|Why can't relativists even
1.0 Where's the beef?
The most obvious objection rational people raise against GR is that, after nearly 100 years of theory, it has yet to produce a
sculpture of four-dimensional space-time. Today, despite all the uproar about how mathematically beautiful this theory is,
the shape of our universe is as elusive as ever. We, the skeptics of the realm, once and for all demand to see the emperor's
The mathematician instinctively counter-argues that an illustration is not necessary or perhaps even appropriate to
understand the large-scale structure of the Universe. If space-time is beyond visualization it is because our cosmos is
a unique, four-dimensional manifold that encompasses everything. Space-time is outside of us, so we are forever barred
from seeing its shape from a bird’s-eye perspective:
“ It is impossible to imagine a four-dimensional space... in general relativity it
became meaningless to talk about space and time outside the limits of the
“ Questions such as 'What is beyond the edge of the universe?' or 'What is the
universe expanding into?' Are as meaningless as asking 'What is north of the
north pole?' ”(p. 555) 
“ such questions as ‘is the universe finite or infinite’ or ‘what caused the universe’
are false and cannot be answered because the point of view from which such
questions arise does not really exist and is unattainable. It presumes that
consciousness can take up a position outside existence as such in order to
observe it - and that the totality of existence can be an object to it ” 
[The questions are false? Boy! Relativists sure do like to cover every base!]
Therefore, it is just as unreasonable to demand a sculpture of a 4-D space-time from 3-D relativists as it would be to
challenge 2-D Flatlanders to produce a 3-D cube.
Nevertheless, the mathematician argues that visualization relies on fallible organs and opinionated testimony. Intuition
and eyewitness descriptions are notoriously inconsistent, subjective, and unscientific. Scientists guarantee objectivity
through Mathematics, a universal discipline that enables proponents to predict the outcome of an experiment, and the
skeptic, to verify claims independently. Not Art, but Mathematics is the language of Physics.
" The language of physics is mathematics." 
" Much of pseudoscience is qualitative hand-waving. Until a concept can be made
quantitative, or at least put on a firm logical foundation, it is not science." 
Such replies raise more questions than they answer. Specifically:
a. It is unnecessary to be on the outside of the Universe to visualize it. The
prosecutor merely has to show the jury a picture of what he has on his mind.
The juror needs to visualize what the Universe looks from afar in order to
understand the prosecutor's theory. The scientific method merely requires
that a theory be consistent with the exhibits presented at the start of the
b. A geometric figure is not something that a prosecutor proves with an
experiment. A geometric figure is an exhibit that the prosecutor points to
and names before he explains his theory. He points to Exhibit A and says
table. The juror shouldn't need an equation to visualize the object table,
and she certainly cannot infer the object alluded to from any equation. All she
needs is her eyes!
c. But then, if space-time is an unimaginable object and can only be
approached through equations, one wonders why so many prominent
relativists attempt to illustrate this alleged entity in their books and
websites. Either space-time is amenable to visualization or it is not. If it is
not, what is it that these experts don’t understand about their own theory?
d. How is a 3-D solid supposed to ‘simulate’ our 4-D cosmos anyways? What
plane can the 2-D genius exhibit to make his fellow Flatlanders visualize a
sphere? Is a circle a 2-D analogy of a sphere? Or perhaps it is an analogy of
a cylinder! The mathematicians spin a circle to construct a sphere and scan
a circle to construct a cylinder. Which is it going to be? And why even attempt
an analogy when, admittedly, Mathematics is the only venue to ‘understand’
the shape of the Universe? Relativists should simply insist that laymen take
e. Yet more daunting about such replies is what they reveal about the
establishment’s understanding of the scientific method. In Science,
specifically in Physics, we absolutely need to start the presentation with
a physical object. Without the corpus delicti, the prosecutors can’t even
start their case.
2.0 Understand or visualize space-time?
Relativists parry these attacks in one of two ways. They either scoff that this is not what physicists mean by ‘4-D’ or
trivialize the objections altogether by alleging that pictorial representations should be taken lightly. Experts rely on
analogies merely to simplify complex mathematical concepts for laymen:
“ One way to understand what the fourth dimension ‘looks like’ is to carefully
examine what the 3rd dimension looks like to ‘creatures’ living in a 2-dimensional
world. If we can understand this, then we can understand some of what the fourth
dimension looks like to us creatures living in the 3-D world by using appropriate
“ White holes pop up in general relativity (which also explains the expansion of the
universe) and that theory as a whole is not easy to understand physically. The only
way most people can understand general relativity is through mathematics” 
“ That doesn't mean that it is impossible to understand the expansion of the universe,
but it does mean that, for most of us, that understanding will be of a different quality
than what we're used to -- it will be grounded in mathematics rather than in physical
Understand a geometric figure? Concepts, we understand. Objects, we visualize! Is space-time a concept or an object?
The only reason the mathematicians can get away with such supernatural and irrational replies is because they haven't
defined the strategic words that make or break their theories.
Before we can establish whether space-time has merits as a scientific proposition, we must settle whether we are dealing
with a real physical object or merely with an abstract mathematical concept. If photons and planets roll or slide on the
surface of space-time, if asteroids are prevented from leaving our beloved Solar System by space-time, it seems that we
are referring to a physical object and not to an abstract concept.
" Einstein's discoveries have shown that due to relativity of motion our space and time
can be mathematically combined into one object — spacetime. " 
If the mathematician is going to treat space-time as both, as an object and as a concept, then for sure he will be able to
explain anything. If, instead, he is compelled to choose, his theory will necessarily collapse at one end or the other. For
instance, if the mathematician is going to argue that the Earth rolls around a roulette generated by the Sun and that this
wall prevents our planet from escaping the Solar System, he must be able to illustrate whatever it is that comes in physical
contact with the Earth. How else are the jurors supposed to understand the theory if they can't visualize the scene the
prosecutor is describing? Under this scenario, space-time is a physical object and not an abstract mathematical concept.
So what is the relativist going to draw if he cannot imagine space-time? On the other hand, if the mathematician presents
space-time as a concept, it is irrational for him to argue that the Earth weighs down and warps a concept.
If the mathematicians decide that space-time is a physical object, the next step is for them to resolve once and for all how
many dimensions this object has. Is space-time 2-D, 3-D, or 4-D? Is it possible for a physical object to be 4-D, or is this just
another ad hoc mathematical concept with no relevance to the physical world?
Copyright © by Nila Gaede 2008
What do you mean you don't understand me? There's
nothing to understand! I have shape just like you, God
damn it! Concepts you understand. Objects you see. All
you need to 'understand' me is your eyes, you fool! I'm
sick of people staring at me as if I were an abstract
clarifying the differences between
relativistic surrealism and Physics