> >> Are points and lines not still mathematical objects
>
> > The point is ?? ?? ?? ????? ("to ti en einai") of the infinity.
> >If you want a definition based on something fresher than Aristotle
> >then:
> > The point is nothing which is still something in potention to
> >become everything.
> >IMHO the Aristotle-based definition is better, but it's personal.
>
> I don't want a definition for points fresher or not than Aristotle.
> I'm trying to ascertain whether lines are made up of points.
Let's see if I can help.
I believe Lester is asking whether a line is a composite object or an
atomic primitive.
One way of asking the question is whether a point sits ON a line or
whether the point is part OF the line.
Of course, since both the point and the line are idealizations,
conceptual constructions out of the human mind that don't have any
independent reality, then one could rightly ask why the hell it
matters, since there is no way to verify either statement through an
external discriminator. Lester doesn't believe in external
discriminators anyway, because that is the work of evil empirics, and
he'd rather spend his day mentally diddling away at issues like this.
But to provide him with some prurient prose by which to diddle
further, let's toss him the idea that we can clearly cleave a line in
two by picking a point (either on the line or part of the line, take
your pick) and assigning one direction to one semi-infinite segment
and the other direction to the other semi-infinite segment --
sometimes called rays. One can then take one of those rays and cleave
it again, and one of the results will be a line segment, which is
distinguished by having two end *points*. Now the interesting question
is whether those end points are ON the line segment or part OF the
line segment. One way to answer this is to take the geometric limit of
one end point approaching the other end point, and ask what the limit
of the line segment is. That should either settle it or send Lester
into an orgasmic frenzy.
VK
> > The point is to ti en einai of the infinity.
> > If you want a definition based on something fresher than Aristotle
> > then:
> > The point is nothing which is still something in potention to
> > become everything.
> > IMHO the Aristotle-based definition is better, but it's personal.
>
> I don't want a definition for points fresher or not than Aristotle.
> I'm trying to ascertain whether lines are made up of points.
You are bringing unacceptably too much of the "everyday sensual
experience" by placing the question like that. Why "points", why
plural? Floor by floor - a high building, foot by foot - 12 feet
stick, something like that? ;-) Neither points nor lines are really
existing, so you may think of them whatever you want - as long as it
helps you to make another step in constructing something more
complicated. Somewhere on the go you may get an intersection with the
real world - or you may not, it is always cool but not required -
unless you are on some applied contract work.
The point is nothing with potential of becoming; that is a simplified
up to profanity hybrid or Aristotle and Hegel, my sorries to them but
it gets us started. Then the line is the point deformed (stretched)
from negative to positive infinity.
Or let's go in the reverse order: define the point using the line. The
line is then an one-dimensional space and the point is vertical
projection of this space onto n-dimensional space.
Both options are as good as two crossed line. The difference is in the
"mindset" they put on you, so some higher constructs are "possible" or
"not possible" here or there.
Actually with your line with many-many(-many) points you are hitting
straight to the hands of Zenon. So can Achilles ever get the tortoise?
And - most importantly and directly relevant to your current worries -
can the bow ever flight? First answer the questions from the "reality
point of view". That will let you to relax your mind for taking non-
existing abstractions as freely as you need - for the given moment and
for the given aim.
SucMucPaProlij
> On the other hand if the point is not defined by the intersection of lines
> how can one assume the line is made up of things which aren't defined?
>
hahahahaha you are poor philosopher. Math can't create the world it can only
(try to) explain it.
To explain something you must fist admit that something exists.
I admit that lines and points do exist.
Every definition puts in relation two or more thing that exist.
Definition of point doesn't create point. It puts point in relation to something
else.
If you define point with intersection of two lines you put in relation:
1) point that you admit that already exists
2) two lines that you admit that already exist
3) and their intersection that you admit that already exists.
Definition also does not create relation between thing. Relation between point,
two lines and their intersection already exists and with definition you only
admit that it exists.
When you say "point is intersection of two lines" then you only admit that there
exist certain relation between point, two lines and their intersection. This
relation will also exist if you don't define it because definition discovers
relations, it does not create them.
Who (beside you) claims that it is wrong to define point with lines and define
line with points?
Definition of point says that there is some relation R1 between point P and
lines L1 and L2
R1 = {(R, L1, L2) | where blabla P bla L1 and blabla L2}
"Line is made up of points" says that there is relation R2 between line L and
point P
R2={(L,P) | where blabla L and blabla P}
Not all relations are in form y=f(x) nor they should be.
It is true that you can define point without intersection of two lines and it is
true that you can define line without points but it only means that there is
certain relation between point and something that is not line, and there is
certain relation between lines and something that is not point.
It is also true that you can't define point using nothing nor you can define
line using nothing because relation between point and nothing is just not
relation and therefore definition that defines something using nothing is just
not definition.
Just as f(x)=x-2*f(x) if perfectly good definition of f(x), "point is
intersection of lines and line is made out of points" is ok definition if you
know how to use it.
Someone is confused with f(x)=x-2*f(x) and someone else is confused with points
and lines :)))))
Eric Gisse
No, I said "it is more complicated than that."
Eric Gisse
> "Eric Gisse" <jowr...@gmail.com> wrote in message news:
>
> 1173852999.161844.238...@l75g2000hse.googlegroups.com...
>
>
>
> > On Mar 13, 5:17 pm, "Tom Potter" <tdp1...@gmail.com> wrote:
>
> > [...]
>
> > I was speaking of Hilbert's formulation of Euclidean geometry.
> > Euclid's formulation is imprecise, and some of his works have errors.
>
> > The words "point, line, on, between, and congruence" are undefined and
> > left to us to determine the meaning within a specific model. The book
> > "The Geometric Viewpoint - A survey of Geometries" by Thomas Sibley
> > would be useful for you, among other things.
>
> >> I suggest that the best definition of point
> >> as far as physics is concerned, would be:
> >> "A point is the intersection of orthogonal properties."
>
> > A vague and un-needed definition. Geometry does well enough without.
>
> >> In other words,
> >> a physical point is where time, x,y, and z spaces,
> >> charge and impedance are referenced.
>
> > But x,y,z is coordinate-dependent, it isn't physical.
>
> You can use whatever coordinate system you like ,
> and whatever units you want,
> but a ***physical point*** is referenced by
> time, x,y, and z spaces,charge and impedance.
No, it isn't.
Physical points don't exist. There are no coordinate systems in
reality.
In physics, it is 3 space positions and time - pick your coordinate
system. Charge and impedance are quantities irrelevant to position.
>
> Leave out an x, y, or z
> and you define a line.
You define nothing. A particle that isn't localized in space can be
anywhere.
>
> Leave out Q,
> and you define nothing.
Knowledge of charge is not required and I have no reason to see why it
would be. Perhaps studying some physics would be in order, so you
could understand how the concept of dimensionality is used.
>
> Leave out a t,
> and you have a static universe.
More like a slice of the universe at a specified time.
>
> Leave out a Z (And a second Q),
> and you have no rotation (Action aka angular momentum).
Point out the charge in r x p if you can.
>
> --
> Tom Potter
>
> *** Time Magazine Person of the Year 2006 ***http://home.earthlink.net/~tdp/http://tdp1001.googlepages.com/homehttp://no-turtles.comhttp://www.frappr.com/tompotterhttp://photos.yahoo.com/tdp1001http://spaces.msn.com/tdp1001http://www.flickr.com/photos/tom-potter/http://tom-potter.blogspot.com
exp(j*pi/2)
Actually, Bob Cain's fundamental problem is that when he looks into a
mirror he sees everyone except himself.
Lester Zick
<blums...@et.uni-magdeburg.de> wrote:
>
>
>On 3/13/2007 6:52 PM, Lester Zick wrote:
>>
>> In the swansong of modern math lines are composed of points. But then
>> we must ask how points are defined?
>
>I hate arbitrary definitions. I would rather like to pinpoint what makes
>the notion of a point different from the notion of a number:
Well I'm not exactly sure what a number is supposed to be. I know
modern mathematikers claim numbers are supposed to be this and that.
However no one seems to understand what this and that is supposed to
mean.
>If a line is really continuous, then a mobile point can continuously
>glide on it. If the line just consists of points corresponding to
>rational numbers, then one can only jump from one discrete position to
>an other.
Just like modern mathematikers can jump from one position to another.
>A point has no parts, each part of continuum has parts, therefore
>continuum cannot be resolved into any finite amount of points.
>Real numbers must be understood like fictions.
Or perhaps like functions.
>All this seems to be well-known. When will the battle between frogs and
>mices end with a return to Salviati?
Perhaps when modern mathematikers concern themselves with truth
instead of fiction?
~v~~
Lester Zick
>On Mar 14, 9:51 am, Eckard Blumschein <blumsch...@et.uni-magdeburg.de>
>wrote:
>> On 3/13/2007 6:52 PM, Lester Zick wrote:
>>
>>
>>
>> > In the swansong of modern math lines are composed of points. But then
>> > we must ask how points are defined?
>>
>> I hate arbitrary definitions. I would rather like to pinpoint what makes
>> the notion of a point different from the notion of a number:
>>
>> If a line is really continuous, then a mobile point can continuously
>> glide on it. If the line just consists of points corresponding to
>> rational numbers, then one can only jump from one discrete position to
>> an other.
>
>That's an interesting (but old) problem. How would one distinguish
>between continuous and discrete? As a proposal, I would suggest means
>that there is a finite, nonzero interval (where interval is measurable
>somehow) between successive positions, in which there is no
>intervening position. Unfortunately, the rational numbers do not
>satisfy this definition of discreteness, because between *any* two
>rational numbers, there is an intervening rational number. I'd be
>interested in your definition of discreteness that the rational
>numbers satisfy.
That there is a straight line segment between rational numbers?
>> A point has no parts, each part of continuum has parts, therefore
>> continuum cannot be resolved into any finite amount of points.
>> Real numbers must be understood like fictions.
>>
>> All this seems to be well-known. When will the battle between frogs and
>> mices end with a return to Salviati?
>
~v~~
Lester Zick
wrote:
>Eckard Blumschein wrote:> If a line is really continuous, then a mobile
Arithmetic forever. Points glide at least as much as you do, Bob.
~v~~
Aaron
> On Tue, 13 Mar 2007 18:43:09 GMT, Sam Wormley <sworml...@mchsi.com>
> wrote:
>
>
>
>
>
> >Lester Zick wrote:
> >> The Definition of Points
> >> ~v~~
>
> >> 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~~
>
> > Point
>
> > A point 0-dimensional mathematical object, which can be specified in
> > n-dimensional space using n coordinates. Although the notion of a point
> > is intuitively rather clear, the mathematical machinery used to deal
> > with points and point-like objects can be surprisingly slippery. This
> > difficulty was encountered by none other than Euclid himself who, in
> > his Elements, gave the vague definition of a point as "that which has
> > no part."
>
> Sure, Sam. I understand that there are things we call points which
> have no exhaustive definition. However my point is the contention of
> mathematikers that lines are made up of points is untenable if lines
> are required to define points through their intersection.It's vacuous.
I'm like not getting it here. Are we just talking about graphing of
functions?
Isn't this splitting hairs or am I missing something?
A point is like a spot and has the same number of information elements
as there are dimensions in the space it models, right?
A line is then all the spots from one spot to another.
If two lines share a spot, big deal. They ahare a spot.
It's just numbers in a co-ordinate system, which in tern is an
abstract device to count numbers and model things we see using math
functions.
It it really more complicated than that?
Lester Zick
wrote:
And if wishes were horses you would ride.
~v~~
Lester Zick
No what you said is "Points, lines, etc aren't defined. Only their
relations to eachother". Your comment that "No, it is more complicated
than that" was simply a naive extraneous appeal to circumvent my
observation that relations between points and lines satisfy your
original observation. Your trivial ideas on complexity are irrelevant.
~v~~
Lester Zick
<som...@arcanemethod.com> wrote:
Actually I'm sure when Bob looks into a mirror he sees very little.
~v~~
Lester Zick
wrote:
>On Mar 14, 1:12 am, Lester Zick <dontbot...@nowhere.net> wrote:
>> On 13 Mar 2007 17:46:20 -0700, "The_Man" <me_so_hornee...@yahoo.com>
>> wrote:
>>
>> >On Mar 13, 12:52 pm, Lester Zick <dontbot...@nowhere.net> wrote:
>> >> The Definition of Points
>> >> ~v~~
>>
>> >> In the swansong of modern math lines are composed of points.
>>
>> >This is true if you consider "modern math" to begin with Euclid.
>>
>> What is this "truth" thingie whereof you so fondly speak?
>>
>> >> But then
>> >> we must ask how points are defined?
>>
>> >Yes, you must ask, since you obviously can't READ.
>>
>> Only because I learned to write before I learned to read.
>>
>> >? However I seem to recollect
>> >> intersections of lines determine points.
>>
>> >Did you even pass higvh school geometry?
>>
>> Obviously you didn't even pass grade school spelling.
>
>Sorry, typo. If the best rejoinder you have is to notice a typo, you
>don't have much.
Well I certainly agree you're sorry. That's a little something.
>> > The intersection of two lines
>> >can be the null set (no intersection at all for parallel or skew
>> >lines), it can be a single point, or it can be a whole line. A
>> >fundamental theorem of linear algebra shows that there are THREE
>> >possibilities for the simultaneous solution to two equations in two
>> >unknowns.
>>
>> Obviously in your case one of the three wasn't learning to spell.
>
>The question wasn't my spelling ability or lack thereof, but YOUR
>ideas about lines.
Oh well. It was a little hard to tell precisely what your comment was
in aid of. Spelling was all that came to mind.
>> >> But if so then we are left to
>> >> consider the rather peculiar proposition that lines are composed of
>> >> the intersection of lines.
>>
>> >You can "consider" anything you please, but the only "peculiar" thing
>> >is that you know nothing about even simple high school geometry.
>>
>> Of course not. Just look what it did for you.
>
>Yes, I can do math, and you can't.
Well bully for you.
>> >> Now I don't claim the foregoing definitions
>> >> are circular.
>>
>> >Sure you do.
>>
>> Oh really? How clever of you to notice, sport.
>>
>> >> Only that the ratio of definitional logic
>>
>> >Why talk about logic, when you nothing about it, either?
>>
>> When I what? Are you quite sure you're off baby formula?
>
>If I'm not off baby formula, what does that say about you? Come back
>when you can pass a college math course, and not be self-important to
>the hamburger-flipping set because you got your GED 90 years ago.
HAHA. You da Man! HOHO.
>> >> to conclusions
>> >> is a transcendental somewhere in the neighborhood of 3.14159 . . .
>>
>> >Who gives a flying fuck if you think lines are made of points, or
>> >not?
>>
>> I don't.
>
>You don't what?
Whatever you said, sport.
>> >You can piss on science and math all you want, but it puts up
>> >buildings and bridges that still stand up, gives us telephones that
>> >work almost all the time, TV sets that we flip on and get 150
>> >channels. You can "doubt" the laws of EM radiation, but we know those
>> >laws are right, 'cause all the shit we build according to those laws
>> >WORKS.
>>
>> And a lotta shit you also build doesn't.
>
>Such as? What - your French Fry broiler is on the blink again? That
>cash register, where you push the little picture of the food idea, so
>that you don't have to know arithmetic - is it broken again? It must
>be a FAILURE of Modern Math!
Don't take it so personally. Anyone can do empiricism. It's not rocket
science. As a matter of fact it's not even science. Exhibit #1: you.
>> >What do YOU produce, Mister Nick Ick? What have YOU accomplished?
>>
>> Just as soon as I learn high school geometry you'll be the first to
>> know.
>
>Start soon; you obviously aren't gifted.
Obviously however for reasons which remain yet to be explained I'm
gifted with you.
~v~~
Lester Zick
<mrjohnpau...@hotmail.com> wrote:
>> If the point is defined by the intersection what happens to the point
>> and what defines the point when the lines don't intersect?
>> On the other hand if the point is not defined by the intersection of lines
>> how can one assume the line is made up of things which aren't defined?
>>
>
>hahahahaha you are poor philosopher.
Obviously. That's why I became a mathematician.
> Math can't create the world it can only
>(try to) explain it.
Which is probably why neomathematikers prefer to make up a world they
can explain so they have something they can explain instead of
something they can't. Makes them feel useful I expect.
>To explain something you must fist admit that something exists.
>I admit that lines and points do exist.
That's nice. Does anyone care?
>Every definition puts in relation two or more thing that exist.
>Definition of point doesn't create point. It puts point in relation to something
>else.
>If you define point with intersection of two lines you put in relation:
>1) point that you admit that already exists
>2) two lines that you admit that already exist
>3) and their intersection that you admit that already exists.
Well I don't already admit points exist in the absence of line
intersections.
>Definition also does not create relation between thing. Relation between point,
>two lines and their intersection already exists and with definition you only
>admit that it exists.
>
>When you say "point is intersection of two lines" then you only admit that there
>exist certain relation between point, two lines and their intersection. This
>relation will also exist if you don't define it because definition discovers
>relations, it does not create them.
>
>Who (beside you) claims that it is wrong to define point with lines and define
>line with points?
Beats me. I was hoping somebody else would. Obviously you don't.
>Definition of point says that there is some relation R1 between point P and
>lines L1 and L2
>R1 = {(R, L1, L2) | where blabla P bla L1 and blabla L2}
>
>"Line is made up of points" says that there is relation R2 between line L and
>point P
>R2={(L,P) | where blabla L and blabla P}
>
>Not all relations are in form y=f(x) nor they should be.
>
>It is true that you can define point without intersection of two lines and it is
>true that you can define line without points but it only means that there is
>certain relation between point and something that is not line, and there is
>certain relation between lines and something that is not point.
>
>It is also true that you can't define point using nothing nor you can define
>line using nothing because relation between point and nothing is just not
>relation and therefore definition that defines something using nothing is just
>not definition.
>
>Just as f(x)=x-2*f(x) if perfectly good definition of f(x), "point is
>intersection of lines and line is made out of points" is ok definition if you
>know how to use it.
>Someone is confused with f(x)=x-2*f(x) and someone else is confused with points
>and lines :)))))
Look. If you have something to say responsive to my modest little
essay I would hope you could abbreviate it with some kind of non
circular philosophical extract running to oh maybe twenty lines or
less. Obviously you think lines are made up of points. Big deal. So do
most other neoplatonic mathematikers.
~v~~
Bob Kolker
>
>
> Obviously. That's why I became a mathematician.
You are not now, nor were you ever a mathematician. Nor will you ever be
one unless you get a brain transplant.
Your postings indicate not only a profound ignorance of things
mathetmicatical but a definite lack of talent for and competence in
mathematics.
Bob Kolker
Lester Zick
wrote:
>On Mar 14, 12:50 am, Lester Zick <dontbot...@nowhere.net> wrote:
>> On Tue, 13 Mar 2007 23:40:39 +0100, "SucMucPaProlij"
>>
>>
>>
>>
>>
>> <mrjohnpauldike2...@hotmail.com> wrote:
>>
>> >"Lester Zick" <dontbot...@nowhere.net> wrote in message
>> >news:2t8ev292sqinpej14...@4ax.com...
>> >> On Tue, 13 Mar 2007 20:48:34 +0100, "SucMucPaProlij"
>> >> <mrjohnpauldike2...@hotmail.com> wrote:
>>
>> >>>> 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 . . .
>>
>> >>>point is coordinate in (any) space (real or imaginary).
>> >>>For example (x,y,z) is a point where x,y and z are any numbers.
>>
>> >> That's nice. And I'm sure we could give any number of other examples
>> >> of points. Very enlightening indeed. However the question at hand is
>> >> whether points constitute lines and whether or not circular lines of
>> >> reasoning support that contention.
>
>O.K. Tell us, Icky-po: What do YOU think lines are made of?
Itsy bitsy little dots.
> What do
>YOU think is a "suitable" definition for point, line, plane, etc.. I'm
>sure Gauss, Euler, Cantor, Cauchy, Riemann, and Hilbert are rolling
>over in their graves with anticipation.
Straight lines are derivatives of curves. At least according to Newton
and his method of drawing tangents. Tell Euler et al. they can stop
rolling. Euler couldn't even get the definition of angular mechanics
right.
>Maybe the crew of my local Burger King will redefine QM next week, and
>the Friendly's will unify all the forces of nature in one theory.
Why bother? I already have. That was the first point of my collateral
thread "Takin Out the Trash".
>> >>>line is collection of points and is defined with three functions
>> >>>x = f(t)
>> >>>y = g(t)
>> >>>z = h(t)
>>
>> >>>where t is any real number and f,g and h are any continous functions.
>>
>> >>>Your definition is good for 10 years old boy to understand what is point and
>> >>>what is line. (When I was a child, I thought like a child, I reasoned like a
>> >>>child. When I became a man, I put away childish ways behind me.....)
>>
>> >> Problem is you may have put away childish things such as lines and
>> >> points but you're still thinking like a child.
>>
>> >> Are points and lines not still mathematical objects and are lines made
>> >> up of points just because you got to be eleven?
>>
>> >> ~v~~
>>
>> >hahahahaha
>> >the simple answer is that line is not made of anything. Line is just
>> >abstraction. Properties of line comes from it's definition.
>>
>> Which is all just swell. So now the question I posed becomes are
>> abstract lines made up of abstract points?
>>
>> >Is line made of points?
>> >If you don't define term "made of" and use it without too much thinking you can
>> >say that:
>>
>> Why don't you ask Bob Kolker. He seems to think lines are "made up" of
>> points, abstract or otherwise. I'm not quite clear about how he thinks
>> lines are "made up" of points but he nonetheless seems to think they
>> are.
>>
>> >line is defined with 3 functions:
>> >x = f(t)
>> >y = g(t)
>> >z = h(t)
>>
>> >where (x,y,z) is a point. As you change 't' you get different points and you say
>> >that line is "made of" points, but it is just an expressions that you must fist
>> >understand well before you question it.
>>
>> Frankly I prefer to question things before I waste time learning them.
>
>Yes -learning things is such a "waste". That's why you know so little.
Well I agree learning erroneous things is such a waste. That's why you
know so much that's wrong.
~v~~
Eric Gisse
*sigh*
It isn't my fault you cannot read for comprehension.
Points and lines are undefined - it is as simple as that. Every
question you ask that is of the form "So <idiotic idea> defines
[point,line]" will have "no" as an answer.
Lester Zick
I guess. Was that what I was looking for? Sure coulda fooled me.
~v~~
Lester Zick
>On Mar 14, 10:13 pm, Lester Zick <dontbot...@nowhere.net> wrote:
>> > The point is to ti en einai of the infinity.
>> > If you want a definition based on something fresher than Aristotle
>> > then:
>> > The point is nothing which is still something in potention to
>> > become everything.
>> > IMHO the Aristotle-based definition is better, but it's personal.
>>
>> I don't want a definition for points fresher or not than Aristotle.
>> I'm trying to ascertain whether lines are made up of points.
>
>You are bringing unacceptably too much of the "everyday sensual
>experience" by placing the question like that.
I do? Funny I sorta thought I'd make the question more explicit.
> Why "points", why
>plural? Floor by floor - a high building, foot by foot - 12 feet
>stick, something like that? ;-) Neither points nor lines are really
>existing, so you may think of them whatever you want - as long as it
>helps you to make another step in constructing something more
>complicated. Somewhere on the go you may get an intersection with the
>real world - or you may not, it is always cool but not required -
>unless you are on some applied contract work.
So this "real world" thingie. What is that exactly? I thought my
observations and questions were about the real world. I have no
interest in neoplatonic mysticism.
>The point is nothing with potential of becoming; that is a simplified
>up to profanity hybrid or Aristotle and Hegel, my sorries to them but
>it gets us started. Then the line is the point deformed (stretched)
>from negative to positive infinity.
>
>Or let's go in the reverse order: define the point using the line. The
>line is then an one-dimensional space and the point is vertical
>projection of this space onto n-dimensional space.
>
>Both options are as good as two crossed line. The difference is in the
>"mindset" they put on you, so some higher constructs are "possible" or
>"not possible" here or there.
>
>Actually with your line with many-many(-many) points you are hitting
>straight to the hands of Zenon. So can Achilles ever get the tortoise?
>And - most importantly and directly relevant to your current worries -
>can the bow ever flight? First answer the questions from the "reality
>point of view". That will let you to relax your mind for taking non-
>existing abstractions as freely as you need - for the given moment and
>for the given aim.
Yeah look, VK, I have a very limited interest in philosophy especially
bad philosophy. If you have some conclusion to draw with respect to my
observations and the question at hand please get to it and omit the
philosophy. Not interested.
~v~~
Lester Zick
>On Mar 14, 2:13 pm, Lester Zick <dontbot...@nowhere.net> wrote:
>> On 14 Mar 2007 10:10:55 -0700, "VK" <schools_r...@yahoo.com> wrote:
>>
>> >On Mar 14, 1:28 am, Lester Zick <dontbot...@nowhere.net> wrote:
>> >> Are points and lines not still mathematical objects
>>
>> > The point is ?? ?? ?? ????? ("to ti en einai") of the infinity.
>> >If you want a definition based on something fresher than Aristotle
>> >then:
>> > The point is nothing which is still something in potention to
>> >become everything.
>> >IMHO the Aristotle-based definition is better, but it's personal.
>>
>> I don't want a definition for points fresher or not than Aristotle.
>> I'm trying to ascertain whether lines are made up of points.
>
>Let's see if I can help.
Oh that'll be refreshing for a change.
>I believe Lester is asking whether a line is a composite object or an
>atomic primitive.
Actually I'm interested in whether vectors exist and have
constituents.
>One way of asking the question is whether a point sits ON a line or
>whether the point is part OF the line.
Like I said before you're not very good at philosophy but you're much
worse at science.
>Of course, since both the point and the line are idealizations,
>conceptual constructions out of the human mind that don't have any
>independent reality, then one could rightly ask why the hell it
>matters, since there is no way to verify either statement through an
>external discriminator.
An external what-inator? Why don't you just call it magic and be done
with it? No need to dress it up like a dog's dinner with all the
philosophical badinage. You're a mystic. So what?
> Lester doesn't believe in external
>discriminators anyway, because that is the work of evil empirics, and
>he'd rather spend his day mentally diddling away at issues like this.
Whereas obviously you don't.
>But to provide him with some prurient prose by which to diddle
You know, sport, if you were even half as witty as I am that might
indeed make you a half wit. However in this instance you're trying too
hard and you wind up appearing more trying than witty.
>further, let's toss him the idea that we can clearly cleave a line in
>two by picking a point (either on the line or part of the line, take
>your pick) and assigning one direction to one semi-infinite segment
>and the other direction to the other semi-infinite segment --
>sometimes called rays. One can then take one of those rays and cleave
>it again, and one of the results will be a line segment, which is
>distinguished by having two end *points*. Now the interesting question
>is whether those end points are ON the line segment or part OF the
>line segment.
Neither. The end points contain the line segment. That's how the line
segment is defined.
> One way to answer this is to take the geometric limit of
>one end point approaching the other end point,
Of course another way to answer this is to ask what defines the line
segment to begin with.
> and ask what the limit
>of the line segment is.
When it gets to zero do be sure to let us know.
> That should either settle it or send Lester
>into an orgasmic frenzy.
Gee with another swell foop you might actually get to the calculus. Of
course Newton and Leibniz and probably a thousand other wannabe's are
waiting in the wings ahead of you and the other neomathematikers.
Sam Wormley
> Look. If you have something to say responsive to my modest little
> essay I would hope you could abbreviate it with some kind of non
> circular philosophical extract running to oh maybe twenty lines or
> less. Obviously you think lines are made up of points. Big deal. So do
> most other neoplatonic mathematikers.
>
> ~v~~
Hey Lester--
Sam Wormley
> Straight lines are derivatives of curves. At least according to Newton
> and his method of drawing tangents. Tell Euler et al. they can stop
> rolling. Euler couldn't even get the definition of angular mechanics
> right.
>
>
Hey Lester
Line
http://mathworld.wolfram.com/Line.html
"A line is uniquely determined by two points, and the line passing
through points A and B".
"A line is a straight one-dimensional figure having no thickness and
extending infinitely in both directions. A line is sometimes called
a straight line or, more archaically, a right line (Casey 1893), to
emphasize that it has no "wiggles" anywhere along its length. While
lines are intrinsically one-dimensional objects, they may be embedded
in higher dimensional spaces".
SucMucPaProlij
> Look. If you have something to say responsive to my modest little
> essay I would hope you could abbreviate it with some kind of non
> circular philosophical extract running to oh maybe twenty lines or
> less. Obviously you think lines are made up of points. Big deal. So do
> most other neoplatonic mathematikers.
>
I think that you think that mathematikers are stupid and it has nothing to do
with lines and point.
I only know that they are convergent because they are limited and monotone but
this is subject for another topic :))))
Bob Kolker
>
> Hey Lester--
>
> Point
> http://mathworld.wolfram.com/Point.html
>
> A point 0-dimensional mathematical object, which can be specified in
> n-dimensional space using n coordinates. Although the notion of a point
> is intuitively rather clear, the mathematical machinery used to deal
> with points and point-like objects can be surprisingly slippery. This
> difficulty was encountered by none other than Euclid himself who, in
> his Elements, gave the vague definition of a point as "that which has
> no part."
That really is not a definition in the species-genus sense. It is a
-notion- expressing an intuition. At no point is that "definition" ever
used in a proof. Check it out.
Many of Euclid's "definitions" were not proper definitions. Some where.
The only things that count are the list of undefined terms, definitions
grounded on the undefined terms and the axioms/postulates that endow the
undefined terms with properties that can be used in proofs.
Bob Kolker
Bob Kolker
>
> Actually I'm interested in whether vectors exist and have
> constituents.
Yes they do, in the mathematical sense. They lead to a successful
description of forces for one thing. The constituents of a vector are
length and direction.
>
> Neither. The end points contain the line segment. That's how the line
> segment is defined.
That is admirably correct. And given the end points of a segment one can
readily define the set of points that make up the line determined by the
end points of the segment. Learn some analytic geometry to see how.
>
> Of course another way to answer this is to ask what defines the line
> segment to begin with.
A pair of points.
>
>
>> and ask what the limit
>>of the line segment is.
>
>
> When it gets to zero do be sure to let us know.
I see you are channeling Bishop Berkeley again. All of hist objections
have been answered by the theory of hyperreal numbers on which
non-standard analysis is based. Berkeley raised cogent objections to
Newton and Leibniz which were finally and complete answered in the late
1950's by Abraham Robinson.
By the way, if lines (or other curves) do not consist of the points on
them, what do they consist of?
Bob Kolker
Sam Wormley
Give me something better, Bob, or are you arguing there isn't a better
definition (if you can call it that).
Bob Kolker
>
> Give me something better, Bob, or are you arguing there isn't a better
> definition (if you can call it that).
You are asking for a definition of an undefined term. There is nothing
better. If one finds a definition of point it will have to be based on
something undefined (eventually) otherwise there is circularity or
infinite regress. We can't have mathematics based on turtles all the way
down. There has to be starting point.
Here is my position. If an alleged definition is no where used in proofs
it should be eliminated or clear marked as an intuitive insight.
Bob Kolker
Sam Wormley
Fair enough--However, for conceptualizing "defining" a point
with coordinate systems suffices.
Bob Kolker
> Fair enough--However, for conceptualizing "defining" a point
> with coordinate systems suffices.
Yes indeed. Point is a tuple of elements from a ring. But even these
have be grounded upon undefined terms.
The fact that RxR with a metric satisfies the Hilbert Axioms for plane
geometry implies that points can be taken to be pairs of real numbers.
The fact that the Hilbert Axioms for the plane is a categorical system
makes me feel warm and fuzzy about identifying a line with a set of
points (number pairs) that satisfy a first degree equation in the
co-ordinate variables.
This is a point (sic!) that Lester Zick is genetically incapable of
grasping.
Bob Kolker
VK
> I believe Lester is asking whether a line is a composite object or an
> atomic primitive.
That is one of things and the most easy one. I believe I already gave
the answer but not sure that he will ever accept it: it is whatever
one wants it to be today thus whatever higher level constructs is one
planning to study. Sometimes for instance it is more benefitial to go
in definitions from surface rather than from point. The line then is
an intersection of two surfaces and the point is an intersection of
two lines. For the final touch it is left to define the surface as a
set of points and we are back to the round of circular definitions :-)
- but - in either case we don't care as we are getting the starting
point we need to move on.
And - hidden for an appropriate moment - he also has an implicit join
of numbers and geometry, so number points and number lines are being
kept close to Euclidic points and lines for the next shot :-)
And what he really wants I guess as a provable definition of a basic
abstraction. So he doesn't want a statement like "Got does exist" but
he wants a statement like "It is rainy today outside" so Lester could
just run outside to say is it true or not and provide his wet/dry
umbrella as an ultimate proof.
So overall it is a rather demanding gentleman :-)
Lester Zick
But it is your fault you cannot argue for comprehension by others.
>Points and lines are undefined - it is as simple as that.
Problem is that when you want to endorse an idea you say "it is as
simple as that" and when you want to oppose an idea you say "it is
more complicated than that" such that we have a pretty good idea what
your opinions might be but no idea at all why your opinions matter or
are what they are or should be considered true by others.
> Every
>question you ask that is of the form "So <idiotic idea> defines
>[point,line]" will have "no" as an answer.
So we should just accept your opinions as true without justification?
Excuse moi but this is still a science forum and not merely a polemics
forum.
~v~~