Showing posts with label William Shakespeare. Show all posts
Showing posts with label William Shakespeare. Show all posts

Sunday, April 19, 2009

These "Damnable Superstitions": Legal Double Standards and Cultural Reflections of Witchcraft and Judicial Astrology, ca. 1200-ca. 1600: Part 7


Cultural Reflections of Witchcraft and Judicial Astrology
in Elizabethan England

The demarcation between astrology and witchcraft not only in early modern intellectual circles but also in the culture as a whole poses a more difficult problem.
The key to this answer may lie in these divergent definitions of astrology and their aforementioned subdivisions. In sixteenth century England, for example, natural astrology would distance itself from the judicial branch and come to be known as astronomy. While natural astrology was certainly accepted by most Elizabethans, the judicial branch lost momentum, in many ways because of Elizabeth’s fragile claim to the throne early in her reign and the uncertainty of England’s future following her death. Elizabeth I never married and produced no natural heir, and the act of monarchical succession was an uneasy topic among the noblemen who could bear the brunt of any future wars involving a struggle among potential successors. Divination had been proclaimed illegal in 1541, but King Edward VI, whose court included an astrologer, repealed this law shortly thereafter. This law was again implemented verbatim in 1550 under Mary, Queen of Scots, and reinforced in 1563, five years into Elizabeth’s reign.[1] Even in the first version, witchcraft is clearly paired with astrological prophecy because both could have serious repercussions for the ultimate future of the monarch if they were to proclaim a certain negative future:

Where dyvers and sundry persones, making theyre foundacon by Prophecies,…have dyvised desecated and practiced to make folke thinke that by theyre untrew gessys it might be knowne what good or evyll things shulde come happen or be done, by or to such persones as have and had noble personages of whome suche fals Prophesies hathe or shulde herafter be set fourthe, wherby in tymes paste many noble men have suffered,…That if any persone prynte or wryte, or ells speake sing or declare to any other persone of the King or of any other persone, after the firste daye of Julie next coomyng, any such false Prophecies…thene everye such offence shalbe deamed Felonye,…[2]

It is necessary to note that neither astrology nor witchcraft is mentioned directly. Prophecy is proclaimed illegal, which, given the circumstance of the practice, could encompass either. The word “Felonye” in sixteenth century English did not necessarily constitute a crime carrying the death penalty.
Therefore, it is highly possible that offenses against this law were penalized differently depending on whether they were considered astrology or witchcraft or whether men or women committed them.

John Chamber, who thought so lowly of astrology that he put it in the same category with witchcraft as a “damnable superstition,” nevertheless preserved their traditional distinctions. While astrology was merely a form of false prophecy, it made no use of demons or devils and was thus not as abominable. Just as the opening of Elizabeth’s reign heralded laws against prophecy, so the last year of her reign renewed the discussion.
In his A Defence of Iudicial Astrologie (1603), Sir Christopher Heydon observed

Astrologie, being an arte…hath no more fellowship with the deuill, then heauen with hell. But that witches cannot be imitated in their deuillish profession, without all these former impieties…and as many inquisitors, as haue written of them, doe al testify with one consent, out of their confessions. And therefore the word of God it selfe, Exod. 22, doeth absolutely decree, That a witch shall not be suffered to liue.[3]


Heydon managed to distance astrological prophecy from witchcraft and equate God’s functioning in the world, as had generations of defenders before him, with “the free moderation both of the course and power of the Starres vnto God.”[4]
Chamber and Heydon may be seen as representatives of two sides of a very divided argument defined as realist versus occultist or science versus superstition. From the modern perspective, the irony is that astrology, an institution with a history as a science, was regarded as a “damnable superstition,” while witchcraft was considered a very valid and very dangerous reality. The great change occurring in sixteenth and early seventeenth century England was the swiftly shifting perception of judicial astrology. Just as natural astrology came to be closer to astronomy, judicial astrology came to be regarded as at best sheer nonsense and at worst comparable to witchcraft. This comparability had always been in the spirit of philosophical discourse rather than legality, but as judicial and natural astrology disconnected from one another and the blanket term astrologia, new niches of study, and thus legality, emerged.

Of course, it must be noted that Elizabeth’s court included an astrologer, and a successful and famous one at that. John Dee was not only a court astrologer for Elizabeth I but a polymath in general, whose library was the envy of many European scholars. To be sure, even with the growing skepticism of judicial astrology, the practice was relatively safe in England, provided that one was in the favor of the authorities. Dee most certainly was, having spent time in captivity at Hampton Court with Elizabeth, where he was known to have cast her horoscope positively. After her ascension to the throne, Dee even astrologically determined the most auspicious moment for her coronation to ensure a long and successful reign.[5] For obvious reasons, astrologers who cast horoscopes favorably tended to hold more sway and avoid illicit controversy.


Elizabeth’s successor James I, was less forgiving. In his own work, Daemonologie
, he discerns between the two concepts of natural and judicial astrology making many explicit references to the Bible. Here, he defines the natural branch as “knowing thereby the powers of simples, and sickenesses, the course of the seasons and the weather, being ruled by their influence; which part depending vpon the former [Astronomie], although it be not of it selfe a parte of Mathematicques [astrology]: yet it is not vnlawful, being moderatlie vsed,”[6] but his treatment of judicial astrology is overtly unforgiving:

The second part is to truste so much to their influences, as thereby to fore-tell what common-weales shall florish or decay: what, persones shall be fortunate or vnfortunate: what side shall winne in anie battell: What man shall obteine victorie at singular combate: What way, and of what age shall men die: What horse shall winne at matche-running…This parte now is vtterlie vnlawful to be trusted in, or practized amongst christians, as leaning to no ground of natural reason: & it is this part which I called before the deuils schole…in the Prophet Ieremie it is plainelie forbidden, to beleeue or hearken vnto them that Prophecies & fore-speakes by the course of the Planets & Starres.[7]


James I insisted that because the Bible forbade it, its practice should be unlawful.
He wrote this when he was the King of Scotland but reaffirmed it as King of England, passing laws prohibiting it. In only the second week of his reign in 1604, for example, the English Parliament made witchcraft a more harshly punishable offense—where it once carried the death penalty only in cases of murder, it was now punishable as a capital offense only if there was intent to harm or if the use of “evil spirits” was suspected.[8] This again was an extension of the crimen exeptum and did not bode well for English women of this period. Because of this double standard, the differentiation between the legality of astrology and the illegality of witchcraft was essentially arbitrary in terms of their intrinsic qualities, and even though certain forms of astrology were censured by various Western European medieval and early modern governments, the act of studying the influence of the stars on human affairs was generally tolerated for astrologers and denied for those accused of witchcraft.[9]

Despite astrology’s many denunciations from the Church Fathers and national secular authorities, the terminology and unconscious discourse of astrological belief persisted well into early modern times.
One outstanding example of its perseverance within popular culture and the unstated but razor thin line between it and the unacceptable offense of witchcraft is demonstrated by the ubiquity of both in the plays of William Shakespeare. Shakespeare’s use of astrological rhetoric in his plays in many ways seems to subconsciously reflect its popularity at the time, but his own faith in it cannot be construed simply by its conspicuousness in his plays. Most uses, in fact, are particular to and exemplary of his characters although, as the Shakespearean scholar Johnstone Parr has cited, there are over two hundred astrological allusions in his plays and all are eventually fulfilled.[10] There are many cases in which characters resign themselves to astrological fatalism or use the stars as an excuse for their extraordinary woe, but in all circumstances their belief in astrology as a science is taken for granted by the audience and never questioned. Witchcraft, however, as seen most explicitly in the play Macbeth, remains a plot point unalterably prejudged as evil by an early modern audience familiar with it only as a crime against nature, society, and God.

Much of the common public awareness of witchcraft is evident in the depiction of witches in plays such as Shakespeare’s Macbeth
. The witches in Macbeth are cast as hideous and villainous, in many ways as inhuman and unearthly as evil spirits, such as when Banquo comments that they are “So withered and so wild in their attire, / That [they] look not like th’inhabitants o’ th’earth / And yet are on’t” (1.3.40-42). Macbeth’s witches are surrounded by an aura of darkness and have an otherworldly quality to them. They describe themselves as “Weird sisters” (1.3.32), or women fused with fate and prone to sacrilegious acts or connected with the black arts, such as when Macbeth greets them “How now, you secret, black, and midnight hags” (4.1.48)? For dramatic purposes the witches are almost inaccessible as actual human beings, seen more as material instruments of gloom, agents of demons, or a means of forecasting one’s demise. Macbeth’s is predicted just so, and it may be that this serves as a lesson to those who endeavor to “tempt fate,” as it were, rather than leave the functioning of the world in God’s hands.

The leader of Macbeth’s witches is Hecate. She is based on the Greek mythological figure representing both witchcraft and the crossroads, or the potential direction of the future.
Mythologically speaking, the relationship between witchcraft and the course of the future, an area obviously engaged by astrological horoscopy, was embodied in the same goddess. This tenuous link between astrological predetermination and the goddess of witchcraft is obvious in her own predilection to assert her power during the full moon. Those accused of being engaged in demonology and witchcraft commonly made reference to the moon as a source of power. Hecate’s association with the moon—in Aristotelian cosmology, the dividing line between the corruptible, changeable world and the immutable perfection of the heavens—links her both to the heavens, the realm of astrological phenomena, and the earth, where sinfulness and corruption prevail. She later chastises the witches in Macbeth for not consulting her before they interfered with his fate. Replying to the First Witch’s observation of her “angerly” disposition, Hecate states,

Have I not reason, bedlams as you are?
Saucy and overbold, how did you dare

To trade and traffic with Macbeth

In riddles and affairs of death,

And I, the mistress of your charms,

The close contriver of all harms,

Was never called to bear my part

Or show the glory of our art? (3.5.2-9)


Hecate specifically criticizes their foretelling of Macbeth’s doom, but this punition can hardly be taken seriously when it comes from the goddess of witchcraft and divination herself.
In terms of witchcraft, the act of divination is described here as an “art,” and without the mythological figure behind it, it is without merit. The act of looking to another supernatural force, such as this pagan goddess, would have been deemed heretical by an early modern Christian audience were it not recognized as depicting the witches as the wholly evil antagonists within the story arc. The metaphysical and meta-dramatic wall that this fiction provided removed all external judgment from the equation among Shakespearean audiences. While witchcraft focused on baseness and materiality, the practice of astrology made use of the exteriority of the heavenly spheres of God, even within the dominion of performance art.

While this use of witches as dreadful characters is expected, the power of astrological predetermination is used in a more neutral way, suggesting neither misdeeds nor illegality.
Several plays contain references to the power of the stars, perhaps most famously in Romeo and Juliet where the title couple receives the epigraph “star-crossed lovers.” A lesser-known quotation comes from The Winter’s Tale, when, upon the proclamation of her prison sentence, Hermione exclaims: “There’s some ill planet reigns: / I must be patient until the heavens look / With an aspect more favorable” (2.1.105-107). Here, the planets not only have influence over human affairs but are actually “reigning” over them. This is language we have seen more often used in the context of God’s power over history and individual events in a human life. King Lear offers one of the most unfavorable depictions of astrology in the entire Shakespearean canon. During his unraveling near the end of the play, after exhausting himself in allocation of fault for the sorry state of his former kingdom, Lear howls out bewailing his fate as if in submission to the universe: “It is the stars / The stars above us govern our conditions; / Else oneself mate and make could not beget/ Such different issues” (4.3.34-37). More subtly, but within the same stratum of reflection, Edmund rebukes astrology as a means of blaming one’s unfortunate state upon something other than oneself:

This is the excellent foppery of the world, that…
we make guilty of our disasters the sun,

the moon, and the stars: as if we were villains

on necessity; fools by heavenly compulsion; knaves, thieves,

and treachers, by spherical predominance; drunkards,
liars, and adulterers, by an enforced obedience of
planetary influence; and all that we are evil in by a

divine thrusting on. An admirable evasion of

whoremaster man, to lay his goatish disposition on the

charge of a star. My father compounded with my

mother under the dragon’s tail and my nativity was

under Ursa Major, so that it follows that I am rough and

lecherous. Fut! I should have been that I am had the

maidenliest star in the firmament twinkled on my

bastardizing. (1.2.118-127)


Edmund clearly disregards his own supposed fate by actively seeking to change it.
This act of free will was crucial to Protestants in general, and despite the seemingly fatalistic attitude of many Shakespearean characters, the influence of the stars was generally viewed not necessarily as a fixed act, but as an influence to be overcome—just as historical Christian thinkers from Augustine to Albertus had said. As Cassius declares in Julius Caesar, “The fault, dear Brutus, is not in our stars, / But in ourselves, that we are underlings” (1.2.140-141). England itself, by the time of the Stuart monarchy, was engaged in a tacit ideological battle—that of the Anglicans, for whom free will was of the utmost importance, and that of the emerging Puritans who, influenced by Calvinism, deferred to the power of God rather than free will. To accentuate the importance of this vital dialogue in pre-modern England, some scholars have suggested that Gloucester and his son Edmund represent the Elizabethan dichotomy of realist and occultist, like their real life counterparts John Chamber and Sir Christopher Heydon.[11] Gloucester symbolizes the pessimistic resignation inherent in those who take the predictions of astrology as the final word, and Edmund embodies the more brash and youthful exuberance of the succeeding generation, which feels that the world is its for the taking. It is no coincidence that Shakespeare constructs these characters as a father-son duo in which the father is incapable of “passing the torch” because Edmund is an illegitimate bastard son and because there exists no common ideological ground between them. A realist to the end, Edmund’s downfall can be construed as a reluctance to accept that which he cannot change, as is evident in his refusal to accept astrology, the absolute edifice of fixed unchangeability according to it critics.

Free will, and its link to astrology, is also addressed in Macbeth, where the concept of the witches’ foretelling of Macbeth’s future is related to prevailing over one’s own fate.
The witches prophesy that Macbeth will become king of Scotland, and Macbeth does not question the veracity of the witches’ prophecies but instead ponders his own role in them and whether or not he must be active for these premonitions to come true:

[Aside] This supernatural soliciting
Cannot be ill, cannot be good. If ill,

Why hath it given me earnest of success

Commencing in a truth? I am Thane of Cawdor.

If good, why do I yield to that suggestion

Whose horrid image doth unfix my hair

And make my seated heart knock at my ribs,

Against the use of nature? (1.3.128-138)


Is direct action necessary to bring these prophecies to fruition, or are they somehow sewn into the fabric of time, unalterable, and thus as predictable as the rising and setting of the sun?
The witches provide the ominous human link between the will of the universe and the path of Macbeth’s individual future. In Macbeth’s first encounter with the witches, no prediction is advanced at all, simply the statement “All hail Macbeth, that shalt be king hereafter” (1.3.50). We may ask whether this is a testimonial of fact or if it is meant to fuel the fire of Macbeth’s ambition. If it is fact, then the question of free will becomes moot because Macbeth’s fate is written in stone, but if Macbeth must take action to fulfill these prophecies, then in retrospect we can never truly know if the witches’ forecast came true or if Macbeth took his future entirely into his own hands. This is the paradox always present in studying the effects of prophecy in the context of both witchcraft and astrology.

Perhaps the most famous lines typifying astrological notions in early modernity are those of Ulysses in Troilus and Cressida, a play set amidst the backdrop of the Trojan War.
Less related to the practicing of astrology or witchcraft than they are to the metaphysical concept of an interrelated cosmos where man and the universe are reflections of each other, these lines help to elucidate the special relationship between the microcosm and macrocosm:

The heavens themselves, the planets, and this center,
Observe degree, priority and place,

Insisture, course, proportion, season, form,

Office, and custom, all in line of order;

And therefore is the glorious planet Sol

In noble eminence, enthron’d and spher’d

Amidst the other, whose med’cinable eye

Corrects the ill aspects of planets evil,

And posts, like the commandments of a king,

Sans check, to good and bad. But when the planets

In evil mixture to discord wander,

What plagues and what portents, what mutiny,

What raging of the sea, shaking of the earth,

Commotion in the winds! Frights, changes, horrors,

Divert and crack, rend and deracinate,

The unity and married calm of states

Quite from this fixture! O, when degree is shak’d,

Which is the ladder to all high designs,

The enterprise is sick! How could communities,

Degrees in schools, and brotherhoods in cities,

Peaceful commerce from dividable shores,

The primogenity and due of birth,

Prerogative of age, crowns, scepters, laurels,

But by degree, stand in authentic place?

Take but degree away, untune that string,

And hark what discord follows. (1.3.85-110)[12]


In the worldview of the Elizabethans, as well as Western society in general before the Scientific Revolution, everything from plants and animals, elements and humors, body parts and professions, had their particular place within the hierarchy of created things.
A change in the status quo or the social stability of the Western world would cause uncontrollable havoc, Ulysses seems to say, and when applied to medieval and early modern views on witchcraft, we can see how the European patriarchy maintained their positions by continuing to denigrate women through a false mythology of devil worship and unnatural occult activities. It is as though even astrology, with its unstable claim to legitimacy, could be applied to the disparagement of women. The intimate relationship between man and the cosmos was a direct product of the fusing of ancient astrological notions and the Christian theological perspective, influenced by Platonism and Aristotelianism. While this standpoint could accommodate the practice of astrology, under certain circumstances, witchcraft had no such “natural place” in the hierarchy of being. This belief linked most astrological claims to the functioning of God in the material universe, and thus astrological rhetoric was employed in an uncontroversial way. Witchcraft never had such a luxury. Shakespeare’s utilization of astrology as a dramatic device employed both as an object of characters’ blame and praise could pass through the early modern audience without fear of backlash whereas his description of witches had to remain entirely wicked to be well received.



[1] Allen, Don Cameron, The Star-Crossed Renaissance: The Quarrel about Astrology and Its Influence in England, New York: Octagon Books, 1941, p. 102.

[2] Smith, Warren D, “The Elizabethan Rejection of Judicial Astrology and Shakespeare’s Practice,” Shakespeare Quarterly 9.2 (Spring, 1958), p. 162-163.

[3] Op. cit. A4r

[4] Ibid. A2v

[5] Bobrick, The Fated Sky: Astrology in History, p. 145.

[6] Op. cit. p. 14.

[7] Ibid. p. 14-15. In this passage, King James I makes reference to the prophet Jeremiah, which probably refers to Jeremiah 23:9-22, in which Jeremiah is troubled over the moral reproach of the current priests and prophets of Israel. Verses 10 and 11 state, “Their course is evil and their might is not right. Both prophet and priest are ungodly; even in my house I have found their wickedness, says the Lord.” Verse 16: “Thus says the Lord of hosts: ‘Do not listen to the words of the prophets who prophesy to you, filling you with vain hopes; they speak visions of their own minds [probably in reference to dream interpretation], not from the mouth of the Lord.’” Verse 21: “I did not send the prophets yet they ran; I did not speak to them, yet they prophesied.” It may also refer to Jeremiah 10:2-3, which states: “Learn not the way of the nations, nor be dismayed at the signs of the heavens because the nations are dismayed at them, for the customs of the peoples are false.” In any case, King James I rejected astrology on Biblical grounds because he viewed astrology as a form of false prophesy, or those who trusted their own faculties of reason over faith in revealed scripture which, as we have seen, could be utilized to denounce astrology.

[8] Barstow, Witchcraze, p. 39

[9] Smith, “The Elizabethan Rejection of Judicial Astrology and Shakespeare’s Practice,” p. 159.

[10] Bobrick, The Fated Sky: Astrology in History, p. 182.

[11] Allen, The Star Crossed Renaissance, p. 167 and 178.

[12] For clarification on this concept, insofar as it has modern psychological implications, see Gustav Jahoda’s work The Psychology of Superstition, Baltimore: Pelican Books, 1969, p. 120-125. He gives a wonderful explanation of the psychology of superstitious behavior in modern times and its ancestor in occult sciences and archetypal representations in the arts and sciences from the Middle Ages and pre-Scientific Revolution times, as well as a succinct Jungian analysis of the Elizabethan worldview.

Monday, April 13, 2009

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

I think that the greatest asset I bring to the table as a soon-to-be graduate student in history is my ability in writing and researching and I said as much in my personal statement. I had decent GRE scores and a pretty good transcript, but it's definitely the writing, researching, and editing that make me a good candidate. What follows is the paper I used as my graduate writing sample, and it has an interesting history. It grew out of a much, much (much) shorter paper I wrote in a senior year class on the late plays of Shakespeare. The original was on the use of astrological discourse and depictions of witchcraft in Shakespearean plays (King Lear, Macbeth, A Winter's Tale, and Troilus and Cressida in particular) and how Shakespeare had to make the witches villainous to escape legal retribution but astrological rhetoric was perfectly acceptable, even though several laws against astrology were current in late Elizabethan England. The conclusion of that paper was that essentially, even though astrology was to some degree illegal in 16th century England, it was popular enough among its people that there was little authorities could do to curb its influence by simply passing a law, and thus it remained in tact, at least as way of speaking about and interpreting events.

For my graduate writing sample, I decided to expand upon the Shakespeare paper I had written, making it even more historically based. Essentially, what resulted was this massive paper (the original was around 8 pages, the current one is 46) that deals with the separate histories of Western witchcraft and astrology, their similar practices despite dissimilar position in the Western European consciousness, and their convergence in popular culture as evinced by writers like Shakespeare. In retrospect, the paper seems a bit too broad, and I think I focus a bit too much on their general histories, perhaps include a few too many unnecessary details, and don't tie together the separate sections of the paper--I think the last section on Shakespeare is probably the strongest section, but it seems somewhat out of place after reading the first two thirds. Many of you who read this blog have already read an earlier version of this paper. This is probably at least the tenth draft and it differers significantly from that one in some important ways: gone are some of the more general descriptions of both astrology and witchcraft as well as some of the less historically relevant literary aspects from Macbeth, and there is a greater emphasis on primary sources, especially the Malleus Maleficarum and the works of King James, Regino of Prum, Charlemagne, Augustine, and Isodore of Seville. I think it's a better paper, though still a little broad. As I mentioned, it's extraordinarily long, so I'm going to post it in seven or eight parts over the course of the next week or so. It is unaltered from the original except that I have removed the footnotes and reinserted them in quasi-MLA format throughout the text, except in the case of relatively important information which I have attempted to reintegrate into the main body. I may or may not post the bibliography later. Enjoy!

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

Introduction: "Damnable Superstitions"

In 1601 the Englishman John Chamber, in his diatribe against astrology titled A Treatise Against Iudicial Astrologie, wrote, “Witchcraft…sometime findeth now and then some hard entertainment, as it well deserueth. But this damnable superstition [judicial astrology], which dishonoreth God, polluteth heauen, deceiueth and seduceth men, goeth without touch or check; the Astrologer escaping, while the Witch is punished, may not that be well said?” (Chamber, C2v) The fact that men and women were engaged in similar applications of the occult, but were regarded differently in terms of legal and social status, was oftentimes the case in Elizabethan England. Chamber’s equation with astrology and witchcraft is a fact sometimes overlooked by historians of both. While the two had separate origins and different historical paths, the parallels in practice, purpose, and their positions in popular social consciousness cannot be ignored.

Witchcraft had long been condemned both by religious and political establishments throughout medieval and early modern history, but the similarities between it and astrology have largely been overlooked due to the institutionalized place of the latter in Western scholarly society. Despite the fact that the judicial branch of astrology—that concerned with divination, horoscopy, and the foretelling of the future—was censured to various degrees throughout its history in Western civilization, it remained an edifice of scientific discourse from ancient times until well into the seventeenth century. In general, astrology was accepted because it was practiced principally by learned and noble men from the same socio-economic class as those who also created the laws governing its performance, and it is no coincidence that very similar acts committed by women were condemned, many times for no other reason than the fact that they were perpetrated by females and regarded as heretical (Barstowe, 16). The patriarchal society of Europe was maintained by excluding these works of women, however comparable they were. As we shall observe in this study, the origins of these two disciplines are poles apart in terms of their cultural and ideological geneses; however, the disapproval of both in the Later Middle Ages and early modern period is a fact we can explain when we examine what kept them apart: 1) the masculine/feminine duality rife in pre-modern Europe and the misogynation stemming from this; 2) the accommodation of astrology within Aristotelian-Ptolemaic cosmology, and its influence on the Christian attitude toward the physical universe; 3) the microcosm-macrocosm relationship; 4) the heretical nature of the late medieval interpretation of witchcraft versus astrology; 5) and the early Christian distaste for nearly all things pagan from which the mythology of witchcraft ultimately arises. This last point excluded Greco-Roman learning, into which astrology was incorporated, and Christianity was able to syncretize. This study will track the categorization and punishment of witchcraft, the modes of astrological discourse in the later Middle Ages and early modern times, their similarity in some practices despite contradictory legal standards, and the positions of both in the popular consciousness of the late sixteenth and early seventeenth century as evinced by the writings of William Shakespeare in particular.

Tuesday, February 3, 2009

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.