The Decline of Scholasticism and the Rise of Humanism: Late Medieval Thought and the Coming Renaissance

That Scholasticism was the primary mode of academic discourse in the medieval university system is an understatement. From the early 12th till at least mid 14th century, it was the only system within which reputable scholars and academics aired their ideas and theories. Just as the Church held a spiritual monopoly over Western Christendom, so too did Scholasticism, combined primarily with Thomist philosophy, hold sway over the scholarly mind, and this entrenchment, over time, led to a gradual erosion of original thinking until by the mid-14th century a serious crisis of stagnation entered Western thought. As we have seen, the "Latin Averroists" along with Albertus Magnus and Thomas Aquinas managed to propel Aristotle to the forefront of the philosophical dialogue, and even though his ascension hit numerous snags along the way (being banned in 1210 and severely restricted in 1231), his preeminence, especially among the Dominican order and its followers, became obvious by mid-century. The inertness of learning did not come about purely because of the rigidity of the Scholastic method so much as by the tyranny exerted over the minds of the period by an authority which was never to be contradicted. Numerous scholars spent decades systematizing and synthesizing Aristotle's works until at last a body of ideas existed that held up both the revealed truths of the Church and the observed truths of nature. But nobody is perfect, and chinks began to appear in The Philosopher's armor as scholars began to find out that the ancient scholar was not always correct and some ideas could still be interpreted, even in spite of the synthesis, as heretical. It became evident that new paths of knowledge had to be explored if any advancement could be made. What was to result over the course of about a century and a half were two dynamically different modes of thought: one which sought to divorce faith and reason and one that brought a more secular and more humanistic approach to Western philosophy.

The status of "mandatory" conferred upon Aristotle in 1255 was to be a short-lived one despite the fact that his works were now readily accessible and nearly sacred in Western Christendom. While Aquinas had been rather reserved in his application of Aristotelian logic to Christian theology, some near contemporary scholars dared to go further, stating that Aristotle's philosophy proved such diverse ideas as the unity of all thought, coalescing in a godhead (such as Siger de Brabant, 1235-1282) and the idea that the individual soul was not immortal but that all souls merged into one upon death (Boetius of Dacia, 1230-1285). The next major test of the Aristotelian corpus came just 22 years later in 1277 when more charges of heresy came up relating to Aristotle's work. However, this time it was not the Philosopher himself, but merely his works that were to be held up for scrutiny. Rather than putting a blanket ban on him, Pope John XXI commissioned the Bishop Etienne Tempiers of Orleans to review Aristotle's writings and bring to his attention any precepts that specifically contradicted the Holy Scriptures. Fortunately for Tempiers, Thomas Aquinas had completed his great compilation of Aristotle fewer than four years prior. In less than six weeks, the bishop brought forth no fewer than 219 propositions which he claimed should be banned. These were taken into consideration by the Pope, and he upheld Tempiers' findings. This prohibition, unlike the one of 1210, would not be as far reaching and ended up applying only to the University of Paris. Many other universities used this to their advantage and several attracted students who would otherwise have gone to Paris, boasting that their university still allowed his teachings. Still, the effect was that some of Aristotle's thoughts would be forever tainted with a brand of heresy and scholars would have to tread into Aristotelian waters at their own risk. And in spite of the ban, the University of Paris continued to be the foremost theological school in Europe. Far from being an inhibition on the minds of medieval scholars, it turned out to be a blessing in disguise, as the hold this philosopher exerted over them began to give way to a more open-ended way to reach new realms of knowledge.

One such way that this new academic freedom led the learned was in the direction of skepticism. This was not so much skepticism in the modern sense as it was in the a skepticism specifically of the entire enterprise of Aristotelian synthesis. Several major thinkers of the late 13th and early 14th century attempted to scrap Aristotle altogether, hearkening back to more Augustinian and Platonic notions of the self, the soul, and the metaphysical nature of the universe. John Duns Scotus (1266-1308), for example, claimed that since the human being was a perfect being made imperfect through sin, we could never truly trust our senses empirically, thus, the only sure path of knowledge was faith in revealed scripture. This did not , as some have suggested, mean that Duns Scotus advocated a complete denial of reason, but that the sphere of reason had no place being used in the arguments raging in the theological arena. This mode of thought was particular to the Francisan order, which found its philosophical inspiration from the likes of Augustine and the Middle Platonists rather than Aristotle and the Averroist, but by the early 14th century, the gap between faith and reason was certainly widening.

It was William of Occam, however, who put together a coherent argument against the use of the Scholastic method, and his critique attempted to completely overturn the technique of linking theological premises through reasoned analysis. Scholasticism had been about plurality--combining multifaceted and disparate ideas into one congruous form. Occam turned this philosophy on its head, stating that "plurality need not be posited without necessity." He viewed all of this reconciliation as unnecessary and posited that Scholastics relied on too many assumptions to link between Aristotle to Scripture. The best theory was the one that required the fewest amount of leaps in logic to validate it. This very simple yet profoundly powerful thesis was an enunciation of what would come to be called "Occam's Razor" or "the law of parsimony." According to Occam, the simplest explanation was always the best one--and of course, for Occam, the simplest explanation for nearly every tenet within the Aristotelian corpus was that God was in control of all action. Occam promoted the idea of the absolute power of God at the expense of almost any other reason-based explanation. This was the greatest affront to Scholasticism in that Scholastics, at their core, believed that one could through reason become closer to God. Occam did not deny the importance of reason, but stated, as Duns Scotus and others had, that it had no place in theology. This is an essential divorce between faith and reason that is still with us to this day, though it would not reach its full peak until the Scientific Revolution. The great irony of Occam's most lasting contribution to philosophy is that, today, the premise of Occam's Razor is often used to disprove the existence of God.

But what of the other direction philosophy was heading during the close of the Middle Ages? For all their differences in opinion, Duns Scotus and Occam, the two most towering figures of the early 14th century, were essentially still working within the Scholastic framework. The modes of thought that would begin developing to the south in Italy, laying the seeds of the Renaissance which would unleash itself upon Europe beginning in the 15th century, were trending in an entirely different direction. Philosophy in general was losing a great deal of consistency in the Later Middle Ages, as it was interrupted by what Barbara Tuchman has called the "calamitous 14th century" which was racked by peasant revolts, religious upheavals, a sharp rise in mysticism, the long and bloody Hundred Year's War, and most of all the Black Plague. The unity of the previous few centuries was long gone and people seemed to seek comfort and consistency in a plethora of areas. What happened in Italy is a subject for another philosophy lecture, but in many ways its roots are firmly planted in the Middle Ages. In terms of philosophy, there is one figure that truly stands out as the early Renaissance champion of a new secular and humanistic outlook on life: Francesco Petrarch (1304-1374).

Petrarch very quickly became disenfranchised by contemporary university professors who insisted on reading the glosses and commentaries of ancient texts as if they were the equal of the original and he complained that the eloquence of the original Latin and Greek (though he knew no Greek) were too muddied and vulgarized by the later writers. By simply asserting that the original texts be held in the highest regard and by demanding access to the unadulterated ones (as much as was possible) Petrarch began the process of rediscovery for which the coming period was named. This was a literal rediscovery: Petrarch became a papal secretary and physically scoured libraries across Europe looking for old and long forgotten texts--and for this, he is thought to be personally responsible for the discovery of no fewer than 10 histories of Livy, several orations of Cicero, and at least one text of Archimedes. What resulted was a much more human-oriented philosophy that emphasized a study of the arts and humanities in their original form, a rejection of the authority of the universities (including Aristotle), and the individual freedom of scholars to discover at will. It is also at this time that the first recorded uses of the term "Middle Ages" appears to describe the preceding period (from medium aevum, Latin for "in-between-age," coined in the early 1400s by humanist scholar Flavio Biondo). This was a disparaging term, implying that the thousand years "in between" the fall of Rome and the rebirth of its cultural, literary, and philosophical greatness in 15th century was essentially a time of little importance and learning. But, of course, the Middle Ages, though crude, were hardly "dark" and the illuminating light of academia shined on even in difficult times. And the modern word, thought to be so influenced by the humanism and secularism of the Renaissance, was in a very tangible way, influenced as much as by the Medieval period as those which followed it.

The Aristotelian Reconciliation: Albertus Magnus and Thomas Aquinas

The primary goal of 12th and 13th century Scholasticism was to reconcile the natural philosophy of Aristotle with revealed truth of Christian scripture. The impact of Christian thought on the philosophy of the Middle Ages need not be mentioned, for not only was it the most important in terms of influence, it was indeed the entire framework within which medieval philosophers perceived the world. However, beginning in the early 12th century, a new force which had hitherto been unknown or at least obscure enough to escape the notice of all but those scholars lucky enough to have access to his work, began to exert its influence on Western thought. Much like the Bible, Aristotle needs no introduction and if the specifics of his philosophy do not precede him, his reputation does. Throughout the course of the 12th and 13th century, he would become so popular and so emulated that he came to be known simply as Ille Philosophus, "The Philosopher," and this is in large part due to the works of Albertus Magnus and Thomas Aquinas, who were able to resolve many of the differences between and synthesize both the corpus of Christian thought and the writings of the ancient thinker.

The path from obscurity to ubiquity for Aristotle's works in the Middle Ages was an arduous one and more complex than can be attempted here, but we may briefly track its movement. Aristotelian philosophy, like most other intellectual pursuits, gradually faded from the collective consciousness of Western Europe following the fall of the Roman Empire as there was a general dearth of scholars to carry on his work and the more academic nature of his writings did not lend itself to study in the generally difficult life led by most from 500-1000 CE. As we have seen, there were areas where his works were preserved: Boethius' translations formed the backbone of later Latin translations and copyists and scribes in the British Isles and in the Byzantine Empire preserved a fair amount in later centuries as well. But likely the greatest location for the preservation of Aristotelian knowledge was the Islamic world, which, if the Appropriation Theory is correct, managed to add to and improve. The greatest of these was the mid-12th century Muslim Spaniard Averroes (Ibn Rushd), who is often regarded as the founder of secular thought in Western Europe. Among Averroes' many accomplishments include his massively influential commentary on the writings of Aristotle, written in 1160, in which he simplified and summarized Aristotle's philosophy, made editorial comments on them to elucidate their oftentimes difficult concepts, and attempted to tease out the meanings behind Aristotle that may be conciliatory to the Islamic religion. What resulted was a sort of medieval Cliff's Notes version of the works of Aristotle that were read across the Islamic world and soon found their way into the hands of eager European scholars. Averroes was so influential that, for a time, Scholastics who were engaged in the process of synthesizing Aristotle with Christianity were known as Averroists.

To Medieval scholars, the most important ideas to be found in Aristotle's works were the ones related to metaphysics and natural philosophy. While too broad to detail here, some of his more notable theories include the concept of the four element (earth, water, air, and fire) composition of matter and their correspondent qualities, humors, zodiacal signs, etc.; the idea of nature as a "plenum," meaning that one could not reach the smallest portion of matter (the word atom comes from the Greek a tomos meaning "uncuttable"); the sphericity of the earth and the cosmos and the idea of a "natural place" for all elements (earth sank to the center, water on top of it, air rose above these two, and fire ascended to the heavens); the perfect circular motion of heavenly bodies and the difference in the nature of physics below the orbit of the moon (the sublunar sphere) and above the orbit of the moon (the supralunar sphere); and the logical hierarchy of "causes" in nature, among many, many others. It became clear early on, that not all of Aristotle's ideas meshed well with Christian doctrine, but Aristotle's authority was already too great and religious figures of the day likely could not have passed laws forbidding his teachings if they had wanted to. But try they did: in 1210 in Paris a council of bishops forbade the teaching of his works in the French university system and in 1231 in Rome Pope Gregory IX ordered a "clean-up" of Aristotle's works so they would become more palatable to medieval Christian sensibilities. The most notable of "The Philosopher's" beliefs that disagreed with Christianity included his assertion that the cosmos was eternal and had no beginning or end (this denied the Creation as well as the Apocalypse), that the soul and the body are interminably linked (this denied the immortal soul and the prospects for salvation and afterlife), and that miracles were impossible (this, of course, denied God's will). This is where Albertus and Thomas Aquinas enter the picture.

Albertus Magnus (c. 1200-1280) was a German Dominican scholar who was the first to attempt a Christian synthesis of Aristotle's ideas utilizing the same format as Averroes. Albertus, who would later be made a Doctor of the Church (one of only 33 people to hold this title in history), had a lifelong thirst for knowledge that never seems to have been satiated and ranged from theology and philosophy to alchemy and astrology, physics and metaphysics to metallurgy and phrenology. During his lifetime, he managed to compile the majority of Aristotle's known works, make insightful comments upon them as they related to the Christian world view, and preserve his work in a relatively complete form upon which later scholars could draw. However, Albertus is generally considered to have failed in truly creating a systematized Aristotelian corpus which could pass muster among the Church powers who insisted on a thoroughly Christianized philosophy. Albertus' greatest contributions to history were not to be his writings on Aristotle but his advocacy of an experimental method and of a compatibility between science and religion--perhaps broader realizations of his attempts with Aristotle. It is fitting that the scholar who succeeded in this more specific and more laborious task was Albertus Magnus' greatest student, Thomas Aquinas.

Thomas Aquinas (c. 1225-1274) was originally from the country-side around Naples and the son of a minor noble who wanted Thomas to enter a Benedictine monastery as his uncle had done. Thomas' early education was at the state-sponsored University in Naples where he developed an early interest in theology. He was more receptive to Dominican ideals as they had placed a greater emphasis on empiricism and rationality and this eventually led him to Paris where he received instruction from the imminent Albertus Magnus. Where Thomas was able to succeed his master's failures was in the great organizational capacity and originality in his thinking. Thomas regarded Aristotle, not necessarily as an ancient pagan philosopher, but as a brilliant thinker who had the Christian-perceived misfortune of being born before the salvation of Christ. And he viewed Christianity not as an island of meaning, new and disparate from other philosophy, but as a completion and fulfillment of the knowledge originally, if only partially, realized by Aristotle. Aquinas was the first to distance himself from the Augustinian viewpoint of deduction: Augustine had explained everything by taking what was known universally (the existence of God, the salvation of Christ, the path to Heaven, etc.) and derived particulars from this. Thomas, on the other hand, using the quintessentially Scholastic tool of reason, began with what could be discerned rationally among particular cases (a particular murder being evil, arriving at a conception of God after reviewing his individual creations of plants and animals, etc.) and used these to arrive at universal conclusions. His verdict on Aristotle was, essentially, that reason and faith, being separate but complementary, could be used in service of one another--reason had helped Scholastic philosophers arrive at proofs and arguments in favor of the existence of God, and faith was now being used to contend that, as far as Aristotle's natural philosophy was concerned, it could not truly contradict revealed truth if the validity of his ideas were discovered in nature. For was not nature the very dominion of God and the expression of His will at creation? Aquinas would follow Aristotle very closely in this respect, and this would lead him on the path to reworking most of the Philosopher's ideas under the illumination of the light of Christianity.

His greatest work in this endeavor was his Summa Theologica, which would contain the entirety of his new philosophical system. Written between 1265 and 1274, it argued nearly every major point of Christian theology with appeal to reason, including especially the existence of God; the Creation; Man and his purpose; Christ and His life, death and resurrection; and salvation. The work is especially known for its enunciation of "The Five Ways" or quinquae viae, five arguments for the existence of God that have a certain Aristotelian ring to them. The first of the Five Ways can be, and has been, read as the most astonishing example of Aristotelian reconciliation in particular and with Scholastic logic in general. The First Way reads, "God is simple, without composition of parts, such as body and soul, or matter and form." Aristotle had, as we have seen, argued for the eternity of the universe, but had conceded that if there was a beginning, it would necessitate the existence of a "prime mover" or a "first cause"--something that got the ball rolling. Aquinas linked these ideas thusly: To cause change is to bring into being that which had hitherto not existed and this can be done only by something that already existed (as fire is needed to cause burning in matter); a thing causing this change must remain constant itself during the change if the result is to be constant; therefore anything in the process of changing was caused by something prior to it; there must be a terminal point as there will be no original cause of changes if we do not; this first cause must be God. These words are essentially Aristotle's, with the phrase "prime mover" changed to "God." This is Thomist Scholasticism and Aristotelian reconciliation at its finest.

Thanks to Aquinas, not only was Aristotle reinstated in the European university system in the Middle Ages, it was made mandatory in 1255. His separation of natural philosophy from theology made the study of both easily compatible and this is viewed as a proto-attempt to reconcile science and religion. Aquinas himself, however, would leave his greatest work unfinished as he died while writing it in 1274. While celebrating Mass, Aquinas had a mystical vision which he would share with no one, but it obviously had a profound effect on him which changed him deeply. "I cannot go on," he said. "All that I have written seems like so much straw to me [mihi videtur ut palea] compared to what I have seen and what has been revealed to me." Aquinas died four months later. Modern observers believe he may have had a stroke or a nervous breakdown. Others that he received a mystical vision from God, providing him with an instant communion with the ultimate reality beyond logical comprehension, which no words could possibly attempt to describe. Whatever the case, even despite Thomas Aquinas' refusal to complete his opus, his new system of philosophy would dominate the remainder of medieval thought and would not find a replacement until the Protestant reformation 250 years later and the revival of Neoplatonism in the Renaissance. And he would almost single-handedly make Aristotle available for intellectual consumption on a broad scale for the remainder of the Middle Ages.

Science/Angels and Religion/Demons and Vice Versa, Part 2

The first problem in interpreting the relationship between science and religion as a war is that it simply ignores the history. Most people are familiar with the most infamous instances of religious persecution of scientific thinkers: Copernicus did not publish his heliocentric theory until he was on his deathbed for fear of the backlash, Galileo was sentenced to house arrest for asserting that the earth moves, Scopes was banned from teaching evolution in Tennessee in 1925, and so on. What is often not told about these stories is that, for the most part, they are the exception rather than the rule. From the fall of the Roman Empire to the rise of humanist Renaissance Italy and the later Scientific Revolution, most scholars involved in anything resembling natural philosophy were also members of the clergy. This is to some degree logistical, as only clerics in the Middle Ages had anything remotely resembling an education to give them the ability to pursue these topics, but nevertheless, the sole harborers of learning in the West during this thousand year time period were religious. Some anti-religious thinkers, such as Richard Dawkins , have suggested that this is simply because they had no other choice in their day, but I think the argument works better in reverse: that because they were religious, and clerical, their choice was to pursue knowledge. The greatest polymaths of the Middle Ages were not just theologians, but also natural philosophers, the closest cognate to "scientist" that existed before the Scientific Revolution (indeed, many scientists were still called natural philosophers as late as the 19th century). A great many supposedly "modern" innovations were rooted in the era when religion allegedly suppressed free thought with an iron fist: the experimental method employing empiricism and rationalism, differential calculus, tools precursory to those still used in modern surgery, the creation of the modern university and peer editing systems, and numerous practical implementations of contemporary technology like the compass, gunpowder, astrolabe, and sextant. This is not to say that the Medieval and pre -Scientific Revolution era was just like ours; it was obviously very different. The Christian religion--in its institutional, cultural, political, and folk varieties--permeated every aspect of medieval life. But it is just as equally erroneous to imagine that religious authorities actively sought to impede scientific progress anymore than they are attempting, or should attempt, to do now. The relationship has been muddied and is more complicated now, but there is no massive religious conspiracy (at least not one with any real power) currently vying to destroy the institution of science.

Once one digs a bit deeper into the hallowed lore of the history of science, particularly the episodes of individual persecution, one finds figures who have been more often than not castigated for theological and political transgressions rather than scientific ones or ones related to freedom of thought. Numerous astrologers in the Middle Ages were punished not because their practices were deemed anti-Christian or as some form of black magic; usually, they were punished because they foretold a future that was unpleasing to the ears and sensibilities of the nobles, kings or popes upon whom they commented. Astrologers often found themselves in the precarious position of interpreting a certain stellar portent to mean that the king would die near the end of the year. Despite being certain of their observations and mathematics, they were often reticent about releasing such information, since, even if it were true (from the medieval point of view), the ruler would not wish this information be made public as it could foment a rebellion or announce to his enemies that the time to attack his kingdom was now. Similarly, alchemists were often persecuted, not because of some religious admonition, but because if the alchemist succeeded in transmuting lead into gold it would ruin his sovereign's gold standard and create rampant inflation or debasement of the currency. These were practical political and economic issues, rather than the fear that Christian leaders would lose their grip on moral authority.

This was not confined to the proto-sciences either. An early and famous instance of the so-called religious persecution of science, came in the 13th century with the imprisoning of Roger Bacon, an English Franciscan friar and natural philosopher famous for, among other things, his works on optics and the refraction of light, detailed astronomical observation, and the anticipation of uses for gunpowder, microscopes, telescopes, and other inventions centuries away. He is also considered as one of the first Europeans to assert the primacy of something resembling the experimental method of science, derived from the likes of Plato and Aristotle, and filtered through Avicenna and other Arab commentators. The history of the man, intertwined with his advocacy of this modern-seeming notion, often contributes to the misunderstanding that he was imprisoned for experimentation in an age when true knowledge was thought to come from contemplation and revelation. This is, essentially, incorrect. The details of his crime and imprisonment are extraordinarily hazy, even by medieval standards. It seems that he was imprisoned at least for a short time, but some sources claim that it may have been up to ten years (based on the fact that he was away from University for that amount of time). But many modern scholars do not even believe he was imprisoned at all: Lindbergh says of Bacon that "his imprisonment, if it occurred at all (which I doubt) probably resulted with his sympathies for the radical 'poverty' wing of the Franciscan (a wholly theological matter) rather than from any scientific novelties which he may have proposed." The point is that, whether he was imprisoned or not, this simply cannot be construed as evidence of religion combating science. Giordano Bruno offers us another striking example. Often considered by less discerning scholars as the "first martyr for free thought," Bruno was burned at the stake, not by religious officials, but by the secular Roman inquisition in 1600. Though he is often known for his early championing of the heliocentric theory as well as for the infinity of the cosmos (which he, it should be noted, arrived at through philosophical rather than scientific reasoning), perhaps his best contribution to science was his work on spatial geometry. But why was he burned at the stake? For the heliocentrism? The geometry? Biographer Luigi Firpo lists his legal infringements as such: holding opinions contrary to the Catholic faith regarding the Trinity, Christ's divinity, the Incarnation, Transubstantiation, and Mass; believing in the plurality of worlds and the infinity and eternity of the universe; and believing in metempsychosis [reincarnation] and the transmigration of souls into other animals. Nowhere was the Copernican theory mentioned, and in fact, the Catholic Church had not even formed a coherent doctrinal opinion on the matter at the time of Bruno's trial. The plurality of worlds is the closest thing approximating a persecution of scientific ideas, but again, this was more a philosophical assertion than a scientific one, for both Bruno and his persecutors, in that a finite world with a definitive beginning (the Creation) and end (the Apocalypse) was doctrinal, and the eternity of the world (meaning universe) was considered erroneous. (This, by the way, had precedent, and was banned by the Bishop Ettiene Tempiers in the famous Aristotelian Prohibition of 1277, which forbade several teachings of Aristotle, including the eternity of the universe - for almost purely theological reasons.)


Most famous of course, was the trial of Galileo, the archetype, if ever there was one, for the story of the crushing hand of religion landing on an undeserving scientific mind. Most modern interpretations of the trial have cast a far more political light on the subject, and while even the most ardent supporter of the religious position cannot deny the humiliation foisted upon Galileo by the bearers of such trenchant dogma (Galileo really did have to recant on his knees and spent the remainder of his life under house arrest, unlike Bruno, for his Copernican weltanschauung), the political calculus inherent in the move is too indispensable in understanding the trial to leave out of the story. The fall of Galileo, according to historian Mario Biagioli , resembled "the fall of the favorite" in that his guilt was seen as a double indemnity of sorts, as Galileo had been among the greatest of his patron's thinkers. In seventeenth century politics, and especially in places without strong monarchs, like the principalities and city-states of Germany and Italy, artists, writers, and scientists, performed all of their work at the behest of a political patron whose financial support ensured the continued success of the lesser person. Galileo's general patron in his early years had been Cardinal Maffeo Barberini, later to become Pope Urban VII. It is possible that with a friend in high places, Galileo believed that he may have been able to escape retribution for publishing teachings contrary to the Catholic faith, which by the 1630s had developed an official opinion on Copernicus: it was OK to discuss his theory as a mathematical abstraction, but the notion that the earth physically revolved around the sun was a heresy. And it did not help matters that Galileo, in his groundbreaking opus majus Dialogue Concerning the Two Chief World Systems, put the Aristotelian/Ptolemaic system, of which Pope Urban VII availed himself, in the mouth of a character named Simplicio. While modeled after a sixth century commentator on Aristotle, the unfortunate connotations of the name did not endear Galileo to his former patron. As Biagiolo put it, it was "patronage dynamics" more than anything that did in Galileo.


The second, and I think more important, problem in interpreting the religio-scientific relationship is the simple fact that there are no monolithic entities for which the blanket terms "science" and "religion" may be applied. Obviously, there are many different religions, each of which has not only widely varying degrees of acceptance and antipathy towards the scientific enterprise, but also widely varying internal differences (just think of Christianity, ranging from papal approval of evolution to political movements designed to remove its teaching from public schools). Science, too, is dynamic. Indeed, it thrives on discord and requires constant disagreement, argumentation, and competition among scientists to arrive at truth. Facts, of course, are purely objective, but entirely different hypotheses and theories may be arrived at by different thinkers. And there are certainly more sub-fields within natural science than there are religions in the world, united primarily (perhaps solely) by methodology. Because of the emergence of impartial, objective scientific knowledge, many of the world's religious believers have had little problem with interpreting their faith's teachings symbolically, and the great scholars of comparative religion Carl Jung, Joseph Campbell, Mircea Eliade, and others have offered up extensive research to show this as among the deepest and most spiritually satisfying ways to worship, as opposed to crude literalism. In short, reducing science and religion to caricatures simplifies their complex relationship.

So, where does this leave us, as 21st century human being living in a world where both institutional religions and academic, practical, and technological science remain the most potent forces in our lives? I think that the one aspect of modern fundamentalist Creationism that truly baffles me is the falsification necessity of science. The historian and philosopher of science Karl Popper said science is only science when its hypotheses, experiments, and theories are falsifiable, that is, can be proved wrong rather than right. What fundamentalist Christian is willing to say with a straight-face that, should new evidence emerge disproving the existence of God, they would accept that science has disproved religion? No one. But this is precisely what a scientific hypothesis puts on the line when it is proposed: peer reviewing scientists devise experiments to test a hypotheses (prove it wrong) and if no one can, the hypothesis is formulated into a theory and tends to be accepted. I recall getting into an argument once with a friend less amenable to the truths of science about the validity of carbon dating, and one of his key arguments was "how can we accept something as fact when scientists simply take for granted that it's true?" which implies that scientists have never really tested whether carbon dating is fact. But of course, by using it in the field and getting consistent result, it's validity is not really in question. If it did not get consistent results, it would be tossed out in favor of a more accurate method. Biologist J.B.S. Haldane, accused of treating evolution as if it were a dogmatic truth, was asked what it would take for him to give up the theory, to which he famously replied, "Rabbit fossils in the Precambrian." This, in a nutshell, is how science works. The religious community does a great discredit to their own beliefs when they set them up for falsification. It is as if those who presume to speak on behalf of all religion are literally "testing their faith", and, if I were religious, I would think it cheapens my belief to subject it to the rigors of scientific testing. Isn't the point of faith that one doesn't know? And if one is not willing to admit the possibility that something is wrong, one cannot subject it to science.

One possible way to march forward has been proposed by evolutionary paleontologist Stephen Jay Gould in his book Rocks of Ages: Science and Religion in the Fullness of Life, which posits a middle ground that he calls NOMA, or "non-overlapping magisteria." Essentially, Gould, an agnostic, describes the relationship he envisions for religion and science as one of mutual respect and admiration in which the ultimate arena of each should remain separate. Religion is the realm and moral and ethical truths, which no amount of scientific knowledge can comment upon, and science is the realm of factual and testable knowledge about the physical universe, against which literalistic interpretations of the Bible should not infringe. To be sure, I am not entirely sold on his position (and neither are many of his most vociferous critics from the scientific and religious spheres) since areas that centuries ago would have found themselves undoubtedly within the dominion of religion, are now considered objectively testable by science. But can we truly believe the most anti-religious thinkers such as Richard Dawkins and Daniel Dennet when they say that, in a sense, God is testable and the verdict declaims that "God almost certainly does not exist"? I think that Dawkins, in his book The God Delusion, was most likely taking the the Creationist position to task and actually subjecting it to the scientific method as the Creationists so wish it be (with predictable results). But, as a true agnostic, I can't abide by a scientific test on something which, I feel by its very definition, is untestable, anymore than I can stand when fundamentalist Christians attempt to peddle their ideology as science. And, considering that I have in the past and in some ways am still somewhat acquiescent to some of the more outlandish claims of peripheral science, I feel that there can still be some limited communication between these two realms--especially when one considers the history and the more congenial relationship occasioned at times in the past. Both science and religion have their angels and demons. Let us hope in the future, that it is the angels of both that prevail.

"Choice, Chance, and the Actions of Others": A Religio-Scientific Interpretation of Free Will

First, imagine the conceivable dimensions of space geometrically: a line connecting two points is the first dimension - it has length but no width or depth. If we add a line branching from this original line, we have created the second dimension - on a plane, these two lines taken as a whole have length and width but no depth. Visualizing the third dimension is the easiest since we live in this dimension, but if we think of this dimension not as a third line on another plane, but as a fold connecting the two original lines, it will help us to imagine dimensions higher than the fourth. So, imagine that we cannot simply draw another line along another plane to give it depth. Now, imagine the third dimension, instead, as a fold of one of the original lines to meet the other line (like a two dimensional ant on the surface of a two dimensional newspaper, or Mario in one of the wrap around screens) being able to seemingly blink from one section to another if we were to fold those two points together. Still, with me? If we imagine the fourth dimension, time or duration, as another geometric line, then the fifth dimension is a line branching from our fourth dimensional line of time. There are infinitely many branches, all of which exist and represent all of the possible future available to us in this universe, but they are inaccessible to us, since we are bound by three dimensions. Getting to any of these branches requires only "choice , chance, and the actions of others", although we can only travel down one of these branches at any given moment. This is another way of saying that free will is our access point to the fifth dimension. We'll return to this notion at the end to demonstrate the conceptual possibility of viewing free will outside the realm of our own three dimensional universe. The implications of these amorphous suppositions have roots in both scientific and religious disciplines, and I wish to explore these in their totality.

I was prompted into deeper thinking about these topics recently because of four things: firstly, the recent posting of my graduate writing sample discusses the concept of free will in the historical context of astrology, witchcraft, the thought of Patristic writers and other pre-modern Christian theologians, and the writings of Shakespeare; secondly, a recent post by my friend Jason on the "implications of omnipotence" and the incompatibility of free will and an omnipotent God; thirdly, my recent, and almost unintentionally relevant, reading of two books on the topic: Science and Creation: A Search for Understanding by theoretical physicist turned Anglican priest John Polkinghorne and Freedom of Choice Affirmed by agnostic humanist philosopher Corliss Lamont; and fourthly, the previous video, linked here and above, which, quite frankly, was mind-boggling to me the first time I watched it, but which illustrates how to visualize dimensions higher than the fourth. This has profound implications for what we may call free will or the freedom of choice. Since I've already posted 15,000 words or so on the first section, we'll jump right into the blog post, books, and end by reconceptualizing the contents of the video within the context of free will.

In the discourse of the modern day discussion of free will vs. determinism, one must begin with the Church Fathers and Christian theologians of the Middle Ages. And, if we begin with the most influential of them all, Augustine, we immediately run into contradictory interpretations of the phenomenon. On the one hand, Augustine seems to deny free will, giving all power over the past, present, and future to God. He states that the number of saved souls is fixed, has been since the beginning of time, and that all are predestined to go either to heaven or hell. But Augustine, perhaps counterintuitively from a contemporary perspective, differentiates between determinism and predestination. The former is an absolute fixity in the future of the universe, which he denies, whereas the second only refers to the ultimate fate of individual souls, whose choices, freely made, determine their final location. The Catholic Church, which holds the existence of free will to be compatible with its doctrine, regards the writings of Augustine as affirming free will, in that he asserts that "any can be saved if they wish." Indeed, the Calvinist view of hard determinism would be diametrically opposed to the Catholic doctrine of free will beginning in the 16th century. The difference is merely in the perspective - our lack of knowledge as to our ultimate fate renders free will a reality, while from God's perspective, it is already known and decided. While contradictory, this nevertheless represents Augustine's and the Church's position, as Augustine constantly refers to free will as the ability of any person to accept Christ and thus be saved through grace. He says as much in his theological treatise "On Free Choice of the Will". The pre-determinism found in his writings is usually contextualized with the contemporary heresy of Pelagianism that Augustine was combating - Pelagius taught that humans could be saved of their own accord and did not need the saving grace of Christ, which Augustine rejected.

If free will is equivalent to freedom of choice, then perhaps the question lies in cause and effect. Here, however, the verdict, both philosophical and scientific, is still out. One of the earliest and most influential conceptions of cause and effect, is Aristotle's "Unmoved Mover," an imagined originator of the universe, defined as the original cause through which all existence may be termed an effect. Though the idea may seem similar to the concept of "God", it must be noted that Aristotle's "Unmoved Mover" was not anthropomorphic and did not play an active role in creation as the Judeo-Christian God did. Thus, it was originally considered incompatible with the creator God until the the great Scholastic Thomas Aquinas. Aquinas did Aristotle one better, or five better as it were. Aristotle had contended that the universe was eternal and had proposed the idea of a hypothetical "Unmoved Mover" as a necessary attribute of any universe that did have a temporal beginning. Aquinas, who as a Christian believed in a finite universe with a definite temporal beginning, took the "Unmoved Mover" concept as a given and as his starting point for his Quinquae Viae, or the Five Ways. The Five Ways, originally conceived as a rational approach to proving the existence of God, also contains major implications for the conflict between free will and determinism. Polkinghorne simplifies them thusly: "1) The existence of change...conclude[s] that there must be a first originator of change; 2) the existence of causation...conclude[s] that there must be a first cause; 3) the existence of coming to be and ceasing to be...conclude[s] that the world's actual continuance requires an unchanging ground of its existence; 4) the existence of gradations and qualities...conclude[s] that there must be one whose perfection is the ground for all partial qualities; 5) the existence of purpose in this world...conclude[s] the necessity of an intelligence directing it." (I plan on posting more on this later). A "first cause" equivalent to God implies a certain top-down control in the matter if we accept Aquinas' version of a "first cause" rather than Aristotle's, though I think Polkinghorne is right when he points out that Aquinas was more concerned with a "logical hierarchy" than a "temporal priority." This continues to muddy the argument and even though the official Catholic position is one of free will, the greatest writings on the matter do not shed any particularly coherent light on the issue.

Science, however, is no clearer. Traditional Newtonian physics is fairly cut and dried. It is classically mechanistic: 1) a body at rest or in uniform motion stays in that state unless acted upon by an external force, 2) force equals mass times the acceleration of a given object (F=ma), and 3) for every action, there is an equal and opposite reaction. These are Newton's three laws of motion simplified, and these, in some ways, also seem to imply determinism. The late 18th century French physicist and astronomer Pierre-Simon Laplace used these physical laws to create his own thought experiment, oftentimes called "Laplace's demon", which posits that if a demon with unlimited calculating power were given the location and momentum of every atom in the universe, he could predict the entire future of that universe. Carried further, this suggests that, of course, no human (Hari Seldon aside) could ever have this knowledge considering our own intellectual limitations, but an infinitely superior being with such power could in fact have such knowledge. Laplace called this being a demon, but what is to stop us in our conceptual language from granting this ability to God? Again, is this not exactly the God described by the Calvinists? This is where the conflict between knowing the future and controlling the future comes into play, which Augustine and other Christians have explained simply as a difference in perception. But, we must push this idea even further. As it turns out, Newtonian physics only describes the universe in general macroscopic terms, and at very small sizes and very fast velocities, it does not describe reality accurately. The determinism of Laplace's demon is overturned by Heisenberg's Uncertainty Principle, which states that if one knows the location of a subatomic particle, one cannot know its precise momentum, and if one knows the momentum of a subatomic particle, its precise location is indeterminate. So much for a demon with a calculator knowing our future - he can never input both variables into his equation. Einstein famously mused, in regards to quantum mechanics, that "God does not play dice." By playing dice, though, quantum physics, at least in this respect, affirms a universe of free choice.

The truth of the matter remains murky, and even more recent scientific discoveries swing the pendulum back in the direction of determinism: certain electrons seem to be able to "communicate" with each other no matter the distance and in certain experiments involving these electrons, effects are quite capable of appearing before causes (according to some). Recent studies by neurobiologists and cognitive scientists in the realm of simple voluntary movement have shown that the brain is aware of the movements we are about to make before our conscious minds are. Chance is another conundrum. What we call chance, may not really be chance at all (though I don't suspect a coin flip in our universe will come up heads ninety-two times in a row) but "infinitely complex order." When odds are calculated in a coin flip, for example, one would say that the odds of a coin coming up heads is 1 in 2, all things being equal. In reality, all things are never equal, and variations in the weight of the coin, the strength and direction of the toss, which side it is on to begin with, how many times it bounces, etc. will have an effect on the outcome. Only the hypothetical continuation of the flip for all eternity will give a statistical average of 1 in 2. Chance is simply infinitely complex order, indistinguishable from what we may call chaos but which is not chaos. In other words, order and disorder are not mutually exclusive, but "disorder" is simply order so complex as to be unpredictable and thus equivalent to what we would call chance. Perhaps free will is this very form of "unpredictability", so complex at a universal scale, that only God Himself is capable of discerning the order from the disorder. The acausal connecting principle synchronicity, by this definition, could be defined as more than chance - it could be a pattern found in the apparent disorder of the universe, a glimpse at the infinite complexity of reality. In short, science is no clearer than religion is on this matter.

Justice is an entirely separate concern. If we ask the question "Do humans have free will?" and the answer is no, does this necessarily imply that the universe is unjust? Some critics point out, I believe with a fair amount of justification, the incompatibility of an omniscient and omnipotent God who nevertheless has endowed us with free will. If an all-knowing and all-powerful God, both established conditions for Christian belief, truly does exist, then His knowledge about the universe, the criticism goes, implies that your choice is really His choice (an effect that can trace itself all the way back to Aquinas' "First Cause" of Aristotle's "Unmoved Mover"), and this lack of control on our part is unjust. The traditional Christian rebuttal would be something to the effect of "God exists outside of time and space and thus His knowledge does not affect your will. All of eternity is a continual unified 'present' from God's perspective, whereas we are forced to perceive the universe temporally and spatially." Implicit in this argument is the fact that, as God exists outside of any conceptual framework we could ever attempt to comprehend, so too is His justice and judgment beyond our comprehension.

In closing, let us return to the thought experiment we began with. Beyond our perceivable three spatial dimensions and the fourth of time, superstring theory posits the existence of 10 dimensions (or 11 if time is included as a dimension rather than a "direction"). The fifth dimension, according to the geometric concept laid out in the opening paragraph, consists of branches extending out from the "line" of time. In the totality of the universe, the point from which we start "contains" all of three dimensional space starting with the big bang and the point where the line ends is the temporal and spatial end of the universe. But, since time is not fixed (at least from our three dimensional perspective), there are an infinite number of "branches" from this line that creates the fifth dimension (heat death, big crunch, etc.). A "folding" of this fifth dimensional line to meet another fifth dimensional line takes us into the sixth dimension, and this would be the equivalent of a warp or wormhole leading to another timeline within our own universe. Then, taking all these branches as a new geometric point (just as we did to the first three dimensions), we could term this "infinity", since every timeline that could possibly exist within our universe exists within this point. We can then draw a line from this infinity to entirely different infinities. How is this possible? Because the first "infinity point" contains only all possible timelines in our current universe and does not contain timelines from other universes (the "multiverse"), where the initial conditions following the big bang are different and create different physical laws (for example, another universe may have a light speed faster than ours or a boiling point of water higher than 100 Celsius or where gravity is stronger than the electro-magnetic force, etc.) Following the original premise, branches and folds produce the eighth and ninth dimensions, which, when collapsed into a point, creates the tenth dimension. No more lines can be drawn from here, since we have already exahausted "all possible timelines for all possible universes". Does this make sense? No, not really. . . just watch the video. It will be easier to understand it conceptually as opposed to reading an imperfect verbal description. So what's the point in describing all these dimensions? Because, according to this conceptualization of supersting theory's "higher dimensions," everything that exists beyond the fifth dimension is dependent upon "choice, chance, and the action of others" in order to exist. All of the possible future timelines (the fifth dimensional branches from our fourth dimensional "line" of time) require our active choice to occur. Or, put another way, the indeterminate nature of the future is simply another way of envisioning the necessity of choice. If we could picture an entity or being that exists in or beyond the 10th dimension, who would necessarily have access to the lower dimensions (as we have access to the second and first), does their knowledge of time, our future, all possible futures, and all possible other universes abrogate our own free will? At least in this respect, I'm not sure that knowledge equals control, even if creation is implied.

I find it telling that Corliss Lamont titled his book Freedom of Choice Affrimed rather than Confirmed. Confirmation presupposes objective knowledge about the subject, and this may prove impossible. This essay was not meant to prove free will valid or invalid, but to shed some light on a new way of thinking about the issue. However, I am certain I feel more confused after exploring this topic over the past week, than less. But when we open new doors we often find ourselves in rooms with completely new mental furniture. And this is never a bad thing.

Tout comprendre, c'est tout accepter. . .

These "Damnable Superstitions": Legal Double Standards and Cultural Reflections of Witchcraft and Judicial Astrology, ca. 1200-ca. 1600: Part 3

Modes of Astrological Discourse, ca. 1130-1600

Like witchcraft, the history of astrology is, of course, far more complex than one simple paper can attempt to contain, but it will be useful to track its basic course of development in the history of Western science. Astrology had many independent origins chronologically and geographically, but the Western vein had its foundation as an organized discipline in Chaldean Babylonia around 3000 B.C.E., was influenced by Persian Zoroastrianism, and was transmitted via the Egyptians to the Greeks by at least 500 B.C.E.[1] Generally speaking, astrology enjoyed unquestioned legitimacy in ancient times because, as a science, it grew out of the priestly tradition it had occupied in Babylon. The Babylonian religion held the sacredness of the stars and planets, and this infatuation with the heavens lent itself to meticulous study. As David C. Lindberg elucidates in his history of the origins of Western science, there were persuasive reasons for believing in astrology in terms of its being a study of celestial influences. “Nobody could doubt,” he writes,

that the heavens were the major source of light and heat in the terrestrial region; the seasons were plainly connected with the solar motion around the ecliptic; the tides were apparently connected with lunar motion; and it seemed clear, once the compass made its appearance (late in the twelfth century), that the poles of the celestial sphere exercised a magnetic influence on certain minerals.[2]

Jim Tester, in his seminal work on the history of Western astrology, argues that Mesopotamian (and through association Egyptian) astrology was “purely descriptive” and was not the scientific enterprise it evolved into by the first few centuries of the Christian era. This original version of astrology was concerned primarily with calendrical matters, and the mathematical techniques and observational precision necessary for constructing tables, nativities, and horoscopes did not exist until around the fourth century in Greece.[3] During this classical golden age, Pythagorean, Platonic, and Aristotelian thought all accommodated astrological discourse within their cosmic frameworks. As the Greek method of rational inquiry was adopted by the Romans, astrological writings flourished during the early empire, especially in Eastern scholarly centers such as Alexandria: Marcus Mailius’ Astronomicon, Dorotheus of Sidon’s didactic five-part poem the Pentateuch, Vettius Valen’s encyclopedic compilation the Anthology, and Julius Firmicus Maternus’ eight book compendium, the Mathesis to name but a few outstanding examples of the era. Towering above them all was the Tetrabiblos (“the four books”) by the Hellenized Egyptian Ptolemy (90-168 C.E.), “the cornerstone of medieval astrology.”[4]

Like much other scholarship in the Latin West following the fall of the Roman Empire, astrology lay dormant for several centuries awaiting rediscovery. A smattering of translations of astrological, medical and other scientific works occurred during the tenth and eleventh centuries, but the explosions of translations that led to the building of a truly medieval version of astrology occurred in the twelfth century. This flowering of learning, often referred to as the twelfth century renaissance, included a great many astrological works, many of which were Greek works preserved, commented upon, and improved by Arab scholars. From 1130 to the 1170s, dozens of astrological writings were translated into Latin by the likes of Abelard of Bath (Al-Khwarizmi’s Tables and several works of Euclid), Plato of Tivoli (several Arab astrological tracts by Al-Battani and Ptolemy’s Tetrabiblos), and above all Gerard of Cremona, of whose more than ninety translations, six are astrological in nature.[5] The foundation upon which medieval astrology stood was derived from relatively few works. Ptolemy’s Tetrabiblos was the one work to which all medieval astrologers seemed to defer, and in conjunction with Ptolemy’s other great work The Almagest, constituted a formidable edifice of authority.[6] The work of the Arab Abu Ma‘shar (often Latinized as Albumasar) titled Introduction to the Science of Astrology was also heavily referenced and was regarded as the most important Arab contribution to the science.[7] Both the Tetrabiblos and the Introduction to Astrology were translated from Arabic to Latin in the 1130s. Ptolemy’s works had survived in the West due to the ninth and tenth century efforts of Arab scholars, and without their preservation, his volumes may never have made their way into European hands. Within the Tetrabiblos, astrology is treated hierarchically and it begins with the general and works its way to the particular. Book I is procedural, describing the movement of the planets and stars, the use of calculations, and how to understand the results. Book II details the collective aspects of astrology that may be generally applied to large populations or nations, and Books III and IV together get to the more specific details of individual astrology, or those things which may be determined by the positions of the stars and planets at the conception, birth, and other important moments in the life of the person whose horoscope has been cast (genethlialogy).[8] Its thoroughly mathematical treatment of the subject removed it from the more legendary position it had held in the Western consciousness and set it on the path as an area of scientific study.

Perhaps the most important translations made during the twelfth century renaissance, and related directly to the rebirth in astrology, were those of Aristotle. From the fall of the Roman Empire until the twelfth century, the medieval cosmos was Biblical and heavily influenced by Platonic thought.[9] Aristotle burst onto the scene contemporaneously with these astrological translations and his view of the universe informed the new medieval astrology. Briefly, Aristotle’s universe was a sphere of dual nature, with the earth at the center and the sphere of fixed stars at the outermost reaches. Physical law acted differently depending on the position within the cosmos. The supralunar sphere, or the entire universe above the moon, was an incorruptible, unchangeable realm where all movement was perfectly circular and in general, predictable. Birth, generation, decay, and death, on the other hand, categorized the sublunar region. It was a world of transience. Many Christians believed that this validated the concept of original sin and that the fall and expulsion of Adam and Eve were evident in the disparity between the upper and lower spheres. [10] This was the same disparity involved in dividing witchcraft and astrology, since astrology, by definition, was occupied with the study of the perfect regions of the universe while witchcraft relied on the most flawed cosmic territory.

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[1]Couliano, Eros and Magic in the Renaissance, p. 25, as well as the Encarta Encyclopedia 2000 entries on “Astrology” and “History of Astronomy.”

[2] Lindberg, David C., The Beginnings of Western Science: The European Scientific Tradition in Philosophical, Religious, and Institutional Context, 600 B.C. to A.D. 1450. Chicago: Chicago University Press, 1992, p. 274.

[3] Tester, Jim. A History of Western Astrology. Woodbridge: Boydell Press, 1987, p. 12 and 13.

[4] Ibid. p. 11-56.

[5] Ibid. p. 152. For a more complete list of scientific works translated during these three-quarters of a century, see Tester’s notes as well.

[6] Wedel, Theodore Otto. The Medieval Attitude towards Astrology. New Haven: Yale University Press, 1920. p. 65 and 67.

[7] Ibid. p. 62.

[8] Tester, A History of Western Astrology, p. 68.

[9] See note 13 in Part 6 for a more thorough description of the Platonic cosmological attitude toward astrology and it adherents in the early Renaissance.

[10] Lindberg, The Beginnings of Western Science, p. 55. The Aristotelian works most responsible for this worldview were De Caelo (On the Heavens), Physica (Physics), and most especially De Generatione et Corruptione (On Generation and Corruption). See also The Basic Works of Aristotle, edited by Richard McKeon, Chicago: Random House: Chicago, 1941.

The Probability of the Improbable

"It is likely that unlikely things will happen."
-Aristotle

A recurrent conversation I seem to have with people is on the balance between analysis and intuition in daily life. I consider myself an incredibly analytical person, always taking in every scrap of information about something and viewing a problem from all angles before I arrive at a decision or a solution. Still, even though I find it difficult not to rationally observe all the information at my disposal, I actually have a rather embarrassing habit of impulsively choosing things on occasion. And it's not dependent on the size of the decision either: sometimes I agonize for several minutes in the morning over what pair of pants to wear, but have made decisions about trips to take and major purchases because they "felt" right. If this sounds ridiculous, it is; but I find it interesting that many, if not most people, make decisions this way. Perhaps even more interestingly is how good the record for making decisions this way is. Given this interpretation of human behavior, one thing that's especially humorous to me, is when something is especially counterintuitive. So, here's a little anecdote I ran across while recently perusing the book How to Think about Weird Things, which illustrates how intuition can sometimes be way off:

When we try to judge the probabilities involved in events, we're often wrong. Sometimes we're really wrong because the true probabilities are completely counter to our intuitive "feel" for the odds. Mathematician John Allen Paulos offers this surprising example of a counterintuitive probability:

"First, take a deep breath. Assume Shakespeare's account is accurate and Julius Caesar gasped 'You too, Brutus' before breathing his last. What are the chances that you just inhaled a molecule which Caesar exhaled in his dying breath? The surprising answer is that, with a probability better than 99 percent, you just did inhale such a molecule. For those who don't believe me: I am assuming that after more than two thousand years the exhaled molecules are uniformly spread about the world, and the vast majority are still free in the atmosphere. Given these reasonably valid assumptions, the problem of determining the relevant probability is straightforward. If there are N molecules of air in the world and Caesar exhaled A of them, then the probability that any given molecule you inhale is from Caesar is A/N. The probability that any given molecule you inhale is not from Caesar is thus 1 - A/N. By the multiplication principle, if you inhale three molecules, the probability that none of these three is from Caesar is [1 - A/N]³. Similarly, if you inhale B molecules, the probability that none of them is from Caesar is approximately [1- A/N]^B. Hence, the probability of the complementary event, of your inhaling at least one of his exhaled molecules, is 1 - [1 - A/N]^B. A, B (each about 1/30th of a liter, or 2.2 x 10²²), and N (about 10⁴⁴ molecules) are such that this probability is more than .99. It is intriguing that we're all, at least in this minimal sense, eventually part of one another."

I'd want to see a study on how long it takes molecules contained in 1/30th of a liter to diffuse into a body of gases the volume of the Earth's atmosphere as well as the likely amount of molecules that are not free in the atmosphere to be sure this is accurate. I guess that's just my analytical nature. However, I'm willing to give the study the benefit of the doubt. I guess that's just my intuitive nature.