1.0   Infinitesimal is not the same as 0-D!

    The idiots of mathematics have developed the incongruous notion that 'infinitesimal' and 'absolutely
    nothing' are synonyms:

    “ We may think of a point as a ‘dot’ on a piece of paper… A point has no length or
       width, it just specifies an exact location.” [1]

    “ A point has no size…Points are infinitely small” (p. 6) [2]

    A dot on a piece of paper has no length or width? An infinitely small point has no size?

    Whenever a mathematician puts an article such as 'a' or 'the' in front of the word point, he is treating it
    as a noun. Is this noun a physical object or an abstract concept? In Physics, the answer is straight
    forward. In Physics, only those things which have shape may serve as nouns. Formless concepts are
    prohibited. Physics and Geometry deal first and foremost with things which have shape.

    Let's see if I can state this in mathematical terms so that perhaps the mathematicians may also
    understand. If it is infinitesimal, the particle or point occupies greater-than-zero ( > 0 ) volume. For the
    purposes of Science, infinitesimal means small. That's all that this word means. It means that the
    observer has trouble seeing it. An infinitesimal dot is necessarily either 2-D or 3-D, but it definitely has
    shape. There are no figures that are 0-D or 1-D in Geometry! When we talk about infinitesimal we are
    referring to a dot and treating the point as a physical object and not as an abstract concept:

    “ If you think about the structure of math as a tree, there has to be something at the
       bottom of the tree, some objects that aren't defined. A point is one of these objects.
       It is undefined. It is just an object. In geometry, people usually think of points, lines,
       and planes as undefined objects (also known as undefined terms).” [3]

    “ Many physical objects suggest the idea of a point. Examples include the corner
       of a block, the tip of a pencil, or a dot on a sheet of paper. Such things are called
       models or representations or pictures of points, although they show only approxi-
       mately the idea in mind.” [4]

    [ Approximately? What idea could you have in mind other than the dot you've just described?]

    If a point didn't have size or dimensions or shape, it would not be a geometric figure, meaning that it
    would simply not be a part of Geometry!


    2.0   All geometric figures have shape

    Before the numskulls of Mathematical Physics can define the word point, it would help if they at least
    got their story straight. Is a point an object or a concept?

    “ 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.”  [5]

    “ Some concepts central to geometry are not defined in terms of simpler concepts.
       The most familiar of these undefined terms are point, line, and plane.” [6]

    Is there no difference between the solid object rock and the abstract concept love?

    The mathematician may argue that Geometry is an abstract science that deals with relations between
    and within idealized figures. He would be a fool to argue that Geometry does not deal at all with figures
    (i.e., shapes). Einstein wasn't a very bright individual, but he figured out this much a long time ago:

    “ In axiomatic geometry the words ‘point,’ ‘straight line,’ etc., stand only for empty
       conceptual schemata. That which gives them substance is not relevant to
       mathematics. Yet on the other hand it is certain that mathematics generally, and
       particularly geometry, owes its existence to the need which was felt of learning
       something about the relations of real things to one another… geometry must be
       stripped of its merely logical-formal character” [7]

    Geometry is a discipline that deals first and foremost with physical objects, shapes, and ideal figures:

    “ Geometry is the study of shape and size.” [8]

    “ Geometry: The branch of mathematics whose primary subject is spatial relationships
       and shapes of bodies. Geometry studies spatial relationships and shapes, while
       ignoring other properties of real bodies (density, weight, colour, etc.).” [9]

    Without shapes, there can be no Geometry. Relations can only be made between shapes, with
    ‘something’ in front of us.


    3.0   Approaching is not the same as being there  

    The mathematicians may argue next that 'infinitesimal' means something different in Mathematical
    Physics because, in fact, it does. In Mathematics, infinitesimal means:

    “ Capable of having values approaching zero as a limit.” [10]

    But clearly, even under the mathematical notion of infinitesimal, the magnitude is still greater than
    zero. Approaching is not the same as being there. Therefore, it is inexplicable why the mathematicians
    routinely confuse tiny with nothing and 'approaching 0' with 0.

    So now, for those of you who just finished visualizing the smallest particle you can think of, as
    homework, magnify it a billion times and divide it in half. If you have trouble seeing my point, please
    feel free to bring your personal SEM  to class; you no longer have to strain your eyes. Make my point
    as big as you like and imagine it the shape of a circle, a square or a pyramid, it doesn’t matter. If point
    wants to join the Noun Club, point will have to submit a portrait for its ID like the rest of the members!
    And if a point is alleged to be infinitesimal, it should have no trouble meeting this requirement (Fig. 1).

    4.0   From Math to Physics

    You may argue, finally, that although my argument has merits, it is ultimately trivial. So what if the
    mathematician confuses abstractions with real objects in his ethereal field? This is a harmless
    semantic issue.

    The problem is that the mathematician stealthily extrapolates these ridiculous notions into Physics:

    “ A point particle…does not have any volume or surface area; it is zero dimensional…
       Particle physics suggests that fundamental particles (quarks, electrons and other
       leptons) may be point particles which can contain mass, charge, spin, and multipole
       moments without occupying any volume.” [11]   Electrons are emitted one by one
       from the source in the electron microscope… As far as these micrographs show,
       you can be confident that electrons are particles…”  [12]

    “ In the infinitely remote past the universe had an infinite radius of curvature but this
       decreased progressively in the course of time to reach a minimum… At some point
       in the past the radius was zero (infinite curvature)” (pp. 79-80)    [13]

    [Minimum? Zero? Which is it? Apparently, in relativity, 0 and > 0 is all the same!]

    The prosecutor can make a movie of an impossible object  – a tribar, the devil’s pitchfork, etc. The
    juror can visualize these shapes on the screen. However, a juror will not be able to understand how
    these alleged objects collide. Touch is an exclusive property of the 3-D world of solids. Impossible
    objects may only be viewed in 2-D. The outlines and contours are visible. The explanation of how
    they collide is at best surrealistic. Indeed, the motion of an impossible object already tasks the
    rational mind. An impossible object is nowhere to begin with. It lacks location. The paper, the ink, the
    computer screen have location, but not the leprechaun or the tribar. Motion consists of two or more
    locations of an object. Therefore, an impossible object cannot be conceived to move. The relations
    actually take place in the observer's brain and not on the screen. This is what we call supernatural.

    On the other hand, the mathematician cannot even imagine let alone illustrate a zero-dimensional
    (0-D) dot or point to begin with. A dot has a minimum of two dimensions: width and height. If the
    prosecutor states that he is going to move a 0-D point, he first has to draw the monster or bring a
    sculpture of one to his show-and-tells. Of course, this is rather a bit difficult. A 0-D dot is a logical
    contradiction. When the prosecutor invokes not an impossible object, but an irrational object, his
    dissertation is not supernatural. It is irrational.  


    5.0   Conclusions

    What the geometers in their immense ignorance never figured out is that the definition of the word
    point has nothing to do with size (infinitesimal). Size inherently invokes another object. We can’t talk
    about size in a universe consisting of a single point. We need at least another one to compare the two.
    Size also requires an observer. Size has to do with measurement and measurement requires an idiot
    known as a mathematician to do the measuring. Without a witness or another point, size is just shape
    or position or length (Fig. 2). Therefore, size is a non-starter, a conceptually invalid parameter to fall
    back on to define the word point.

    more rantings about the infinitesimal point if you haven't had your fill...
The infinitesimal point
The alleged ‘0D’
mathematical point from
a bird's-eye perspective.

The same point
under the SEM
Adapted for the Internet from:

Why God Doesn't Exist



Fig. 2    

The only object in the Universe
    Without anything to
    compare it against, the
    sole object in the
    Universe has
    a single property: shape.

Fig. 1   

The 'infinitesimal' point of Mathematical Physics under the microscope
You will
someday, my
dear. Dr. Al is
now busy
trying to see it.
Why don't I
ever get to
see the stiff's
belly button?
What did you
expect, Bill? It's
infinitesimal!
It's so tiny!
But I can barely
see it, Dr. Al.

    ________________________________________________________________________________________


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        Copyright © by Nila Gaede 2008