The Rape of Cassandra

Author’s Note: This is first in a series of posts. Though they can be read independently, they were written with this order in mind: The Rape of CassandraMice on a Galley: A Review of AgoraHypatia Miscellanea


To Athena

(Homeric Hymn to Athena)

I begin to sing of Pallas Athena, the glorious Goddess, bright eyed,

inventive, unbending of heart

pure virgin, savior of cities

courageous, Tritogeneia. Wise Zeus himself bare her

from his awful head, arrayed in warlike arms

of flashing gold, and awe seized all the gods as they gazed.

But Athena sprang quickly from the immortal head

and stood before Zeus who holds the aegis,

shaking a sharp spear: great Olympus began to reel horribly

at the might of the bright-eyed Goddess,

and earth round about cried fearfully,

and the sea was moved and tossed with dark waves,

while foam burst forth suddenly:

the bright son of Hyperion stopped his swift-footed horses a long while, until the maiden Pallas Athena had stripped the heavenly armour from her immortal shoulders.

And wise Zeus was glad.

And so hail to you, daughter of Zeus who holds the aegis!

Now I will remember you and another song as well.

 

 

Athena Mourning 450 BCE

ATHENA: Do you know the insult done to me and the shrine I love?

-Aeschylus, Agamemnon

It is as if she is radiating fear, or that anxiety is a virile contagion. Some ancient animal sense, some herd instinct flashes through me. The white tailed doe.

“I’m sorry. I’m a little disorganized,” she needlessly says. “It’s this math. I hate it.”

“Take your time, we have as long as you need,” I respond. I look over the hundred digit poster of pi that’s on the wall. I have looked it over hundreds of times. With some students I tutor, I use the poster as a prompt to talk about infinite, or irrational numbers. Not with her. Despite my curiosity, I do not ask why she hates math. The question has no meaning.

“Give me a paper… a thesis, any day, and I can write it like that,” she snaps her fingers. “Ask me an anatomy question or psychology, and I’ll answer you right away, but math… I don’t know how you do it- ugh.” She is shuffling through her bags looking for her math notebook. Her hands shake, her eyes are watery. She is bloodless. My breath tries to emulate her hurried gasps, and I consciously slow it. Fear feeds on itself.

“Don’t be scared,” I say. “You’ll get through this.” I smile at her.

“Help me,” and she looks up at me. She looks into my eyes, and her eyes are lensed with tears. What I say next will determine whether they flow or recede.

I know of no subject with the possible exception of Speech that can cause such a physiological response in a person. It is worse than fear, it is dread, it is the fear of fear, and the fear of feeling fear. This student is experiencing the exact response she would have to a predator, to a snake. It is no surprise that she has avoided the subject, that it is odious to her. Mathematics has bitten her, has wounded her, and she remembers. She is not alone.

Her kind is legion. Sheila Tobias writes in Overcoming Math Anxiety that this intense fear of mathematics has limited the opportunities of millions of adults and that their negative experiences in mathematics can haunt them throughout their lives. It is part of our American culture that we do not give into fear and that we respond to it with defiance. Mathematics seems to be the exception. We not only accept as fact that math must cause dread, we tell ourselves a myriad of harmful myths to rationalize it.

Chief among these is the lateralization of brain function. This is the Right Brain/ Left Brain myth. There are many brain myths, such as the myth that we only use ten percent of our brains, but I think this one is the most harmful. Stemming from a misunderstanding of the split brain experiments performed by Sperry and Gazzaniga in the 1960s, the Right Brain/ Left Brain myth stipulates that people fall into one of two categories either Right Brain dominant or Left Brain dominant. Right Brain dominated people are said to be more creative and intuitive, whereas Left Brain dominated people are logical and analytic. The dangerous and fallacious conclusion is this: If you are Left Brained, you can do mathematics, if not then you can’t. When asked about astrology, Arthur C. Clark responded “I don’t believe in astrology; I’m a Sagittarius and we’re skeptical.”, and we should receive any such dictatorial theory with the same spirit, but we haven’t, and we don’t.

Roger W. Sperry and Michael S. Gazzaniga discovered some important things. They found out that the left and right sides of the brain process information independently. They discovered that they processed information differently. What they didn’t discover was that people are dominated by one hemisphere or the other.  This “fact” was “discovered” and popularized by the army of self-help writing vultures circling society’s anxieties. What was discovered is something that shouldn’t be surprising- we use both hemispheres of our brains all the time. Our experience of consciousness comes from a complex interaction of both types of data processing. As John McCrone writes in “Right Brain” or “Left Brain” – Myth Or Reality?,“whatever the story about lateralization, simple dichotomies are out. It is how the two sides of the brain complement and combine that counts.” He is perhaps too optimistic with his appraisal the myth when he states: “at least there seems no prospect of a return to the old left-right caricatures that inspired so many self-help books exhorting people to liberate their right-brains and avoid too much sterile left-brain thinking,”(2000).

If it is only a myth, why does it survive and resonate with so many? For the same reason that many myths survive- it provides a simple etiology for the state of the world: “I can’t paint because I’m a left brain person.”, “She always gets lost because she is right brained.”, “Math is for left brain, boring people.” Now, we all have our strengths and weaknesses, and there is certainly such a thing as talent, but we are not, for the most part, dictated by our biology. The myth of brain dichotomies is comforting to many because it provides a simple anodyne for the unsanitary and undemocratic fact that all people are not equal.  It provides the implicit assurance that any weakness one may possess is necessarily offset by a strength. Most harmful is the way it rationalizes and maintains the status quo and prevents challenges to it.

This dichotomy is taken as such a truism, that it is apparent in our very architecture. Here is a map of the tutoring department at the college I work at:

Room 116 is devoted to languages, social science, literature and the subjects falling under Humanities. Room 115 is devoted to mathematics, statistics, and the sciences. There is a wall between them. I realize that, in this photo, the arrangement of the subject is the reverse of that purported in the myth, but remember that the orientation of this map is arbitrary. The thing to note is this- we have so fully incorporated this myth into our culture that we no longer think to question it. We are so often consciously and unconsciously reminded of it that most people take it as fact.

If a lie is repeated enough times it would become widely accepted as truth.

-attributed to Joseph Goebbels.

This myth is most destructive when combined with another pernicious misbelief. Here is a typical list of right brain characteristics (taken from the Herald Sun, October 9, 2009 Right Brain v Left Brain), Right: uses feeling, believes, appreciates, fantasy based, impetuous. Compare this list of attributes to this poem written by Mrs. E. Little in response to the initial stirrings of the Women’s Rights movement and published in Godey’s Ladies Book in 1848:

The Rights of a True Woman

The right to love whom others scorn,

The right to comfort and to mourn,

The right to shed new joy on earth,

The right to feel the soul’s high worth …

Such women’s rights, and God will bless

And crown their champions with success.

When reading this poem, it is important to remember that the rights mentioned in the poem are the only rights assumed by a “true woman.” A “true woman” only has these characteristics. Certainly these are good characteristics, but the author is binding women by these rights and denying her any others. So what is the conclusion of the comparison between poem and the characteristics? The True Woman is Right-Brained.

The synthesis of the Right Brain/ Left Brain myth and the True Woman myth is a truly dangerous and largely unquestioned lie that runs rampant throughout our society. Furthermore, it is a self fulfilling stereotype.

University of California Santa Barbara mathematics professor, John Ernest states the results of a 1976 study of high school students: “[both genders] have a fair amount of trouble doing math, and most of them do not like the subject very much.” If both genders are equally poor at mathematics, then what is the explanation for this:

From the same study: “The difference between them was that boys stuck with math, because they felt their careers depended on it and because they had more confidence than girls in their ability to learn it.”  Why is there this difference in confidence, and where did it come from? I would like to emphasize the point that it isn’t biological: “No one has yet identified a ‘math lobe’ in the brain.” If the answer isn’t internal, it necessarily must be external, and it is: “Researchers can only measure performance on tests, and we know much more now than we used to about how much performance is influenced by beliefs, perceptions, prior experience, and self-esteem.” (Tobias, 1993).  It is societal.

There is a common bias to dismiss the effect society has on educated people. We believe that our knowledge and cleverness buffers us from the stereotypes. We think that because we know words and phrases like peer pressure, discrimination, mores, folkways, and words ending in ‘ism’, we are protected from them, like knowing the names of demons. However this is dismissive and untrue. Temple University mathematics professor, John Allen Paulos, writes in Innumeracy, “whether or not a department has a mathematics or statistics requirement is the most important single determinant of where a woman will attend graduate school to study political science,”(2001).

Math anxiety is a serious thing. It truly affects people’s lives, and I think it is most harmful to women.  In my personal experience, it manifests itself differently in women than in men. The anxiety is most often displayed as frustration and anger in males, and fear and despair in females. From a tutoring perspective, this presents very different challenges. In a tutoring session, anger can be used creatively: The tutoring session can be recast as a confrontation between the student and the problem, and the belligerent side of anger used as a catalyst to get the student to confront and overcome the difficulty.  Fear is far harder to deal with. When a student feels real physical dread of mathematics it is very hard to get the student to refuse the natural instinct to run and to stay with the problem.

I’m going to quote a long passage from Malcolm Gladwell’s book, Outliers: The Story of Success. I encourage you to read the full passage.  Though Outliers is not specifically about mathematics, this passage captures the essence of mathematical learning better than any other I have come across, and I believe its example is invaluable. (For clarification, I have used Wolfram|Alpha to make reproductions of the graphs featured in the book):

A few years ago, Alan Schoenfeld, a math professor at Berkeley, made a videotape of a woman named Renee as she was trying to solve a math problem. Renee was in her mid-twenties, with long black hair and round silver glasses. In the tape, she’s playing with a software program designed to teach algebra. On the screen are a y and an x axis. The program asks the user to punch in a set of coordinates and then draws the line from those coordinates on the screen. For example, when she typed in 5 on the y axis and 5 on the x axis, the computer did this:


At this point, I’m sure, some vague memory of your middle-school algebra is coming back to you. But rest assured, you don’t need to remember any of it to understand the significance of Renee’s example. In fact, as you listen to Renee talking in the next few paragraphs, focus not on what she’s saying but rather on how she’s talking and why she’s talking the way she is.

The point of the computer program, which Schoenfeld created, was to teach students about how to calculate the slope of a line. Slope, as I’m sure you remember (or, more accurately, as I’ll bet you don’t remember; I certainly didn’t), is rise over run. The slope of the line in our example is 1, since the rise is 5 and the run is 5.

So there is Renee. She’s sitting at the keyboard, and she’s trying to figure out what numbers to enter in order to get the computer to draw a line that is absolutely vertical, that is directly superimposed over the y axis. Now, those of you who remember your high school math will know that this is, in fact, impossible. A vertical line has an undefined slope. Its rise is infinite: any number on the y axis starting at zero and going on forever. It’s run on the x axis, meanwhile, is zero. Infinity divided by zero is not a number.

But Renee doesn’t realize that what she’s trying to do can’t be done. She is, rather, in the grip of what Schoenfeld calls a “glorious misconception,” and the reason Schoenfeld likes to show this particular tape is that it is a perfect demonstration of how this misconception came to be resolved.

Renee was a nurse. She wasn’t someone who had been particularly interested in mathematics in the past. But she had somehow gotten hold of the software and was hooked.

“Now, what I want to do is make a straight line with this formula, parallel to the y axis,” she begins. Schoenfeld is sitting next to her. She looks over at him anxiously. “It’s been five years since I did any of this.”

She starts to fiddle with the program, typing in different numbers. “Now if I change the slope that way…minus 1 . .. now what I mean to do is make the line go straight.”

As she types in numbers, the line on the screen changes.

“Oops. That’s not going to do it.”

She looks puzzled.

“What are you trying to do?” Schoenfeld asks.

“What I’m trying to do is make a straight line parallel to the y axis. What do I need to do here? I think what I need to do is change this a little bit.” She points at the place where the number for the y axis is. “That was something I discovered. That when you go from 1 to 2, there was a rather big change. But now if you get way up there you have to keep changing.”

This is Renee’s glorious misconception. She’s noticed the higher she makes the y axis coordinate, the steeper the line gets. So she thinks the key to making a vertical line is just making the y axis coordinate large enough.

“I guess 12 or even 13 could do it. Maybe even as much as 15.”

She frowns. She and Schoenfeld go back and forth. She asks him questions. He prods her gently in the right direction. She keeps trying and trying, one approach after another.

At one point, she types in 20. The line gets a little bit steeper.


She types in 40. The line gets steeper still.


“I see that there is a relationship there. But as to why, it doesn’t seem to make sense to me… What if I do 80? If 40 gets me halfway, then 80 should get me all the way to the y axis. So let’s just see what happens.” She types in 80. The line is steeper. But it’s still not totally vertical.


“Ohhh. It’s infinity, isn’t it? It’s never going to get there.” Renee is close. But then she reverts to her original misconception.

“So what do I need? 100? Every time you double the number, you get halfway to the y axis. But it never gets there…”

She types in 100.


“It’s closer. But not quite there yet.”

She starts to think out loud. It’s obvious she’s on the verge of figuring something out. “Well, I knew this, though… but… I knew that. For each one up, it goes that many over. I’m still somewhat confused as to why…”

She pauses, squinting at the screen.

“I’m getting confused. It’s a tenth of the way to the one. But I don’t want it to be…”

And then she sees it.

“Oh! It’s any number up, and zero over. It’s any number divided by zero!” Her face lights up. “A vertical line is anything divided by zero — and that’s an undefined number. Ohhh. Okay. Now I see. The slope of a vertical line is undefined. Ahhhh. That means something now. I won’t forget that!”

Over the course of his career, Schoenfeld has videotaped countless students as they worked on math problems. But the Renee tape is one of his favorites because of how beautifully it illustrates what he considers to be the secret to learning mathematics. Twenty-two minutes pass from the moment Renee begins playing with the computer program to the moment she says, “Ahhhh. That means something now.” That’s a long time. (2008)

This is the story of a math student. Studying mathematics is a long, difficult process. It is tedium and torture interspersed with sporadic epiphanies of such brilliance that they justify the effort that came before them and renew one’s desire to venture onwards. I often think of studying mathematics as climbing a succession of mountains. The climb is hard and exhausting, but upon reaching a summit, the vista’s beauty inspires you to continue, to attempt the next peak, and with each crest, you see farther and clearer. To understand and enjoy mathematics, this trek is necessary. Imagine the student with math anxiety attempting this journey, sticking with one problem for twenty-two agonizing minutes knowing that she is a right-brained woman in a left-brained man’s field, and throughout it all, her body reminding her that she is in imminent mortal danger.

[Mathematicians] resemble those that gaze out from the tops of high mountains whose summits are lost in the clouds. Objects on the plain below have disappeared from view; they are left with only the spectacle of their own thoughts and the consciousness of the height to which they have risen… -Denis Diderot

There is a nasty and ridiculous response that rears its head whenever someone is audacious enough to suggest that sexism or gender inequality is in fact a thing. It is the inevitable argument by example. It goes like this: “A bias against women does not exist in mathematics; my high school chemistry teacher, Mrs. Representativeforallwomen, was a scientist and a woman.” We should all be able to see the absurdity of the speaker’s conclusion, but to draw attention to that fact I am going to list the first names of the entire 2010 faculty of Stanford University mathematics department, one of the most prestigious mathematics departments in the world. You will see that some of them are indeed women:

Ricardo, Simon, Gregory, Daniel, Isabelle, Emmanuel, Gunnar, Ralph, Brian, Craig, Amir, Persi, Yakov, Solomon, Robert, Søren, Pierre, Eleny, Renata, Vladislav, Yitzhak, Joseph, Steren, Jun, Joan, Tai-Ping, Rafe, Peter, James, Grigori, Maryam, Donald, Robert, George, Lenya, Richard, Leon, Kannon, Ravi, András, Akshay, Brian, Melanie

Out of the 43 faculty members, 6 are women. That’s about 14%. Have I proved anything? No, but it most provoke our curiosity why there is such a disparity between the percentage of the faculty that is female, 14%, and the percentage of people who are female, 51%. If the reason for this schism is not biological, which it isn’t then what is it?

A 2010 report by the American Association of University Women titled Why so Few: Women in Science, Technology, Engineering, and Mathematics provides some answers: “In schools and in homes the environment that is created serves to subtly and perhaps in some cases not so subtly discourages girls or encourages them to focus on other areas, even if they might have a brimming interest and ability in science.” Sheila Tobias provides us with examples of the practical manifestation of this phenomenon:

Fathers… are more likely to help with math homework than mothers. Even teachers, expecting more in mathematics of their boy students than of their girls, ask higher-order questions of boys and encourage males to discover alternative solutions while inhibiting girls’ mathematical creativity by insisting that they follow the rules.(1993)

We do not encourage our female students to continue their studies in mathematics. We don’t provide clear female role models in these areas. We believe myths about women being incapable of math. Consciously or unconsciously we reinforce these attitudes and create an atmosphere that implies math is not for girls.

Most tragic is the fact that these prejudices shape the world in their image. The constant repetition and reinforcement of the notion that math and science are only for the biologically selected discourages and prevents encouragement for many. Fewer women then go into these fields, and the myth appears true. Less women scientists and mathematicians mean less female role models for students considering the fields. It means simple intimidation by gender inequality. There is no shadowy plan against women here; there is simply the self-fulfilling prophecy of some myths run rampant.

My own sister has experienced these prejudices. When she asked her adviser about pursuing science, her adviser advised her against it. The reason? She was a “language person” was the response. Implicit in “language person” is this pernicious logic: language person= right brained= a woman. A person in authority attempts to shape someone’s future based on falsehoods. I wonder how many woman have been turned away from sciences because their advisers, teachers, friends, or parents told them they were “language persons.”

How it Works, XKCD by Randall Munroe

Having failed to embed it( wordpress currently does not support vimeo embedding), I’m placing a link to a video by physicist, educator, and skateboarder, Yung Tae Kim addresses several of the failings of our education system, and provides some suggestions for reform. While these concerns apply to every aspect of education, I feel that they are especially pertinent to science and mathematics education. I think the entire video is brilliant, however if you are pressed for time I would suggest skipping to:

1:40 – a discussion of the problem of depersonalization and class size. Keep in mind how this atmosphere may affect individuals with math anxiety.

5:00 – a shocking statistic regarding the credentials of many science teachers.

10:28 – the negative effects of some common teaching practices. I feel these practices may be especially harmful to women.

Here is Dr. Tae’s Building a New Culture of Teaching and Learning

Why are such harmful attitudes so prevalent in our society? How have we let them flourish? Why aren’t there more women in science and mathematics? Many of these beliefs have become entrenched in our culture through their long history. It is a legacy that begins fourteen hundred years ago with the first recorded female mathematician.

In order to understand something, you must go to its origins.

– Aristotle

St. Paul at Epesus from the Doré Bible, Gustave Doré 1865

In 391, the Christian emperor Theodosius I made paganism illegal. Shortly thereafter, by decree of Patriarch Theophilus, the Serapeum of Alexandria was looted and destroyed.   A temple to the god Serapis, it was renowned in the ancient world. The Roman historian Ammianus Marcellinus, a contemporary to the Serapeum’s destruction, described it as “splendid to a point that words would only diminish its beauty.”  However, its importance in 391 went far beyond its aesthetics. After the inadvertent destruction of the Great Library of Alexandria by Julius Caesar in 31BCE, the Serapeum became the shelter for many of the surviving books. The Great Library of Alexandria was the greatest repository of knowledge, and for a time the most academically vibrant place in the ancient world. It would remain the single greatest accumulation of knowledge achieved until the Renaissance, thirteen hundred years later. With its destruction, human knowledge was set back hundreds of years. It would take millennia for science and mathematics to recover. The destruction of the Serapeum and the surviving books set the recovery back even further.

Watching this tragic event was a 21 year old woman whose brilliance was equal to any displayed in those books, and whose end was just as tragic. Hypatia of Alexandria, history’s first recorded female scientist, was an anomaly of her time.  The ancient view of women was terrible. In Athens, women could not leave their homes, accept inheritance, or buy things and they were bound to marriage for survival. The story of Pandora suggests that not only were women created as a punishment for men, but that women are the cause of all evils in the world. The story of Genesis goes so far as to blame women for the existence of death.  In the Timaeus, when Plato outlines his theory of reincarnation, he tells us that wretched men are punished by being reborn as women: “Of the men who came into the world, those who were cowards or led unrighteous lives may with reason be supposed to have changed into the nature of women in the second generation.” But here in 391, watching the holocaust of the achievements of the ancient world is 21 year old Hypatia. A woman dressed in the strictly male robes of scholars. A woman who had the audacity and keenness to lecture to halls of men about science, astronomy, logic, philosophy and mathematics – subjects considered beyond all reach of the female mind.

Hypatia in The School of Athens, Raphael 1510

There was a woman at Alexandria named Hypatia, daughter of the philosopher Theon, who made such attainments in literature and science, as to far surpass all the philosophers of her own time. Having succeeded to the school of Plato and Plotinus, she explained the principles of philosophy to her auditors, many of whom came from a distance to receive her instructions. On account of the self-possession and ease of manner, which she had acquired in consequence of the cultivation of her mind, she not unfrequently appeared in public in presence of the magistrates. Neither did she feel abashed in going to an assembly of men. For all men on account of her extraordinary dignity and virtue admired her the more.

-Socrates Scholasticus

The vast majority of Hypatia’s work has been destroyed or lost to the tides of history. However, what remains is of such remarkable quality and importance that it is truly surprising that she was indeed more prolific. She was a mathematics professor at the Museum of Alexandria, a position first held by the single greatest mathematics writer of all time, Euclid. This is comparable to the “Newton’s Chair” of physics at the University of Cambridge, formerly held by Stephen Hawking.  Her lectures were extremely well regarded and men would travel vast distances to study under her.

Woman Teaching Geometry in Adelard of Bath's translation of Euclid's Elements 1309-1316

Most of what we know about her personality, reputation and research comes from one of her students, Synesius of Cyrene who became bishop of Ptolemias in Libya. Through his writings we know that Hypatia was involved in the invention of the astrolabe (used for astronomy and navigation), the planesphere (an interactive star chart), the hydroscope (similar to a periscope, used for seeing under the water), and the hydrometer (an instrument for measuring the density/ specific gravity of liquids).

An Astrolabe

Most of her mathematical writings are believed to have been in the form of class notes and textbooks to her students, which have been lost. However two of her treatises have survived. In On the Conics of Appolonius, she popularizes and extends Appolonius work on conic sections. After Hypatia’s death, this area of mathematics would be forgotten and ignored until the seventeenth century. Her most important work is a commentary on Diophantus’ Arithmetica. Diophantus who lived in the third century, is considered “the father of algebra.” He invented the concept of using symbolic notation in mathematics, an invention without which mathematics would be hopelessly impaired. The academic tradition of commentaries required the commentator to copy the entire work by hand adding annotations and enhancement. Of the surviving copies of Diophantus’ Arithmetica, it is theorized that all are derived from Hypatia’s commentaries and therefore include her additions. She is as much an author of the work we now call Arithmetica as Diophantus. Without her work we would no longer have his and science and mathematics would be centuries behind.

Furthermore Hypatia was a philosopher, and she passed along her neoPlatonist beliefs to her students. At the height of her career, letters addressed simply to “The Muse” or “The Philosopher” would be delivered unquestioningly to her. This influence is clear in Synesius, who was a forerunner in combining Platonism with Christianity – a practice which would become dominant in the middle ages, and is still seen today. Central to her philosophy was scientific rationalism, and this was a liability for her because in the fourth century, an ecclesiastical campaign against science would lead to one of the greatest tragedies of the ancient world.

Hypatia by Masolino da Panicale 1428

It is important to remember that Hypatia was unique in her world. There were no other female scientists, lecturers, inventors, mathematicians, or philosophers at that time. As far as we know, there had never been. It was assumed that there couldn’t be. Hypatia’s opportunity to become a scholar and public figure was provided to her by her father, Theon of Alexandria; a man who is remarkable for his belief in and love of his daughter.

Reserve your right to think, for even to think wrongly is better than not to think at all.

-Theon of Alexandria

Theon was himself a distinguished mathematician and astronomer at the Museum of Alexandria. He may even have been its director. His greatest works are his commentaries on Ptolemy’s astronomical work, Almagest (assisted by Hypatia), and Euclid’s Elements (perhaps the most significant work of mathematics ever published). Like Hypatia, it seems that most of his writing was for his students, and for them he made significant clarifications and enhancements to the Elements. He was concerned with the quality of his students, noting that many could not follow geometric demonstrations. He felt that academics was losing its rigor. Perhaps in response to these fears, he took a special interest in his daughter.  He was determined to help Hypatia develop into the “perfect human being.”

Theon made sure that Hypatia received a formal education in the arts, literature, science, and philosophy. He immersed her in the intellectual world of Alexandria, and personally tutored her in mathematics. Theon knew that Hypatia would face harsh criticism due to her gender, and to equip her against these, he had her trained in speech and rhetoric. When her competencies exceeded his, she travelled to Athens to study at the school founded by the philosopher Plutarch.

Theon invented as series of exercises and calisthenics for Hypatia to practice. He cherished her, and tried to cultivate her in all dimensions. Theon’s belief in his daughter should still be inspiring. She may have been naturally intelligent and talented, but it was her father’s support and encouragement that allowed her to blossom. Success does not spring from a vacuum.

All formal dogmatic religions are fallacious and must never be accepted by self-respecting persons as final. –Theon of Alexandria

By the end of the fourth century and into the fifth century, by necessity of Roman law, Roman citizens were converting to Christianity. Throughout the empire, heresies were being purged, and the heretics assassinated. It had become popular propaganda that non-Christian beliefs were weakening Roman character and had to be annihilated. In Alexandria, this was the task of the bishop Cyril.

Saint Cyril of Alexandria by Ignaz Franz Platzer, 1717-1787

Cyril of Alexandria was ideal for this position. He seems to have had a gift for inciting the passions of his followers. In 412, he was consecrated as a successor to his uncle, Theophilus, but only after his supporters rioted violently against his opponent. His first act was the persecution of the Novations (a sect that denied the authority of the pope), and the plunder of their churches. Shortly thereafter, he instructed his followers to drive the Jews from Alexandria.

The expulsion of the Jews incensed the Prefect of Alexandria, Orestes, who moved against Cyril. In defense of the Bishop, five hundred monks travelled to Alexandria from Nitria several miles south of Alexandria. With this influx, Cyril’s power in the city rivaled Orestes’ and things became violent. At one riot, a monk named Ammonius injured Orestes with a thrown rock. Orestes had Ammonius arrested and tortured to death.

Cyril brought Ammonius’ remains to the cathedral, and honored the monk as a martyr. The monk’s death, and Cyril’s fiery passion galvanized his supporters, and rioting in Alexandria became continuous. The most infamous of these riots was led by Peter the Lector in 415. It had a specific target.

Hypatia was the perfect victim. She was a friend and supporter of Orestes. She represented the paganism that the Christians were attempting to purge. She taught the knowledge of the decadent, sinful Greeks. Her Platonism and scientific rationalism were in opposition to the Chrisitian dogma. Most importantly, she was an example of the corrupting influence of that knowledge- She was a woman who didn’t know her place, and she was corrupting the young men of Alexandria.

Hypatia was torn from her chariot by a bloodthirsty mob as she was returning to her home from the Museum. She was stripped of her clothes as they dragged her through the streets and into the Cathedral of Alexandria. On that hallowed ground, she was held by the rioters as they tore her skin from her bones with oyster shells. The strips were burnt piece by piece as she died.

Hypatia by Charles William Mitchell, 1885

Let your women keep silent…-1 Corinthians 14

Cyril would later become Saint Cyril, and go on to author the seventeen volume On Adoration in Spirit and in Truth. Both titles seem tragically ironic to me.

Hypatia’s murder represents more than just the loss of a great human. With her assassination, the academic spirit in Alexandria was broken. Historians mark the end of Greek mathematics with her death. A millennium would pass before science and mathematics regained its vigor. The Dark Ages would soon begin.

Hypatia is often mentioned as an inspiration for woman, and she is. However, I think the truth of her legacy is much darker. There would not be another woman mathematician for over twelve hundred years until Elena Lucrezia Cornaro Piscopia received her doctorate in 1678. Saint Cyril and Peter the Lector’s message seems to have rung loud, clear, and long. They laid the precedent: “It is dangerous for a woman to study science and mathematics, to be a scholar and an author. Society doesn’t want you, and will expel you. It is not natural and not Christian.” Their misogyny and anti-intellectualism have sounded throughout history and still echo today. How many fathers like Theon decided against schooling their daughters out of a fear that they would follow Hypatia’s fate? If only Hypatia were not murdered, perhaps her story would have served as inspiration for thousands of girls instead of as a warning.

Rape of Cassandra, Red figure pottery, C, 370-360 BCE

The most important event of classical mythology occurs during the sack of Troy after the Greeks have succeeded with their gambit of the Trojan Horse. Amidst the chaos of Troy’s collapse and the massacre being carried out by the Greek troops, Cassandra, daughter of Troy’s King Priam, Priestess of Athena, Seer of Troy, and the one Trojan who knew they were doomed, sought sanctuary in the Temple of Athena. There she grasped the statue of Athena with both arms. In classical tradition this should have meant that she was untouchable, that Athena had granted her asylum. But something went horribly wrong. Ajax the Lessor, a hero of Greece, burst into the temple, raped Cassandra at the feet of Athena, and abducted her.

This trespass of one of the fundamental codes of the Hellenistic religions enraged the gods who cursed the Greeks. This curse was the reason the Heroes of Troy met such difficulties in returning home. Hesiod in Works and Days marks this as the event that turned the gods away from men, and ended the age of heroes and mythology. The gods were so disgusted by Ajax actions, that they washed their hands of us. In Hesiod’s words, humanity entered a period of unstoppable degeneration in which “there will be no help against evil.”

Hypatia’s murder has cast a similar shadow. We have all been cursed for what was done in that cathedral. We had the opportunity to mature as a species and make strides for equality and rationality, but it was lost to dogmatic hatred. Our heritage is a sixteen hundred year old handicap, and it is time to make amends. Do not passively allow dogmatic thinking to limit the world we live in – this is our responsibility.

Fable should be taught as fable, myth as myth, and miracles as poetic fancies. To teach superstitions as truths is horrifying. The mind of a child accepts them and only through great pain, perhaps tragedy, can the child be relieved of them. Men will fight for superstition as quickly as for the living truth – even more so, since a superstition is intangible, you can’t refute it, but truth is a point of view, so it is changeable.

-Hypatia of Alexandria

Bibliography

Ceci, Stephen. “Women and Math | Psychology Today.” Psychology Today: Health, Help, Happiness Find a Therapist. http://www.psychologytoday.com/blog/exploding-myths/200912/women-and-math (accessed September 20, 2010).

Chapman, J. “St. Cyril of Alexandria.” In The Catholic Encyclopedia. Vol. 4. New York: Robert Appleton Company, 1908.

Elfman, Lois. “Report Examines Why Women Are Under-represented in STEM Fields.” Higher Education News and Jobs. http://diverseeducation.com/article/13640/ (accessed September 20, 2010).

Ernest, John. “Mathematics and Sex.” American Mathematics Monthly 83, no. 2 (1976).

“Faculty.” Department of Mathematics – Stanford University. http://math.stanford.edu/directory/faculty.html (accessed September 28, 2010).

Gladwell, Malcolm. “Rice Paddies and Math Tests.” In Outliers: the Story of Success. New York: Little, Brown and, 2008.

Lienhard, John H. “Hypatia’s Mathematics.” University of Huston. http://www.uh.edu/engines/epi215.htm (accessed September 22, 2010).

McCrone, John. “‘Right Brain’ or ‘Left Brain’ – Myth Or Reality?” Rense.com. http://www.rense.com/general2/rb.htm (accessed September 20, 2010).

Mertz, Janet E. “Why Females Remain Underrepresented in Mathematics at the Highest Level.” American Society for Cell Biology Newsletter (August 2009): 7-9.

O’Connor, J. J., and E. F. Robertson. “Theon of Alexandria.” School of Mathematics and Statistics, University of Saint Andrews, Scotland. http://www-history.mcs.st-and.ac.uk/Biographies/Theon.html (accessed September 24, 2010).

Paulos, John Allen. Innumeracy: Mathematical Illiteracy and Its Consequences. New York: Vintage Books, 1990.

“Right Brain v Left Brain.” Herald Sun. http://www.heraldsun.com.au/news/right-brain-v-left-brain/story-e6frf7jo-1111114603615 (accessed September 20, 2010).

“The Left Brain/ Right Brain Myth : Neurophilosophy.” ScienceBlogs. http://scienceblogs.com/neurophilosophy/2007/10/the_left_brain_right_brain_myt.php (accessed September 20, 2010).

“The Split Brain Experiments.” Nobelprize.org. http://nobelprize.org/educational/medicine/split-brain/background.html (accessed September 20, 2010).

Tobias, Sheila. Overcoming Math Anxiety. New York: W.W. Norton, 1993.

Williams, Danielle. “The Life and Legacy of Hypatia.” http://hem.bredband.net/b153434/works/hypatia.htm (accessed September 22, 2010).

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About Webster

Transitionally, I’m a math student and tutor en route to becoming a math professor. Permanently, I’m a mathematics enthusiast. I study mathematics professionally, and as a leisure activity. At the time of writing this, I’m a generalist. I have let to reach the depth of understanding that requires specialization. Though I eagerly await that time, I do enjoy the ‘now’ and find there is bountiful food for thought at any level.
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5 Responses to The Rape of Cassandra

  1. Melody says:

    Hi Webster! I am with annabelle and I have wanted to look at this so many times but I havent had time until now, thank god. I want to give you my most sincere heartfelt congratulations for your joyous, wondrous, creative, enthusiastic, spiritual, inquisitive approach in challenging the status quo of the field of mathematics.

    I’m so proud of you! But I have to say that I have seen research that has suggested that gender differences in mathematics do not become apparent until around 8th grade. Some neuroscience research suggests that the onset of menses leads to iron deficiencies in females and that iron is an essential component for sustained concentration in frustrating subjects.

    Therefore, it is my advice to this age group that they take a supplement of iron at least once a week to give them this edge that male counterparts don’t ahve to ddeal with. This does not deny all of what you have written. IT may make it more difficult for females to survive problems of accelling at math. Please check my references though since I do not remember the origin of these studies.

    Love you!

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