1.0   Recap

    Geometry is a science that studies relations between shapes. We cannot do Geometry unless we have form
    before us. Likewise, Physics deals first and foremost with shape and form. You may want to theorize in the
    abstract all you want (e.g., black hole, dark matter, point particle), but when we go to the lab, you'd better have
    something more than just a mathematical abstraction.

    The foregoing analyses demonstrate that the word point is not undefined or indefinable, but rather that it
    enjoys several irreconcilable definitions which cannot be invoked simultaneously during a given dissertation.
    The reason mathematicians claim that a point is undefined has to do solely with their blatant disregard for the
    scientific method. They have no intention of using the word point consistently since this would instantly
    convert Geometry into a non-science and derail any theory founded upon it (e.g., General Relativity). Thus,
    Euclid begins with a point having no extension (dimensionless figure), insinuates that it is really a location,
    and then goes through the motions of building lines and solids with this abstraction. It is bad enough that he
    substitutes the concept location with the object dot. It is beyond words when he moves the location and tells
    us that it is now at a new location. Weyl  begins by assuming that his point is a 'here and now', a half-breed
    whose mother is a location (here) and whose father is a second (now). (p. 11) [1] Since he can't use such
    hogwash rationally, this abstract 'here and now' soon suffers a metamorphosis. It converts from location to
    dot. Weyl slides this dot and paints a swath he calls a line. Or he places a series of them in a row and swings
    them around to scan a plane. To a mathematician it doesn't matter. At the end of the presentation he is going
    to convert the dot back into a location anyways to get his 'point' across. Kaufmann tells us that a star shrinks
    so much that it converts into an infinitesimal, 0-D concept known as a singularity. (p. 470) [2]  Others postulate
    that virtual points twinkle on and off between 3D dots and non-dimensional locations. [3]  And Hawking
    constructs his universe by integrating 4-D points. (pp. 23-24) [4]  What do we find in each of these points?
    What else but the verb event. The mathematicians have not chosen between a dot, a position, a location, and
    ordered pair, and an event. The mathematicians have chosen all of them simultaneously.

    Poincaré realized this inconsistency early in the 20th Century:

    " Mathematics is the art of giving the same name to different things." [5]

    This allows the mathematicians to select the definition best suited to explain the theory that they are
    promoting at the moment. Having reviewed the various mathematical proposals for the word point in vogue
    today, it is clear that none of them passes a rigorous examination.


    2.0   How then should we define this mysterious figure? What really is a point?

    One popular answer is that we should leave certain words alone. We have inherited very bad habits,
    traditions, and customs, and old habits are hard to shake. We were told in primary school that words normally
    have to be defined, we know not why, and few ever gave it much thought. So when someone asks you to
    define the word table, your mind draws a blank. How do you define a table anyways? I sit at one every day, I
    eat on it, I place things upon it. The one I have at home is made mostly of wood and a bit of metal, which I think
    is aluminum. My local carpenter customized it especially for me. So how should I answer the question?
    Should I focus on how it was built, on its material constitution, on what it is, on what it is used for? In the end,
    you get such a brainstorm rush that you resolve to leave table undefined. Yeah! That's the ticket! The word
    table cannot be defined. It is one of those 'whatchmacallit?' primitive words. Yeah! And curiously, so are the
    words tree, rock, coconut, and every word you can think of. For some strange reason it is very difficult to
    define objects.

    The correct answer is that for the purposes of a scientific theory -- meaning a rational explanation -- you
    cannot and don't define objects. A physical object is something you point to and name. Imagine being
    marooned on a lost island with someone who doesn’t understand your language. How do you begin to teach
    her your mother tongue? Certainly, you won't begin by defining sophisticated concepts such as love and
    acceleration. You begin by pointing to a tree and saying tree. Then, you point to a rock and say rock.
    Eventually, you can perhaps communicate that you should try to knock a coconut from the tree with the rock
    to kill your hunger. If you want the ET to understand your narrative or explanation, you absolutely must begin
    by pointing to the relevant objects and naming them individually like Adam did with the animals (Gen. 2:19-20).
    We cannot and do not 'understand' objects. We can at best understand a definition or an explanation. An
    object is something you 'visualize'. We understand movies (theories)  and visualize photographs (exhibits).

    So please do not judge me too harshly if I now treat you as if you were an alien who just arrived on Earth from
    another planet. I will attempt to perform a feat that no one has been able to do in the last 3,000 years. I will
    attempt to ‘define’ the word point unambiguously. This is a very difficult thing to do, so please have patience
    and allow me to prepare my props a little. I’m a bit nervous. But, here it goes.

    I did it! Halleluiah! I am saved! I can’t believe it! I was able to show WHAT a point IS! Just to think that it took
    3000 years to ‘define’ the word point sends goose bumps down my neck. Well shiver me timbers!

    For the purposes of Physics, a point is nothing but a dot. After we illustrate it, point to it, and name it, we can
    proceed to describe and define it as scholarly as we can:

    point: An infinitesimal, typically round or spherical object that has no importance whatsoever
                in Physics; a dot.

    For the purposes of Physics, the point is nothing more than a hypothetical subset of objects, conceptually, a
    tiny stand-alone chunk of an object, a two or three dimensional dot. This is all that a point is. That is all that we
    have in front of our eyes. If you wish to think of a point as an elephant in the horizon or as an atom at the tip of
    your nose, that is your prerogative, but in the end it is just an infinitesimal spec. In Physics, a point is just as
    easy to 'define' as any other object. There is nothing special about a point that would warrant the
    mathematicians to condemn it to anonymity or to spend 3000 years of research on it only to tell you that they
    cannot define it. A point has the simplest shape known in Geometry: we typically imagine it as a circle. If a
    point is alleged to be a geometric figure, it must meet a single requirement: shape. Without shape we are not
    even talking about an object or about Geometry.


    3.0   Is this 'definition' useful, Bill?

    The idiot of Mathematics now asks whether this 'definition' of mine is useful. What is the purpose of defining
    the word point in such a way that makes it irrelevant?

    I am terribly sorry if this definition disappoints the mathematicians and doesn't meet their expectations, but in
    Science and in Physics we don't give a damn whether a stupid mathematician can use a definition. This is
    WHAT a point IS. If the mathematicians cannot use this exhibit to explain their theories, perhaps they should
    brainstorm one they can and then proceed to use it consistently. If the mathematician is referring to a location,
    he should call it a location so as to avoid misleading the jurors, and not say 'point', insinuate a 'dot', and talk
    about 'locations' and 'ordered pairs' for the rest of the presentation. And finally, if every mathematician on
    Earth, living or dead, were to vote against my method of 'defining' this most crucial of geometric figures on
    which Relativity, Quantum, and String Theories rest, it does not change the fact that a point is nothing but a
    dot.


    4.0   This is your personal version of a dot

    The stupid idiot of Mathematics attempts to make one last stand. He tells you now that these arguments are
    irrelevant. Mathematicians have been using their 'undefined' point for centuries. Who am I to come in and try
    to change this tradition so late in the game? They may argue that the point that I am proposing is simply my
    personal version.

    Again, they miss the 'point'! This is not my version of a point. This is what a point is for the purposes of
    Physics, Science, and Geometry. Geometry deals first and foremost with shapes such as a dot and not with
    abstract concepts such as a location. The mathematicians can talk about a location all they want, but first they
    must have a dot! Without the dot, they have absolutely nothing. The mathematicians cannot extrapolate any
    conclusions they draw from their ridiculous, malleable 'point' onto Physics or Science. They are barred from
    using the word point (as they conceive it) anywhere in Physics, Science, or Geometry. So now, what is it that
    you didn't understand you stupid relativist?
Point
So then,
what is a point?
Adapted for the Internet from:

Why God Doesn't Exist

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    Last modified 01/17/08


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Mmmmmh. Medicine
Man not know point
either. What mean point?
Primitive Bill
still pondering 'What is the point?'