There can be only one Wandering Toward a

James E. Beichler

fQXi essay competition

March 2017

There can be only one!
Wandering Toward a Goal:
How can mindless mathematical laws give rise to aims and intention?
Abstract: “ ie e does ot a de , it is not like the proverbial drunken sailor who let go of the light
pole that is holding him up and tries to walk away, and it certainly does not wander toward any specific
goal. “ ie e does ot spe ifi all k o
hat ha d atu e ill deal it i the futu e e plo atio s. The
general goal, if it can be called that, is to describe nature as truthfully as possible. Science goes where
nature and the universe lead and explains what nature and the universe present to science. Science is a
straightforward logical process by which human thought evolves and sometimes revolutionizes how we
view our world. In general, the only thing that could be construed as a goal in science is a complete
understanding of how nature works and presents itself to us. In other words, science answers to nature,
nature does not answer to science and especially not to any specific goal in the minds of scientists or
others. Given this, once the obtuse nature of the given question is determined and the given question is
translated into common English, the answer is just as easy as the question is ridiculous. The answer is

simply that mathematical laws cannot give rise to aims and intentions which are normally considered
aspects of consciousness. However, this raises the new question of why the given question is so obtuse
in nature and needs to be translated to an answerable question, while answering this new question is
significantly telling.

Introduction
There are no such things as natural mathematical laws; mathematics is based on logical mental
systems which were originally abstracted from nature and our experiences of the external
world. To the contrary, mathematicians have traditionally purified and distanced their subject
from nature, physics and the natural world through a conscious prog a alled igo izatio .
There has, in fact, been an open discussion over the past few recent decades whether
mathematics is built into nature at all or whether it is a completely human created discipline or
way of thinking. That discussion has never been conclusively ended, while there is no reason to
believe that rigorized mathematics should be able to explain anything and/or everything that
occurs in nature, so mathematics could not possibly provide the final answers to the scientific
quest to understand and explain nature.
Our abstract mathematical systems and the theorems that describe them must be internally
consistent and thus internally provable, but not absolutely provable. Even if mathematical laws
did exist they would not be mindless because all of mathematics is a product of mind and/or
the i d s i te p etatio a d o de i g of atu e. The question ho a

i dless
athe ati al la s gi e ise to ai s a d i te tio appears to turn nature on its head in its
inference that consciousness (in the form of aims and intents) must either be a product of, if
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not emerge from, natural mathematical laws and that is just Bad Science (BS). Mathematics is
based on provable theorems, or rather specific logical systems based on given theorems whose
internal logi al o siste
is p o a le. The gi e theo e s a o l e p o e , a o di g to
Gödel s theo e , goi g outside of the o igi al theo e to a la ge a d o e o p ehe si e
system. Science is instead based on explanatory hypotheses and theories that are also
i te all o siste t, ut a e e e p o e , o l e ified fu the o se atio of nature
and experimentation.
Mathematics, and this is far truer for advanced mathematical systems than it is for simple

atu al athe ati al systems such as the counting numbers, is only a product of the mind
and our mental interpretation of the external world around us and nothing more. It does not
represent some mythical or even mystical reality beyond the reality from which it evolved – our
material reality as represented by science. Human minds interpret nature as fundamentally
mathematical when in fact the mathematical systems originally developed from nature were
extended beyond nature and natural boundaries of thought and are thus only expressions
which can suggest new physical possibilities for science to investigate, not automatically create
true physical realities. So the question How can mindless mathematical laws give rise to aims
a d i te tio is no more than an elaborate mathematical case of mistaking the finger pointing
at the oo fo the ealit of the oo , i ed ith a i fo atio al it of putti g the a t
efo e the ho se .

What is everyone really looking for?
The real question being asked should e Why would anyone try to elevate mathematics above
physics, nature and the real substantial world of experience? because such a radical change in
science presents a direct challenge to validity of the scientific and experimental methods, both
of which are the major pillars, like mathematics, upon which science rests. Only two valid
reasons for this come to mind: (1) Human ego believes and even dictates that humans either
can and/or should be able to control all facets of nature and the natural world, a statement that
is almost religious instead of scientific in its suppositions and implications (Did God not give

dominion over the natural world to man?); and (2) the existence of two different and seemingly
incompatible theoretical paradigms in modern physics which have so far defied unification and
the assumption that such a unification would be a theo of e e thi g , the existence of
which is also ultimately related to human ego – as if we have already evolved enough
consciously to know everything.
This seeming failure has brought into question what constitutes normal science through
observation and the scientific method and initiated a search beyond the normal methods of
science – should we base science on mathematics instead of observation? – to develop a new
and unique way to unify the paradigms. Some scientists have interpreted this failure to mean
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that nature is somehow wrong and that the science they have built upon mathematics, which is
logically sound according to human derived logic, represents the real and an even greater truth
of nature in spite of the reality of nature and thus feel that they must find some illusive and

imaginary goal toward which mathematics is wandering. This is pure human ego at work, not
science. All of this is unnecessary because unification has been completed, the people asking
this question have just nor yet realized it.
These two reasons lead to thei o pa ado si e hu a ego s goal of o t olli g all of atu e
cannot possibly work unless a unified theo of ph si s, the h potheti al theo of e e thi g ,
even if it is only a step toward the reality of such a theory, is reached and all attempts to do so
have failed utterly over the past ten decades. It seems that some scientists have wrongly
concluded that imagined ends justify the means, which means throwing out time and
experience validated scientific methods. These failures can only be explained and accepted by
human ego if our ultimate physical reality can be reduced to an illusion, bits, mathematics, a
computer program or simulation, a hologram in the mind of some undefined being, a Super
Intelligence or Cosmic Consciousness, the matrix, an experiment conducted by advanced
undefined super beings, and so on. Humans always look for excuses for their failures because
the human ego cannot comprehend the simple fact that nature rules the universe and humans
do not rule nature (by mathematical law, physical theory or otherwise).
George Gamow, a world renowned and respected physicist spoke on this same issue more than
a half e tu ago, efo e the sea h fo a thi al theo of e e thi g e a e popula .
Mathematics is usually considered, especially by mathematicians, the
Queen of all Sciences and, being a queen, it naturally tries to avoid morganatic
relations with other branches of knowledge. Thus, for example, when David

Hilbert, at a "Joint Congress of Pure and Applied Mathematics," was asked to
deliver an opening speech that would help to break down the hostility that, it
was felt, existed between the two groups of mathematicians, he began in the
following way:
"We are often told that pure and applied mathematics are hostile to
each other. This is not true. Pure and applied mathematics are not hostile to
each other. Pure and applied mathematics have never been hostile to each
other. Pure and applied mathematics will never be hostile to each other.
Pure and applied mathematics cannot be hostile to each other because, in
fact, there is absolutely nothing in common between them."
But although mathematics likes to be pure and to stand quite apart
from other sciences, other sciences, especially physics, like mathematics,
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and try to "fraternize" with it as much as possible. In fact, almost every
branch of pure mathematics is now being put to work to explain one or
another feature of the physical universe. This includes such disciplines as
the theory of abstract groups, non-commutable algebra, and non-Euclidian
geometry, which have always been considered most pure and incapable of
any application whatever. (Gamow, 1980: 24)
Ga o ited the uestio as a diffe e e et ee pu e a d applied athe ati s a d
o luded that the a ot e cannot be hostile to each other because, in fact, there is
absolutel othi g i o
o et ee the . I his o
a , he ad itted that a st a t
rigorized mathematics is a wonderful thing, but it is different from non-rigorized physical
mathematics and need not necessarily lead to real physical situations or even be of any
specific use in describing physical reality.
Gamow obviously had the greatest respect for mathematics and its use as a tool in physics and
science. Later in his book, he explained how mathematics was so powerful a tool that it could
be used to turn a person or even a universe inside-out, so physical objects could be considered
from different relative perspectives in the scientific search to explain them. However, he did
not suggest and certainly did not mean to imply that everything in mathematics, especially
advanced abstract mathematics, could or should even be used to explain reality or that

everything in mathematics would necessarily have a true physical correlate. It should be clear
that rigorized abstract mathematics can also lead physics and science astray in their search for
natural truth and that includes how consciousness and the physical world interact at a
fundamental level. It seems that mathematics, the Queen of science, should worry about
cleaning its own house instead of trying to overthrow physics, the King of science, in an ill
thought out oup d etat. We a dis o e i the e d that atu e is athe ati al, ut e ill
never be able to show that mathematics is nature because that could not and would not be
true.

Mathematical rigor leads to physical Rigor Mortis
It seems strange that anyone would even suggest that mathematical laws rule nature or are
even more fundamental to reality than nature when everything dealing with nature has been
stripped from abstract theoretical mathematics over the past two centuries. Throughout
history, many scholars have succumbed to the notion that mathematical abstractions are
themselves the reality they describe in their overly enthusiastic attempts to reduce physical
reality to mental abstractions. This historical undercurrent in the normal advance of science is
especially evident through the rigorization process in mathematics. Rigorization is a general
movement to purify the discipline by stripping all references to physical reality from which
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athe ati s o igi all a ose a d ase all of athe ati s o a igo ous a d pu el logical
foundation. Any relationship to or dependence upon physical reality was purposely stripped
from mathematics during the rigorization process which began in the eighteenth century.
Abstract non-physical concepts such as the non-commuting variables that were later adapted
for use in quantum mechanics only emerged after the rigorization of mathematics. So
mathematical systems based on non-commuting variables may be internally logical, but that
neither means nor guarantees that such mathematical relationships are physically viable and/or
complete with respect to external physical reality.
In other words, the mathematical concept of non-commuting pairs did not evolve from either
strictly physical knowledge or the mental interpretations of real physical processes. Therefore,
non-commuting variables should automatically be considered non-physical and purely
mathematical by definition. They might prove sufficient to describe specialized subsets of
reality, but they do not necessarily describe reality in the whole. In cases where they do
describe parts of reality, they are not reality itself but mere mental conveniences created by the

human mind. The mere fact that they yield experimental results when applied to the physical
world is no absolute guarantee that they alone determine a unique unchallengeable and
complete picture of local reality, as assumed in the quantum theory, let alone all of reality. Even
then a picture of reality is not itself reality, a mistake most scientists make when they allow
their theories to become immutable and unvarying absolute laws of nature. Buddhists have
always warned their followers not to mistake the finger pointing at the moon for the moon
itself and that warning now needs to be heeded by physicists. Yet it would seem that
igo izatio has o o e to ph si s u de the guise of its of i fo atio .
The story of the rigorization or purification of calculus and later of all of mathematics
has been well documented because it has been glorified by philosophers and mathematicians
alike. Yet what is right for the goose in not always right for the gander, as the old saying goes.
Mathematicians and philosophers take great pride in the purified mental edifices that they
have constructed. Of all the natural philosophers of the seventeenth century, Newton went
fu the a d del ed deepe i to the fu da e tal atu e of ph si al thi gs tha a othe
person only to have that aspect of his overall physics washed away. Even Whitrow, who has so
ell do u e ted Ne to s use of ti e i the development of his calculus of fluxions, has given
an adequate account of the historical process of cleansing mathematics of its inherent physical
reality as seen through the eyes of a philosopher although he quotes a mathematician (Carl B.
Boyer) as his source.
In direct opposition to this point of` view, it is now generally agreed by

mathematicians that the difficulties concerning the foundations of the calculus
first exposed by Berkeley adequately resolved until last century when Cauchy,
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Dedekind, Cantor, Weierstrass and others imparted a far greater precision to the
basic concepts than had been hitherto obtained. These mathematicians all
adhered to the formalist view of the nature of the subject. In particular, they
rejected the Newtonian conception of calculus as a scientific description of the
generation of magnitudes. Consequently, the gain in precision which they
achieved was accompanied by the elimination of temporal concepts. For
example, the modern definition which identifies the limit of an infinite sequence
with the sequence itself has deprived the mathematical problem of whether a
variable reaches its limit of all meaning. As a result the limit concept has been
finally divorced from its intuitive dependence on the concept of motion. Thus,
although the ideas of time played so central a role in the rise of the new
mathematical analysis in the seventeenth century, two hundred years of
discussion concerning its foundations ultimately culminated in the paradoxical
esult that the e aspe t hi h led to its rise was in a sense again excluded
from mathematics with the so- alled stati theo of the a ia le hi h
Weie st ass had de eloped. [C.B. Bo e , op. it., p.
] The a ia le does ot
represent a progressive passage through all of the values of an interval, but the
disjunction assumption of any one of the values in the interval. Our vague notion
of motion, although remarkably fruitful in having suggested the investigations
which produced the calculus, was found, in the light of further elaboration in
thought, to e uite i ade uate a d isleadi g.
Thus, the wheel has turned full circle and mathematical analysis is now
characterized by its neo-Plato i eli i atio of ti e . Whit o ,
In his final sentence and conclusion, Whitrow essentiall hit the ail o the head
elati g
the process of stripping physics and their physical origins from the calculus and mathematics by
the eli i atio of ti e to a Plato i o ld ie . Although the e a e defi itel so e Plato i
elements in science and physic today, science tends to be more Aristotelian in its reliance on
observations of nature and physical reality. Unfortunately, the internal mental concept of time
is not necessarily equal to or the same as the natural and physical reality of time in the external
world. So this process necessarily introduces the possibility of an error into science each and
every time that the new purified mathematics is applied to physical situations.
Even then, the story of what happened to the calculus after Newton is still more
i te esti g a d detailed tha so fa i plied. Lei iz s
ols fo a ious athe ati al
operations were adopted in direct step with the process whereby the basic concept of relating
change to time was expunged completely from the calculus. Kramer takes great pride in this
accomplishment, as do all mathematicians and logicians, but physicists and scientists should be
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extremely wary of this practice because it is no more than an attempt to strip nature from
science and subsequently subject nature itself to the vagaries of the human mind and
consciousness as already attempted by Plato and Descartes. The one point that Whitrow and
Kramer would agree on, although they may have different views on the significance of this
practice, is that the elimination of time and all references to physical reality from the calculus
that dominated the development of calculus after Newton was a good thing. Neither they nor
anyone else would see in this practice the possibility of a divergence between mathematics and
the physical reality explained by science. This practice went even further and affected all
mathematical systems, not just the calculus, as well as physics itself.
Newton developed his concepts of absolute space and time to give the infinite and
infinitesimal limits a physical reality that his intuition said existed in nature, while later
mathematicians redefined calculus in terms of the philosophical limits, devoid of physical
content, that they preferred. The later success of the Newtonian calculus stripped of its
physicality convinced a whole new generation of thinkers that further abstraction was good and
proper in mathematics and physics. The rigorization and abstraction of mathematics further
and further away from its physical origins became a priority in the academic discipline of
mathematics, which served to greatly accelerate progress in mathematics, but at the same time
abstract mathematics became less likely to be used in physics or that it ever could be used in
physics to describe the real world.
The mistake of natural philosophers and those that followed was in thinking that
abstraction from physical reality to a sort of logical mental reality would affect neither physics
and mathematics nor the relationship between them adversely. The historical fact that Leibniz
began his development of his version of the calculus from purely philosophical considerations
after learning his mathematics from Huygens was no help as far as physics was originally
concerned. To some thinkers the philosophical approach may have seemed to come more
easil si pl e ause Lei iz s
ols a d o e latu e e e easie to use, ut i ealit it
as a fool s t ap fo hi h ode ph si s has had to pa dea l . That attitude has now come
back to haunt physics especially now that physics reached an impasse in the rush and
su se ue t failu e to u if ph si s esulti g i the false a d u atu al idea that athe ati s,
which has been so successful through rigorization, should or could lead physics, by way of
example, into a new era of understanding and unification. Instead, rigorization has led to
specific problems in physics.

The arrow that time forgot
The rigorization of calculus has ultimately led to one of the greatest mistakes in the history of
science, which alone demonstrates that mathematics could never be equated to nature or held
in regard to a higher reality than nature. Ti e held a spe ial pla e i Ne to s ph si s hi h
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has gone unrecognized by later generations of scholars and scientists because time became just
another variable in rigorized calculus, i.e., time lost its physics through the rigorization of
calculus. In this regard, nearly all modern scholars have either implied or stated that science
was essentially indifferent to the concept of time until the development of thermodynamics in
the mid to late nineteenth century. Scientists merely assumed the background flow of time
without being more specific. Yet for more than a century, comments have been made about
the dis o e of ti e s a o , o e possi le ay to interpret entropy in thermodynamics, as
the first theoretical indication that time always flowed toward the future. It has been claimed
time and time again that before the emergence of the concept of entropy the physical notion of
time, as used in physics, could not distinguish between the forward or backward direction of
the flow of time. Yet that so-called fact is absolutely false. Ne to s se o d la of otio is
usually used to exemplify this claim since the applied force and the consequent acceleration
can be either positive or negative due to their direction while time never enters that
consideration.
In other words, the direction of time had never, according to everyone with any knowledge of
the su je t, ee i luded i Ne to s la s of otio , ut that lai is u t ue. The di e tio
of ti e as a esse tial pa t of Ne to s al ulus of flu io s , ut mathematicians had so
successfully stripped the calculus and by proxy physics itself of their connection with the
forward flow of time that scientists no longer understood the intimate connection between
time and motion that Newton had constructed. In the rigorized mathematics of calculus, the
derivative, in this case the instantaneous speed, is defined as

.
The variable t approaches but never reaches zero although the variable x can go to zero in the
calculus case which rigorized calculus. In pure Newtonian physics, this would have a completely
different interpretation that would render the necessity of defining a logical limiting case
unnecessary.
Newton would have merely said that relative measures of x and t could both go to zero as
necessary to define instantaneous speed, at (or through) a point in space along a continuous
line, because behind that framework of relative time going to zero the absolute time
framework ran on universal time which could never go to zero. So defining the limit in this
ma e as u e essa i Ne to s al ulus of flu io s . The poi t is that the flo of ti e
as al a s o i g fo a d ithi the a solute ti e f a e o k i Ne to s o igi al ph si s of
motion, so the belief that entropy supplied the first historical instance in physics that
guaranteed the forward motion of time is absolutely untrue. The concept was literally built into
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his se o d la of otio th ough the al ulus of flu io s . The igo izatio of
invented this previously non-existent problem for physics.

March 2017

athe ati s

Yet Ne to s spe ial ole i o eptualizi g ti e as a ph si al ua tit a d thus e de i g the
concept an essential part of physics has still been noticed by some in the modern physics
community, although the real significance of his action has not been noticed.
The crucial position that time occupies in the laws of the universe was not made
fully manifest until the work of Newton, in the late seventeenth century. Newton
p efa ed his p ese tatio ith a fa ous defi itio of a solute, t ue a d
mathematical time, [which] of itself, and from its own nature, flows equably
ithout elatio to a thi g e te al. Ce t al to Ne to s e ti e s he e as
the hypothesis that material bodies move through space along predictable paths,
subject to forces which accelerate them, in accordance with strict mathematical
laws. Having discovered what these laws were, Newton was able to calculate the
motion of the moon and planets, as well as the paths of projectiles and other
earthly bodies. This represented a giant advance in human understanding of the
physical world, and the beginning of scientific theory as we understand it.
(Davies, 29-30)
Davies account is accurate as far as it goes, but no one would normally guess it to be accurate
gi e the othe histo i al a ou ts of Ne to s o k p e iousl ited. But the Da ies is a
open-minded modern physicist who is willing to look beyond the common body of physics at
the concepts that have been dismissed by his contemporaries.
This would seem just a minor infraction of mathematics in history and physics except for the
fact that this notion had a very important and significant effect on the later development of
ode ph si s, a el i the o ept of ha ge a d ho it as t eated i the HUP.
However, that story cannot be told without noting another important mathematical error of
logi that has ad e sel affe ted s ie e a d ph si s, )e o s pa adox.

)e o’s parado
The greatest error perpetrated by mathematics and mathematical thought is also one of the
most famous cases of philosophical mischief in the history of western science – )e o s pa ado .
This paradox represents a simple logical error that has haunted philosophy, mathematics and
science for over two millennia and remains, except here, unsolvable. Yet mathematicians and
philosophers keep making the same kind of logical error under the same as well as different
circumstances while expecting their abstract mathematical systems to outwit and rule over
nature, the real world, which need not answer to their logic. Zeno (c.490-450 BCE) defined the
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essential problem facing the newly developing science of his day as well as our modern era –
how e dete i e a a st a t otio of spa e so that it ould e pa titio ed i to dista es
and time which will allow a viable and workable definition of motion in the form of speed and
changing speed. However, no one seems to have learned the lesson that Zeno so eloquently
defined – simply because Zeno lied and his lie has been perpetuated for more than two
millennia.
It may be too harsh and even a bit cynical (as well as incorrect) to say that Zeno lied,
because he undoubtedly did not mean to do so. Modern scholars though cannot hide behind
such an excuse. Their sin is worse because we now know that space and time are physically
different whereas mathematicians see space and time as just two variables in an equation.
Zeno did not have a full comprehension of the concepts of space or motion that he needed to
develop his arguments correctly. The simple fact that )e o s arguments are still considered as
paradoxical today by modern philosophers and mathematicians who have not yet solved either
the mysteries of his mistakes or their application to the modern concept of space and time only
amplifies his mistake, whether a lie or not, and creates what is more than likely the greatest, if
not the longest lived, fallacy in all of science and human.
)e o de eloped a u e of a ious pa ado es that de o st ated the i possi ilit of
motion. If his arguments were true, then the belief in the plurality of all things and the concept
of change is grossly mistaken contrary to the evidence of our senses and experiences. Modern
abstract mathematicians follow this same path and does not take into account our sensations
and experience of the real world in their logical deliberations. In particular motion must be
nothing more than an illusion. These ideas are still supported by a few scholars and
philosophe s toda ho elie e that ealit is o e a d u ha gi g a d hat e e pe ie e as
ha gi g ate ial ealit is just ou o s ious ess i te a ti g ith the o e to eate the
illusio of the te po al o ld i ou i ds. “i e ealit is o e a d u ha gi g i )e o s
fundamental ideology, there neither is nor could be such a thing as a discrepancy between
being and non-being.
)e o s philosophi al ethodolog as uite si ple. He assumed the reality of motion
then using it demonstrated that the assumption would lead to physical impossibilities.
Therefore, his basic assumption that motion was real was false because he was actually
defining change of position or change of time alone, depending upon which examples he used,
without the other interacting with the former in any manner. In the end all that Zeno actually
de o st ated is that spa e a d ti e ust e o side ed togethe to eate ha ge if the
nature of motion is to be understood. At best, Zeno and the other Greek philosophers saw
otio as a pu e u diffe e tiated ha ge i ti e o spa e, oth of hi h e e e ual e ause
the had ot ee diffe e tiated et ee , athe tha a ha ge i oth si ulta eousl .
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However, this fact does not alter their culpability in differentiating change in positions in both
space and time.
Logi al a gu e ts o p oofs of the t pe used )e o a e k o as reductio ad
absurdum o p oof
o t adi tio a d a e o l as t ue as the o igi al statements upon
which the arguments are based, something like mathematical theorems. However, even though
the a e alled p oofs , the esse tiall p o e o l a si gle pe so s o g oup s elief as
expressed by their original assumption) of what is logical a d hat is ot. These p oofs a e
eithe a solute o u i e sal, so the ust e take
ith a g ai of salt . The ost fa ous of
his paradoxes are deals with a race between Achilles and a tortoise, an arrow in flight and
motion toward a fixed object. All of these represent essentially the same argument under
different circumstances, so only explaining any one of them is enough to refute Zeno. In
mathematics, this is similar to a limiting technique such as that by which calculus is defined: A
derivative is the limit of an average speed as the change in time goes to, but never reaches,
zero. A similar limit is used to define a metric-element in the Riemannian geometry of surfaces:
The smallest measurable size of a metric-element is defined as it approaches, but does not
reach, zero. In both cases, the abstract rigorized mathematics is not realistic because nature
treats the zeros of size (location or localized in space) and time differently.
The simplest of )e o s examples to picture is the movement o
otio of a pe so
toward a stationary goal or object. The reality of motion is assumed. However, before the
person can move all of the way to the goal the person must cover half of the total distance.
Before the person can move the rest of the way toward the object he must complete half of the
e ai i g dista e, a d so o a d so o . This epetitio of o e e ts ep ese ts the
edu tio to a su dit i )e o s logi al a gu e t. Logi all speaki g ho e e , the pe so
never reaches the object or goal even though motion was assumed real because there are an
infinite number of decreasing half-distances between the starting point and the end point of
the journey. This result contradicts the original assumption that motion is real, so the original
assumptio
ust e false a d otio is p o e i possi le. As sill as this a gu e t is, it has
perplexed thinkers for two and a half millennia. The modern mathematical system of calculus
did not solve the problem until the end of the eighteenth century with the notion of a limit
while the philosophical problem is still very real for philosophers who still debate the paradox
today.
Yet they are all missing the essential point of the paradoxes. Zeno lied. He cheated. He did not
really assume motion. No solutio is the solutio to )e o s pa ado e ause he used a
unrealistic mathematical model for motion, i.e., a mathematical model that did not conform to
or follow nature. His arguments either made no reference to time change when distance
change was used as an example, or to distance change when time was used as the example
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while true natural motion is impossible without the change in spatial position occurring over
some interval of time. What Zeno really assumed was a simpler case of a change in position
onl , hi h does ot o stitute eal ph si al otio . What he eall p o ed as that spa e
could not be easily subdivided ad i fi itu in a geometric sense of the word, what later came
to called in mathematics the limit of a series. In other words, he was unable to distinguish
whether a physical geometry of either distance or measurement should be based on the points
that make up space or the extended distances through space. Since no one in all of history
seems to have really understood the true meaning of his paradoxes and proofs,
mathematicians, scientists and philosophers have consistently failed to understand the true
meaning of the abstract concept of space that they have been using for the past two and a half
millennia. As strange as it may seem to the modern mind, Isaac Newton came closer to
understanding that duality than anyone else in his time or since, perhaps because spirituality
and science were closer in his mind than in the minds of modern scientists.
The single major fundamental problem of both modern physics and mathematics today is how
we take account of both discrete points in space and extensions in space simultaneously and
this was the whole point or lesson that should have been lea ed f o )e o s pa ado .
Understanding this mistake is especially important, in fact essential, for understanding the HUP
of modern quantum physics and the relationship between the quantum, matter and spacetime. The same fundamental problem is also a concern in Riemannian geometry which is solely
based on extension in the form of the metric-element since Riemann specifically ignored pointelements in his geometry of surfaces.
These last two failures present as much of a problem in modern mathematics as in physics and
are the main if not only reason that physics has not yet been unified by any of the scientists or
mathematicians who have tried so desperately to do so over the past century. This
fundamental problem is also related to consciousness in that it is the human consciousness that
has failed to distinguish between point and extension because human consciousness has not
yet risen to the level of understanding how they are intimately related to generate our material
reality. In the end, the lesson to be learned from this is that rigorized mathematics and logical
thinking can easily mislead science and has, in fact, led physics astray on many occasions, so it
cannot and should not be used to model consciousness where such mistakes could not be
discerned.

One fundamental mathematical error repeated over and over again
So what is true for mathematics is not necessarily true for physics, yet there are still specific
and significant correspondences between the two because mathematics originally emerged and
evolved as a method to analyze and understand nature and the physical world. For example,
the mathematical definition upon which the mathematical system of calculus is based, the limit
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of Δ /Δt as Δt→ , may be mathematically possible, but it is not physically possible. Δt is
always approaching but can never be 0, hile Δ is oth app oa hi g a d ould eventually
reach zero while still corresponding to Δt, even when it is not zero. We simply do not know of,
nor have we ever observed, a real physical situatio he e Δt o the s allest possi le time
duration has been zero, nor could we because the act of observation itself assumes non-zerotime duration. Newton knew this and when he invented calculus he took that fact into
consideration such that absolute time, where time can never go to zero duration, always
existed in the background of relative time as used in physics where actual observed and/or
measured time duration could go to zero at a corresponding point in space. That is why his
physical calculus differed from purely mathematical rigorized calculus (which is based on the
ideal philosophical concepts of Leibniz), at least philosophically, if not in reality itself, beyond
the physicality of our natural world, that is if anything like reality beyond the physical and our
natural world even exists.
Newtonian calculus then morphs and evolves into the differential geometry of a surface of
Riemann and the same fundamental problem of the difference between a zero point and a
measurable extension raises its ugly head once again.
Geo etric slope of a poi t o a curve → derivative calculus
derivative calculus → differe tial calculus
differe tial calculus → differe tial geo etr
a d differe tial geo etr → geo etr of curved surfaces that are ot flat

In keeping with this evolution of ideas and concepts, the differential geometry of Riemann is
based upon the concept of a metric-element (extension along a single dimensional line, twodimensional area, three-dimensional volume or of higher dimension) defined by Δs= d n2)1/2,
where n is the number of dimensions, i the li iti g ase he e Δs→ . In other words,
Riemannian geometry addresses the concept of the shortest possible measurable extension to
eith3er side of a non-measurable discrete point, i.e., Riemannian point-elements, but says
nothing about the discrete point or point-element itself. This concept is then elevated to the
overall problem of differential geometry for the case of analyzing n-dimensional surface
curvature near and approaching the discrete point center of a surface, without actually stating
how curvature varies through and/or at the point.
Newton related the fact that time or time duration can never be zero and time always moved
forward in his concept of absolute time, and while Ei stei s de elop e t of spe ial elati it
got rid of absolute space in physics and science, we still, in any if not all practical instances,
think in terms of an absolute physical time. We still think of time as continuous and always
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moves forward no matter how small a duration of time we are talking about, including a
moment of zero duration. Riemannian geometry is only about spatial measurements and has
nothing to do with time. Yet nature tells, quite simply, that motion would be impossible if time
were to go to zero duration, so we assume in physics that it cannot, at least in relativity physics.
The situation is different in quantum physics where time duration can go to zero and energy
would still be expended of changed simultaneously, which is physically impossible.
In relativity theory, this notion is evident in the concept of time dilation. Since mass can never
go to infinity according to special relativity, i.e. it would take an infinite amount of energy to
propel an object with non-ze o ass to the speed of light, Δt i the al ulus defi itio of
instantaneous speed could never go to zero. The instantaneous speed of a material object with
non-zero mass would therefore always be finite and less than the speed of light, c, according to
special relativity. Relative to a non-zero massive object, the speed of light would then represent
on infinity (indefinite) of sorts with respect to speed (always approaching but never being able
to reach that limit). This is true for relative space, but it is also true if an absolute reference
frame were still allowable and definable, however this or any new concept of an absolute
space, based on the infiniteness of the relative speed of light, would look different in many
respects from the older Newtonian concept of an absolute space or time.
If this same standard is then applied to quantum theory, then the uncertainty (certainty) of an
e e t a e e e %
% , a d si e ΔEΔt≤ħ/ the u e tai t i e e g ΔE ould e e e
g eate tha
%, o athe ΔE ould e e e i fi ite as i plied ΔE≤ħ/ Δt. This fa t
changes the whole interpretation of the HUP, in fact the uncertainty could not be an
uncertainty since an uncertainty could only range between 0 and 100%, not 0 and infinity.
Technically, the HUP is about the statistical concept of expectancy which can range between 0
and infinity, rather than uncertainty, and the expectancy value is proportional to the square of
the uncertainty, which better fits the physical situation.
Otherwise, if ΔE a o l app oa h infinity, without any hope of ever reaching infinity, then the
same must be true for the u e tai t i
o e tu , Δp, si e

E = ∫ dp/dt d .
“o ΔE is at least p opo tio al to ∫ Δp/dt d fo a gi e ua tu e e t. It is athe st a ge
that this integral contains all of the components that the HUP contains, only the HUP splits
these components apart as if they have no physical relationship to each other when in fact they
do. This relationship from calculus all but proves that the HUP is actually a form of anti-calculus
which is paradoxical because calculus and other continuous mathematical methods are used to
calculate supposed physical realities as represented to us by the HUP.

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The two mathematical relationships that define the HUP can only be split apart philosophically
and mathematically, where different standards are at play, but never in nature and thus never
in physics as demonstrated by the above formula relating energy and momentum. Splitting
apart of the uncertainty components in the two major formulations of the HUP is therefore
completely unnatural. So when experiments are conducted and interpreted in terms of the
HUP, a completely unnatural (unreal) situation is forced upon the physical reality of the
quantum event in question, which introduces an unnatural uncertainty into the observed
physical reality. The uncertainty is thus limited to the physically discrete point and has
absolutely nothing to do with any measurable duration, be it position, time, momentum or
energy, with which physics actually deals.
This would be every bit as true for quantum theory is it is true for classical physics, which would
mean that, consequently, position Δ could never go to zero, which is not born out in physics
because zero points of position are only necessary in physics when talking about the concepts
of center of mass (linear motion) and center or rotation (circular motion). Otherwise, there are
no zeros of position, or discrete points in measurable space itself and thus in physics. So while
space and time are conceptually two completely different things, energy and momentum are
tied together quite intimately, which means that the uncertainties in energy and momentum
must be somehow related even if the uncertainties between location and time are not. This
reduces the whole and complete nature of the uncertainty problem to an obfuscation of the
original problem of logically defining instantaneous speed at the very foundations of physics.
This causes yet another paradox between quantum theory and quantum mechanics which is
based upon the ability to measure values which yield zeroes (and infinities) across the board in
the uncertainties. This whole argument demonstrates that the uncertainties of quantum
mechanics are a purely mathematical problem stemming from the purely mathematical
interpretation of what we call physical reality rather than the physical interpretation of a real
physical event. This mathematical interpretation does not exactly equate to physical reality
and, in fact, introduces a mathematical uncertainty into physics which is not really there in
physical reality. There is no uncertainty in the physical reality posed to us by nature and our
universe.
On the other hand, the HUP and quantum mechanics are thought to be completely nongeometrical and non-relativistic by design, if that is even possible from a natural and realistic
perspective, although non-relativity implies a geometry of non-relativistic discrete points such
as that posited by a Newtonian-like absolute space. Furthermore, Newton postulated that
absolute space is Euclidean while quantum theory defaults to a Euclidean flat geometry for
cosmological and other practical purposes without ever calling it Euclidean. In any case, any
absolute space would correspond to, if not be equivalent to, a collection of discrete points in a
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flat Euclidean three-dimensional space. So, essentially, if not for all intents and purposes,
quantum space is just a rehash of Newtonian absolute space, at least for the case of quantum
mechanics and the HUP.
We know that time has points (moments) and extension (duration) from the physical point of
view, but that is all we can say about the similarities between time and space. Space has a
measurable (extension or extendable) geometry, but time cannot be measured in the same
sense even though we can indirectly include it in a mathematical formula in relation to distance
(c2t2 = x2 + y2 + z2), so we can say that it has points (moments) and extension (duration), again
like geometry. So the space-like structure of our world is implied, but it is not guaranteed. The
bottom line becomes the simple fact that nature is subject to interpretation by the human mind
and consciousness even though we do not directly know or experience consciousness under
normal circumstances. Nor do we directly know or experience mathematics, which is created by
human mind and consciousness, so mathematics is also subject to interpretation by mind and
consciousness when applied to nature and the real world. However, in the end, no matter how
accurately minds and consciousness seem to interpret nature, nature itself makes the final
decision whether our interpretation of nature is correct or not, not the human mind,
consciousness or mathematics, which also exist at the whim and according to the rules of
nature.
It should be obvious that mathematics alone cannot and should not be trusted as a final arbiter
or method for explaining either our experiential reality or the mind and consciousness
experiencing and interpreting that reality. Bet ee )e o s pa ado , the loss of a y physical
connection to mathematics through the process of rigorization, the misinterpretation of time in
ph si s, a d a e tu of g oss isi te p etatio s of the HUP, a possi le athe ati al la s
that we could discover have been totally discredited and disqualified as fundamental enough,
within the context of our natu al o ld of e pe ie e a d o se atio , to gi e ise to ai s a d
i te tio , let alo e the o ept of o s ious ess to a d hi h ai s a d i te tio s poi t o
imply. However, solving the fundamental problems touched on but nor solved in these
examples of how to simultaneously accounts for point and extension, whether disguised as
discrete and continuous, quantum and relativity, or point-element and metric-element, does
lead to a completely unified field theory which neutralizes the basic reason for even asking the
gi e uestio ho a
i dless athe ati al la s gi e ise to ai s a d i te tio ? Whe e
then does the answer to exploring consciousness and its relation to our experienced reality lie?
It can only be found in a true unification of physics, based on physical principles and not
mathematics alone, whether pure and rigorized or not.

The point-wise unification of relativity and quantum

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Quantum theory in the form of the HUP and quantum mechanics drives a stake directly through
the very heart of nature and the fundamental nature of the concept of change , so asi to
physics, by dividing the natural connection on between space and time upon which our physical
reality and universe are founded. It may be logical to do this in the sense of mathematical
rigorization and the rigorization of physics, but ti is not such a good idea and has inhibited the
advance of physics for far too long. It does so by using matter as the pawn and plaything of
momentum and energy. In this sense, the HUP is based solely on mathematical rigorization and
not on true experiences and observations of nature and thus overly limits physics and nature in
an unnatural manner. So, although there are flaws in relativity theory, under these condition
ua tu theo has ee the eal fl i the oi t e t as fa as u ifi atio is o e ed.
Given the different formulations of the HUP, which basically define the modern quantum
theory, there are several ways to proceed that allow other physical models of reality to be
included or unified with the quantum. By setting these two equations equal, as they are equal
to the same quantity, we get

and then by simplifying
.

It ould see f o HUP s e p essio of u e tai t that i gi g space and time together
supp esses the ua tu effe t as e e plified the disappea a e of Pla k s o sta t,
rendering the event physically real for consideration by classical physics.

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For example, when the condition that