Exposing oneself to older ideas has many benefits.  Such a statement is almost a cliche for someone in my line of work, but then every so often the reality of this truth hits one afresh.  The old world had much wisdom that we have lost.

One idea that struck me with particular force recently has to do with the early Church’s link between the reality of sin as it relates to fact of death.  For Adam and Eve, sin brought death, and their progeny inherit bodies of death.  After the Fall, sin now results from death.  That is, we sin because we know we will die.  Sin often originates in our rebellion against death.

We do this unfortunately, in a variety of ways.  We distract ourselves endlessly with extended consumption.*  When men reach my age they buy sports cars and get trophy wives in an attempt to feel young and powerful again.  All of us feel the need for self-preservation, so when we see a chance to “extend ourselves” and grow our kingdom we seize it, whether that means invading another country or cutting someone off in traffic.

The futility of such actions is obvious on a biological level — we will die.  But such actions do more than merely delay the inevitable.  By making death more distant, we lose our dominion over it and thereby give it more power over our lives.

This is the main theme of Philippe Aries’ book The Hour of our Death, which stands as a greatly expanded version of his Western Attitudes toward Death.  In that book he talks about the idea of a “tame” death in a more thematic manner. In this work, in minute and at times fascinating detail Aries gives the reader a multi-faceted look at how western man has died since the early Middle Ages.

I will try not to repeat myself too much from the review linked above.  He begins his study under the heading “The Tame Death.”   Essentially from the early Middle Ages, our approach to death consisted of . . .

• A belief that death “politely” let one know of its imminent arrival.  This blessed those about to die, for it gave them a chance to say goodbye and reconcile with friends and family.
• Rituals that governed the process of death for the dying, which included last rites
• The rituals having the effect of “taming” death*

Aries concludes his first chapter by writing,

The fact that we keep meeting instances of the same general attitude toward death from Homer to Tolstoy does not mean we should assign a historical permanence exempt from variation.  .  . . But for 2000 years it resisted pressures in a world subject to change . . . this attitude toward death is like a bulwark of inertia and continuity.

It has by now been so obliterated from our culture that it is hard for us to imagine or understand it.

Thus, when we call this “familiar” death the tame death, we do not mean to say that it was once wild and is now domesticated.  On the contrary, we mean that it has become wild today when it used to be tame.

This “wild” state of death came about in distinct stages.

1. Perhaps because of the plague, the later Middle Ages depicted the gruesomeness of death and the reality of death much more frequently in their artwork.  Death was far from “put aside,” but assumed a more terrible aspect.
2. The late Renaissance made death more about the Last Judgment than redemption in their art.  Perhaps this happened as Renaissance culture knew that it had drifted from its medieval roots and sought through a kind of force — like shaking a patient — to regain some ground.
3. Many Protestants abandoned this Catholic practice, but as is typical in such cases, swung the other way entirely.  Death no longer brought terror, but neither could it allow for mourning.  Some Puritans, for example, had encouragement to remarry within a month or two of the decease of their spouse.  Rather than fix the “problem” of death, this approach attempts to give death an unreality, which makes it ultimately abstract and impossible to tame.
4. The scientific age believed that cemeteries were unhealthy places.  Burials stopped happening in or beside churches (located within the town) and got moved outside town limits.  Now, too, rituals involving the dying were in jeopardy, because of the risk of disease, infection, etc.  In suffering “medicalization,” death left the field of the Church and entered the field of science.
5. The Romantic era of the “beautiful death” attempted to correct the Enlightenment approach.  But like the Puritans before them, they unintentionally swung unhelpfully in the other direction in two main ways: 1) The “beautiful death” imposed a burden on the dying to “get it right” — be tranquil, be composed, be “natural,” etc., and 2) In returning death to the provence of nature they believed they entered a beneficent realm.  But nature in truth (at least according to Aries) is arbitrary, and cannot be “tamed” on its own terms.  Thus, the impossibility of taming death in nature.
6. The modern era has abandoned rituals of almost every kind that guide cultural practice.  Our societies do not pause in any way for death, unless it is perhaps the death of a statesmen or our military.  Other deaths in society do not register.  As the “ends” of our communal life have secularized, so too has death been secularized.  The whole notion of a “communion of saints,” or a “cloud of witnesses” has disappeared utterly from nearly all Protestant churches.  Without this sense of continuity or ritual, death has free reign, no controls, and again, becomes more terrible in aspect.

Aries published his book in 1981, perhaps the height of the modern medicalization of death.  With the advent of hospice care and other less invasive end of life medical practices we begin to move back in a more positive direction.  But we have a long way to go.

One key way back to a more proper understanding of death will involve a theological shift, as I hinted above.  If we persist in the idea that God resides “up there” while we remain “down here,” we will never understand death.  The same holds true for the departed.  Without the communion of saints, death will continue its lordship.  I quote extensively from Stephen Freeman’s Everywhere Present below to illustrate the point and show us the way forward.

At the time of my visit [to the St. Saba monastery] one of the brotherhood had “fallen asleep” two weeks earlier.  “We never say that a monk has died, ” our guide told us, and I suddenly imagined the unspokenness of death I knew so well [from living in America].  He continued, “We always say, in the words of Scripture, that they have “fallen asleep.”  But most we say this because we see them so often.

Now I knew I was in a different place.

“You see them?” I asked.

“Sure,” he said.  “They appear to monks all the time.  It’s nothing to see St. Saba on the stairs or elsewhere.”  The witness of the monk (who happened to be from San Francisco) was not a tale of the unexpected.  These were not ghostly visits he described, but the living presence of the saints who inhabit the same space as ourselves.  It is a one-storey universe.  Such stories . . . can be duplicated all over the monastic world.

The doctrine of the ancient Church is quite clear in this matter.  Those who have died are separated from us in the body, but the Church remains One.  There is not one church in heaven and another on Earth.

Dave

*Who doesn’t love Amazon Prime?  But my countenance fell upon reading a recent ad of theirs for same day shipping — “Patience no longer required.”

How does one know if your faith is “really real?”  Christians can sometimes get hung up unnecessarily on this question, but it’s an easy one to ask.  When you don’t have a dramatic night/day testimony it can seem all the more difficult to answer.  The Church can complicate matters by sometimes venerating the Damascus road kind of conversion of the overtly evil man immediately transformed.  Such people have more certainty, we assume, and so have greater faith and a more profound Christian experience.

But aside from the exceptional experience of St. Paul, very little in the history of Christian spirituality suggests this as the norm. Every significant spiritual writer I am aware explains that God almost always works slowly over time through the mundane aspects of life.  Growth in holiness comes by putting one foot in front of the other.  It makes sense then (barring exceptions of course), that those who had an early start and never traveled in the wrong direction for long periods of time would be further up the mountain than even the “dramatic” converts.

Two recent works I encountered bear this out.

We have no equivalent to Malcolm Muggeridge in the west today.  To get him we would probably have to combine G.K. Chesterton, Truman Capote, and David Brooks.  He made his career as a journalist first, but later became a social “man about town” who rubbed elbows with the media and intellectual elite of English society.  He then rejected much of the pomp and circumstance of his life and converted to Christianity.  He wrote many books, perhaps his most famous being his autobiography, Chronicles of Wasted Time, a work spread out over three volumes.  In the first volume, “The Green Stick,” he tells the story of his early life, and his embrace of the liberal left.

Throughout the book Muggeridge’s wit and panache shine through.  He gleefully pokes himself and his profession.  He had gone from devotee to gargoyle, happily mocking all our pretensions.*  Typical of his style is how he discovered as a reporter how to distill all momentous political speeches to just a few phrases.  “We decided that there was no need for politicians to finish their sentences,” he writes,  “with their end being implicit in the beginning.”  Such phrases are,

On this historic occasion when . . .

There can be no one here present who . . .

We have just passed through an ordeal that . . .

No thinking man will underestimate the . . .

While there are many circumstances which . . .

While recognizing the reality of . . .

It is surely incumbent upon all of us to . . .

Such is the choice that at present confronts . . .

It is idle to think that politicians can . . .

It rests with the common people to . . .

With head erect and clear purpose we . . .

One feels the sham nature of so much of our modern existence reading Muggeridge. Having drank deeply from the world, he can expose it all the more readily.  This brief clip illustrates not only his fabulous voice (and who wouldn’t want the life of sitting around, smoking, and giving one’s opinion on everything), but also his abhorrence with that which most fascinated the 20th century.

Muggeridge takes his title from the Russian legend of the Green Stick, so dear to Tolstoy.  In this story, should anyone find the Green Stick he would have the power to remove all suffering.  The simplicity of the idea charms anyone, but of course nothing is ever that simple.  Muggeridge as a boy talked of his wish for the same Green Stick, which may have helped lead him down socialist paths in his younger days.  One can’t fault him for this, but it strikes me that occasionally Muggeridge’s rejection of so much he experienced led him to oversimplify in the other direction.  Even his brief quote in the clip above reveals this flaw.  Power is not evil in itself, obviously, for we rejoice in God’s own power. Naturally no one on earth perfectly uses power, and most abuse it in great or small ways.  Some of the greatest saints of the Church divested themselves entirely of earthly power.

But Muggeridge would, I think, rejoice to see power rightly used to crush evil or to bring justice.  And this is not mere theory.  On rare occasions (like king St. Louis IX) Christian rulers have used power and worldly status for good ends without it getting to their heads.  So power can be redeemed.  Of course Muggeridge could have said something like, “Power is so dangerous, and so rarely used well.  We in the modern world, with it’s deadly combination of technology and our uncertain moral compass, are particularly unsuited to use power, and we should seek to limit its use whenever possible”

But he didn’t.

Muggeridge’s style easily engages the reader, and he mixes humor with profound insight almost perfectly at times.  I recommend him.  But he also comes across at times as someone with a bit too much baggage. He has a hard time appreciating things in general — perhaps he ruined his palate with the life he led.  A convert to Christianity somewhat later in life, I think he still struggled (as I and so many of us do) to see things clearly as they really are.

The Discourse and Sayings of Dorotheos of Gaza are not as entertaining to read as Muggeridge, but one senses quickly that his writing comes from a much different place.  His stories have an endearing simplicity, though perhaps lack penetrating insight.  His instructions about the spiritual life seem immediately obvious, but then, the best kind of teaching usually has this quality.  What really struck me, however, about reading this on the heels of Muggeridge was how Dorotheos comes across as so unencumbered, so free of the “issues” that run rampant in modern experience.  He led a simple, unadorned life with monks in the wilderness, and this gives him an almost perfect freedom.  If nothing else, it shows how the dramatic, worldly convert is not better off, and often has less to teach the Church, than the slow and steady Christian who has lived the Christian life with others for countless years.  The clarity and simplicity of the Discourses reminds of Dante, who knew something akin to Dorotheos when he ended his journey by seeing God as a single point of light.

Dave

*This, I’m sure, was the true purpose of the medieval gargoyle — they had little to do with scaring anyone.  They were meant to mock us, to humble us, to poke fun at the culture around us.  That’s why I hate the famous Darth Vader gargoyle on the National Cathedral, which pats our culture on the back in a cutesy way.  I suppose though, that’s what happens when we have a “National” cathedral which serves ultimately as a monument to ourselves.

Very few would place Bach anywhere outside of one of the top musical masters in history.  He has universal praise and admiration for his talent, innovation, and inspiration.  Personally for me, Bach stands at the top, with Beethoven a very close second.  I have yet to read a full-fledged Bach biography, but those that I have glanced at so far turned me off by phrases like, “A man of great musical genius and simple faith,” or “His outstanding musical ability contrasts with his unadorned faith,” or some other such sentiment.

Certainly having a “simple” faith should be praised, if by the term one means something akin to purity of trust, or as Aquinas might have used the term, i.e. “unclouded.”  But I doubt that the authors intend this meaning of the word. Instead I get the impression that they mean something like, “Bach poured his genius into his music while rubber-stamping his faith.” Jaroslav Peikan’s Bach Among the Theologians dispels these notions once and for all, and shows Bach to have thought deeply about theological concerns, which he expressed not in letters, memoirs, or treatises but in his music.

Pelikan first sets the context of Bach’s music within the Reformation as a whole.  Living on this side of the Reformation many may take certain things about worship for granted.  Before the Reformation, churches had musicians, “striving for perfection in the true style of this music, a a performance far removed from subjective expression and concert effectiveness” that often centered around Gregorian chant.  The dissolution of this heritage opened up new possibilities for good and evil.  Granted, Pelikan admits that Protestant worship music might tend to take on a “performance” character, and hence the horrifying “worship leader” stereotype, which must be one of the worst inheritances of the Reformation. On the other hand, we had the introduction of congregational singing and participation in the service.  And while I do think that the Reformation should have kept the baby and at least some of the bathwater from their medieval past, the changes allowed Bach to develop music along a “concert-like” character and forge a whole new style of church music.

But Pelikan does not start his work here.  Instead he contextualizes Bach’s work within the Church calendar as a whole.  Luther himself kept many so-called Catholic “trappings,” with the Church calendar as a whole. Of course the vast majority of Bach’s works were commissioned for worship settings, and the church calendar dictated at least something of the tone and style of Bach’s work.  Here we can make two conclusions, one rather obvious, and the other less so:

• Artists in the modern era often talk of the need for them to be free to create what they wish.  I think this idea would have struck people in earlier eras as rather odd.  The artist had a job like anyone else. We should not assume that strictures such as “commissions,” and “orders” restrict creativity. Unquestionably, the west’s greatest artists (Machiavelli, Bach, Rembrandt, etc.) did their best work under such so-called “limitations.”
• “The liturgical year is the context in which the Church commemorates, day by day, all history.”  Pelikan reminds us that the Church calendar doesn’t merely provide a convenience, it expresses a theology of time.*  The major festivals of the church with one exception (Trinity Sunday, the latest addition to the calendar) celebrate not doctrines, but events.  The cycle of four seasons integrate our experience with that of creation as a whole.  This formed the subtle, sometimes unseen backdrop to Bach’s work.  Since much of Bach’s work, then, got commissioned to commemorate events, the possibility of more emotional and experiential content in his music.

Bach never wavered from his staunchly confessional Lutheran perspective.  He appears not to have thought much about ever joining a different church.  Some might use this to support the “simple faith” thesis of Bach, but Pelikan shows that Bach interacted with many different prevailing ideas of his time and yet was captured by none of them. Bach admired Frederick the Great and Enlightenment rationalism, with its emphasis on balance and symmetry, and muted sensibility.  We see this influence in his Well Tempered Clavier, and The Art of the Fugue to great effect (Pelikan also points out the geometrical symmetry of some of his cantatas).  This is the kind of Bach music that gives you a contented sense of completion.

But unlike other somewhat contemporary artists (perhaps like Vivaldi, for example), Bach’s range extended far beyond “rationalist” confines.  To the dismay of some of his Lutheran patrons, Bach admired some aspects of the emerging Pietist movement, which stressed the importance of subjective religious experience. Pietists occupied almost the opposite point on the spectrum from the rationalists, yet Bach felt comfortable here too.  He could see that just as reason has a place in God’s economy, so too does subjective emotional experience.  Bach applied his understanding in his St. Matthew’s Passion, where he emphasizes the suffering of Jesus the individual.

In emphasizing such “subjective” emotions, Bach went against some of his staunchest Lutheran supporters (which undercuts whoever sees Bach as a mere tool of his patrons).  But in St. John’s Passion Bach picks up on that gospel’s different perspective.  In John’s narrative the resurrection receives far more attention, and the resurrection is not just Christ’s victory, but that of all mankind.  So he makes St. John’s Passion more magisterial and universal in scope.  In these different emphases Bach paid heed to the differences in the texts themselves. Matthew’s gospel has the most Old Testament references so might be described as the gospel that gets the most context, hence, the most particularity.  John wrote his gospel much later after the fall of Jerusalem, and so his account gives us more universal, grand themes.  Again we see Bach not merely as a musician in a vacuum, but using music to express theology (as I suppose all music does in one way or another).

And finally, the wilder, unhinged Bach of the B Minor Mass . . . 

Pelikan reminds us that we will not see the modern view of the artist as the man freed from all limits in Bach no matter how hard we look, however.  Yes, he innovated and tweaked sensibilities.  Yes, he refused to let one particular theological perspective bind him  But his “sacred” works (Pelikan recognizes that with Bach the line between his “sacred” and “secular” works is very thin indeed) all answered to the liturgy of the Church and its measurement of time.  If the four seasons of the year give us different perspectives and priorities, so too the Church calendar gives time itself a context.  In rooting us to all of time and mapping it out for us, the Church reminds us that God has something to say about all of our experience in His world. God’s limitations, then, are much broader, wider, and deeper than any freedoms we might imagine we grant ourselves.  No matter how hard we may try, none of us can break free from the limitations of time itself.

Dave

*This gives us a hint as to why controversies in the church surrounding say, when Easter should be celebrated seem arcane and irrelevant to us, but had much greater importance to them.

The back cover of this book by James K. Thompson proclaims that, “there are few comparative studies available” of theories of decline,” whereas “growth” gets all the attention.  This seems false to me. Hollywood can’t go more than a few weeks without making a movie about huge disasters and the end of all things.  Americans, at least, seem to be continually questioning themselves and pondering our place in the cosmos.  Historians too, going back to Thucydides at least, seem in general more drawn to decline than growth.  And admittedly for me, the title Decline in History: The European Experience in itself got me to look at the book in the first place.  It seems that I, like everyone else, have decline on the brain.

Thompson sets out to first examine two basic approaches to decline taken in the 20th century, and then see via synthesis whether or not he can come up his own grand theory.  In past centuries theories of decline had their roots in the actions of men, and here I don’t mean “mankind” generally but men as political leaders most particularly.  Not much else got examined.  In the early 20th century Spengler and Toynbee changed this standard approach and saw the actions of people in general against a back drop of a process of growth and decay that had either the dread inevitability of death about it (Spengler) or the great likelihood of human actions adding up to eventual failure (Toynbee).

Enter into the arena the Fernand Braudel, a patient, meticulous genius who rebelled utterly from the standard way of viewing decline.  He looked at everything but people and instead focused on climate, the soil, geographical positioning, and observed slight changes over time.*  So, Portugal was doomed not so much by what it did as by the fact that their forests could never keep up with their shipbuilding, thus leading to an inevitable overextension in their soil.  The Mediterranean itself never had high quality soil.  So while (perhaps following Toynbee) this initially presented a great challenge and brought out an inspired response from those who lived there, no amount of human ingenuity could fundamentally change nature.  The receding tide of Mediterranean dominance was written under the soles of their feet.

Other 20th century historians followed Braudel armed with a Marxist approach that focused on social class, such as Michael Mann.  Success in any civilization raises the standard of living for the middle class.  This middle class then aspires to join the aristocracy, or at least emulate their habits.  This results in exploitation of the lower classes and with that, an attendant social and political decay.  Thus for Braudel and Mann, success, exploitation, and decline all go together, whether in the soil or in the mass of humanity.

Thompson attempts to glean from these approaches (with a few others thrown in as well) and come up with his own approach.  I liked his broad spectrum approach, and some of his examples show give great illumination into what happens with decline across different civilizations.

Historically rises in power, and shifts in power, tend to have two main characteristics.  One is proximity to the coast, for coastal regions will lead to fruitful contact with other civilizations.  The second factor in significant and sustained growth lies in the coastal region’s proximity to another great power of different aspect, allowing for progress arising out of a dynamic synergy.  So Greece’s proximity to Egypt presaged a shift from the Fertile Crescent to the Mediterranean.  Venice’s location on Italy’s northeastern coast gave them beneficial interaction with Byzantium.  So Venice’s decline in power might have less to do with Venice and more to do with the Moslem conquest of Byzantium by 1453.  Now the possibility of fruitful interaction ended, and the “center of gravity” shifted away from the Mediterranean towards the Atlantic.  This gave Portugal the early advantage in the next growth cycle.

But for Thompson growth and decline involve more than geographic position.  Portugal’s quick rise had something to do with geography, but also to the dominance of the aristocracy with a high-born and heroic ideal.  As De Tocqueville states, aristocratic societies will eagerly jump into the fray when competition, honor, and glory beckon.  They are bred for that sort of thing, and perhaps this explains (along with their geography) why   Thompson then suggests that perhaps Portugal held onto their empire for longer than we might expect due to the tenacity of the peasant class seeping into the Portuguese ethos.  But it was this lack of a strong merchant middle-class that meant that they could not really implement their enormous gains and diffuse them into the whole of society.  Imagine one getting first to Thanksgiving dinner, gorging oneself, but lacking proper digestion.  Everything would sit in the belly with none of the nourishment passed to the body, immobilizing the unfortunate eager diner.

Thompson shows himself torn between the deterministic Braudel/Mann and the more fluid Jonathan Israel, who focused on politics.  It does appear, however, that he has little time for theories of growth and decline that focus on individual rulers.  He offers a lengthy summary of Charles Diehl’s work on Byzantium, whose “traditional interpretation” focuses mainly on the influence of their emperors.  Thompson prefers other sociological factors, namely,

A transitional state, between Antiquity and the medieval world, one too whose quixotic obsession with preserving the imperial ideal [agreeing with Toynbee’s spiritual analysis of Byzantium] caused it to clash continuously with new economic, social, and political developments, thus, not altogether surprisingly, can be seen to have experienced the type of decline associated with both types of civilization.

Based on Thompson’s brief summary, I think I would have more sympathy with Diehl than he.  But Diehl himself suggests an interesting point of confluence between the political and sociological perspectives when he argues that at a certain point, Byzantium issues lay beyond the help of any one ruler.  Eventually concrete sets in that requires a catastrophe to loosen.  I like this approach of synthesizing different approaches, but few historians have the necessary nimbleness of mind, personality, and the patience of research to achieve this.  Perhaps that leaves us layman needing to seek out different writers with different strengths and different points of view.

*I have tried (feebly) to read Braudel and failed on multiple occasions.  How he gathered his research, how he had the patience to do so, is beyond me.  I do think, however, that while his methods have much to commend them, writing history without focusing on people seems too clever by half.

If you were like me you grew up thinking that math stood as the most obvious, least abstract, and therefore most inherently “atheistic” of the disciplines.  Literature involved interpretation, who knows what happened in the past with History, but math was always math, brutal, hard, and cold.

Long after my last math class I found out that in ye olden days, Greek philosophers considered math the most inherently religious of the disciplines.  It involved, after all, abstractions, universals, unchanging reality, and perfection, the very things inherent in the spiritual realms.  After the Greeks, some of the greatest mathematical advances came from deeply religious people like Pascal and Newton.

A strength of Naming Infinity, by Loren Graham and Jean-Michel Kantor, is that it looks at some of the deepest questions about the truths in Math through one obscure group of people at the turn of the 20th century.  In Russia at that time a group of monks arose who engaged in a practice called Name Worshipping.  The roots of this practice go back to the “Jesus Prayer” prevalent in Eastern Orthodox spirituality, where a person repeats the prayer, “Lord Jesus, have mercy on me a sinner” continually to achieve greater spiritual awareness.  Name Worshippers went further, believing that “the Name of God is God.”  The name of God contains His character, so speaking the name of God revealed God Himself.

The church labeled this practice heretical.  God’s name stands for God Himself to be sure, but the church’s  main criticism of this practice stemmed from the seemingly “magical” qualities the monks attributed to the name itself.  And of course, since the name of God gets rendered differently in different languages, it could open up the charge of polytheism.

Naturally the monks accused of heresy had good arguments in their defense, denying that they believed literally in the divinity of the letters or sounds themselves.  Rather, the name of God stood as the most important signifier of divinity in the world (the idea of “signs” would prove to be a link to mathematical innovation). The book frustrates somewhat on this topic, because although this so-called “name worship” will have an indirect link to the story the authors tell, it gets dropped early in the book.  Still, the authors are not Church historians or theologians, and probably rightly step out of the way of an issue they wouldn’t understand well.  This is one weakness of the book — the authors introduce an esoteric and unfamiliar concept and then drop it for the vast majority of the story.

The real root of the book deals with a mathematical and not a theological controversy (though theology remains indirectly involved in the story).  On one side we had the French, who stressed “continuity,” the idea that to get from one mathematical point to another, one must pass through all intermediate points.  Math then, is a closed system, a measurable system, where numbers have a concrete reality that cannot be manipulated.

Russians occupied the other side, the more interesting one for me.  They stressed “discontinuity,” or the idea that reality is not as set in stone as we think, and thus, reality can be manipulated.  We can call reality into being through the creation of numbers, or sets of numbers. In the west at this time determinism held sway over many scientific and mathematical minds.  A Russian priest and mathematician, Pavel Florensky, led the opposition to this school of thought.  He preached discontinuity in all fields, not just in math.  Here the book frustrates yet again, for they back off from going into any real detail linking mysticism and math.  I think the central idea of the Russian school had to do with the concept of naming sets of numbers (linked to set theory), and hence the connection to the heretical school of Name Worshippers.  To quote the authors,

To take a simple example, defining the set of numbers such that their squares are less than 2, and naming it “A,” and analogously the set of numbers such that their squares are larger than 2 and naming it “B,” brought into existence the real number the square root of 2 (emphasis mine).  Similar namings can create highly complex new sets of real numbers.  . . . When a mathematician created a set by naming it, he gave birth to a new mathematical being.

If math dealt with more than finite possibilities, then “real reality” too had to be more than just finite.  The connections of math with religion become obvious, as creation happened in Genesis 1 via the Word, via naming (this idea is present in Egyptian texts as well).

Freed from normal approaches to mathematical questions, the Russian school made key advances in math.  They also taught in new and unusual ways.  One student recalls that,

Luzin would start from the outset by posing to his students who were hardly out of high school problems of the highest level, problems that stymied the most eminent scholars.

The authors add,

One characteristic of the Russian school stood out — the conviction of the best Russian teachers that the most fruitful attack on problems was direct and straightforward, without any preliminary, long, and heavy reading.  In other words, start from scratch.  By doing so one got an almost physical feeling of being directly in contact with mathematical objects and experienced the sensual pleasure of having to fight intellectually with one’s bare hands.  One of the great mathematicians of the time, Israel Moisseivich Gelfand, “We should study this topic before it has been tainted by handling.”*

Here we sense the mystical side of math where one bypasses “matter” to get right in touch with “reality.”  It sounds thrilling, but I don’t understand it.  I never was any good at math, but this sounds appealingly very little like the math I had in high school.  But one also might sense its weaknesses.  The great Luzin (mentioned above) would sometimes brag that he “never solved equations anymore.”  That is, math resided for him not in reality, but perhaps in some gnostic fairy world.  Math need now always have a direct physical application to have value.  The training of the mind itself has great value.  But math must, I think, have some “physical” applications to root us close to the Incarnation.

But though I found the book oddly structured, and though it bounced around too much from topic to topic, the book has great value in exposing western laymen like myself to a whole new way of thinking about math, and about reality itself.

Dave

*This whole approach reminds me of Dostoevsky’s theories on reality as it applied to gambling.  In his story The Gambler, it seemed to me that he thought the interaction of the human will could influence the games played.  It was never about mere statistics.  Likewise, I had a friend who swore that he developed a “system” to win on roulette, which seems like a game one must lose if played for any length of time.  Yet he assured me that over the course of more than a year, with 10+ trips to a local casino, that he had come out ahead $880.

Many of us know the anecdote of the composer with the rebellious son who could always annoy  his father by playing an incomplete scale on the piano.  No matter what occupied the composer at the time, he would go to the piano and complete the scale himself.

True or not, the story testifies to our need for completeness.  Reading Charles Hill’s Grand Strategies: Literature, Statecraft, and World Order made me think of this story, but with a slight twist.  I imagine Hill at the piano playing a complete scale, but with the last note much quieter than the others.  It’s there, but so faint that one would feel bound to go the piano and play the final note at its proper volume.  Meaning and wholeness requires balance, symmetry, and perhaps also, a strong finish.

Hill had a long career as a diplomat that spanned the Cold War and beyond and so has authority to speak on his subject.  What drew me to the book was his idea that good diplomacy went far beyond political science theories of realism, idealism, and the like.  Good diplomacy requires good literature, which touches us in areas beyond politics.  Problems in diplomacy arise when we seek mere political solutions to political problems.  As in C.S. Lewis’ “First and Second Things,” one only gets political solutions by basing them on something more foundational.  Hill believes that great literature gives us the foundations for real wisdom, and thus, real understanding of problems.  He quotes Henry Kissinger towards the end of the book, who said,

I put a proposition to you all: we have entered a time of total change in human consciousness of how people look at the world.  Reading books requires you to form concepts, to train your mind to relationships.  You have to come to grips with who you are.  A leader needs these qualities.  But now we learn from fragments of facts.  A book is a large intellectual construction; you can’t hold it all in your mind all at once.  You have to struggle mentally to internalize it.  Now there is no need to internalize because each fact can be called up instantly on the computer.  There is no context, no motive.  Information is not knowledge.  People are not readers, but researchers, they float on the surface.  Churchill understood context.  It disaggregates everything.  All this makes strategic thinking about the world nearly impossible to achieve.

Hill impressed me with the idea behind his book, and he displays a wide knowledge of western civilization’s literary heritage.  Many times I marked pages where I gained fresh insight and had my perspective challenged, but in the end the book left me frustrated at the missed opportunities Hill leaves on the table.  He conveys the message that great literature helps us understand the world and ourselves, but this note strikes me as far too wimpy and obvious given what the book could have achieved.

As Kissinger mentioned, statesmen should prioritize context.  Hill does a good job with this in his section on ancient literature.  He weaves in Aristotle’s assertion that the family gives the state its foundation, and then looks at the Illiad and the Odyssey, which have marriages at their center.  He fans out to Aeschylus, whose Oresteia  trilogy has the breakdown of family bonds nearly destroy the state.  He traces this up through De Tocqueville, who saw family, and especially women and mothers, as bulwarks of the familial stability needed for any state.  But democracies in particular need family stability due to their decisive emphasis on individual rights.

So far so good — my eyes got opened to a theme that unifies so many different thinkers across time.  But Hill draws no conclusions from this, he has no application.  He has no stories or anecdotes about how this insight helped him, or how it can help anyone else form a “grand strategy.”

Hill makes the importance of context brilliantly in his section on Walt Whitman.  If we know the opening lines of the The Illiad  and The Aeneid Whitman’s, “I sing the song of myself,” suddenly strikes one like a thunderclap.  We see that Whitman means to destroy, or perhaps remake, the whole concept of epic literature.  His exaltation of the “eternal now” of the individual has an enormous impact on how Americans think of themselves. You, the I, are now the epic, which brings us right up to social media today.  But again, to what end?  Hill hints at the potentially destructive impact of Whitman’s attempts to make the past obsolete, but never draws out the consequences for American diplomacy.  Many Europeans argue, for example, that Americans act rashly without proper understanding of context and history, but Hill never addresses this.  But now not just Americans, but much of the western world appears ready to formally and radically redefine the concept of marriage and family.  What will this mean for our diplomacy as a nation, especially in sensitive areas of the globe that reject this redefinition as blasphemy?  Hill compares the hopeful message of the Oresteia with American Eugene O’Neil’s recapitulation of the same themes in Mourning Becomes Electra.  O’Neill rejects Aeschylus’ hopeful conclusion.  Why, and to what end?  Again, Hill offers us nothing.

For someone so adept at drawing conclusions based on texts, and for someone so experienced in putting forth ideas and proposals, I cannot believe he lacks the ability to make grand strategic pronouncements.  But Hill plays it very close to the vest and misses a great opportunity to share whatever wisdom he has.  His great specific insights never come full circle.

Similarly, Hill frustrated me by never questioning the logic of the state itself.  He has high praise for the Peace of Westphalia, which in his view ended the cycle of violence from religion and clan and created the state.  This parallels what happened in the Oresteia and the symmetry appeals to Hill and to myself.  But has the state in fact limited violence?  Maybe it has, but it should not be assumed.  What problems come with the creation of states?  Aeschylus assumes the good of the state as almost a given, but that’s understandable given his medium.  Aeschylus also lived in one of the great golden ages of civilization, and the state no doubt shone brightly in its virtues in his lifetime.  Hill has no such restrictions of medium, and has the benefit of the hindsight of history.  He should have done more.

Hill tantalizes in doses.  The individual notes he strikes promise much.  But he fails to deliver on the promise of his title.

In 1893 Frederick Jackson Turner changed our study of American history with a speech to the American Historical Association entitled “The Significance of the Frontier in American History.”  His talk helped propel him to national prominence.  But naturally all that attention also made him a target for criticism.  In his speech Jackson proposed that the concept and reality of the frontier had done more than anything else to shape American history and American consciousness.  As the frontier disappeared in the late 19th century, he argued we might expect to see a new phase in our national development.

Jackson begins his speech by defining the frontier as the boundary between “savagery and civilization,” and states that the American frontier differentiates itself from other places by lying at “the hither edge of free land.”  In the days of earliest settlement in the 17th century, the east coast formed the frontier of Europe.  Then, as our national identity took shape, areas in the west became our own frontier.

While initially the French rather than the English engaged in the most direct trading with Indians, Turner argues that the trading trails themselves inevitably drew English colonial civilization westward.  Trails to sources of salt (used as a preservative) then assumed vital importance, leading to a still more inexorable march of civilization.

But the frontier did more than this, serving as the first real “melting pot” in American history, long before the wave of 19th century immigration.  In short, frontier expansion created the first sense of “composite nationality,” the first sense of what it meant to be American as opposed to European.  One could have the north and the south at odds, but “the west could not remain sectional.”  Of course this new sense of national identity led to a new political identity.  Turner claimed that, “this nationalizing tendency of the West that transformed the democracy of Jefferson into the national republicanism of Monroe and the democracy of Andrew Jackson.”

Perhaps most crucially, the frontier had a decisive impact on the growth of democracy.  Turner cites several examples of how frontier/western sections of colonies and states continually pushed a progressive agenda, especially in terms of expanding the right to vote.  Turner quotes from one early 19th century representative from western Virginia who spoke in Congress,

The Old Dominion has long been celebrated for producing great orators; the ablest metaphysicians in policy; men that can split hairs in all abstruse questions of political economy.  But at home, when they return from Congress, they have negroes to fan them to sleep.  But . . . a western Virginia statesman, though far inferior in logic and metaphysics and rhetoric to the old Virginia statesmen, has this advantage, that when he returns home he takes off his coat and takes hold of the plow.  This gives him bone and muscle, sir, and preserves his republican principles uncontaminated.

This may give us a clue as to why we never had any success regulating frontier expansion.  We attached the frontier so strongly to our national identity that to go without a frontier meant repudiating ourselves.  Or perhaps, as Turner suggests, the frontier functioned as a “safety valve” for the landless, the immigrant, the economically distressed.  Without this, democracy might tend towards eating itself from within.  In the absence of an external threat or safety valve, Turner surmised that democracy might turn into a mere vehicle for discontent.  The self-reliant virtues that made us great would weaken us when we turned inward.

Turner’s essay raises this crucial question without answering it — can democracy survive without a frontier?  Rome’s history suggests it, as do the words of Alcibiades when he urged Athens to attack Syracuse:

Nicias must not divert you from your purpose by preaching indolence, and by trying to set the young against the old; . . . The state, if at rest, like everything else will wear herself out by internal friction. Every pursuit which requires skill will tend to decay, whereas by conflict the city will always be gaining fresh experience and learning to defend herself, not in theory, but in practice. My opinion in short is, that a state used to activity will quickly be ruined by the change to inaction; and that they of all men enjoy the greatest security who are truest to themselves and their institutions even when they are not the best.

There exists however, the opposite theory.  Some argue that the rapid expansion of republics, and not their “rest,” that leads to a “time of troubles.”  In the example above, for example, the Athenians did not rest, did attack Sicily, and this led to catastrophic disaster.  Or we might bypass the question somewhat and declare that the problems experienced by Rome and Athens are human problems and not particular to democracies.

In any case, this question needs further thought.

The introduction to the essay explained Turner’s influence, and also his critics.  I have no problem with such a bold idea as Turner’s drawing criticism.  This is the purpose of bold ideas — to inspire conversation.  What I have a problem with is the nature of some of the apparent objections.  Some complain that Turner should have devoted more study to the period after the closing of the frontier.  But this seems silly.  He studied one particular period, and not another.  Not studying the time after the closing of the frontier doesn’t mean his ideas are false.

Some complain that Turner overlooked other factors in America’s growth.  “You never mention southern agrarians or eastern capitalists!  For shame, Turner, for shame!”

I can’t stand these kinds of objections.

Turner only claimed that the frontier explained the heart, not the whole body.  To say, “You never mentioned southern agrarians” is entirely without meaning, unless one means to say that Southern agrarians form the key to understanding America.  Otherwise all you’re doing is whining that someone didn’t say something about your own pet field of study.  It’s not an argument.

We should do better than this.

I also mistrust the argument that no “heart” of American history can be found at all.  In this vein, Turner’s thesis is false by definition, and again, not proved wrong via an argument.  This declaration sounds like a rejection of History itself.  Such people may be old and grumpy long before their time, or perhaps they resent the mere effort of trying in the first place. For if those that try to find meaning happen to do so, others who reject it might feel threatened.  Such people would appreciate Homer Simpson’s advice . . .

I think any biographer of Pascal has a difficult task.  Brilliant, ill, and aristocratic, Pascal lived much of his life up in his head.  The Abbe Jean Steinmann does a passable job with his life, though I found myself bored at times and skipped or glazed over portions of his work.

I do give Steinmann credit, however, for bringing out some of the remarkable aspects of Pascal’s mind.  The 17th century witnessed an intellectual explosion that has no equal afterwards.  A list of intellectuals from that time still should dizzy us — Newton, Descartes, Hume, Hobbes, Galileo, Leeuwenhoek, Boyle — the list could go on and on.  We talk flippantly about the “pace of innovation” today and yet surely we can’t begin to hold a candle to that era.  While I have no familiarity with most of the names on the list of 17th century notables, Pascal stands out to me as the most passionately Christian of the lot, and he was no slouch with math either.  He invented the calculator and gets credit for advances in projective geometry and probability theory.

Having not read it all, the book gets no full review, but it did inspire a few thoughts. . .

• Euclid

Euclid had a profound impact on Pascal’s early life.  One might almost say Euclid “inspired” him.  Euclid got Pascal to see the world and use his mind in wholly new ways.  I know that Abraham Lincoln also had a similar experience with Euclid.  When we consider that every major intellect probably from the Renaissance onwards cut his (or her) teeth on Euclid, we might surmise that perhaps only Plato and Aristotle have had more influence from the ancient world.

And yet, for whatever reason, Euclid has fallen off the face of the earth.  Why do we not use Euclid for geometry classes?  The answer is likely not, “Well, modern geometry texts hold the students attention much more effectively.  They’re more exciting, more memorable.”  Chronological snobbery probably has something to do with it.  Some might add that geometry has advanced beyond Euclid and we have new ways of approaching the subject, thanks to thinkers like Descartes and Einstein’s.  But (in keeping with Jacques Maritain’s dictum) the only way to fight against the tradition is to first know the tradition.  In my own math education I had never had a whiff of the story of math, or knew how anyone in the past solved any problems.  For me math meant memorizing formulas.  Contrast this with Steinmann’s description of how discovering, on his own, how the angles of a triangle must equal 180 degrees changed Pascal’s early life.*

• Math and Theology

Over the last few years I have often heard comments like, “We should learn to read the Bible as literature,” or “We must learn to see the poetry in theology.”   I concur with both sentiments and applaud the drift away from viewing Scripture as a list of isolated proof texts.  But I never hear how math or science should impact our theological thinking.  Some use science to “prove” aspects of the Bible, but I have yet to hear someone show how thinking “mathematically” can help you think theologically.

This is unfortunate, and perpetuates misperceptions about math and science.  If God invented both literary and scientific minds surely both lead to him, not just in the details, but in the “big picture” as well.

Enter Pascal, whose wonderful imagination (good for lots of things besides literature) led him to make theological conclusions based on his genius for math and science.  Pascal argued for the idea of vacuums, against much of the establishment of his day.  But he took the issue further, arguing for the infinite divisibility of matter, which then became a springboard for the proper place of reason in faith.  We see him use math in other ways, such as the “spiritual perfection” of numbers showing the fallenness of the world.  For Pascal some things are simply just self-evident and beyond reason, but his “math sense” led him to these ideas.

Whatever we think of some of Pascal’s conclusions, if we taught math as Pascal learned it, I think we would see math and science rejuvenated, and our theology enriched.

• Dominion

Pascal’s illness meant that he lived only a few short years after starting to take his faith seriously.  We need not call it a “conversion experience,” but clearly Pascal had some kind of experience in the last few years of his life that intensified his faith and changed his life.  Some see Pascal rejecting reason, math, etc. in his latter years.  I wouldn’t go that far — I would say that Pascal may have been going through a recalibration period that tragically got cut short by his death.

I wrote elsewhere about the concept of dominion and I will try not to repeat myself too much.  The Pensees have brilliant insights, but they lack a fullness that you see in more mature Christian thinkers (granted, of course, that it was very much an unfinished work).  Pascal’s brain (and his heart) burned at fever pitch.  I don’t blame Pascal for this.  Had he lived longer I’m sure he would have written something monumental and deep.  As it is, of course, the Pensees are a classic, but Pascal did not have enough distance from math and reason to welcome it back fully into his thought, this time in the proper place.  For example, he wrote that, “Curiosity is only vanity. We usually only want to know something so that we can talk about it.”  Surely this is too harsh.  Those who want to talk about their discoveries might do so mainly with the intent of enjoying them further, for enjoyment increases when we share it.  Pascal seems a bit too jaded, a bit too sure of himself as a “new convert,” and this portrait of him shows that he may not have been at home with himself either.

But all in all Pascal’s life should strongly encourage the right brained that yes, they can do more than defend Creation by design.  Their mathematical insights can give rise to profound truths about the world.

*Alas, Steinmann fails to mention how Pascal did this, just that it happened.  Maybe he expects us to figure it out on our own, like Pascal.

^ Some great quotes from Pascal . . .

All of humanity’s problems stem from man’s inability to sit quietly in a room alone.

When a soldier complains of his hard life (or a labourer, etc.) try giving him nothing to do.

The heart has its order, the mind has its own, which uses principles and demonstrations. The heart has a different one. We do not prove that we ought to be loved by setting out in order the causes of love; that would be absurd.

Knowing God without knowing our wretchedness leads to pride. Knowing our wretchedness without knowing God leads to despair. Knowing Jesus Christ is the middle course, because in him we find both God and our wretchedness.

Jesus is a God whom we can approach without pride and before whom we can humble ourselves without despair.

Man is to himself the most wonderful object in nature; for he cannot conceive what the body is, still less what the mind is, and least of all how a body should be united to a mind. This is the consummation of his difficulties, and yet it is his very being.

Man is equally incapable of seeing the nothingness from which he emerges and the infinity in which he is engulfed.

We know truth, not only by reason, but also by the heart.