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.

 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 hasa 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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