New Source Concepts for ‘Matter’

“Reality is the real business of physics”.    Einstein

“Just as Newton shattered the medieval crystal spheres, modern quantum theory has irreparably smashed Newton’s clockwork.  We are now certain that the world is not a deterministic mechanism”.    Nick Herbert

Democritus was the first Greek philosopher to theorize that matter was composed of atoms, which he pictured as small indivisible pieces of solid matter called ‘atoms’ from the Greek word ‘tome’ meaning “uncuttable”.  This postulate remained in place throughout the early 20th century, whereupon physicists discovered that these atoms where composed on smaller charged components.  This sub-atomic paradigm isn’t composed of material at all, instead, what we find are charged relations, energy, force fields of charged relations. This is why the human eye or any medium embodying linear stress isn’t the proper instrument to explain the subatomic world of charged relations; hearing is!  Given the wests predominant use of linearity, physicists aren’t going to understand what they ‘see’ until their taught how to listen.  Let me explain.

The atom is composed of protons, electrons, neutrons.  This is known as the nucleus, its organized in the shape of a football or doorknob.  It is primarily spherical or distorted into essentially the same particle in different energy states.  They are bound together by a force called a pion.  The exchange of pions creates the strong nuclear force that binds the atomic nucleus together.  The creation of atom smashers allowed us to discern families of particles held together by strong/weak forces alternating.  These high energy particle accelerators permitted the discovery that each family particle (either weak/strong) had anti-particles.  Until the 1960’s, chaos theory was used to explain this behavior. It was ‘quark‘ theory that was used to explain the behavior of particles in the nucleus subject to the strong force. Hundreds of particles have been discovered to exist in the heart of the nucleus.  The hundreds of different particles that make up the nucleus come from varying combinations of quarks & antiquarks. For instance, the proton & neutron are made up of three quarks each.  Even the pion is made up of two quarks.  Between 1968-1984 we discerned a total of 6 quarks with basic properties known.  This is called the quark level organization.  This means that everything in the universe is explained in terms of combinations of quarks and their force fields.

Wait, it gets better.

Each quark comes in three distinct colors making a total of 18 varying quarks. Wait.  Each quark has an antiquark, so the total is 36.  We postulate that the force binding the components of the quark are called gluons, they carry the charge between quarks.  These relations are called quantum electrodynamics (QED) * quantum chromodynamics (QCD). 

Why is this significant?

Welcome to a new post-Cartesian, Newtonian/Kantian world of the dematerialization of matter.  a1a2


In Remembrance of Isaac Newton: Discovery, Intuition & Knowledge

“To myself, I seem to have been only like a boy playing on the seashore, and diverting myself and now and then finding a smoother pebble or a prettier shell than ordinary, while the great ocean of truth lay all undiscovered before me.”  Newton

The late great Catholic thinker Peter Drucker once remarked that the single greatest skill one’s parents can depart upon their child is the demonstrative capacity to be effective.  There are antecedents to this that most educators ignore, given our exclusive propensity toward positivist endeavors, we ignore the very culture in which discovery or the skill of discovering is learned.

An American Protestant theologian, named Francis McConnell (d. 1953), wrote in his diary of a powerful experience he had in elementary school.  He was assigned algebra homework and the very last question perplexed him enough that he went to bed without finishing it. Upon waking, an image came to mind of its solution.  He immediately recognized that his subconscious mind was working on the equation while asleep.

The term ‘intuition’ has been irrevocably damaged by Immanual Kant.  For Kantian epistemology, intuition is akin to sense perception of a given exterior object.  In reality, the term encapsulates much more.  The agnostic psychologist Carl Jung had a much better appreciation of how intuition is shaped within the contours of extraordinary exertion. For when the ‘entire’ person engages reality the subconscious mind works to assemble data that is preconscious or precognitive.  These relations aren’t empirical or positivist, but they exert influence on perception, conception and judgment.  Strictly speaking, these intuitions are embodied as an emotional reserve shaping resolution.  Remember the agrarian adage, “when the whole person is engaged, there is no work!”

It was the same for Isaac Newton.


The Achievement of Einstein


Isaac Newton’s epitaph is worthy of great discernment, he revealed that if he achieved any success in his endeavors its because he stood on ‘the shoulders of giants’.  That very humility is often missing from contemporary leaders, especially those who devote their lives to a vocation in the sciences.

It was no different with Albert Einstein.

Albert Einstein’s best known achievement was his 1905 paper on relativity.  His protagonists was Immanuel Kant.  But it remains Cornelius Lanczos who best encapsulated the achievement that is Albert Einstein.  Dr. Lanczos wrote the following:

“What Einstein did was not a formal accomplishment.  He did not approach the problem from the standpoint of finding some mathematical equation which will describe a group of phenomena.  Something much more fundamental was at stake, namely, the critical evaluation of the cultural foundation of theoretical physics.  Certain things which were always taken for granted, were put under scrutiny and their falseness proved.  This was no longer mere physics and mathematics. . . Here started that dogged uphill fight of Einstein which lasted ten years and which is perhaps unparalleled in the entire history of the human mind; a fight which did not arise from any experimental puzzle of the mind.”

From Dr. Cornelius Lanczos collected works titled  Albert Einstein and the cosmic world order 1966.

Summary of his achievements, 2005 symposia Library of Alexandria

Big Bang: Empirical, Ideal Prescriptions & Its Consequences


Astronomers today are in a unique position to experience a new reality, namely the impact of the Big Bang on our Universe.

When we look out in space we see things in the immediate past.  Objects that we witness visually are about 1.4 seconds in the past.  Looking at stars and other celestial objects permits us to view it going back about 9 minutes.  If we look at our nearest star we’re witnessing it 4 years in the past.  Viewing our nearest galaxy (Andromeda), its about 2 million years back. With the help of telescopes, we witness events that are 10 billion years old. If we look at quasars, we are looking at objects immediately after creation.

Dr. Edwin Hubble’s 1929 ‘red shift’ doppler effect spectra means that since the Big Bang, everything in the universe is shifting outward, moving away from each other.  Einstein’s work told of how the total gravitational force of all mass produces a universe that must be understood in terms of ‘curved space geometry’, meaning that all objects in the universe follow curved trajectories.  This has great impact on western understanding of cosmology, time and the assumptions underwriting our Big Bang.

For Einstein, if our universe is negatively curved, it is an open universe, meaning that mass moving along gravitational lines of curved space would exit from our universe.  But, if it is positively curved, meaning ‘closed’, then the universe curves back onto itself.  Currently, this is the main postulate of contemporary cosmologists, even though divergent work is being done by rival cosmologists who are unable to reconcile such postulates to the demands evidenced in ‘closed’ systems as delineated by Einstein.

Albert Schweitzer on Meaning & Life Itself.

“The meaning of life is arrived at . . . by dark gropings, by feelings not wholly understood, by catching at hints and fumbling for explanations. ”   Alfred Adler 1930

“To grow in youngness is a blow.

To age into sickness is an insult.

To die is, if we are not careful, to turn from God’s breast, feeling slighted and unloved.

The sparrow asks to be seen as it falls.

Philosophy must try, as best it can, to turn the sparrows to flights of angels, which, Shakespeare wrote, sing us to our rest.”  Written by Ray Bradbury.

Reverence for Life

Albert Schweitzer Reverence for Life 

The moment of personal transformation for Dr. Albert Schweitzer, a conversion and metanoia:

Albert Schweitzer, born on January 14, 1875 in Alsace, Germany (now a part of France), was the son of a Lutheran minister and member of a family of ministers, scholars and musicians, which included a famous cousin, Jean-Paul Sartre. As a child, Schweitzer played the organ and piano, and was only nine when he first performed at his father’s church. His musical talent earned him international recognition. Although he dedicated his life to the healing profession, he continued to perform as an organist throughout his life, even publishing a book on organ construction and a biography on Bach.

In 1893, Schweitzer enrolled at the University of Strasbourg. He received a doctorate in philosophy in 1899 and a teaching degree in theology the following year. Following in the footsteps of his father, Schweitzer became the pastor of Saint Nicholas Church in Strasbourg and worked at the Theological College of Saint Thomas for nearly a decade. During that time, he published, among other works, a scholarly text entitled The Quest of the Historical Jesus.

In 1904, Schweitzer experienced a turning point in his life after reading an article published by the Paris Missionary Society, which highlighted an urgent need for physicians in Gabon, a French colony in Africa. The article so moved him that he immediately decided to pursue a medical career, much to the disappointment of his family, colleagues and friend – the only exception being a rare woman named Helene Bresslau, whom he eventually married. A determined Schweitzer re-entered the University of Strasbourg in 1905 at the age of 30, funding his medical education with fees from concert performances and lectures. Eight years later, he graduated with specialisations in tropical medicine and surgery. Incredibly, the Paris Missionary Society initially rejected his application to join its programme in Africa, fearing that other ‘liberals and radicals’ would follow suit. However, the Schweitzers agreed to raise their own funds to cover the first two years of expenses, which caused the Paris Missionary Society to relent. In March 1913, Dr and Mrs Schweitzer left for Africa to build a hospital at Lambaréné in the French Congo, and according to historical records, the work had started in a modified chicken coop.


Schweitzer’s arrival in Africa was beset with challenges. Within a year, World War I broke out, and being German citizens, the Schweitzers were considered enemies of France. In 1917, they were interned as prisoners of war, first in the Pyrenees, then in a former mental institution at Saint Remy, where Vincent van Gogh was confined during his last months of life. Upon an early release, the Schweitzers returned to Europe and remained there for the next six years. During that time, Dr Schweitzer maintained his medical skills as well as his pastoral and musical interests, writing several texts, including On the Edge of the Primeval Forest, The Decay and Restoration of Civilization, Civilization and Ethics, and Christianity and the Religions of the World. Schweitzer finally returned to Lambaréné in 1924 and remained there for the rest of his life. Unfortunately, his wife Helene could not remain by his side, as she had contracted tuberculosis during their earlier stay at Lambaréné, and was not well enough to withstand the rigorous living conditions in the jungles of Africa. It was a difficult separation for the family, and Schweitzer had to make do with letters and infrequent visits. In due course, their daughter Rhena moved to Africa to work with her father and eventually took charge of the mission.

While being transported upstream on the Ogowe River from Lambaréné, Schweitzer honed his philosophy of ‘reverence for life’. He reasoned that the morality of man should extend to the entire creation of the universe and that relationships should be both deepened and widened, with each person acting in accordance with his beliefs, as he himself had done. Schweitzer also believed that all should live a portion of their lives for others. His philosophy embraced not only humans but also all living creatures, as was demonstrated by the multitude of animals that populated the hospital grounds.


In the Beginning Was the ATOM

Listening to the great MIT cosmologist Alan Guth describe the universe expanding within a fraction of a second from the size of an atom to a marble remains incredulous.  My initial thought was how does he know?  Believing in the big bang required a very large leap of faith.

The great cosmologists of the 20th century also though so too, like Einstein.  He stubbornly refused to believe it.  The work of managing this hypothesis fell to a Belgian Roman Catholic Priest named Georges Lemaitre, who was an accomplished astronomer and physicist. He theorized that the Universe expanded from the proposition that it was launched from a primeval atom, a process that he later termed ‘the big bang’.  Why is this significant?  Because at the time of his work, the vast majority of accomplished (read tenured lol) professional physicists assumed the universe to be static, with no beginning or end; a view identical to Aristotle.  Father Lemaitre, being a well trained Thomas, just couldn’t accept that premise.  Alone he worked out complicated mathematical results demonstrating the beginning of the universe based on Einstein’s own theory of general relativity.  Note, this was done after Edwin Hubble’s astronomical observations of 1929 which proved that Lemaitre was right about an expanding universe.

On March 17 of 2014, the Harvard-Smithsonian Center for Astrophysics held a conference examining background imaging of cosmic extragalactic polarization (B.I.C.E.P.), meaning evidentiary support for gravitational waves confirming the existence of major theoretical components of Einstein’s theory of relativity, evidence supporting ‘the big bang.”

B.I.C.E.P. also supports cosmic inflation, a mechanism by which the early universe expanded from the size of an atom to that of a marble (Alan Guth).  So the ‘Big Bang’ is verified by B.I.C.E.P. but also from decades of data on background microwave radiation (embers of the big bang) as well as high-energy particle collisions from the Large Hadron Collider (a replica of the big bang.)

So, what’s the big deal?

The big deal is this:  the big bang didn’t happen in a void, it didn’t occur in ‘nothing’. It had to be spawned in some kind of pre-existent medium, like quantum foam (an idea).

So, we’re off to the races again, but this time on firmer ontological ground.

Eric Hoffer: the True Believer

From social philosopher Eric Hoffer’s “The True Believer” (1951):

There is in us a tendency to locate the shaping forces of our existence outside ourselves. Success and failure are unavoidably related in our minds with the state of things around us. Hence it is that people with a sense of fulfillment think it a good world and would like to conserve it as it is, while the frustrated favor radical change. The tendency to look for all causes outside ourselves persists even when it is clear that our state of being is the product of personal qualities such as ability, character, appearance, health and so on. “If anything ail a man,” says Thoreau, “so that he does not perform his functions, if he have a pain in his bowels even . . . he forthwith sets about reforming—the world.”

The Integrative Person, Mind

In this highly engaging book, André Gushurst-Moore surveys twelve of history’s greatest men of Anglo-American letters: Thomas More, Jonathan Swift, Samuel Johnson, Edmund Burke, Samuel Taylor Coleridge, John Henry Newman, Orestes Brownson, Benjamin Disraeli, G. K. Chesterton, T. S. Eliot, C. S. Lewis, and Russell Kirk. Along the way, he explores several interrelated themes, all intended to illuminate “the common mind.”

What is this common mind? It is that which rests upon the uniformity of human nature, and which encompasses qualities and values shared by people throughout history simply by virtue of their common humanity. Predicated on this is the idea of common sense and a properly formed conscience, the “faculty that negotiates . . . moral action.” The accumulation of insights and wisdom imparted by such a conscience over the centuries represents what Gushurst-Moore then calls “the wisdom of the integrated person” and “the integrated wisdom of the group”—what we might call “custom” and “tradition.”

As Gushurst-Moore explains, the common mind is really an “integrative” mind, bringing together the best of the modern, the medieval, and the classical. In the works of Thomas More, with whom these essays start, it is reflected in the influence of Plato and Aristotle, Augustine and Aquinas, Cicero, Lucian, Thucydides, and Sallust. In short, the common mind is “the mind of Europe, the settled mind of the West.”

Its opposite is “the disintegrative mind.” This is the mind of the sophist, the Pyrrhonist, Ockhamist nominalist, radical skeptic, and deconstructionist—anyone who denies universal truths and attempts to annihilate meaning by seeking to “fracture the connection between common sense . . . and language.” Dangerous stuff, this—and characteristic of so many thinkers of the Left.

In the twentieth century, we have witnessed the bloody legacy of the disintegrative mind: It is one of alienation, fragmentation, and death. And at the societal level, it has resulted in a “decline of civility and manners,” the “celebration of the violent, the cruel, and the outré,” and a general “denial of beauty and decorum” in art and literature.

Like many people, Gushurst-Moore wonders where we went wrong. How did we lose “a society of gentleness, order, politeness, and restraints”? But the purpose of his book is neither diagnostic nor prescriptive. Rather, it is a celebration of men over the centuries who have opposed the disintegrative mind and whose literary works aimed at evoking “a familiar, older, and more gentle social order.”

Various interrelated themes guide the author. Happily for the reader, Gushurst-Moore—currently Second Master at the Benedictine “Worth School” in West Sussex, England—is adept at elucidating the themes on which these men of letters concur. They have the effect, he says, “of commenting on each other, across the barriers of time.” The result is an extended meditation on the qualities of the common mind.

To be sure, not all of the figures profiled have the same partisan allegiances. But all have an abiding respect for humane learning and the Western tradition. Their acceptance of universal truths and their recognition of the reality of a flawed human nature transcend “classes, circumstances, and individuals.” And whether considering More in the fifteenth and sixteenth centuries, Coleridge in the eighteenth and nineteenth centuries, or Kirk in the twentieth century, Gushurst-Moore reminds us that their struggles are also our struggles today.

Each of these writers—through what he calls works of “conservation, defense, restoration, and recovery”—constructed imaginative “visions of order.” They demonstrated how the common mind could help illuminate, redeem, and rehabilitate the “fragmented consciousness and disintegrated world of modernity.”

In some ways, this book can be considered a eulogy to the classical Christian humanism of the West—to the idea that liberal education should have a moral purpose and that literature should be the principal means through which men develop the moral imagination. This is, of course, Cardinal Newman’s educational ideal: producing “moral aristocrats capable of independent reflection, and guided by the integrated personality itself.”

It’s interesting to note that it’s not just traditional drama, fiction, and poetry that serve this formative purpose. Gushurst-Moore also sees an important salvific role for other forms of literature. For example, literary fantasy “opens up the possibility of the supernatural in a culture that has lost its religious bearings.” And, he adds, it can be especially effective since it is often written in simple language—accessible and easy to understand—while imparting moral lessons or great wisdom.

This also explains his inclusion of Russell Kirk in this collection of profiles. In Kirk’s essays, he often explored how “writers such as Tolkien, Lewis, Charles Williams, and the science fiction writer Ray Bradbury, use fantasy and myth to remind people of the norms from which their society departs.” But he also wrote imaginative fiction himself—his so-called “Gothic romances.”

What’s more, Gushurst-Moore considers Kirk’s life itself a “redemptive work of art”: Here was the Bohemian Tory inveighing against modernity from his Italianate mansion in the little town of Mecosta. For Kirk, he explains, “conservative” was more than a political label; it stood “for a whole attitude to life, including the religious, philosophical, political, literary, and the everyday.” It was simply the “natural political position of the common mind.”

It’s worth remembering that considerations of the political in this book are incidental, as this is primarily a work of literary analysis and philosophical reflection. In fact, throughout, it is clear that the author has a vocation—to teach others about literature and educate them about the higher things.

In his introduction, for example, Gushurst-Moore provides a close reading of Philip Larkin’s poignant “Going, Going” with its images of a disintegrated world. Later, he offers a miniature thematic study, looking at how Brownson and Disraeli, for example, both wrote about the folly of trying to impose one country’s political constitution on another country without, in Brownson’s words, any regard for the latter’s “sentiments, convictions, consciences, manners, customs, habits, and organization.”

Gushurst-Moore’s descriptions can be wonderfully apt. He calls Brownson an American version of Thomas Carlyle or John Ruskin: “voluminous, verbose, thunderous, and prophetic.” When considering the heroic couplet, he says it is where “[t]he spirit of Voltaire and the spirit of Rousseau come together,” deeming it “the literary correlative of an abstract political constitution imposed on any nation, whatever its customs and traditions.” At other times, he is unexpectedly droll: “It is difficult, at the best of times, to think of Coleridge, the inveterate opium-eater, as a conservative.”

In the end, Gushurst-Moore concludes with a thoughtful essay on the future of the common mind in the West. And he leaves us with a lasting impression of the thoughts and ideas that he has gleaned from the great works of these twelve giants of humane literature—in the hope of inspiring us, presumably, to make similar efforts to defend the common mind.

Yet perhaps the book’s most important message is that, despite the disintegration and fragmentation of the modern world, we are compelled to remember that which makes us human—and which binds us to other men. Or, as Chesterton says, “we need a rally of the really human things.”

In the meantime, what is left? Eliot tells us: “Only the fight to recover what has been lost.”

From ‘The New Criterion’ September 2014.

Amazon:  ‘The Integrative Mind’

Realist Philosophy & Math

Philosophy of mathematics, which might seem like some boutique academic specialty, has played a remarkable role in the history of Western thought. To Plato, for example, mathematics provided the very model of knowledge, of truth apprehended with certainty not by the senses but by the mind. St. Augustine learned that lesson from the neo-Platonists of his day, which allowed him to take a crucial step toward his religious conversion, for it made intelligible the possibility of a non-material god. “How is pure mathematics possible?”—the famous question at the heart of the Critique of Pure Reason—was Kant’s way of asking in an aphorism what the world must be like if it can be described by mathematical physics. Mathematics raises, in an acute way, the question of how (or whether) we can bridge the gap between our knowledge and the objects of our knowledge.

The mathematician and philosopher James Franklin is a leader of the “Sydney School,” which has developed an account of mathematics that he sets out in An Aristotelian Realist Philosophy of Mathematics. “Aristotelian” means not that it strictly follows or develops Aristotle, but that it is recognizably in the same ballpark. He presents it as a middle way between two poles—broadly classifiable as Platonist and nominalist—that have dominated the subject and dictated the terms in which it is discussed. He therefore begins with an ancient question about the status of universals, those general properties (such as shape, number, mass) whose relationships are the proper subject matter of systematic knowledge.

For a hardcore Platonist, universals—which include the objects of mathematics—constitute a realm of entities that exist independent of minds and outside space and time. Platonist views of mathematics have had an enduring appeal. The mathematician hunkered in a foxhole, earning his pay, finds it difficult to set aside the prejudice that he is grappling with something real—to keep up morale, if nothing else. And if mathematics concerns unchanging entities detached from the messy and confusing world of the senses, we can begin to explain and justify the belief that mathematical knowledge is necessary and certain.

To a nominalist, only particular individuals exist. Words purporting to denote universals are conventional labels. Nothing real corresponds to the boundaries they draw, which are nothing but convenient ways of organizing our experience (thus far). Franklin holds that universals are real, not because they inhabit some special realm of their own but because they refer to real properties of things. What universals exist can be discovered by investigation. Blue is one, goes the argument, because there is an ensemble of physical properties one of whose effects is that bodies which possess them will, in appropriate circumstances, look blue. The facts that the normally sighted make similar judgments about what is blue and can agree about how to line up shades of blue along the color spectrum testify that blue corresponds to something real. The inability of different people to compare their subjective experiences of color is beside the point.

Mathematics presents difficulties for each of these views. A Platonist, for example, must explain how we physical creatures can have access to a world of non-spatial, nontemporal entities and how knowledge about that other realm could be relevant to the world we live in. Applied mathematics is also a challenge to nominalists: Why are propositions about things that do not exist so uncannily useful? Aristotelian realism, which places applied mathematics at the center of its account, must explain universals that are “uninstantiated.” Many notions of mathematics, such as high-order infinities, do not seem to be realized in the physical world; indeed, if the world is finite, even large numbers are not the numbers of anything. In what sense, then, can these be “real properties of things”?

Part I of Franklin’s book, “The Science of Quantity and Structure,” argues that Aristotelian realism is adequate to give an account of mathematics and that this account, uniquely, justifies two striking claims: that the objects of mathematics include real properties of the physical world and, accordingly, that “there are necessary mathematical truths literally true of physical reality.” Part II, “Knowing Mathematical Reality,” ranges widely over questions of epistemology, such as understanding, visualization, explanation, and non-deductive reasoning (evidence other than proofs for or against mathematical assertions). It includes an outline for a program to explain how, building on inherent mathematical abilities—such as babies’ perceptions of multiplicity—we can acquire higher-level knowledge of abstract and unperceived mathematical structures.

“Quantity” begins with the counting numbers: one, two, three . . . Any account of them must begin with Gottlob Frege’s tour de force, The Foundations of Arithmetic (1884). It is a deep inquiry into the notion of number, a brilliant demolition of competing theories, a founding document of analytical philosophy, and a treat for anyone capable of enjoying a first-rate mind at work.

A number, Frege says, cannot be a property. What would be the number of the Iliad? One (poem)? 24 (books)? 15,693 (verses)? To count we need not just the stuff being counted but also a “criterion of identity” that specifies what it is about that stuff that one should count—for example, the criterion of “being a poem” or of “being a book of a poem.” Frege concludes that since a number is not a property—nor, he also argues, a mental state—it must be a (nonspatial, nontemporal) thing.

Not so fast, says Franklin. If we accept the reality of universals, including those that express relations, there is a third possibility, one that doesn’t require belief in mysterious Platonist objects: The number of verses in the Iliad is the relation between the Iliad and the universal “being a verse.” As Frege says, however, we must give an account not only of numbers (“There are three cows in the barn”), but also of number theory (“For every n there is a prime number greater than n”). Franklin does not address that explicitly. I suspect he would respond that number theory is about the structure of arithmetic; in his account, structure requires no Platonist objects either.

Much advanced mathematics concerns non-quantitative notions—such as symmetry and continuity—that have been called structural. We may know it when we see it, but structure is difficult to define in the abstract. Franklin offers the following: Structure is what can be defined in terms solely of part/whole relations and logic. In particular, structure is about how things are related, regardless of what those things are. (A highly technical aside: Second-order logic is required to characterize many important mathematical structures; that potentially requires some hefty philosophical and mathematical commitments that one might prefer to avoid when laying a subject’s groundwork.)

Everything rests on the contention that mathematical entities can be literally exemplified in the world. Franklin’s running example is the structure of a graph. Leonhard Euler, the greatest mathematician of the eighteenth century, introduced the notion of a graph to solve the Königsberg Bridge Problem. Through the city of Königsberg runs the river Pregel, which contains two islands. The city had seven bridges, each connecting an island either to one bank of the river or to the other island. It was believed impossible to take a walk that crossed every one of the bridges exactly once; and Euler proved this was true by proving a fact about a certain graph. Franklin argues that the city of Königsberg literally has the structure of that graph and that Euler’s proof therefore demonstrated a necessary truth about the physical world.

A graph may be visualized as a collection of dots on paper (call them nodes) and line segments joining some of the pairs of points (call these lines edges, and call the points an edge joins its end points). The structure of a graph is a universal—the end-point relationship among nodes and edges. If we say that each of Königsberg’s four land masses (two river banks, two islands) counts as a node, that each bridge counts as an edge, and that the end points of a bridge are the land masses it connects, we have identified a graph structure of which, says Franklin, Königsberg is literally an instance. Euler proves that there is no path in that graph—no way to proceed successively from one node to another by following edges that connect them—on which every edge appears exactly once.

An obvious objection is that the example seems to have been cherry-picked. Königsberg might literally be a graph, but we often represent a complex situation with some structure that has been deliberately and radically simplified—for example, treating a fluid made of particles as if it were a continuous substance. In that case the real world is not an instance of what’s analyzed and Franklin’s account seems to get no purchase. I’ll attempt an abbreviated version of his response. Consider a coin, whose exact outline is complex; it’s certainly not a Euclidean circle. The exact outline of the coin nonetheless realizes some mathematical structure and without leaving the world of mathematics we can establish necessary relations between it and other structures. For example, we can consider those structures that represent “a figure no more than x% out of round” and establish, by proof, upper and lower bounds for their areas. And it’s quite plausible to assert that some real coin literally exhibits the property of being “no more than five percent out of round.”

The ability to reason in this way about not-fully-known structures typically depends on the structures’ being “stable”—that is, having properties that are relatively insensitive to variations in the structure. Stability is a mathematical property that can be established by mathematical means.

It is striking that the landscape described more than fifty years ago in Stephan Körner’s well-known book Philosophy of Mathematics, An Introductory Essay looks so much like the one visible in the up-to-date Stanford Encyclopedia of Philosophy. The main non-Platonist contenders are listed, then and now, as: logicist (mathematics is nothing but logic), formalist (mathematics is the manipulation of symbols according to specified rules), and intuitionist (mathematics consists of constructions performed in the minds of mathematicians). Each has been philosophically fruitful and has motivated significant developments in mathematics. (I wonder if there is a field in which philosophy has had a more beneficial effect on practice.) And they remain at a stand-off, each able to present formidable criticisms of the others.

Franklin claims to offer a way out of the impasse and his book seems to me—a professional mathematician with an amateur interest in philosophy—an important one. A short review cannot do justice to the variety of problems considered and the interesting angles of attack offered by his realist point of view.

An epilogue, titled “Mathematics, Last Bastion of Reason,” places the discussion in a larger context. Readers of this journal needn’t be reminded of the fashionable anti-rationalisms and irrationalisms that have flourished in the arts and in the humanities. Franklin notes that popular versions of even hard sciences “have caught some unpleasant philosophical diseases”—as when quantum mechanics, which makes predictions verified to spectacular degrees of accuracy, is “coated in prose about ‘reality dependent on the observer.’ ” Mathematics, he says, has always provided support for views that “exalt the capacity of the human mind to find out the truth” and has been “a perennial thorn in the side of opinions that abase human knowledge, and claim it is limited by sense experience, cultural experience, or one’s personal education and perspective.” Franklin gets into the ring with Mr. Frege, et al. not only to hash out ancient philosophical disputes but to take a stand for the very possibility of objective truth.

Absorption: The Gift of Digital Mediums

Remember the old saying, ‘when the entire person is involved, their is NO work‘. 

Digital/electric mediums are returning man to a nomadic state.  We can witness this return away from specialization in hybrid mediums that use digital media.  If we can get monolithic institutions like education to return to the business of shaping human capital, then we can actively participate in the revolution of contemporary aesthetics. 

Here’s what Dr. Edmundson from the Univ. of Virginia recently wrote in Hedgehog Review:  “Modern life avails one of plentiful opportunities to be mesmerized, enchanted, visually inebriated now:  The condition is not hard to bring on.  In a culture that asks too often to ‘pay attention’, we need rest and release, and we can find both through the mesmerizing powers of current electronic culture.  Ideally, paying attention should be rewarded by absorption, but when absorption isn’t found, or no one teaches us how to achieve it, then being mesmerized will have to do.  Being mesmerized is all about wish fulfillment.  It’s about  becoming the soldier, the knight, becoming the sports star, or princess.  It is a turning away from reality.  To be absorbed is to intensify one’s connection with ‘the real’, in the hope of shaping it for the better.  The engaged/absorbed doctor wants health for the patient, the scientist want’s to add to the stock of knowledge, the poet hopes to bring beauty, truth and pleasure to another.  

These people are not cheering themselves on or inflating their sense of self.  They are acting out of love for the world, and, in return, they receive one of life’s best gifts:  the shaping of an indissoluble self.”