PHALLACIES IN FYSICS

Volume I The untold story of

Classical Science

James E. Beichler, Ph.D.

© 2011

Only available as an Amazon Kindle ebook, 2013

Introduction The simple truth that every generation rewrites history does not mean that the historical record

changes all that much beyond the discovery of lost documents. It merely reflects the simple reality

that different groups at different times regard different parts of the historical record more important

and significant for the present state of science (which is itself constantly changing) than those who

wrote the previously accepted history. In other words, what is really significant in the history of

science is a reflection of the current attitudes and paradigms of science happen to be at any given

time, but attitudes constantly and sometimes radically change as science progresses.

Since the present dominant paradigm of physics is the quantum, the emphasis in the history of

physics for the past half-century or more has been to drown or neglect any long term historical

trends that lead to the alternative of relativity, continuity and the field interpretation of physical

reality. This does not necessarily reflect a conscious effort made by historians and scholars, but more

of a realistic assessment of what is more interesting to the greater number of scientists at any given

time. In other words there is no conspiracy to hide the historical truth. However, history can be

subconsciously and unintentionally used to promote one scientific worldview as opposed to another.

Since the quantum theory is the dominant paradigm in physics, those issues that deal more

directly with the opposing worldview of relativity have been unnecessarily downplayed. In spite of

the importance of general relativity there are far fewer, and the numbers are staggering, histories of

the development and philosophy of relativity theory than there are of the development and

philosophy of quantum theory. Scientific issues that pertain more to relativity than the quantum are

also shortchanged in the historical research and publications that follow from that research. In

particular, the emphasis on the historical development of the concepts of space and time, but

considered to be continuous rather than discrete throughout the history of science have been

neglected.

Furthermore, since the quantum presents a completely new and original idea that is thought to

be unique in history, there is no real call to lend it a more historical countenance. Yet it is not unique

in history and something liked it was expected if not predicted by Newton two and a half centuries

earlier. Unfortunately this truth is very nearly unknown within the history of science which wholly

and completely accepts the simple phallacy that Newtonian science was overthrown at the height of

its success and had nothing to do with the revolution that replaced it. In truth Newton’s science was

never replaced by the quantum theory or any other paradigm and the Second Scientific revolution

was a direct result of the successes of Newton’s science, among other things.

Quantum theory does not make any reference to the pre-history of individual events (material

interactions) in the micro world. Each event is unique to a particular time (instant) and place – this

was amply demonstrated by EPR. However the history of science shows us that the concepts of

space and time are essential and crucial to the development of science and cannot so easily be

ignored on any level of reality including the quantum level, a fact that quantum theory implies could

not possibly be true. Also, when the historical trends to develop and understand the physical nature

of space prior to relativity and the quantum are studied the development of relativity and even

general relativity look as if they were inevitable, a fact which seems to most to be an almost anti-

quantum interpretation of the historical record since relativity is based on continuity and the

quantum is discrete.

According to history, the (original) Scientific Revolution took place between 1540 (Copernicus

and the heliocentric system are developed) and 1687 (Newton publishes the Principia) and a Second

Scientific Revolution took place between 1900 (Planck publishes his paper on the quantum) and

1927 (the Solvay conference where Heisenberg’s quantum mechanics won the day over Einstein’s

objections). Yet an earlier first scientific revolution (the Zeroth) took place well before the

seventeenth century.

The true first scientific revolution began about 600 BCE (Thales founds natural philosophy to

explain the world) and ended about 350 BCE (Aristotle wrote his Physics which defined the limits

and scope of what would become science). The road to science was defined by this first revolution:

physics would evolve around the study of motion, matter and matter in motion at the most

fundamental levels of reality.

All of these revolutions are thought to have been precipitated by specific crises, which is

essentially true. The crises that lead to the Zeroth Revolution dealt with the failure of religion to

account for natural phenomena and physical events in the world of experience and the realization

that mind could interpret reality logically relative to itself instead of relative to the whims and fancies

of the gods.

The crises that lead to the Scientific Revolution of the seventeenth century have been identified

but only partially and then not very accurately, while the specific crises that initiated the Second

Scientific Revolution have been completely misidentified because the real revolution of the early

twentieth century went wrong, or at least took a slightly wrong turn, which has set up a new

revolution in the near future. The failures and inadequacies of each revolution to come to a

completely satisfactory conclusion against the backdrop of a constant evolution of science always

become the seeds for the next revolution. So the failures of the Second Scientific Revolution planted

seeds for the coming revolution.

Phallacies are fallacies that have grown to influence science and history so completely that they

have become phallic symbols that are extremely difficult to eradicate. They may have originally

emerged during the normal course of advancing science through normal evolutionary channels, but

they eventually become the worst enemies of true scientific progress. Only a new revolution will

overthrow them. These are all, however, historical phallacies, and physics has enough of its own

phallacies.

For example, entropy is the ‘arrow of time’ and marks the first instance in science that

differentiates the forward flow of time. This is a phallacy since Newton’s original second law of

motion incorporated the forward flow of time. Einstein was the first to use space curvature in

physics. This is also a phallacy since Clifford was developing an electromagnetic theory based on a

Riemannian curved space a half century before general relativity and Clifford’s work is still an

important piece of the puzzle to unify physics. According to contemporary history and beliefs,

Clifford never published his theory, had no followers, his ideas died with him, he had no influence

on the later development of physics and his ideas were untenable during his life time.

Again, these are all phallacies that actually endanger the future of science and physics. And

finally quantum theory overthrew Newtonian science. This again is not true. In fact a whole batch of

phallacies have been spawned in physics over the last century by direction (or misdirection) that

modern quantum theory has taken. When these historical and physical phallacies are identified and

studied a remarkable thing happens, physics becomes one undivided whole just the way Newton

planned, with no fundamental differences between the quantum, relativity and Newtonian physics

and the rest of science.

Chapter 1

It’s all Greek to me, you and everybody

1.1 The Zeroth Scientific Revolution

1.1.1 An unorthodox but truer interpretation of history

According to the conceived view of historical scholarship as well as tradition, western

intellectual development began with the ancient Greeks more than two-and-a-half millennia ago.

Natural philosophy, which would later evolve into science, began a few centuries later. Although

most scholars of all denominations have known of these events, no one has yet tried to call this

period of radical change in human thought a scientific revolution even though that is exactly what it

was.

The well accepted model of a scientific revolution holds that revolutions follow from the

solution of particular ‘crises’ that the older scientific paradigms of science fail to solve. On the basis

of this model alone, the ancient Greek revolution in scientific thought could not have been a

scientific revolution simply because of the technicality that there were no ‘crises’ in the previous

scientific paradigm.

Natural philosophy or the philosophy of nature (from Latin philosophia naturalis), is a term

applied to the study of nature and the physical universe that was dominant before the

development of modern science. It is considered to be the precursor of natural sciences

such as physics. (Wikipedia)

However, this is far too narrow a viewpoint to justify not recognizing this revolution for what it

really was.

A crisis is simple to find. The fact that no science, rudimentary or otherwise, existed before the

Hellenistic era of Greek culture but did after the era, is in itself a ‘crisis’. In yet another sense, Greek

religion was no longer able to account for the physical state of the world in the minds of the Greek

thinkers. The mythological gods of mount Olympus were the previous paradigm for explaining the

whims and fancies of nature and they were beginning to die away in the minds of men as humankind

learned more about nature and the world about them. Of course there was no ‘previous scientific

paradigm’ according to all present definitions of science, but science is just one type of cultural

paradigm of human thought. It is well known that a true scientific revolution affects culture as much

as science so why can a true scientific revolution not be cultural in a broader context and scientific in

a secondary role as this period was? It is undoubtedly true that Greek ‘natural philosophy’ was the

‘science’ of its day within the cultural context of that period in human history.

Within a broader and richer definition of science as a natural human endeavor that makes

logical and verifiable sense of nature and the world around us, this was a scientific revolution that

began with a simple challenge to archaic religious and supernatural explanations of physical events

and phenomena. Emotional interpretations of the world fell before logical and rational explanations

of nature even if those explanations were incomplete by present standards. There is no hard and fast

rule that restricts scientific revolutions to final answers. If there were, then even the first Scientific

Revolution would not have been a scientific revolution, while there is no logical reason to believe

that the present paradigms of science, products of the Second Scientific Revolution, are absolute and

complete. Otherwise, the two scientific revolutions that modern scholars have documented and

explored are already numbered so this early Greek emergence could only have been the Zeroth

Scientific Revolution, an appellation which fits quite nicely since the road to modern science was

first defined toward the end of this revolution even though a true science, by modern standards, had

not yet been developed.

Over the next few hundred years after this revolution began, philosophers agreed that the most

fundamental property of nature was change, but the type of change that could be used to describe

nature was in doubt until Aristotle. In his book Physics, which is Greek for ‘nature’, Aristotle tried to

logically explain nature by reducing the world to its most common elements, matter and motion. Yet

Aristotle did not develop a proper theory of motion because neither he nor anyone else had

developed a proper background framework for understanding motion – space and time.

Aristotle accepted the fundamental idea of change as the best way to explain nature from earlier

Greek philosophers, but more specifically interpreted the fundamental commonality as the change

of position of material bodies that was thought to constitute motion. Given then that everything

tangible is a form of matter, Aristotle deduced that any logical explanation of phenomena and events

in the natural world could be reduced to matter in motion. This leap of reasoning was actually a

fantastic conceptual advance over previous ideas and proved far more than Aristotle could deal with

given the level of conceptual mathematics he had at hand, but he still set the standard for future

science to develop.

So the concept of motion remained ill defined for philosophical purposes for the next two

millennia. A large part of science and philosophy over that long period of time has been dedicated to

defining and expanding out logical concept of motion, but a large part has also been dedicated to

understanding the basic background concepts of nature that contribute to motion, i.e., space and

time. From a heuristic viewpoint, Aristotle was unable to develop a workable theory of motion due

to his philosophical prejudices and the conceptual limitations of his time. On the other hand, such

changes in human attitude take generations to complete while the essential fundamental nature of

these changes fuel the revolutions in human thought that are necessary for true progress.

Nor was the alternate question of what is moving solved by Aristotle. Aristotle thought that

matter was continuous. He called his model of matter the Plenum. There were no voids in the world

because nature abhorred voids so there could only be continuous matter, which further complicated

the concept of motion. How could individual bodies of matter move if everything was filled with

matter with no non-material gaps between the denser bodies of matter that we commonly sense?

The Plenum manifested itself as different kinds of matter that occupied their natural places in the

world, which allowed Aristotle to completely dispense with the notion of space. In a sense, the

plenum was his space. Yet his was not the only theory to explain the world.

Democritus had earlier developed the first atomic theory of matter. Atoms of primordial matter

bounced around within the void, causing all of the physical phenomena that we observe in nature.

The differences of view between Aristotle and the atomists mark the first recognition that the

continuous and discrete natures of reality are incompatible. Like Aristotle, Democritus and the

atomists formed no real concept of space. The first abstract concept similar to modern abstract

concepts of space was only developed as part of the scientific revolution in the late sixteenth century

of the Common Era.

1.2 The birth of science

1.2.1 Rough beginnings

1.2.2 Natural philosophy

1.2.3 The emergence of formalized mathematics

1.3 The concept of space in Greek antiquity

1.3.1 What a revolting idea!

1.3.2 The pre-Euclidean sense of space

1.3.3 The Euclidean sense of space

1.3.4 The paradoxical nature of motion

1.3.5 Distinguishing something from ‘no-thing’

1.3.6 Plato’s cave and Aristotle’s plenum

1.3.7 The Greek heritage

1.4 No time for change

1.4.1 Zeno’s phallacy

1.4.2 Solving the phallacy

1.5 The two-legged beast of natural philosophy

1.5.1 Reality is in the mind

1.5.2 Mind interprets an external reality

1.6 The nascence of physics

1.6.1 The deeper structure of scientific revolutions

1.6.2 Zeroth and counting

Chapter 2

Middling ages between birth and rebirth

2.1 Primed for intellectual change

Toward the end of the nineteenth century, Ernst Mach (1838-1916) expressed the opinion that

science only began with Galileo. By the time that Mach wrote about the history of science, the social

and historical concepts of revolutions had long been ensconced in the story of humankind and the

idea that science had undergone a revolution in the seventeenth century was more than a century

old. Mach was, of course, speaking of the science of mechanics, but just as well meant the Scientific

Revolution as a whole. As he said,

Having passed successively in review the principles of statics, we are now in a position

to take a brief supplementary survey of the development of the science as a whole. This

development, falling as it does in the earliest period of mechanics, - the period which

begins in Grecian antiquity and reaches its close as the time when Galileo and his younger

contemporaries were inaugurating modern mechanics, illustrates in an excellent manner the

process of the science generally. All conceptions, all methods are here found in their

simplest form, as it were in their infancy. These beginnings point unmistakably to their

origin in the experiences of the manual arts. To the necessity of putting these experiences

into communicable form and of disseminating them beyond the confines of class and craft,

science owes its origin. The collector of experiences of this kind, who seeks to preserve

them in written form, finds before him many different, or at least supposedly different,

experiences. His position is one that enables him to review these experiences more

frequently, more variously, and more impartially than the individual workingman, who is

always limited to a narrow province. (Mach, Science of Mechanics, 77-78)

Mach clearly placed the start of the Scientific Revolution in the early seventeenth century with the

work of Galileo and the dissemination of new ideas throughout the civilized world was a necessary

part of the revolution.

But in all deference to Mach’s opinion, it is more commonly believed today that the Scientific

Revolution, which is considered the beginning of science, began with the development of the

heliocentric system by Nicholas Copernicus’ and published in his 1543 book De revolutionibus orbium

coelestium (On the revolutions of the celestial spheres). However, Copernicus’ book was little known outside

of a tight-knit community of astronomers for several decades until further advances in theoretical

astronomy were made by Tycho Brahe (1546-1601), Johannes Kepler (1571-1630) and Galileo

Galilei (1564-1642).

Pierre Duhem (1861-1916) expressed a completely different and opposing interpretation of the

history of science. He rediscovered and popularized the earlier work of natural philosophers during

the middle Ages and Renaissance which appeared to show that science had evolved slowly over the

centuries. Many others, even before Mach, had denigrated the possibility of any real contributions to

the development of modern science before Copernicus or Galileo. Unlike these others, Duhem

sought to demonstrate the evolutionary approach to the development of science by studying and

enlightening others about the essential contributions of natural philosophers in the Roman Catholic

Church through the work of such churchmen as John Buridan (c.1300-1360), Nicole Oresme

(c.1323-1382) and Roger Bacon (c.1214-1294).

Duhem concluded that the work of these men anticipated the later discoveries of Galileo and

others. In his own words,

… the mechanics and physics of which modern times are justifiably proud to proceed, by

an uninterrupted series of scarcely perceptible improvements, from doctrines professed in

the heart of the medieval schools. (Duhem, Origins, 38)

The historical perspectives of both Mach and Duhem were quite modern in the sense that their

opinions marked the differences between those who now think that science progresses’ by either

evolutionary advances or revolutionary leaps. In reality both the evolution and revolution of ideas,

attitudes and concepts are common to the progress of science and play off of one another.

In any case, the first abstract theory of motion that could be considered scientific by modern

standards was not developed until about 1300 at Oxford University in England. It took scholars

nearly seventeen centuries from the time of Aristotle to develop the necessary conceptual tools

(minimal as they were) to accept Aristotle’s new ideas and interpretations of nature. Quite simply,

neither the rudimentary physical concepts nor the methods of analysis developed by Aristotle and

the Greek philosophers measured up to the task of furthering science.

In the end, they applied their analytical concepts to statics alone (constancy) even though they

considered change more fundamental. This enigmatic way of approaching reality was probably due

to their misunderstanding of the concept of motion. Later philosophers and scholars only had

Aristotle’s erroneous theory of motion, which required the continuous application of forces, to work

with compounded by any lingering doubts regarding the reality of motion fostered by Zeno’s

paradoxes.

Greek civilization fell to the onslaught of a growing Roman Empire within a few centuries after

Aristotle and a later decaying Rome crumbled under the assault of various Vandal and Germanic

hordes in the fifth century of our Common Era or CE. Christianity in the form of the Roman

Catholic Church then filled the intellectual gap as Europe fell into the bleak realities of the Dark

Ages. Central authority over geographically extended groups of people fell apart as did commerce

and communications between diverse settlements, towns and cities. Education and scholarship

suffered terribly and the only knowledge of the Greek philosophers that survived the subsequent

sackings of Rome were hidden away in monastery libraries. Obviously, any science and technology

that survived did very little to progress or advance science much during this period of European

history and what did survive did so in small isolated pockets of humanity.

Renewed contacts with the Muslim world and the Far East in the form of commerce and later

the crusades reignited European intellectualism and learning by the end of the twelfth century and

original Greek texts and their Arabic translations with commentaries were again made available to

European scholars during the thirteenth. However, all European scholars were also Churchmen

because the only available form of formal education was sponsored by the church and only for

members of the church. What little was known of Platonic, Aristotelian and other Greek

philosophies during the previous centuries was magnified a thousand fold by the newly translated

resources and sources that became available toward the end of the thirteenth century, inspiring new

developments and advances in science.

All those centuries ago, the Greeks had discovered that the natural world of experience was

fundamentally geometrical and the geometry of choice was an abstraction of three-dimensional

space as defined, catalogued and categorized by Euclid in the late third century BCE. So, physical

concepts such as weight, force, speed, acceleration and impetus all occurred within either an abstract

geometrical world (similar to Plato’s world of Forms) or against it as a background (similar to

Aristotle’s material world filled by the Plenum).

In other words, the earlier Greek natural philosophers had no real logical concept of space or

time as they later came to be understood although they did sort of ‘beat around the bush’ with more

intuitive concepts. When these physical concepts became more formalized on a ‘scientific’ or logical

basis during the Middle Ages, early science finally began to develop along lines that are similar in

many respects to modern science.

So the questions that a new generation of scholars asked and had to answer were different than

those considered by the Greeks. Was space was merely a background reference frame (Platonic) or

was it in some way interacting with real experienced events and phenomena (Aristotelian), directly

influencing those physical events and phenomena? In other words, was space either active in

passive as described by the world geometry? As if to complicate matters further, these ideas were

intermingled with religious concepts since Catholic natural philosophy had become the apparent heir

to Greek natural philosophy.

Thus the Churchmen and scholars of the late Middle Ages and Renaissance, the new natural

philosophers of the day, also had to distinguish where the boundaries fell between religious and

non-religious concepts of nature and the natural world. Catholicism was a boon to natural

philosophy because it maintained educational facilities to train all natural philosophers and kept

natural philosophy alive during the rougher periods of history, but the boon offered by the Catholic

Church was two sided. Real science had a very difficult birth because it had to separate itself from

the Church and religion to thrive and advance on its own merits.

2.2 May the force impetus be with you

2.3 From mover to pure motion

2.3.1 Analysis of motion

2.3.2 Early religious analysis of space

2.4 Quantified but still dualistic space

2.3.4 The abstract nature of time

2.3.5 Time as measured

2.3.6 Time falls out

Chapter 3

Scientific Revolutions

3.1 The revolving door of science

3.1.1 Identification as such

The seventeenth century did not just harbor the ‘First’ Scientific Revolution, this period of time

in the history of science and the world was home to ‘The Scientific Revolution’. This chain of events

defined the very concept of revolutions as well as scientific revolutions – the political revolutions in

America and France that it inspired came more than a century later. At the time, it was generally

thought by everyone that the revolution was a completely unique occurrence and nothing like it had

ever happened before. Afterwards, the general theme of the events led to the conclusion that

nothing like it would ever happen again. The revolution constituted a singular and unique chain of

events compared to the history of the rest of humankind.

To those who contributed and/or experienced the revolution and those who interpreted the

events at a later date, it was completely unique and defined what it meant to have a revolution,

whether scientific, political or otherwise. It was never foreseen as just one in a group of recurring

revolutions over a lengthier period of time and certainly not a common event in the annals of the

human race. It just happened, only once and forever. The revolution was neither planned nor

executed according to some ultimate purpose or goal. It can also be assumed that everyone thought

it so unique and special that no one would ever have suspected that a Second Scientific Revolution

would ever occur in the future.

According to the well studied and documented structure of scientific revolutions, this

revolution must have been caused by some crisis or crises that could not be solved within the older

paradigm of natural philosophy. If crises in physics need to be identified to justify the existence of

this revolution, they could be easily identified as a crisis of the calendar (astronomy) and the crisis of

motion (pure physics). At least these were the major defining crises of the time from the worldview

of historical hindsight, but when and by who were they first considered ‘crises’?

This interpretation of historical events is quite straight forward and well documented, so it only

seems that there is no reason to question it. The fact that Mach and Duhem could have expressed

such opposing views of the overall progress of science from Aristotle to Newton and the fact that

the discrepancies between the evolutionary and revolutionary view of scientific progress have not

been adequately addressed, even though they were first expressed at the end of the nineteenth

century, should set off more than a few intellectual alarms.

In other words, do revolutions in science result from overcoming specific ‘crises’ or do

revolutions result from the successes of the overthrown scientific paradigms to develop important

fundamental questions that can be answered in new ways? Do evolutionary and revolutionary trends

in science work together as if they are partners in the overall progress of science or is real progress

in science just a case of one or the other? In either case, the so-called ‘crises’ themselves only

develop against the backdrop of evolutionary advances and the successes in science yet they are only

interpreted later as ‘crises’ relative to older science by the new science that later emerges. From the

evolutionary point-of-view, the ‘crises’ were only temporary roadblocks to the advance of science

that occasionally crop up and need to be overcome, while the so-called ‘crises’ only become ‘crises’

relative to the radical new revolutionary ideas that solve them.

The successes of evolution and revolution are both determined by hindsight in the end, so

revolutions are only what they are relative to later science. So, according to still later science earlier

revolutions can take on new meaning under different circumstances that only become apparent a

long time after the revolution took place. So it is possible to reevaluate the period from Thales to

Aristotle in light of still later evolutionary advances that place all of science within a greater and

more general context and discover that that period in time actually amounted to the first (Zeroth)

scientific revolution. The Zeroth Revolution was followed by a falling back or retrograde motion or

even a Dark Ages of scientific thought out of which emerged a new set of evolutionary trends that

preceded and anticipated the Scientific Revolution of the seventeenth century.

If truth be told then either viewpoint is just as valid as the other, but as you look at what

Newton accomplished in his publication of the Principia in 1687 and what science was like a mere

century earlier, then there can be no question that a radical revolution in thought did indeed occur.

The prevalent thoughts and worldviews of scholars in Europe and later throughout the world

radically changed, revolved or were simply and completely overthrown during the seventeenth

century. The change was so radical that it is difficult for modern scholars let alone educated

individuals to completely understand and accept how complete this change was, yet science has

undergone a similar change in just the last century although this change is unique in its own rights.

The change was not in science alone, but drastically affected every facet of culture even though

those changes were driven by the changes in science.

Yet it should be evident to anyone studying the historical record that this revolution was far

more than an ordinary paradigm shift in physics alone, although that is the normal interpretation

that scholars have held fast to for the past several centuries. Physics may have dominated the

revolution, but not exactly the physics which came out of the revolution. Indeed, the major outlook

of the world as a whole, the human worldview, changed with a good many auxiliary changes. For

example, religion and science were split apart and natural philosophy became the province of science

alone.

The scientific method emerged over a period of a century, which included the experimental

method. The experimental method developed as the most fundamental tool in the arsenal of science,

beginning with its earliest inception in the work of William Gilbert (1544-1603) on magnetism and

Galileo Galilei’s (1564-1642) gravitational experiments which ranged from the rate of falling objects

at the Leaning Tower of Pisa to his inclined plane experiments three decades later and continuing

through Isaac Newton’s (1642-1727) optical experiments with light and prisms as reported in his

book Opticks, first published in 1704.

The new scientific method emphasized the art and accuracy of prediction from theory. The

verification of scientific facts and knowledge through observation and experiment rather than the

acceptance of ‘facts’ based on faith as well as the repetition of experiments became the standard for

the new endeavor of science. Before this method was instituted the validity of ‘facts’ and even what

were thought to be absolute truths were based only on the reputation of the scholar stating the

‘facts’ or claiming the ‘truth’ of his statements.

This older practice was called scholasticism and similar practices still exist in scientific and

scholarly thought as idealized in the notion of ‘phallacies’ that haunt modern science. The revolution

also included the rise of the scientific societies and their practice of publishing the results of

scientific experiments and research for the dissemination of new knowledge amongst all people.

Johannes Gutenberg had built his first printing press in 1450 and that technology was used with the

greatest effect during the Scientific Revolution.

The minds of brilliant thinkers were opened to a new freedom of thought and they began to

question all sorts of things that had never before been open for question or debate, not just a

narrow number of topics in science that the earlier natural philosophers and scholars had

questioned. Scientists were no longer interested in ‘why’ things occurred, but rather in ‘how’ they

progressed forward from immediate causes. First causes as implied by the ‘why’ question were not

of real importance to scientists – they were left to religion.

This attitude was more or less institutionalized in the objectification of science. The very way

that scholars and scientists conducted science changed radically. The use of mathematics and

mathematical (algebraic) equations to build models mimicking real situations came into use for the

very first time as did the new analytical geometry invented by Descartes. And finally, new

technologies such as the telescope and microscope that extended the reach of human senses into

worlds that had never before been viewed were invented and rapidly improved.

3.1.2 Beginnings

3.1.3 Seeing reality as it is for the first time

3.2 The right stuff

3.2.1 The survival of mathematics

3.2.2 Breathing new life into mathematics

3.2.3 The mathematics of pure motion

3.3. Descartes at the center of the circle

3.4 Newton versus Cartesian philosophy

3.5 Newtonianism

Chapter 4

Revolution redesigned

4.1 The Revolution’s true nature

The real Scientific Revolution concerns the change in human thought as a whole. This change

existed just below the surface of the Scientific Revolution as normally recorded and since studied by

scientists, historians, philosophers and other scholars. Real scientific revolutions deal primarily with

the fundamental concepts and ideas that bridge the gap between science as a human created system

and the world itself as it actually exists as opposed to the scientific theories which are actually

secondary to these fundamental concepts.

The ‘crises’ which seem to signal the coming revolution are thus no more than superficial

manifestations of deeper underlying core issues that are about to be resolved. This interpretation of

scientific revolutions rings truer with Thomas Kuhn’s concept of a gestalt paradigm shift than just a

fundamental change in simple theories to explain nature and overcome specific ‘crises’. Quite

literally, the relationship between humans and nature, the internal and external realities, undergoes

radical changes during scientific revolutions.

Academics normally document, study and write about the outward effects of the underlying

intellectual revolution that was the ‘First’ Scientific Revolution. So, as important as they were,

Newton’s three laws of motion, his planetary system, all of celestial mechanics, Galileo’s law of

freefall and all the rest are just theories while the real revolutionary concepts deal with mind and

matter on one hand and space and time on the other. These theories merely address the ‘hows’ of

reality exposing itself to us, through our senses. How science regards mind, matter, space and time

affects our scientific theories of reality, but theories can change without fundamental changes in

mind, matter, space and time themselves. We call this evolution or the normal stepwise progress of

science.

In other words, matter, space and time do not change in nature because they are constants, only

the human mind that interprets the sensations of matter, space and time, changes over a period of

time while scientific revolutions account for the changes in the mind that interprets reality. Changes

in the constantly evolving human mind (internal reality) and matter against the background of space

and time (the external reality) characterize revolutions because they radically alter the theories that

make up science at any given time in history.

The human mind is not a constant (unless you count that it is constantly changing) although

nature as a whole is constant. Even if nature as a whole was not constant then the fundamental

principles and background of nature must be constant or there could be no science. This state of

affairs has only become more obvious in the longer run of history that includes present ongoing

changes in science over the past three or four decades.

Within this grander historical context, science has always been and still is an attempt to logically

differentiate between the internal world (our human subjective mental reality) and the external world

(of objective matter, space and time). Our so-called picture of the world, our scientific worldview

that dominates the paradigms that control the day-to-day functions of scientific endeavor, is

constantly evolving and revolving as time passes. Yet something still remains constant within that

‘change’.

In essence, the common dualities that have dominated the rise of science throughout the

Zeroth and first Scientific Revolutions are mind and matter as well as space and time. The world of

matter that we sense and interpret in mind gained the upper hand from the purely mental picture of

our world when Aristotle based science on observation rather than Plato’s notion of mental forms.

Aristotle then saw change as the most common principle in the world of matter and addressed the

causes of change. However, he was trapped by the logic of Zeno’s paradox and a less than

rudimentary concept of time that he inherited from his fellow natural philosophers. So it took the

newer generations of natural philosophers another two millennia to sort out the concept of motion

and then develop new ideas of abstract space and time.

The ‘crises’ of the calendar (time) and motion were only the superficial results of the more

fundamental dualities of mind/matter and space/time that plagued science just prior to the Scientific

Revolution. But history goes forward even while the characteristics of the revolving itself are also

evolving. Descartes established new criteria to differentiate between mind (the internal) and matter

(the external) according to his own beliefs, but then so did Newton by objectifying and relativising

science without stressing the importance of a relational view of space and time, thereby relegating

the subjective aspects of humanity by default to religion and metaphysics. This was the real crux of

the Scientific Revolution – it was a mix of mind and matter expressed as changes in our

interpretations of space and time. These were the theater in which reality played out the script of

nature.

4.2 The Cartesian Dilemma

4.3 Newtonian mind

4.3.1 Mind with a small ‘m’

4.3.2 In the mind of philosophers

4.3.3 Life and the occult forces

4.3.4 A new ploy to package natural ‘change’

4.4 Absolute, relative and debatable

4.4.1 Newtonian space in general

4.4.2 Theological implications

4.4.3 Dynamical implications of absolute space

4.5 Newtonian space as substance

4.6 Time for calculus, or not?

4.6.1 Space from motion

4.6.2 Motion from space and time

4.6.3 It’s about time

4.6.4 Time after time

4.7 Getting down to issues

4.7 Seeds of revolutions past, present and future

Chapter 5

Divergence, reduction and rigor

5.1 The Queen is dead; long live the Queen

5.1.1 Rigorization

Mathematics has long been regarded the queen of the sciences for the vastly important role that

it plays in scientific modeling and calculations. Technically, mathematics is not a science in itself

although it is the most valuable tool that the sciences can utilize to describe nature. Obviously,

mathematics is directly related to the world in which we live. Mathematics originated in nature, but

during the eighteenth century and thereafter a movement grew to rigorize mathematics and place it

on a sounder logical basis by stripping mathematics of all references to its origins in nature.

Mathematics slowly evolved into a purely sterilized mental construct independent of nature and the

real world.

Mathematicians openly sought to extend mathematics beyond its natural limitations and create

something far more than had ever existed in nature or any of reality. This movement was considered

by all to be a good thing, but it did not proceed without introducing new problems for science.

Once a mathematical system was rigorized and extended beyond its natural limits, there was no

guarantee that the mathematical system so developed would have physical counterparts in the real

world. In fact many mathematical systems do not have natural counterparts. Mathematics did not

just go beyond nature, but began to diverge from its physical origins in wholly new ways, just as new

complexities do not always follow the rules that applied to the chaotic situations out of which they

emerged.

In fact, just as scientific changes can be interpreted as the convergence of ideas in new ways, the

aftermath of a scientific revolution can been characterized by a new divergence of ideas. This is also

true of the evolution of mathematics, especially in conjunction with its relationship to physics and

science. This notion can be readily applied to the case of the Scientific Revolution of the

seventeenth century and the major divergence that took place between Newton’s physical calculus of

‘fluxions’ and the newer more generalized calculus of variations. In many ways this rigorization has

been good for science, but it sometimes seems as if rigorization in mathematics is trying to replace

science and the scientific method even though there is no mention of rigorization in the scientific

method.

Mathematicians have purposely created a mental distinction, a mental distance of sorts, between

their abstract mathematical ideals and the physicists’ abstractions of observed physical reality and

nature. This distinction is clearly indicated in the most general of works on the history of

mathematics. Yet no one has taken into account the possibility that abstracting mathematics from

physical situations and then reapplying that mathematics to the same or other physical situations

might introduce problems in the physics or physical models.

Scientists and mathematicians alike have been guilty of relying upon the basic assumption that

the mathematics is the reality, or at least reflects some unspecified underlying reality that strictly

follows the mathematical model rather than physical models. In other words, each and every purely

mathematical model assumes that it is correct and any observations of nature, although not

incorrect, are at least inaccurate if not incomplete if they fail to agree with the mathematics. The

assumption is built into the model whether the person constructing that model is aware of the

assumption or not.

In the sense that other physical quantities undergo variations (change) relative to variables other

than time; the abstraction of differentiation in calculus to delete its special reference to time was a

good and proper thing to do. There are many different types and classifications of variations in the

physical world other than just the variation of distance over time that science uses to depict motion.

The example of physical motion just provided a motivation as well as a simple as well as necessary

and sufficient model to encourage the original development of a more general calculus of variations.

On the other hand, motion still holds a special place within calculus for two very specific reasons:

(1) extensions in space and time are the standards by which physical continuity is ultimately defined,

and (2) space and time are natural fundamental quantities unlike nearly all other quantities to which

calculus can be applied.

For all intents and purposes, space and time are the most fundamental structural components

of physical reality itself, the other being the matter that represents the ‘thing’ that is moving and the

mind interpreting the motion. Other physical quantities that can act as variables for the purposes of

integration and differentiation vary over either space or time even if only indirectly. All other

physical quantities are either characterized or defined by their variations over space and/or time, but

space only varies over time and time seems to vary over nothing else. Time has traditionally been

associated more directly with the notion of ‘change’ simply because it seems to vary over nothing

else, while it also seems to be constant at some level of passage through the common notion of the

present moment and thus the need, even today, for something akin to absolute time.

These are standard matters of concern in the history of science. They have been studied and

analyzed by historians, scientists and other academics, all of whom stand by their interpretations as

representations of a true and accurate historical picture. Yet it seems that no one has ever queried or

otherwise attempted to analyze the unintended consequences of these events on history. How did

separating differentiation and the rest of calculus from its historical roots in the physics of motion

and thus its relationship to time by a philosophical process of abstraction change the relationship

between the mathematics and physics involved? This question needs to be answered now because

physics is entering a new period of revolution and fundamental change.

5.1.1 Calculus rigorized

5.1.2 Reconvergence can cause unforeseen problems

5.1.3 A reality check

5.2 Reduction and abstraction

5.2.1 The mysterious ‘Queries’

5.2.2 An alternative view of history

5.2.3 Newton’s Queries speak for themselves

5.3 Newton’s quantum leap

5.3.1 The real revolution

5.3.2 Inertia

5.3.3 Fluxions

5.3.4 The leap

Chapter 6

Betwixt and between

6.1 The nineteenth century experience

The nineteenth century is one of the most intriguing periods in scientific history and it may well

be the most diverse and complex period in the whole history of human thought. Far more radical

changes took place – ranging from theoretical science to cultural issues – between 1840 and the

1870s than during the period from 1900 to 1930 when the Second Scientific Revolution is normally

said to have occurred. Before 1840 there was no such thing as a scientist, but after 1840 science

became a profession in its own right and the term ‘scientist’ became part of the common cultural

lexicon.

Science literally became its own reality. Natural philosophy ruled until the Scientific Revolution

and Newtonian physics ruled until the 1840s, although it was still called Natural Philosophy. Physics

did not become an independent academic discipline after Newton, but that is exactly the point.

Natural philosophy only evolved into physics in the 1840s when the other branches of science

parted ways and began to develop along their own lines of specialization.

A new ‘philosophy of science’ rose out of these ashes of natural philosophy as well. Science

began a new era of introspection, self-criticism and self-analysis that was not really possible as long

as science was natural philosophy. As long as science was natural philosophy there could not be a

separate philosophy of natural philosophy, so as science emerged from natural philosophy the

philosophy of science also emerged. After this parting of ways occurred, an explosion of knowledge

began, which was second only to the later decades of the twentieth century.

In physics alone, two whole new theoretical subdivisions developed – electromagnetic theory

and thermodynamics – both of which required a revolution in thought itself. Both new areas of

scientific endeavor benefited greatly from new analytical methods in science and mathematics. In

fact, the new analytical period of physics and the sciences was paralleled by the rise of a more

analytical style of mathematics – the rigorization of mathematics was beginning to pay big dividends

– which found its way back into physics and science, further compounding the effect.

Never has there been a more diversely unique expansion of science into previously taboo

regions of knowledge until perhaps the last few decades of the twentieth century. Even then,

modern science, as twentieth century science is known, is only beginning to open to the diverse

scientific possibilities that were first explored in the later nineteenth century. Yet modern scientists

and scholars are only slightly aware of these new trends in science (at least in so far as they are

scientific), if at all, even though they have had a profound influence on modern science and

especially on modern physics. Many scientists still do not think that subjects such as the physics of

mind and consciousness are legitimate scientific subjects even though they first appeared in the late

nineteenth century.

It is hard to believe that the Second Scientific Revolution did not begin until 1900 with science

changing so radically after 1840, but 1900 is the universally accepted date for the beginning of the

revolution. The emergence of thermodynamics and electromagnetism as complete theories in

physics within two decades of 1840 is considered part of classical Newtonian physics before the

revolution. Yet both were at odds with Newton’s original ideas of physics. Being at odds with

Newton’s physics, as prescribed by the Principia, these two new branches in physics created the

problems that eventually ignited the Second Scientific Revolution.

In hindsight though, the revolution is beginning to less like a clear-cut revolution in science that

emerged due to the two crises that supposedly ignited the revolution in thought that became the

Second Scientific Revolution. Deeper underlying problems that had been noted by Newton himself

in the Opticks and later compounded by advances in mathematics and new discoveries make for a far

better revolution than the two crises which were actually just the ‘flotsam and jetsam’ riding atop the

deeper issues about material reality.

6.2 The decade of change

6.2.1 The 1840s

6.2.2 Mathematics follows pace

6.3 The interim decades

6.3.1 More chaos in scientific circles

6.3.2 The nether region between Mind and Matter

6.3.3 Atoms and molecules

6.4 Implications have their way with science

6.4.1 Mind

6.4.2 Revolting times

6.4.3 Crises or just problems

6.5 The revolution before ‘the’ Revolution

6.5.1 Trying on a new mindset

6.5.2 Popular science in the eyes of the populace

6.6 Science does mind after all

6.6.1 Paranormal phenomena challenge the boundary

6.6.2 A less paranormal response

6.6.3 Mixing mathematical and scientific metaphors

6.6.5 The scientific backlash

6.6.6 A science of mind almost emerges

6.6.7 Success at last

6.6.8 The fuse is lit

Chapter 7

The untold revolution in space theory

7.1 From real-world geometry

7.1.1 Which ‘myth’ is which?

A large number of major myths and phallacies permeate the common historical interpretation

of the rise of the non-Euclidean geometries especially regarding their relevance to physics and

connection with other historical events during the nineteenth century. Getting the history of the

non-Euclidean geometries right should hold a much higher priority among modern historians since

they play such a large part in the Second Scientific Revolution, so the fact that so little historical

research is done in this area is of the utmost importance and indicates how little emphasis is placed

on the overall fundamentality of the concepts of space and time in modern physics.

The bottom line is that the full and complete story on the development of the non-Euclidean

and hyperspatial geometries has never been told, probably because it is not necessary for

understanding the rise of the quantum which dominates modern science. For example, modern

historians and scholars would say that measurement only became an issue in science with the

development of quantum mechanics, but if truth be told the issue of measurement actually emerged

in the 1880s with reference to the possibility that space could well be non-Euclidean even though it

seemed (was measured as) for all intents and purposes perfectly Euclidean. This fact can easily be

verified by referring to the first ever article on ‘measurement’ in the 1880s edition of the Encyclopedia

Britannica.

The true importance of the non-Euclidean geometries in influencing our modern views of

physical space cannot be understated even though a lot of the information regarding their early

development and acceptance is either misleading or completely forgotten against the background

and strength of the present quantum paradigm. Quite simply, quantum theory has absolutely no

need for the concept of space curvature and non-Euclidean geometries since the dominant particle

theory, the standard model, a priori assumes the necessity of a flat Euclidean space.

Furthermore, quantum mechanics which is based on the Heisenberg uncertainty principle is

effectively if not completely a non-spatial theory. It specifies direction (in so far as direction can be

specified at a single point in space) in only one dimension. The uncertainty principle was clearly a

theoretical attempt to end the dependence of physics on both the geometry and fundamental natures

of space and time. Under these circumstances, all of the popular versions of this important and

relevant story have been limited by over-rigid standards of what appeared in only the most

prestigious scientific publications and all other historical resources have been overlooked.

A good example of how the history of physics has been corrupted by ignoring the importance

of the non-Euclidean geometries is readily demonstrated by the attempt to delete a well known

historical episode in which Johann Karl Friedrich Gauss (1777-1855) attempted to measure the

curvature of space from the top of three mountains during a land survey in 1826. In 1972 the

historian of science Arthur Miller published an article claiming that Gauss never attempted to

measure the curvature of space. The story, according to Miller, was a “myth”. For evidence he cited

the facts that Gauss never published his non-Euclidean theory and that there is no evidence that

Gauss ever told his contemporaries of his experiment after he completed the survey.

Miller contended that the story was developed after Einstein published his general theory of

relativity in order to show that Einstein’s concept of space-time curvature had a historical precedent.

Somehow, a historical precedent would have made Einstein’s ideas more palatable. Although others’

opinions have not been as radically wrong as Miller’s, they have ranged far and wide on both sides of

the controversy, there has been a great deal of debate over this and similar historical incidents

dealing with the non-Euclidean geometries. These debates are totally fabricated nonsense, since the

easily available historical record clearly shows that both non-Euclidean geometries and hyperspaces

were popular and well discussed during the latter decades of the nineteenth century. In fact, they

formed an important part of the science of the era.

Until recently it has been difficult getting any other more realistic opinion or more accurate

interpretation of the history of non-Euclidean geometries published, especially in so far as they

relate to the development of general relativity. The stranglehold of the quantum and its influence on

other scholarly endeavors is too strong. However, with the latest advances in cosmology and

astrophysics that seem to indicate the fundamental nature of space-time curvature as well as the

discovery of Dark Matter and Dark Energy, the quantum paradigm is losing some of its traditional

luster and general relativity is being held in higher regard.

Decades of failures of the quantum theory to produce a comprehensive unified theory that

replaces gravity theory in either of its present forms (Newtonian or Einsteinian) have also served to

weaken the quantum stranglehold on physics. Therefore, a more complete, comprehensive and

realistic history of non-Euclidean geometries within the context of physics rather than just

mathematics is now called for, if not long overdue.

7.1.2 Raising questions

General relativity is based on a Riemannian geometry that was first developed in the 1850s.

Einstein had the highest praise for the foundational work of Riemann as expressed in Riemann’s

original paper on non-Euclidean geometry. As such, general relativity is routinely considered the first

physical theory to utilize this non-Euclidean structure for space, a fact which is patently untrue. That

supposed fact is a ‘phallacy in fysics’ as well as a gross representation of science and cultural history.

If the misinformation that people usually hear was true then the whole development of non-

Euclidean geometries was no more than a mere exercise in mathematical abstraction, which is also

patently untrue. The non-Euclidean geometries were intimately tied to the concept of physical space

throughout their period of development, which included the whole of the nineteenth century.

The most common interpretation of general relativity today claims that the Riemannian

curvature of space-time is an intrinsic property of space so there is no need for a higher embedding

dimension (the extrinsic case) of space. However, space curvature in the nineteenth century was

considered extrinsic by default since the distinction between internal (intrinsic) and external

(extrinsic) curvature, the latter of which requires a higher fourth dimension of space, was not made

at the time. The idea of intrinsic physical curvature was a later development of relativistic physics.

Otherwise it seems that all reference to the physical reality of space-curvature before 1900 has been

very nearly erased from histories of the era in spite of the vast popularity of the prospect that space

could be curved in a higher dimension.

Years before Bernhard Riemann was even born (1826) other attempts were made, some

successfully, to develop a more classical (non-algebraic) non-Euclidean geometry. These attempts

were made to reconcile the theory of parallels, otherwise known as Euclid’s fifth postulate, since

there seemed to be a possibility that this postulate was false. Euclid’s Elements (c.300 BCE) presents

an internally consistent geometrical system based on theorems, postulates and axioms as well as

methods of proving their logical truth and internal consistency.

However, the parallel postulate stands out because it is the only part of the system that is stated

without proof. This postulate states that

… if a straight line falling on two straight lines makes the interior angles on the same side

less than two right angels, the two straight lines, if produced indefinitely, meet on that side

on which are the angle less than two right angles. (Euclid, 48)

Because this postulate stated that the lines were to be extended indefinitely it was questioned

whether the postulate represented a real situation rather than an infinite and thus unknown situation,

lending an air of ambiguity to the Euclidean system of geometry. The lines are ‘assumed’ to remain

parallel out to infinity, which is the problem because there is no way to prove that assumption. If

they do not remain parallel, there is no way to locally measure the angles accurately enough to

distinguish the resulting angular difference between the opposite interior angles of a line cutting the

parallel lines.

This discrepancy was noted by Giovanni Girolamo Saccheri (1667-1733) who analyzed the

problem in 1733. He actually came very close to developing the notion of the non-Euclidean

geometries, but failed in this respect. Yet he did arrive at three different hypotheses regarding

different possibilities for geometry. The measured angles between an intersecting line and two

parallel lines could form (1) right angles, (2) obtuse angles, or (3) acute angles. The first example, of

course, corresponds to Euclidean geometry where the lines remain parallel and equidistant out to

infinity on a flat Euclidean surface.

The second example corresponds to what later became the branch of non-Euclidean geometry

(hyperbolic where the lines diverge at infinity) developed by Lobachevski and Bolyai independently

of each other, while the third hypothesis would later become Riemannian geometry (spherical or

elliptical where the lines converge at infinity). It is very interesting to note that Saccheri arrived at

many of the same results as Lobachevski and Bolyai, but failed to recognize their truth so he did not

develop a formal geometrical system. Saccheri’s work languished in obscurity until it was

rediscovered and expanded after the fact by Eugenio Beltrami (1835-1900) in the 1860s.

Sometime later, Johann Heinrich Lambert (1728-1777) arrived at the same results. By 1766 he

was able to demonstrate that Saccheri’s third hypothesis resulted from parallel lines on a sphere

while the second hypothesis resulted on an imaginary sphere, thus introducing hyperbolic functions.

He also successfully computed the area of a hyperbolic triangle. For both Lambert and Saccheri,

geometry was real and represented the reality of our material world. So Lambert completely rejected

the third hypothesis as physically impossible while he didn’t even refute the second hypothesis.

Lambert not only noticed that the sum of the angles of a triangle was less than 180o in this new

hyperbolic geometry, but strangely enough the angle sum of a triangle increased as the area of the

triangle decreased.

In 1795, John Playfair wrote a commentary on Euclid’s Elements in which he restated the parallel

postulate in a new and different form. His new statement of the postulate has become known as

Playfair’s axiom: “At most one line can be drawn through any point not on a given line parallel to

the given line in a plane.” This statement has the advantage that it is simpler and it emphasizes the

distinction between the different geometries. Other mathematicians also completed fundamental

work on the problem, but their work did not lead them to develop non-Euclidean geometries. These

include the researches and contributions of Adrian-Marie Legendre (1752-1833), who showed that

the sum of the angles of a triangle cannot be greater than two right angles in 1794 (Elementes de

Geometrie), thus duplicating some of Saccheri’s work.

However, when he tried to demonstrate the opposite proposition, that the sum cannot be less

than two right angles, he made a fundamental mistake and included a statement equivalent to the

parallel postulate, indirectly using the postulate to prove itself. Legendre spent several decades trying

to come to terms with the parallel postulate, but got no further than this and never attempted to

develop a non-Euclidean geometry. So fundamental questions were raised regarding the accuracy

and consistency of Euclid’s geometry while some basic alternative properties of alternate geometries

were described up until the end of the eighteenth century, but no attempts were made to develop

alternative geometries.

While the work of these men was done independently without any direct contact with each

other, the next group of mathematicians had a great deal of interplay centered on Gauss. Ferdinand

Karl Schweikart (1780-1859) is known for investigating this new geometry, which he called “astral

geometry” in a note that he wrote to Gauss in 1818. He described the strange characteristics of his

new astral geometry and suggested that it might even be the true geometry of space. Gauss’ reply

showed that he, for one, agreed.

In fact, Gauss claimed that all he needed was a constant and he could do all of the elementary

geometry for the new system. More importantly, this letter and the response indicate that these two

men were perfectly willing to toss out traditionally accepted Euclidean geometry and consider the

possibility that the real geometry of the world was non-Euclidean. The new geometry was obviously

far more to these men than a mere mathematical abstraction that amounted to little more than an

idle curiosity for the philosophically-minded scientist.

Schweikart’s nephew, Franz Adolph Taurinus (1794-1874) also became interested in the

problem and began his own search for answers. He corresponded with both his uncle and Gauss

regarding the problem. He was unable to demonstrate or prove mathematically that the Euclidean

geometry alone was true and thus came to accept the viability of other possible geometries,

publishing his work in Theorie der Parallellinien in 1825 and Geometriae prima elementa the following year.

In the latter book, Taurinus admitted that a third geometry existed in which the sum of the

angles is less than two right angles, which he called ‘logarithmic spherical geometry’. This particular

geometry was equivalent to the hyperbolic geometry that would be ‘discovered’ later by others. His

second geometry was possible on either an elliptical figure or a sphere, thus anticipating Riemann’s

geometry. Between these geometries based on the surfaces of regular conic figures, there were an

infinite number of possible geometries, a fact which Taurinus considered important. Yet he still

considered Euclidean geometry the geometry of physical space.

For his part, evidence shows that Gauss had pondered the problem before these latest

developments during his school days and discussed the possibilities with his friend Wolfgang Farkas

Bolyai (1804-1833). But Wolfgang was never able to develop his own thoughts on non-Euclidean

geometries into a consistent system of geometry and later tried to dissuade his son János (Johann)

from wasting his own time on the problem. He did, however, publish a book on the foundations of

geometry, the Tentamen (Tentamen iuventutem studiosam in elementa matheosos introducendi), in 1831. It was

an attempt to establish a rigorous and systematic foundation of geometry, arithmetic, algebra and

analysis. During his life, he kept up a correspondence with Gauss that was every bit as important as

his contributions toward a non-Euclidean geometry.

7.1.3 Gauss and the physical curvature of space

7.1.4 The first formal non-Euclidean geometry

7.2 … To real world-geometry

7.2.1 Geometry generalized

7.2.2 The band plays on

7.3 A new dimension of thought

7.4 World geometry as a purely mental construct

7.5 World geometry as sensations of reality

7.5.1 Helmholtz sees it differently

7.5.2 A spectrum of influences

7.5.3 Group theory

7.5.4 Another direction

7.6 World geometry as material reality itself

7.6.1 Posers and opposers

7.6.2 Solving the universe

7.6.3 Clifford’s missing theory

7.6.4 A tragic ending to the theory

7.6.5 Too many phallacies regarding Clifford

Chapter 8

Nature’s new playing ‘field’

8.1 A substantial improvement for space

While the development of non-Euclidean geometries changed the ‘playing field’ for the

scientific concept of space and added the mathematical characteristic of ‘curvature’ to what was

otherwise just a passive background framework for physical phenomena to play out, it still lacked

any substantiality on which to explain other physical characteristics that seemed necessary for a true

physics of space. For Newtonian space, that role had been filled, literally, by various forms of aether,

the latest being the ‘luminiferous aether’ thought to transport light waves.

These ideas and concepts were all the more important during the last decades of the nineteenth

century because Newtonianism had been so successful that scientists began to speculate, a precursor

to the hypotheses that initiated the Second Scientific Revolution, on the true nature of matter where

only a notion of matter as the source of mass for gravity and inertia had existed before.

Newton expressly stated the need for some form of substantial presence within space in the

Opticks to explain matter and elaborated on the issue as well as he could, given the state of science at

the time. He realized that his theory of gravity did not explain matter, but merely how different bits

of matter interacted at a distance. The views he set forth in the last edition of the Opticks (1730) to

be published could be considered his last and most advanced since it represented his final word on

the subject undertaken shortly before his death and not published until after his death.

The very fact that four editions of the Opticks were published over nearly three decades with

the Queries being rewritten and expanded in each succeeding edition demonstrates their speculative

nature on issues that Newton deemed extremely important for science. Newton was trying to point

out the direction of future science and he did so successfully. These were Newton’s last words on

the subject of physics.

The need to give space some substantial reality for carrying or propagating ‘force’ was mostly

due to the fact that ‘action-at-a-distance’, which referred to the transport of natural forces and not

just electromagnetic light waves across vast distances to react and interact with material bodies,

seemed a ridiculous concept. However, some form of substantiality was also needed to understand

how inertia could arise from trying to move a material object through empty space. It seemed that

something substantial must correspond to space itself, point-by-point, to resist motion of material

bodies through space and create inertia.

The discovery of physical ‘fields’ by Michael Faraday replaced any necessity that science might

believe it had to invent various forms of aether to render space itself ‘substantial’ and thus answered

the age-old problem of action-at-a-distance. This fact alone rendered the discovery of the ‘field’ or

‘fields’ the single most important advance in science since science was first developed by the Greeks

in the form of natural philosophy because ‘fields’ offered an explanation why matter need not be

continuous and a vacuum could exist between the fundamental bits of matter, whatever fundamental

form the smallest possible material bodies matter might take.

The fundamental concept of a physical ‘field’ thus preceded and was a necessary step in the

evolutionary trends that later developed the need for the discrete quantum. Quite simply, discrete

bits of (quantized) matter could exist without the loss of continuity of space and time that was

needed to explain many of the others concepts upon which physics and science were founded. In

other words, the universe only need be filled with bits of matter and fields. Nothing else was

necessary.

Einstein just took this notion one step further and reduced the bits of matter to field densities

(curvature). In fact, quantum theory needs relativity to survive as a valid theory even though

quantum theorists would never admit it. Instead, they rely on entanglement which is really no more

than relativity and continuity on the quantum level of physical reality. ‘Proof’ of this view can be

found in the necessity to develop ‘quantum fields theories’ even though the concepts of the

quantum (discrete reality) and the field (continuous reality) are diametrically opposed to each other

in the minds of nearly all scientists and philosophers who have ever thought on the subject.

Empty space in the form of the vacuum, even such as the quantum vacuum, need only support

the existence of a physical ‘field’ of varying potential (density) which would become either potential

energy or ‘force’ when interacting with material bodies, depending upon which interpretation you

used for any particular physical event. Under these circumstances, the ‘field’ concept slowly

subverted the very need for the mental crutch of any type of aether, especially the luminiferous

aether, well before Albert Michelson (1852-1931), whether working alone or with Michael Morley

(1838-1923), could carry out his famous experiments of 1887, only to find that there was no

luminiferous aether. The field concept was subverting the aether concept well before Einstein did

away with any need for aether or any like substance in 1905.

The very concept of a ‘field’ is the single greatest contribution to science and human thought

since the Greeks. The ‘field’ is an existent ‘something’ that was totally new and unsuspected, yet it

has always been there and interpreted as something else, usually as some form of aether. The field

concept is so fundamental that its complete significance has not yet been recognized even though

the concept itself is approaching an age of nearly two centuries. The field is neither an invented

thing nor a mental construct developed merely to model reality, but has a real existence that was first

described by Michael Faraday in the 1830s.

The field concept is the unique intuitive product of Faraday’s insights into nature; however that

is not meant to imply that Faraday developed the concept within an intellectual vacuum with no

outside influences. Faraday simply recognized the reality of the field when he noted the simple

structure of a magnetic field in the patterns of iron filings reacting to the magnetic field surrounding

a simple permanent bar magnet. The filings seemed to form lines that he called ‘lines of force’,

which drew a simple picture of the field’s shape.

Technically, these are not lines of ‘force’ but rather field lines that indicate the structure, shape

and intensity of the magnetic field at every point in space. In other words, Faraday was the first

person to recognize that a field has structure and varies with distance as it is extended in space.

Although they have no independent ‘material’ existence, fields affect or influence matter under the

proper physical conditions. Even today the field is taken for granted and the physical concept of a

field is thereby unnecessarily diminished to a secondary role, especially in the quantum theory. Yet

the field concept is still one of the single greatest advances in science since science was first invented

by the Greeks and one of the greatest advances in the ongoing evolution of human thought.

Unlike space which is passive and does not interact physically with matter, the field is dynamic

in its interactions with matter and is therefore ideal for modeling forces mathematically. The field is

a ‘thing’, not a ‘no-thing’ like space, and as such it is the first true physical ‘thing’ discovered in more

than three millennia. Every field is characterized by an internal structure and external extension in

space even though fields are completely non-material. The field is not space itself, nor is space a

field as such, yet as far as we know no point of space is devoid of field so space and field seem to be,

at least for all practical purposes, coexistent.

Although the concept of a field of potential offers a simple solution to one of the oldest and

most intractable of problems in science – ‘action-at- a-distance’ – it was not invented to solve that or

any other problem. The field was actually ‘observed’ and thus discovered by Faraday. In that sense it

was not just a simple act of discovery just as no one ever ‘discovered’ gravity. It was a ‘realization’ or

‘awareness’ of the field’s existence, just as humans once became aware that gravity existed. In a strict

sense, the ‘realization’ that fields exist is every bit as significant as the ‘realization’ that gravity exists.

So what is a field? It is extended, has structure and fills all of space, but it is also, in a sense,

extension itself, structure and all of space simultaneously. Dimensionality could just as well be a field

property and not be a characteristic of space, which is ‘nothing’, but there seems to be no way to

determine this. When the field interacts with matter it gives rise to force and/or energy, depending

upon one’s interpretation of the physical conditions under which the interaction took place. So the

field consists of varying potential and potential is what precedes both potential and kinetic energy.

The field is fully capable of simple mathematical modeling because of its ability to interact

dynamically with matter. Beyond that, little is known.

There are three traditional types of field – electrical, magnetic and gravitational. However, the

electric and magnetic fields have been combined into one single field called the electromagnetic field

by Michael Faraday and James Clerk Maxwell. Faraday believed that the gravitational field could also

be added to the electromagnetic field, or rather that they had a common source, and conducted

experiments to verify this fact during the 1850s. However, if gravity and electromagnetism are part

of a single more fundamental universal field, then the interactions with matter that might verify the

existence of the single field would necessarily be so subtle that he was unable to discover them. They

were simply beyond his capabilities as an experimenter, but more likely beyond the technology of his

time to measure.

So fields are patterns of pure potential, a simple fact that allows modern scientists to prescribe

an imaginary probabilistic interpretation of reality to the concept of fields even when reality is not

probabilistic itself. It is always probable that the field can be taken advantage of or realized by an

interaction with matter at any point in space given the proper physical conditions. However, this fact

of nature does not mean that the probabilities which are calculated relative to individual points in

space and assigned by humans to those points are ‘real’ in any meaning of the word or by any stretch

of the imagination. Reality is not a statistical game played by scientists and scholars and the field is a

real measurable quantity. As such, historians have sought out the work of other thinkers who may or

may not have influenced Faraday’s concept of the field and debated the extent to which they

influenced Faraday’s discovery.

8.2 Early influences on the origins of field theory

8.3 The straw that broke the camel’s back

8.4 Do revolts cause ‘crises’?

8.4.1 From evolution to revolution

8.4.2 The missing part of the story

Bibliography