1.0   The versatile (and so very useful) line of Math

    The mathematicians of the world want you to believe that a line is simultaneously an itinerary, a distance, a
    geometric figure, a row of apples, a trough plowed by one apple, and a series of numbers. They go back
    and forth between these irreconcilable concepts during the same presentation. They take a point, which is
    not a dot, but a location, they make 'it' streak across space, and call it a line. Then, they begin to twirl, shift,
    scan, and translate this itinerary and to find points -- meaning locations -- on these locations. The
    mathematicians tell you that this itinerary is straight, when they really mean that it is rectilinear. Actually, it is
    neither straight nor rectilinear because the mathematicians are talking about a movie. They are pointing to a
    roll of film, which they casually stretched out on the blackboard and which they incongruously replaced
    with a geometric figure known as a line, which now becomes a pictorial representation of that trajectory,
    and finally end up twirling this avatar or reification. If the itinerary curves, the mathematicians call it a
    geodesic, and continue telling you that it is straight. Then they tell you that your eyes deceive you. The
    'line', meaning the itinerary, may look curved to you, but is actually straight in Flatland and in the superior
    world of four dimensions:

    " space-time is not flat, as had been previously assumed: it is curved or 'warped'...
      bodies like earth are not made to move on curved orbits...instead, they follow the
      nearest thing to a straight path in a curved space (p. 29)...   The mass of the sun
      curves space-time in such a way that... the earth follows a straight path in four-
      dimensional space-time. " (p. 30) [1]

    " For two-dimensional inhabitants of this two-dimensional world the space is finite,
      or closed, but without boundaries. They are living on a spherical two-dimensional
      space of radius R. For these imaginary beings, who know nothing of the third
      dimension, a voyage of exploration in the same direction ('straight line') in their
      space leads to a surprising result, already experienced by those sailors who
      made the first circumnavigation of the Earth." (p. 71) [2]
    "
    It is just you, who is stuck in between these two worlds, lost somewhere in Solid-land, that believes he is
    staring at curved paths. The Flatlanders and Hyperlanders know better. If you want to see a genuine
    'straight' geodesic, you will have to live in Flatland or inside a tesseract.

    At the end of their presentation, the mathematicians tell you that this alleged geometric figure is continuous,
    when they actually mean that it is made of segments or parts. They say it is a rigid structure, and then begin
    to find points within and along this entity. They tell you it is the shortest geometric figure or entity
    imaginable, but that it is itself made of points and that between two points you can always find another
    point, meaning a location, meaning a number. They have been doing Math like this for the last 2500 years.

    So Bill? Why is it that you say that the mathematical physicists of the world are bunch of stupid morons?

    Let's run the claims made by the mathematicians by again in fast forward so that they don't accuse me of
    putting words in their mouths:

    a.        two points

    Everyone knows that two points determine a line”  [3]

    b.        a distance: the separation between two points

    “ the curve that minimizes the distance between two points is clearly a straight line
      segment” [4]

    c.        a row of discrete dots

    A discrete line is a line made up of dots with space between the centers of the dots.”  [5]

    d.        a row of vacant locations

    an exact ‘here,’ a point is space…The endpoints of all vectors…form a straight
      line (pp. 11, 18)  [6]

    e.        a set of ordered pairs

    “ Each point in the plane is now a location in the Cartesian plane and is represented
      by an ordered pair.”  [7]

    f.        a set of coordinates (lines made of cross-hairs)

    “ point lattices may be taken to refer to points in a square array, i.e., points with
      coordinates” [8]
     
    g.        a geometric figure: an elongated rectangle made of a single piece  

    “ all the points which we obtain finally fuse together into a linear continuum, in
      which they become embedded, giving up their individual existences” (p. 16)  [9]

    h.        distance traveled (displacement): the trajectory of an object (typically a point)

    “ the line traced by a point in spacetime (a car) is a succession of events (the
      car observed at successive intervals) called the ‘worldline’ (of the car).” (p. 66)  [10]

    i.        a collage: footprints left by one object on a medium

    the tracks shown in Fig. 1 were obtained, which seemed to be interpretable only
      on the basis of the existence in this case of a particle [11]  (Have patience... the
      paper may take a little bit of time to load!)

    Of course, if a line can be so many things at once, we can see how the mathematicians should have no
    problem explaining anything and everything. But what have they understood?


    2.0   The dull line of Physics

    In Physics, it is not remotely as complicated as all of this. In Physics, a straight line is very simply an
    elongated, straight, rectangular geometric figure (Fig. 1). That’s all that we have before us.

    line: An ideal geometric figure, usually a continuous rectangle, far greater in width
    than in height, and which has no importance whatsoever in Physics or in Science.  
    Whether straight or curved, in Physics, a line consists of four  edges.

    In Science, we don't define what a geometric figure is. In Science, we point to it. The foregoing definition is
    merely a description of what you're staring at below:

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    Last modified 02/07/08


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    The standalone line of Physics is more or less what has heretofore been known as a line segment. A line
    segment is 2-D and consists of two ends rather than of two endpoints. In Physics, there is no figure that is
    infinite! If you're looking for an infinite geometric figure, they sell those only at the Math Asylum.

    I’m sorry if this simple geometric figure disappoints the mathematicians, but that is all that a straight line is.
    For 2500 years the mathematicians have been staring at this rectangle and still declare that they have no
    idea what it is. So I slice through this Gordian knot with my 10-lb hammer and solve the riddle once and for
    all. A line is physically a rectangle. That’s all it is. That’s all we have before us. That's what you're staring at.

    Now, whether this version of the word line is useful is another matter. Physics doesn’t care if an object is
    useful to the idiots of Mathematics. This ‘useful’ feature is one that the mathematicians have concocted to
    justify their ridiculous physical interpretations to laymen. The scientific method requires the mathematician
    to conceptualize before he uses. This definition conduces to radically different results than those reached
    by relativity, quantum, and string theories.

    Once again, the mathematician may attempt to dismiss these arguments as irrelevant. He may try to
    convince you, perhaps, that the mathematicians of the world have used their flexible line for ages and that
    they've done quite well with it. Who am I to change such a long tradition? They will add that this is merely
    my version of line and that it has nothing to do with Math.

    The idiot of Mathematics who falls back on such argument has very little gray matter in his head to deal with
    such issues. This is not my version of a line. This is what a line is for the purposes of Physics, Science, and
    Geometry. Geometry is a science that deals first and foremost with shapes. A mathematician can talk all he
    wants about a series of locations or numbers and about finding infinite numbers between two locations on
    his infinite itinerary, but in Geometry he is first required to put something on the board. A location is nothing
    without something in it. Otherwise, the mathematician should come to terms with the fact that he has no
    authority to extrapolate any conclusion he infers from the mathematical line into Physics. The line of
    Mathematics has nothing to do with the real world.

    Therefore, a mathematician is denied the use of the word line in any scientific context. He cannot say line,
    expect the jurors to visualize an elongated rectangle, and explain his theory with a series of locations. This
    is not only unscientific (inconsistent use of a key term), but irrational. So to answer the mathematician, yes,
    it is not business as usual!

Fig. 1   Line
On my right, I have
a straight line, and
in my left hand, a
straight geodesic.
Don’t believe
them, Bill. A
straight line is
made of points,
like this one.
A point is a cross
between two lines, which
I hold on my right. A
straight line is made of
points and looks like this
curve.
I don’t know
what to believe
anymore!
Adapted for the Internet from:   Why God Doesn't Exist
So then, what is a line?