| Adapted for the Internet from: Why God Doesn't Exist |
- 1.0 Relativists allege that the tesseract is a geometric figure
In his website, Bogomolny shows you what a tesseract is. Actually, he explains to you how you should 'understand' this
alleged 'geometric figure.' He doesn't point to a tesseract. He asks you to watch a movie. Bogomolny does the entire thing
in steps. This relativist systematically constructs:
- • a line by scanning a point
• a plane by scanning a line
• a cube by scanning a plane
- At the last level, he ends up with the tesseract and tells you that:
- “ If we trace a point from one position to another along a straight line we shall get a
segment whose dimension is 1…From a segment we can obtain a square. Translate
the segment in the perpendicular direction…Similarly, to obtain a cube, translate the
square in a perpendicular direction… Tesseract is obtained in the same fashion by
translating a cube along a fourth perpendicular direction. The tesseract’s dimension
is 4.” [1]
Note that this description invokes the physical notion of dimension (length, width, and height) and not the mathematical
definition (the number of coordinates needed to locate a point). Bogomolny is alluding to a static physical object alleged
to have a fourth perpendicular direction. He is talking about a geometric figure that has 4 spatial dimensions and not one
that has 3 spatial plus 1 temporal 'dimension.
Bogomolny's 'geometric' view of the tesseract is not his particular opinion, but the standard version of relativity:
- " the tesseract is the 4-dimensional analog of the (3-dimensional) cube…The tesseract
is to the cube as the cube is to the square, or more formally, the tesseract can be
described as a regular convex 4-polytope… a tesseract is in principle obtained by
combining two cubes " [2]
" A tesseract is an example of a four-dimensional object." [3]
" the ‘hypercube’ - is a solid figure in 4-D space bounded by eight cubes, just as
a cube is bounded by six square faces." [4]
" The above figures show two visualizations of the tesseract. The figure on the left
is a projection of the tesseract in three-space…and the figure on the right is the
graph of the tesseract symmetrically projected into the plane…A tesseract has 16
polytope vertices, 32 polytope edges, 24 squares, and eight cubes." [5]
" a four-dimensional cube, known as a tesseract" [6]
- It is therefore indisputable that relativists perceive the tesseract to be a 4-D geometric figure and not as an abstract
space-time. In some of these websites, the visitor is able to rotate this strange figure with a mouse, and certainly you
cannot talk about twirling or scanning an abstract concept such as love. It is important to establish this point because
we don't want the mathematician to deny everything at the end of the presen-tation.
2.0 In relativity, time is equal to height
The obvious problem with the tesseract is that there is nothing 4-D about it. The picture everyone draws and points to is
unambiguously a two-dimensional image of a 3-D object. Not one of these misguided fanatics can imagine, let alone draw,
a line running perpendicular to the other three. If they could, they would do it in the lab to 'prove' their 'theory.' These folks
just did it the relativistic way: by the stroke of a pen. This confirms that talk is cheap.
A second problem is that these relativists insinuate or outright state that there is a difference between a spatial and a
temporal dimension. The geometric figure that they are alluding to does not have time as the fourth dimension as relativity
proposes. Unlike space-time, the tesseract is alleged to have a fourth spatial dimension:
- " Take the non-infinite cube and extrude it in yet another direction perpendicular to the
first three. But how can we do this? It is impossible to do within the restrictions of the
third dimension (which will I refer to as realmspace in this webpage). However, within
the fourth dimension (which I call tetraspace), it is possible. The shape that results from
this extrusion of a cube into tetraspace is called a tesseract, which is a 4-hypercube...
width, length, height, and a fourth measurement, which I call trength... If you expanded
the tesseract infinitely, it would cover four-dimensional space." [7]
- " In a 4D world, there is another directional axis which is perpendicular to the X, Y, and
Z axes. We shall label this axis W, and call the direction along this axis the fourth
direction…It is important to understand that the W-axis as depicted here is perpen-
dicular to all of the other coordinate axes. We may be tempted to try to point in the
direction of W, but this is impossible because we are confined to 3-dimensional space....
Some claim that it is impossible for us to visualize 4D, since we are confined to 3D, and
therefore cannot directly experience it. However, I believe that it is indeed possible to
develop a good idea of what it looks like. The key here is that what the 4D being sees in
its retina is 3-dimensional, not 4-dimensional. The 4th dimension is inferred. But since
we have a good intuitive grasp of 3D, it is not that difficult to understand what a 4D
being sees in its retina. From there, we just need to learn how to infer 4D depth." [8]
- [4-D depth? This fellow hasn't even learned kindergarten stuff such as the difference
between length and depth. He mixes dimensions (length, width,and height) with vectors
(depth, breadth, and elevation), and probably wouldn't know the difference between
width, latitude, and breadth. Yet he intends to teach you how to visualize the 4-D!]
- But then, if this is true, it raises two more fundamental questions. If a the tesseract is supposed to be a geometric figure,
it cannot serve as an analogy for space-time, which is supposed to be a dynamic mathema-tical concept. It can at best
serve as a simile, example, or mockup of space-time. However, if the tesseract is a geometric figure, the prosecutor
should point to it and not have to explain it.
The second issue is that we have a blatant contradiction in relativity. Hawking and Heidmann testify that there is no
difference between a spatial and a temporal coordinate:
- " In relativity, there is no real distinction between the space and time coordinates, just
as there is no real difference between any two space coordinates." (p. 24) [9]
" The giant leap forward in relativity theory stems from the fact that space and time are
treated on an equal basis." (p. 68) [10]
In fact, relativists routinely replace the dimension of height with the number line known as time:
- " To be able to represent conditions graphically we suppress one space-co-ordinate,
assuming space to be only two dimensional, a Euclidean plane.” (p. 150)… Every
world-displacement x has a definite duration t(x) = t (this takes the place of ‘height’
in our geometrical argument)” (p. 158-159) [11]
" The other two spatial dimensions are ignored or, sometimes, one of them is indicated
by perspective. (These are called space-time diagrams…" (p. 24) [12]
- So now your job is to determine which of these two groups of people are the idiots. Either there is a difference between
time and height or there isn't. And whoever is wrong has not learned the fundamentals in his first year of high school
Physics.
3.0 Math is not the language of Physics
In the real world, the world of Physics, there are only three dimensions: length, width, and height. We're done. There's
no more science than this.
However, relativists tell you that the discipline of Mathematics allows for extra dimensions.
- " As far as we know, the space we inhabit consists of these 3 dimensions, and no
more. We might think that space has to be 3-dimensional, that it can't possibly be
anything else. Physically, this may be true, but mathematically, there is nothing
special about the number 3 that makes it the only possible number of dimensions
space can have." [13]
" there is no fourth spatial dimension in the real world. In relativity theory there are
four dimensions, however: three of space and one of time, but it is impossible for
our human senses fully to visualize what this means. Only through mathematics
can we get down to a rigorous treatment." (p. 68) [14]
" we don't have the four-dimensionsal equivalent of Abbott's three-dimensional sphere
to show us the way to 4-D. (In mathematics, moving into ever higher dimensions is a
walk in the park." [15]
This last statement unwittingly synthesizes the crux of the problem. In Mathematics, the fourth dimension is a piece of cake,
but not so in Physics. What relativists did was assume that there is a fourth dimension. Then, without any justification, they
tell you that in such a world you would be able to stretch a line perpendicular to the other three.
The trick in Physics is to demonstrate this baseless claim in the lab. If, as the mathematicians like to say, the only way to
confirm a 'theory' is through an experiment, here they have a chance to put their money where their mouths are. The test is
simple. They should produce a mockup or a statue of a tesseract. If the mathematicians cannot produce the leprechaun, it
shows just how different Math is from Phyz. Traditional and contemporary Geometry is a vain attempt to blend Mathematics
with Physics.
4.0 The mathematicians insist that there is a 4-D tesseract despite that you cannot see it
Relativists insist that, for mysterious reasons, you will have trouble ‘seeing’ the tesseract and, therefore, they would rather
forgo bringing a mockup to their show-and-tell:
" This structure is not easily imagined but it is possible to project tesseracts into three-
or two-dimensional spaces…" [16]
" Here's a fun way to start visualizing the 4-dimensional regular polytopes…And we can
understand the 4d regular polytopes in the same way!" [17]
Like Bogomolny, these individuals ask you to watch a movie of how this 4-D object is constructed gradually!
The problem is that all of these fanatic relativists are talking about a volume and not about a physical object. Relativists have
never zeroed in on the problem because they still can't tell the difference between an object and a volume.
Other relativists prefer to say that they can't see a 4-D object to save themselves the embarrassment of falling into the
emperor's clothes argument. They tell you, rather, that you are supposed to 'understand' the tesseract. These relativists
prefer to explain the tesseract, you know, like show you a movie of how to construct one. They cannot point to a photograph
of one because whatever you see is going to be a 2-D plane or a 3-D solid.
Unfortunately for them, if a tesseract is a physical object, there is nothing to 'understand' about it. Objects we see with our
eyes. Before we can 'understand' a circle, we must know what the word circle refers to. The prosecutor must first point to a
circle. Then he can describe and explain all he wants.
So it appears that you will not be able to see a tesseract within your lifetime. You have two choices. You either believe what
the mathematicians are telling you or you conclude that they are a bunch of idiots and that Mathematics is not the language
of Physics. Now the ball is in your court.
5.0 The tesseract is a concept
Now let's get to the underlying problem with the tesseract. An object has shape. By this I mean that it is contoured all
around by space. The tesseract doesn't meet this criterion. Relativists explain that you must see the tesseract in steps.
At no point can you see the entire object. You can only see 3-D portions of it gradually. Therefore, admittedly, the tesseract
doesn't have shape. It cannot be classified as either a geometric figure or as a physical object because this is the definition
of the terms figure and object. In the best of cases, the mathematicians have to find a new classification for the tesseract that
doesn't involve the misleading term object. An object has shape and is conceptually static. You do not need to see an object
move before you can call it an object. If you allow the word object to include concepts which are constructed dynamically,
you will not be able to use this word consistently in a dissertation. You will invariably end up with a circular definition. You
would need a concept to define an object and an object to define a concept.
In Physics, an object consists of a still image. The prosecutor points to Exhibit A – a chair, a picture of a chair, or an example
of a chair – and the jury stares at it and sees a figure. A juror should have no reason to listen to an explanation or to watch a
movie to ‘understand’ what a chair is. If relativists want to ‘visualize’ a cube, all they have to do is open their eyes! There is
nothing to ‘understand’ about a physical object. It is the ‘concept’ chair that a prosecutor needs to explain and that the juror
needs to understand. Objects we see. Concepts we understand. The ‘object’ chair only requires that you use your eyes. The
tesseract is not an object, as relativists allege, but a concept:
- “The fourth dimension is not so much a thing as it is an idea. This is like the fact that
the number 3 isn't really a thing in and of itself.” [18]
- This is the reason they have to explain the tesseract. So if the mathematicians tell you that a tesseract is an object and instead
of pointing, they ask you to listen to an explanation, you can safely close your eyes. You are in for a lengthy explanation.
| Relativists explain geometric figures |
| Folks. This magi- cal geometric figure is called the tesseract. Allow me to explain it to you before you place your orders. |
| You’re always so skeptical! |
| It's odd that he needs to 'explain' a geometric figure, don't you think? |
- Module main page: GR's 3-D Tesseract
- Pages in this module:
- 1. This page: Relativists explain geometric figures
2. Relativists haven't decided whether a tesseract is a 4-D figure or its 3-D shadow
3. Relativists say that you are too stupid to see a tesseract with your eyes
4. What really is a tesseract?
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- Copyright © by Nila Gaede 2008