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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
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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.
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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."
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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
5 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.
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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
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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
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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
9 his se o d la of otio th ough the al ulus of flu io s . The igo izatio of athe ati s
invented this previously non-existent problem for physics.
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
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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
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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
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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 space-time. 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 point-elements 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
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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-zero-time 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, two-dimensional area, three-two-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.
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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
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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.
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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.
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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,
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For example, when the condition that the ratio of the uncertainty in position to time is less than
o e ual to the speed of light Δ /Δt ≤ , Ei stei s e uatio s fo spe ial elati it a e easil
(algebraically) derived. On the other hand, when that condition is relaxed and the Work-energy theorem applied, Ne to s second law of motion (F = dp/dt) can also be derived. These
derivations should demonstrate that quantum mechanics and classical physics are completely compatible as well as indicate the direction to take for their unification
In other words, suppressing Pla k s o sta t o i i g the diffe e t ua tu e p essio s for space and time results in a reality described by Newtonian physics and general relativity. When it is suppressed in this manner, quantum theory is closed with respect to classical physics a d ould e e e de i ed f o elati it theo , just as Pla k s o sta t ould e e just pop up out of any relativistic considerations of material reality in either three-dimensional space or four-dimensional space-time. This split can also be looked at from another perspective. The HUP splits space and time apart mathematically and tries to interpret a new unnatural mental
ealit f o this split. I stead it add esses eithe spa e Δx) and a pseudo-time element of momentum (Δp) and/or time (Δt) and a pseudo-space element of energy (ΔE) simultaneously. The mental split of space from time creates uncertainty (which does not really exist in nature)
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binding constant of time to space. This point-by-point quantum space represents an absolute space in the context of Einstein's relative space in special and general relativity, which also explains why the two have not yet been unified. The correct interpretation of the HUP is not as a
Δ
x
Δ
p>
ħ/2
OR
Δ
E
Δ
t>
ħ/2
situation, but instead as a
Δ
x
Δ
p>
ħ/2
AND
/
OR
Δ
E
Δ
t>
ħ/2
situation. Choosing OR yields quantum mechanics, but choosing AND yields classical physics
given special conditions. From these new interpretations of the HUP, new conclusions can be reached that change the quantum paradigm and allow unification with relativity once the point/extension problem with Riemannian geometry is fixed.
This fact has resulted in the false belief that relativity and quantum theories will always be mutually incompatible (when they are only mutually incompatible with regard to three-dimensional space) and cannot be unified intact, while retaining the major characteristics and concepts of each theory. It is true that quantum indeterminism has no place in a continuous world, just as a discrete point cannot exist along a continuous line (it would form a
discontinuity) or surface, yet an infinite number of discrete physical 0-D point/twist Voids make up a continuous space-time manifold.
So the continuous world of relativity can remain deterministic (in its extension) while the quantum world of the discrete point remains indeterministic (at least inside discrete points and only inside discrete points) in quantum absolute space. Under these circumstances, it is safe to conclude that the HUP is merely a physical limiting condition, not unlike the purely
mathematical rigorous definition of an instantaneous velocity, that applies when circumstances (specific physical conditions) are experimentally established to unnaturally and thus artificially separate changes in time and three-dimensional space. Doi g so ould i oke Pla k s
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The quantum theory and relativity theory have now been unified, or at least the fundamental logical basis for their ultimate unification has been laid and this has only been made possible by noting the physical discrepancies that rigorized mathematics and pure mathematical thought has introduced into physics.
Advancing and unifying physics
From this point onward, all that is necessary to unify all of physics is merely noting that discrete points in the quantum absolute space are equivalent to 0-D point/twist Voids in the Riemannian relative space-time continuum. Einstein and Schrödinger had very nearly finished unification in the early 1950s, but they were so intent on interpreting the anti-symmetric and non-symmetric tensors as ultimately electromagnetic in nature, they missed the fact that they had actually predicted the existence of Dark Matter (Schrodinger, 1950) and calculated the effect of Dark Energy on material particles. (Einstein, 1952)
Given the historical fact they were on the track of Dark Matter and Dark Energy rather than electromagnetism or the quantum, how then could they have modified this new structure to include the rest of physics?
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whereby our four-dimensional double-polar spherical space-time continuum is embedded in a physically real five-dimensional single-polar spherical Riemannian manifold.
The single field density tensor S manifests in two different ways in 4-D space by splitting
into two parts, representing point and extension, along the fourth direction of space. The point manifestation is far weaker and becomes the gravito-gravnetic tensor G while
four-dimensional extension manifests as the much stronger the electromagnetic tensor F. These
split again into two parts when reduced to our commonly experienced 4-D space-time. For electromagnetism, the symmetric Faraday tensor emerges and for Gravity the anti-symmetric Schrödinger-Einstein-Cartan tensor emerges. When space and time are split apart to yield classical physics, these emerge as the Lorentz force for electromagnetic and Heaviside force for Gravity. The Faraday tensor is a primitive rank two tensor so there could be still more physics to emerge from the single field tensor F5-D, while the Schrödinger-Einstein
anti-symmetric tensor G5-D splits into the Einstein non-symmetric tensor (normal metric + DE) and a
constant equal to ΛCDM. Splitting space from time yields Newtonian classical physics but also
22
immeasurably small variations independent of one another which manifests their (space-time)
i di g o sta t ħ into observable and measurable quantities.
Just as the single field model accounts for the quantum and relativity simultaneously as products of the physical nature of space-time, the Standard Model of particles is completely uploadable into the single field model with only a change in the definition of particles. Real material particle must and can only have half-spin to conform to the geometrical requirements of the five-dimensional space-time continuum, while other Standard Model particles (non-half-spin) are either intermediate (between their quantum event creation and decay into real particles) if their existence can be verified by experiment, explained by some other means within the context of the single field theory or are just non-existent artifacts of the rigorized mathematics used for calculations in the Standard Model (gravitons, super-symmetric particles). Photons are the four-dimensional extensions of three-dimensional discrete points that lie along classical Maxwellian electromagnetic wave fronts, i.e., the quantum equivalents of wave-front points in Huygens Principle. Even a single complete model of the atom, consisting of both the nucleus and outer electronic shells, emerges based solely on the quantized curvature of a space-ti e sheet of i fi itesi all thi pa allel th ee-dimensional surfaces stacked in the fourth direction of space. (Beichler, 2015) From this basis a complete model of our universe
emerges, even a physical model of life, mind and consciousness.
Finally, the question of consciousness
Now, given this unification model, called the single (operational) field theory or SOFT, a new model of consciousness in our universe emerges from the very beginning, the Big Bang. According to the Big Bang model our present universe originated from a singularity that emerged from the absolute void about 14.3-14.6 billion years ago. The actual age of the universe is not important and in fact is not the given age. That age was determined from the original metric only geometry which is a geometry of measurements. The predicted singularity point, a philosophi al o-thi g o e a athe ati al othi g, would have been emerging from
the o-thi g of the o igi al a solute Void fo an infinite amount of time before it became mathematically infinite and discrete, a nothing over a nothing, enough within itself to become a 0-D point Void with virtual three-dimension-ness when time and space first began as bound by the constant of ħ.
That 0-D point Void would only grow large enough to have measurable although infinitesimally small extent, as predicted by general relativity, after another infinity of moments. In other words, the given or predicted age of the universe only takes into account the time when
23
or indefinite infinity of time. In any case, with single field theory we can now turn the tale around and instead of looking back in time to the singularity, we can look directly at the singularity and see how it could have logically expanded to become our present
physical/material universe.
It is logical to suppose, in the absence of any physical clues or evidence, that the singularity first morphed into a 0-D point Void which somehow differentiated itself from the absolute Void and so wanted to collapse or enfold back into that Void. It must have had some kind or type of primal-awareness of itself to do so, but it was virtually three-di e sio al so it ould t ollapse or enfold back into the absolute Void. Instead, the attempt to do so caused it to duplicate itself as virtual torques in both directions of the fourth dimension of space characterizing new 0-D point Voids. This action rebounded back or unfolded into the virtual three-dimensions of space and created new 0-D point Voids in both directions of all three dimensions.
This process gave the original 0-D poi t Void a t ist si ulta eousl spi i g i all th ee dimensions) and gave the original a twist that dynamically stabilized the 0-D point/twist Voids and guaranteed their discrete nature relative to one another. This enfolding/unfolding process then duplicated itself each and every moment of time at each and every 0-D point/twist Void until an infinity of these discrete points yielded the first measurable three-dimensional extensions and measurable time. Only then did the metrics of general relativity and the
quantum theory become valid enough to accurately describe the continuing explosive period of cosmic inflation.
This explosive rate of expansion continued unabated until quantum fluctuations or weaknesses in the three-dimensional surfaces caused a blow-out (like a balloon expanding beyond its elastic limit and blowing-out). Those first quantum blow-out points became protons, no anti-protons were formed, which began the end of cosmic inflation and gave our universe its initial material characteristics. Secondary quantum fluctuations resulted in a second partial blow-out, only this time electrons, characterized by the maximum curvature of a surface possible without actually blowing out, were formed. And then a third blowout yielded neutrinos, which have the smallest possible amount of measurable curvature and no more. After this occurred, the duplicating 0-D point/twist Voids began compactifying space in all four dimensions which necessitated the initiation of spatial elastic constants between them. Thus the electric permittivity between three-dimensional points of space and the magnetic permeability between four-dimensional points of space were born and the first electromagnetic waves were created in the form of the Cosmic Microwave background.
24
all of our material universe emerged. However, each individual 0-D point/twist Void was also characterized by an inherent semi-physical primal-awareness of itself and the collective nature of that primal-awareness emerged as a semi-physical pre-consciousness potential field.
Over the course of eons of time, this pre-consciousness field influenced matter to form ever more complex systems until a sufficiently high level complexity system with special properties called life emerged with minimal levels of both mind and consciousness. The pre-consciousness field also continued and continues to act through quantum discrete points on living or animate matter to evolve ever more complex forms of life with higher and higher levels of mind and consciousness until Homo sapiens emerged as a complexity of mind with larger and more complex brains approximately 100-200 thousand years ago.
Now that our best science, in the form of the latest unification of physics, has come of age and we are beginning to understand the reality of our world as a five-dimensional space-time continuum, we are approaching the evolutionary emergence of a new and even more complex level of consciousness. Science can no longer progress unless an understanding of the
consciousness that observes and interprets our three-dimensional material/physical world to create physics is itself included in that physics as a four-dimensional spatial extension of our three-dimensional bodies and minds.
Conclusion
25
surface curved in the higher dimension, the higher embedding dimension is shown to be and must be a single-polar spherical space. (Beichler, 2012)
The concept of a five-dimensional space-time continuum represents the true physical being of our universe in that the higher embedding dimension is not a mathematical gimmick that was specifically designed for the sole reason of developing a workable physical model of reality. The embedding space is real and necessary to give our three-dimensional material universe it the specific physical characteristics that we observe in nature and interpret through our minds and
o s ious ess e e if ou i ds a d o s ious ess a ot et di e tl se se the highe
dimension of space. From this perspective, which is the basis of unifying the quantum and relativity as well as classical electromagnetism, thermodynamics and Newtonian physics, (Beichler, 2012, 2013, 2014, 2015, 2106), consciousness and all of its aspects can be fully explained without ever having to refer to rigorized mathematics which has only served to mislead science due to its own shortcomings.
However, not all is lost. In reality, the false interpretation established by the forcing of the HUP upon natural events at the quantum level can also be used to indicate the extent to which physical reality can allow the separation of simultaneous spatial and temporal measurements of the fundamental processes of natural reality. When this is taken into consideration, relativity and the quantum theory can be shown to be completely compatible and thus unifiable. Then, as the Riemannian metric geometry that is used in general relativity is expanded to account for the point-elements (discrete geometrical points on surfaces that Riemann purposely ignored) in conjunction and coordination with his metric-elements (extensions of lines, areas and volumes), a newly enhanced Riemannian geometry can completely account for the quantum and the unification of the quantum and relativity. (Beichler, 2012)
In othe o ds, Ei stei s u ified field theo has ee o pleted and it is far closer to a
theo of e e thi g tha a othe theo i the histo of ph si s. I fa t, it i ludes a e
model of physical evolution which incorporates the biological evolution of life, mind and
consciousness, that is based on thermodynamics rather than the guesswork and speculations of modern physicists who have yet to see the light, have thus been unable to unify physics and have sought excuses to explain why they have failed. These excuses have taken the form of wild ideas, concepts and assumptions, for example, that their mentally derived mathematical laws rule the universe rather than simply observing the universe and letting nature show us how she
o ks as spe ified the ost asi e sio of the s ie tifi ethod .
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