| A mathematician sculpts solids point by point |
| Adapted for the Internet from: Why God Doesn't Exist |
1.0 Geometric figure or volume?
The mathematicians are ultimately not concerned with genuine geometric figures. They have no interest in
circles, triangles and squares per se. Mathematicians are concerned with relations. They are interested in
parameters such as area, diameter, length of a side, height of a polygon, radius, etc. A square is otherwise a
stale object for them. It has no purpose or meaning to a mathematician if he cannot study its internal
relations or use it for something.
It was the internal relations of the basic planes and solids that captured the imagination and fascination of
the Greeks. When Plato and Euclid talk about a sphere, they really have in mind a volume. They want to
figure out, for example, how to calculate the volume a sphere displaces. This is the type of activity that gives
a mathematician a rush. The Greeks had otherwise no use for the square or the circle as mere objects.
Likewise, the early mathematicians defined solids specifically for the purposes of establishing relations. A
cube and a sphere have absolutely no importance to a geometer strictly as figures.
Hence, the mathematicians developed definitions useful to their line of work and which are unrelated to
Physics or to the real physical world. This explains why they have never found a need to define the word
plane correctly. They can perform their mathematical operations even with faulty definitions and
conceptualizations because the mathematicians never have to produce the goose that lays the golden
eggs. A mathematician produces nothing tangible in his entire existence!
One of the earliest purposes for which the mathematicians found planes useful was to calculate volumes.
The mathematician takes a square, scans it through space, and tells you that you end up with a cube.
However, when you attempt to reproduce his experiment in your basement, you always end up with
something else. First, you realize that you cannot scan a square because in Physics a square is not a stand-
alone figure. But assuming you could, you still don't end up with a cube. You end up with a stack of
squares! Is a pile of paper equivalent to a box? The mathematicians really have to be kidding!
What the mathematicians are doing in effect is 'scanning' an area and 'constructing' a volume. The side of
this 'cube' is not a surface you can stand on, but rather a distance-traveled, a movie of the alleged area at
different locations.
Let's put all of this in mathematical terms so that the mathematicians may also understand what it is that
they are doing. The mathematician erroneously believes and misinforms you that he took a square,
multiplied it by a length, and ended up with a cube:
cube = square * length
However, the units he attaches to his result makes you suspect that he lost a screw somewhere in his head:
- 14 cubic meters or 14 m³
What the stupid fool actually did was scan an area and build a volume:
volume = area * distance-traveled
We are not talking about cubes or squares, which means that we are not yet talking about Geometry. We are
talking about building a volume by scanning an area. A cube is a static geometric figure. A volume is a
dynamic concept we build by expansion or shrinkage. A rubber ducky is a physical object and may be said
to belong to Geometry. The amount of water it displaces is a volume. A volume has nothing to do with
Geometry and all to do with Math. Only the idiots of Mathematics confuse one with the other.
It is using 'constructions' that the mathematical morons arrive at their dynamic 'geometric figures' with
which they live today. All of the 'figures' of Mathematical Physics are conveniently both static and dynamic.
The mathematician points to a cube and tells you that it is a geometric figure. We have no problem with this.
He tells you next that he 'constructed' this cube by scanning a plane or integrating dots. Now we do have a
problem. This last claim amounts to a volume. A volume is not the same 'thing' as a cube. A volume is a
dynamic concept. A cube is a static object.
This duality comes in very handy to a mathematician, especially when he attempts to give a physical
interpretation to an equation. He has unwittingly established the foundations that enable him to jump back
and forth between architecture and motion.
- 2.0 Euclid's 'sphere': Twirling the semicircle
- One of the most popular 'constructions' of Mathematical Physics is the ever present sphere. There are
several ways in which the mathematicians 'construct' the volume of a sphere. Euclid did it the old-fashioned
way. He took a semicircle and twirled it around an axis (Fig. 1):
- “ When a semicircle with fixed diameter is carried round and restored again to the same
position from which it began to be moved, the figure so comprehended is a sphere.”
(Bk. 11, Def. 14) [1]
“ a sphere may be generated by revolving a semicircle through 360º about its diameter
as the axis.” [2]
“ A surface of revolution is a surface generated by rotating a two-dimensional curve
about an axis.” [3]
Unfortunately, what Euclid and his contemporary disciples are proposing ends up being nothing like a
sphere. Euclid is talking about a movie rather than about a photograph. Do the following experiment at
home, but always under the supervision of a trained mathematician. Take a clothes-hanger and mold it so
that it looks like a semicircle. Twirl it around 'its diameter as the axis.' Did you end up with a sphere? A
sphere looks more or less like a bowling ball or like a globe. If you ended up with a warped clothes hanger,
you now should know the difference between Math and Phyz! The mathematical morons are not talking
about a sphere or about dimensions or about a surface of anything. Again, they are explaining the
technique that enabled them to come up with a volume.
- ________________________________________________________________________________________
- Last modified 02/17/08
- Copyright © by Nila Gaede 2008
3.0 The 'sphere' of Modern Math: An empty shell made of locations
Euclid's modern day disciples have come up with better mousetraps. They don't always twirl semicircles.
Sometimes they open up an umbrella of points (Fig. 2):
- " a sphere is the set of all points in three-dimensional space (R3) which are at
distance r from a fixed point" [4]
- Other times they have a single point (meaning location) orbiting a center.
- " The sphere itself now consists of all points satisfying the equation: x² + y² + z² = r² " [5]
The equation definition of a sphere invariably requires that you to construct one point at a time.
- And yet other times, people visualize the sphere as a series of piled up rings (Fig. 3):
- " A sphere is a sequence of concentric circles laying top to bottom on each other" 52b [6]
So one of the questions that rational people raise is whether a sphere is supposed to be made of parts or of
a single piece. Is a sphere a segmented or a continuous object? Will a sphere that is made of smaller
components be ideally smooth? For instance, pursuant to these specifications, Wolfram illustrates a disco
ball, which Wikipedia specifically qualifies as being 'a roughly spherical object'. Is this what a sphere is? A
million-sided polyhedron? Is a sphere something we construct over time or is it something you point to and
visualize in a single stare? Are we supposed to imagine a statue or a statue in the making?
Fig. 1 Sphere: The movie Twirling the semicircle |
| I could not visualize you in one go, so I had to construct you piece by piece. When God does not bless us with the ability to conceptualize, we must build our own dreams and visions. |
| A relativist ‘constructs’ a sphere by spinning a curved clothes hanger. When the mathematician is finished, she ends up with a curved clothes hanger and not with a sphere. Relativists confuse a movie of how a sphere was built (dynamic) with a sculpture (static). The sphere of the mathematicians belongs neither in Geometry nor in Physics. |
Fig. 2 Sphere: The photograph equidistant dots (or locations) |
Nevertheless, notice that none of these proposals results in a bowling ball. The mathematicians are not
talking about a solid. They are talking about a 'hollow.' The sphere of Mathematics is an empty balloon.
But it is not even a balloon. The rubber of this alleged balloon is not made of matter. The entire surface is
merely a collection of locations. There is absolutely nothing occupying each of those locations. Each
'point' comprising the 'surface' of the mathematical sphere is an abstract ordered triple (x, y, z). When you
peel mathematical onion to the core, you always end up with zip! There is nothing you can sink your teeth
into. The sphere of Mathematics is not a physical object because it has no shape. According to the
specifications, there is nothing in front of you.
The mathematician says 'So what? We deal with concepts. This enables us to communicate ideas without
being distracted by architecture.'
Aaahh! But then you cannot extrapolate your nonsense to Physics. If you want to cross the line into
Physics, you must absolutely leave your abstract garbage behind. You cannot use your sphere in our
discipline. It is okay if you want to brainstorm some nonsense in your petty world of make-believe. We
have no problem with that. But if you want to theorize about something in the real world, you now will be
required to use the sphere of Physics: the bowling ball. And if your theory cannot work with the solid ball
we put in front of you, whatever you concocted in the fantasy world of Math is irrelevant. There is no such
sphere as the abstract mathematical sphere anywhere in the Universe! Yet this is exactly the sphere
which the idiots of Mathematics use to reach ridiculous syntheses such as the black hole. The
mathematical moron does not compress a ball such as a star. He shrinks its volume. He compresses its
mass. That's why the stupid idiot doesn't see any problem with shrinking this volume to 0 and calling the
result a singularity, insinuating in the process that the singularity has something to do with Physics. The
idiot of Mathematics has no street smartness, no natural curiosity to question whether such hogwash has
anything to do with reality. He accepts the conclusions merely because the results follow from his
equations.
4.0 Conclusions
The fundamental problem with the 'construction' techniques used by the mathematicians is that they
don't produce geometric figures. Instead, they result in volumes. The mathematician is not interested in a
sphere. The mathematician is at best interested in the volume displaced by the sphere. The second
problem with 'constructions' is that you cannot see them in a single stare. You must sit through an eternal
movie of a sculptor chiseling away one point at a time. The dynamic 'figures' of Mathematics are not stand-
alone statues you can touch in the lab. They are abstractions you must watch at the movies. Since the
sphere is alleged to be made of 'infinite points,' this movie does not have a very happy ending. The
'solids' of Mathematics are perpetually under construction. But even if we accept the 'equidistant points'
as a photograph, this version contrasts with the dynamic twirling semicircle that Euclid had in mind.
These version conduce to different physical interpretations and really constitute an attempt to embody
both static and dynamic features into one 'geometric figure.' This leads me to conclude that we have to
revise any inferences drawn from the sphere of Mathematics in the last 4000 years.
The sad history of the 'solid' known as the sphere has been a gradual disappearance of matter: from
dense bowling ball to hollow balloon and from a shell to a little dot (that is really an abstract location) still
going around in an incessant attempt to enclose a volume of nothing. The mathematicians no longer
point or even describe WHAT a sphere IS. They explain how they are building it!
Fig. 3 Sphere: The photograph piled up rings |
| If you want the sphere to be smoother, all you have to do in Mathematical Physics is dig your fingernails in it like this to generate more points. |
- Module main page: A mathematician says that solids are hollow
Pages in this module:
- 3. This page: A mathematician sculpts solids point by point