Tag Archives: Euclidean Geometry

Happy Birthday, Omar Khayyám!

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By Adelaide Hanscom, from Edward Fitzgerald's The Rubaiyat of Omar Khayyam, 1905, public domain via Wikimedia Commons

Since Edward FitzGerald published his translation of The Rubáiyát of Omar Khayyám in 1859, Omar Khayyám (May 18, 1048 – December 4, 1131) has been known, especially in the western world, first and foremost as a great poet, eloquently expressing the joy and beauty of life and our own struggles to live it with a sense of love and meaning. It’s a humanist work, with Khayyám writing much as an Epicurean or Skeptic here and a Stoic there, freely doubting and wondering at everything, unshackled from the orthodoxy one might expect from a famed teacher and writer of his time and place. Yet Khayyám, a devotee of Avicenna, took his Islamic faith very seriously and thought deeply about the nature of his God and humankind’s proper relationship to him.

Khayyám, born in Persia in 1048, was most famed in his own time as a mathematician, astronomer, and scientist. He wrote some of the most important medieval works in geometry and algebra, and helped reform the calendar, an even more accurate one than the Gregorian calendar we use today. But he was also an accomplished philosopher, and scholars are working on resolving the apparent contradictions between this work and his poetry.

One thing I’ve gotten from my research on Khayyám (which, thus far, is not nearly enough): for all his prodigious learning and accomplishments, Khayyám honestly acknowledges the limits of human understanding. He tells us that while the great work of discerning the truths of the universe is a great, noble, and necessary endeavor, we do well to keep in mind that we can never know everything, through science, religion, or any other means. So, Khayyám seems tells us, we do well to work, to wonder, to seek, to do right, but also to live for today:

At first they brought me perplexed in this way
Amazement still enhances day by day
We all alike are tasked to go but Oh!
Why are we brought and sent? This none can say’. (Rubā‘iyyāt, Tirtha 1941, 18, from IEP)

‘As Spring and Fall make their appointed turn,
The leaves of life one aft another turn;
Drink wine and brood not—as the Sage has said:
“Life’s cares are poison, wine the cure in turn.” (Sa‘idī 1994, 58, from IEP)

Learn more about this great poet and thinker at:

How ‘The Rubáiyát of Omar Khayyám’ Inspired Victorian Hedonists ~ by Roman Krznaric

Omar Khayyam ~ by J. J. O’Connor and E. F. Robertson for the School of Mathematics and Statistics at the University of St Andrews, Scotland

‘Omar Khayaam, 1048–1131 ~ The Poetry Foundation

Omar Khayyam: Persian poet and astronomer ~ by the editors for Encyclopædia Britannica

Umar al-Khayyam (Omar Khayyam) – by the editors for Muslim Heritage

Umar Khayyam ~ by Mehdi Aminrazavi and Glen Van Brummelen for The Stanford Encyclopedia of Philosophy

*A version of this piece was previously published at Ordinary Philosophy

~ Ordinary Philosophy is a labor of love and ad-free, supported by patrons and readers like you. Any support you can offer will be deeply appreciated!

Happy Birthday, Omar Khayyám!

Posted on by

By Adelaide Hanscom, from Edward Fitzgerald's The Rubaiyat of Omar Khayyam, 1905, public domain via Wikimedia Commons

Since Edward FitzGerald published his translation of The Rubáiyát of Omar Khayyám in 1859, Omar Khayyám (May 18, 1048 – December 4, 1131) has been known, especially in the western world, first and foremost as a great poet, eloquently expressing the joy and beauty of life and our own struggles to live it with a sense of love and meaning. It’s a humanist work, with Khayyám writing much as an Epicurean or Skeptic here and a Stoic there, freely doubting and wondering at everything, unshackled from the orthodoxy one might expect from a famed teacher and writer of his time and place. Yet Khayyám, a devotee of Avicenna, took his Islamic faith very seriously, and thought deeply about the nature of God and our relationship to him.

Khayyám, born in Persia in 1048, was most famed in his own time as a mathematician, astronomer, and scientist. He wrote some of the most important medieval works in geometry and algebra, and helped reform the calendar, an even more accurate one than the Gregorian calendar we use today. But he was also an accomplished philosopher, and scholars are working on resolving the apparent contradictions between this work and his poetry.

One thing I’ve gotten from my research (which, thus far, is only beginning and therefore not nearly enough): for all his prodigious learning and accomplishments, Khayyám honestly acknowledges the limits of human understanding, and seems to tell us that while the great work of discerning the truths of the universe is a great, noble, even necessary endeavor, we do well to keep in mind that we can never know everything, whether through science or religion. So, Khayyám seems tells us, we do well to work, to wonder, to seek, to do right, but also to live for today:

At first they brought me perplexed in this way
Amazement still enhances day by day
We all alike are tasked to go but Oh!
Why are we brought and sent? This none can say’. (Rubā‘iyyāt, Tirtha 1941, 18, from IEP)

‘As Spring and Fall make their appointed turn,
The leaves of life one aft another turn;
Drink wine and brood not—as the Sage has said:
“Life’s cares are poison, wine the cure in turn.” (Sa‘idī 1994, 58, from IEP)

Learn more about this great poet and thinker at:

Umar Khayyam –  by Mehdi Aminrazavi and Glen Van Brummelen for The Stanford Encyclopedia of Philosophy

‘Omar Khayaam, 1048–1131 – The Poetry Foundation

Omar Khayyam – Encyclopædia Britannica.

Avicenna (Ibn Sina) – by Sajjad H. Rizvi for The Internet Encyclopedia of Philosophy

Umar al-Khayyam (Omar Khayyam) – for Muslim Heritage

*A version of this piece was previously published at Ordinary Philosophy

~ Ordinary Philosophy is a labor of love and ad-free, supported by patrons and readers like you. Any support you can offer will be deeply appreciated!

In Memory of Hypatia of Alexandria

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Detail of the death portrait of a wealthy woman, c. 160-170 AD near modern-day Er-Rubayat in the Fayum, public domain via Wikimedia Commons

Detail of the death portrait of a wealthy woman, c. 160-170 AD near modern-day Er-Rubayat in the Fayum, public domain via Wikimedia Commons

Hypatia’s birthday is somewhere between 350 and 370 AD; a range of dates indicating great uncertainty, to be sure, but original sources that old are hard to come by, especially from a city as turbulent and violence-torn as the Alexandria of her day. The day of her death is better known, sometime in March of 415 AD. Since the latter date is more precise, we’ll break with our birthday remembrance tradition here and celebrate the memory of Hypatia in the month of her tragic and violent death instead of on the date of her birth.

She was a mathematician, astronomer, teacher, and philosopher who wrote commentaries on important works in geometry and astronomy with her father Theon, likely contributing original work of her own. Hypatia was a Neoplatonist, a philosophy with mystical overtones which posits that everything derives its being from the One, an ultimately conscious yet nonmaterial, non-spacial entity which is the pure ideal of everything that is. She was a scholar and teacher in a field and in a male-dominated world, and historians from her day to ours emphasize her extraordinary talents and her femininity with a nearly equal mix of awe and bemusement.

So let us remember and honor Hypatia for her great contributions to human knowledge and to the history of women’s liberation, living proof that women are equals in intellect and courage.

And let us also remember her sad death as a cautionary tale against those who inflame popular sentiment to seize power for themselves. Hypatia met her death at the hands of a mob caught up in the anti-pagan hysteria of the day, an at least partly political religious hysteria shared by Christians, Jews, and pagans alike; Alexandria itself was caught up in a power struggle between political and religious factions. The mob of extremists who dragged Hypatia from her carriage, stripped and then tortured and killed her by tearing off her skin with broken roof tiles, and then defiled her body were inspired by their partisanship with theocratic bishop Cyril to kill this pagan philosopher also admired by many Christians, this mathematician and astronomer (then often equated with sorcerer), this woman who dared teach men, this friend of Cyril’s rival Orestes, civic leader of Alexandria. According to Hypatia scholar Micheal Deakin, “Cyril was no party to this hideous deed, but it was the work of men whose passions he had originally called out. Had there been no [earlier such episodes], there would doubtless have been no murder of Hypatia.”*

Learn more about the great Hypatia of Alexandria:

Hypatia: Mathematician and Astronomer – by Michael Deakin for Encyclopædia Britannica

‘Hypatia of Alexandria‘ – by Michael Deakin for Ockham’s Razor radio program of Radio National of Australia (transcript), Sun August 3rd 1997. (click ‘Show’ across from ‘Transcript’)

‘Hypatia of Alexandria‘ – by Beckett Graham and Susan Vollenweider for The History Chicks podcast

‘Hypatia of Alexandria‘ – by J J O’Connor and E F Robertson for the School of Mathematics and Statistics of thr University of St Andrews in  Scotland website.

“Agora” and Hypatia – Hollywood Strikes Again – by Tim O’Neill for Armarium Magnum blog, Wed May 20, 2009

Hypatia, Ancient Alexandria’s Great Female Scholar – Zielinski, Sarah. ‘Smithsonianmag.com, Mar 14, 2010.

…and about Neoplatonism

Wildberg, Christian, “Neoplatonism“, The Stanford Encyclopedia of Philosophy

~ Ordinary Philosophy is a labor of love and ad-free, supported by patrons and readers like you. Please offer your support today!

* Versions of this piece were originally published here at Ordinary Philosophy one and two years ago. As you can see from past comments, some took issue with my characterization of Hypatia’s murder as, at least in part, inspired by anti-pagan and anti-science religious extremism which in turn, could make her appear as an ideological martyr. One of the most impassioned critics of this piece accused me of perpetuating a partisan and ideologically-motivated distortion created by the anti-clerical John Toland in 1753. This critic insisted that Hypatia’s death was entirely the result of politics, not religion, and therefore any retelling of her death that even hints at religious persecution is likewise just more myth-making. I respond, in brief, that one: the circumstances surrounding her death are still the subject of much scholarly debate given the paucity of contemporary sources and two: that it seems ahistorical to separate out the political from the religious. In Hypatia’s time and indeed, throughout much of history, the religious and political were intertwined and thus, impossible to consider as fully separate issues. I do agree, however, that modern accounts of Hypatia’s murder tend to emphasize the religious and anti-science persecution elements without enough consideration of the political aspects, which is why I include a variety of resources and articles for the reader to consider. I’ve also edited it lightly for clarity, and removed a section in which I drew a parallel between the circumstances which led to Hypatia’s violent death and a timely political news story.

Happy Birthday, Omar Khayyám!

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By Adelaide Hanscom, from Edward Fitzgerald's The Rubaiyat of Omar Khayyam, 1905, public domain via Wikimedia Commons

Since Edward FitzGerald published his translation of The Rubáiyát of Omar Khayyám in 1859, Omar Khayyám has been known, especially in the western world, first and foremost as a great poet, eloquently expressing the joy and beauty of life and our own struggles to live it with a sense of love and meaning. It’s a humanist work, with Khayyám writing much as an Epicurean or Skeptic here and a Stoic there, freely doubting and wondering at everything, unshackled from the orthodoxy one might expect from a famed teacher and writer of his time and place. Yet Khayyám, a devotee of Avicenna, took his Islamic faith very seriously, and thought deeply about the nature of God and our relationship to him.

Khayyám, born in Persia in 1048, was most famed in his own time as a mathematician, astronomer, and scientist. He wrote some of the most important medieval works in geometry and algebra, and helped reform the calendar, an even more accurate one than the Gregorian calendar we use today. But he was also an accomplished philosopher, and scholars are working on resolving the apparent contradictions between this work and his poetry.

One thing I’ve gotten from my research (which, thus far, is only beginning and therefore not nearly enough): for all his prodigious learning and accomplishments, Khayyám honestly acknowledges the limits of human understanding, and seems to tell us that while the great work of discerning the truths of the universe is a great, noble, even necessary endeavor, we do well to keep in mind that we can never know everything, whether through science or religion. So, Khayyám seems tells us, we do well to work, to wonder, to seek, to do right, but also to live for today:

‘At first they brought me perplexed in this way
Amazement still enhances day by day
We all alike are tasked to go but Oh!
Why are we brought and sent? This none can say’. (Rubā‘iyyāt, Tirtha 1941, 18, from IEP)

‘As Spring and Fall make their appointed turn,
The leaves of life one aft another turn;
Drink wine and brood not—as the Sage has said:
“Life’s cares are poison, wine the cure in turn.” (Sa‘idī 1994, 58, from IEP)

~ Ordinary Philosophy and its Traveling Philosophy / History of Ideas series is a labor of love and ad-free, supported by patrons and readers like you. Please offer your support today!

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Sources and Inspiration

Aminrazavi, Mehdi and Van Brummelen, Glen, ‘Umar Khayyam‘, The Stanford Encyclopedia of Philosophy

‘Omar Khayaam, 1048–1131‘. The Poetry Foundation

‘Omar Khayyam‘. In Encyclopædia Britannica.

‘Omar Khayyam‘. In Wikipedia, The Free Encyclopedia.

Rizvi, Sajjad H. ‘Avicenna (Ibn Sina)‘. The Internet Encyclopedia of Philosophy

‘‘Umar al-Khayyam (Omar Khayyam)‘. Muslim Heritage

In Memory of Hypatia of Alexandria

Posted on by

Detail of the death portrait of a wealthy woman, c. 160-170 AD near modern-day Er-Rubayat in the Fayum, public domain via Wikimedia CommonsHypatia’s birthday is somewhere between 350 and 370 AD; a range of dates indicating great uncertainty, to be sure, but original sources that old are hard to come by, especially from a city as turbulent and violence-torn as the Alexandria of her day. The day of her death is better known, sometime in March of 415 AD. Since the latter date is more precise, we’ll break with our birthday remembrance tradition here and celebrate the memory of Hypatia in the month of her tragic and violent death instead of on the date of her birth.

She was a mathematician, astronomer, teacher, and philosopher who wrote commentaries on important works in geometry and astronomy with her father Theon, likely contributing original work of her own. Hypatia was a Neoplatonist, a philosophy with mystical overtones which posits that everything derives its being from the One, an ultimately conscious yet nonmaterial, non-spacial entity which is the pure ideal of everything that is. She was a scholar and teacher in a field and in a male-dominated world, and historians from her day to ours emphasize her extraordinary talents and her femininity with a nearly equal mix of awe and bemusement.

So let us remember and honor Hypatia for her great contributions to human knowledge and to the history of women’s liberation, living proof that women are equals in intellect and courage.

And let us also remember her sad death as a cautionary tale against those who inflame popular sentiment to seize power for themselves. Hypatia met her death at the hands of a Christian mob caught up in the anti-pagan hysteria of the day; Alexandria itself was caught up in a power struggle between civic and religious authority. The mob of extremists who dragged Hypatia from her carriage, torture and kill her with roofing tiles, and defile her body are inspired by their partisanship with theocratic bishop Cyril to kill this pagan philosopher, this mathematician and astronomer (then often equated with sorcerer), this woman who dared teach men, this friend of Cyril’s rival Orestes, civic leader of Alexandria. According to Hypatia scholar Micheal Deakin, “Cyril was no party to this hideous deed, but it was the work of men whose passions he had originally called out. Had there been no [earlier such episodes], there would doubtless have been no murder of Hypatia.”

From a certain millionaire we all know* who rose to power whipping up populist support throughout his presidential race with extremist racial and religious rhetoric, back to Hypatia’s time and beyond, power-hungry opportunists plead innocence from the very violence they inspire. Yet it appears hard to justify that plea when reason and the lessons of history plainly reveal the nearly inevitable results of fomenting sectarian strife. Extremism in the defense of liberty or anything else is a vice** because of the way it drives away reason and sympathy, and after all, nothing is as liberty-destroying as mob violence and death.

* ‘What If Trump Wins?’ by Jeet Heer in New Republic, Nov 24, 2015

** in reference to the quote ‘Extremism in the defense of liberty is no vice’ from Barry Goldwater’s 1964 presidential nomination acceptance speech 

Read more about the great Hypatia of Alexandria:

Deakin, Michael.’Hypatia of Alexandria‘ from Ockham’s Razor radio program of Radio National of Australia (transcript), Sun August 3rd 1997. (click ‘Show’ across from ‘Transcript’)

O’Connor, J J and E F Robertson. ‘Hypatia of Alexandria‘, from the School of Mathematics and Statistics, University of St Andrews, Scotland website.

‘O’Neill, Tim. ‘“Agora” and Hypatia – Hollywood Strikes Again‘. Armarium Magnum blog, Wed May 20, 2009

Zielinski, Sarah. ‘Hypatia, Ancient Alexandria’s Great Female Scholar‘. Smithsonianmag.com, Mar 14, 2010.

…and about Neoplatonism

Wildberg, Christian, “Neoplatonism“, The Stanford Encyclopedia of Philosophy (Spring 2016 Edition), Edward N. Zalta (ed.)

~ Ordinary Philosophy is a labor of love and is ad-free, supported by patrons and readers like you. Please offer your support today!

~ A version of this piece was originally published here at Ordinary Philosophy one year ago

Happy Birthday, Omar Khayyám!

Posted on by

By Adelaide Hanscom, from Edward Fitzgerald's The Rubaiyat of Omar Khayyam, 1905, public domain via Wikimedia Commons

Since Edward FitzGerald published his translation of The Rubáiyát of Omar Khayyám in 1859, Omar Khayyám has been known, especially in the western world, first and foremost as a great poet, eloquently expressing the joy and beauty of life and our own struggles to live it with a sense of love and meaning. It’s a humanist work, with Khayyám writing much as an Epicurean or Skeptic here and a Stoic there, freely doubting and wondering at everything, unshackled from the orthodoxy one might expect from a famed teacher and writer of his time and place. Yet Khayyám, a devotee of Avicenna, took his Islamic faith very seriously, and thought deeply about the nature of God and our relationship to him.

Khayyám, born in Persia in 1048, was most famed in his own time as a mathematician, astronomer, and scientist. He wrote some of the most important medieval works in geometry and algebra, and helped reform the calendar, an even more accurate one than the Gregorian calendar we use today. But he was also an accomplished philosopher, and scholars are working on resolving the apparent contradictions between this work and his poetry.

One thing I’ve gotten from my research (which, thus far, is only beginning and therefore not nearly enough): for all his prodigious learning and accomplishments, Khayyám honestly acknowledges the limits of human understanding, and seems to tell us that while the great work of discerning the truths of the universe is a great, noble, even necessary endeavor, we do well to keep in mind that we can never know everything, whether through science or religion. So, Khayyám seems tells us, we do well to work, to wonder, to seek, to do right, but also to live for today:

‘At first they brought me perplexed in this way
Amazement still enhances day by day
We all alike are tasked to go but Oh!
Why are we brought and sent? This none can say’. (Rubā‘iyyāt, Tirtha 1941, 18, from IEP)

‘As Spring and Fall make their appointed turn,
The leaves of life one aft another turn;
Drink wine and brood not—as the Sage has said:
“Life’s cares are poison, wine the cure in turn.” (Sa‘idī 1994, 58, from IEP)

~ Ordinary Philosophy and its Traveling Philosophy / History of Ideas series is a labor of love and ad-free, entirely supported by patrons and readers like you. Please offer your support today!

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Sources and Inspiration

Aminrazavi, Mehdi and Van Brummelen, Glen, ‘Umar Khayyam‘, The Stanford Encyclopedia of Philosophy

‘Omar Khayaam, 1048–1131‘. The Poetry Foundation

‘Omar Khayyam‘. In Encyclopædia Britannica.

‘Omar Khayyam‘. In Wikipedia, The Free Encyclopedia.

Rizvi, Sajjad H. ‘Avicenna (Ibn Sina)‘. The Internet Encyclopedia of Philosophy

‘‘Umar al-Khayyam (Omar Khayyam)‘. Muslim Heritage

In Memory of Hypatia of Alexandria

Posted on by

Detail of the death portrait of a wealthy woman, c. 160-170 AD near modern-day Er-Rubayat in the Fayum, public domain via Wikimedia CommonsHypatia’s birthday is somewhere between 350 and 370 AD; a range of dates indicating great uncertainty, to be sure, but clear original sources this old are hard to come by, especially from a city as turbulent and violence-torn as the Alexandria of her day. The day of her death is better known, sometime in March of 415 AD. Since the latter date is more precise, we’ll break with our tradition here and remember Hypatia in the month of her tragic and violent death instead of on the date of her birth.

She’s a mathematician, astronomer, teacher, and philosopher, who writes commentaries on important works in geometry and astronomy with her father Theon, likely contributing original work of her own. Hypatia is a Neoplatonist, a philosophy with mystical overtones which posits that everything derives its being from the One, an ultimately conscious yet nonmaterial, non-spacial entity which is the pure ideal of everything that is. She is a scholar and teacher in a field and in a world that’s male-dominated, and historians from her day to ours emphasize her extraordinary talents and her femininity with a nearly equal mix of awe and bemusement.

So let us remember and honor Hypatia for her great contributions to human knowledge and to the history of women’s liberation, living proof that women are equals in intellect and courage.

And let us also remember her sad death as a cautionary tale against those who inflame popular sentiment to seize power for themselves. Hypatia meets her death at the hands of a Christian mob caught up in the anti-pagan hysteria of the day; Alexandria itself was caught up in a power struggle between civic and religious authority. The mob of extremists who drag Hypatia from her carriage, torture and kill her with roofing tiles, and defile her body are inspired by their partisanship with theocratic bishop Cyril to kill this pagan philosopher, this mathematician and astronomer (then often equated with sorcerer), this woman who dared teach men, this friend of Cyril’s rival Orestes, civic leader of Alexandria. As Hypatia scholar Micheal Deakin quotes: “Cyril was no party to this hideous deed, but it was the work of men whose passions he had originally called out. Had there been no [earlier such episodes], there would doubtless have been no murder of Hypatia.”

From the current presidential primary race, in which a certain millionaire is whipping up populist support* with extremist racial and religious rhetoric, back to Hypatia’s time and beyond, power-hungry opportunists plead innocence from the very violence they inspire. Yet it appears hard to justify that plea when reason and the lessons of history plainly reveal the nearly inevitable results of fomenting sectarian strife. Extremism in the defense of liberty or anything else is a vice** because of the way it drives away reason and sympathy, and after all, nothing is as liberty-destroying as mob violence and death.

Ordinary Philosophy is a labor of love and is ad-free, entirely supported by patrons and readers like you. Please offer your support today!

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Read more about Hypatia:

Deakin, Michael.’Hypatia of Alexandria‘ from Ockham’s Razor radio program of Radio National of Australia (transcript), Sun August 3rd 1997. (click ‘Show’ across from ‘Transcript’)

O’Connor, J J and E F Robertson. ‘Hypatia of Alexandria‘, from the School of Mathematics and Statistics, University of St Andrews, Scotland website.

‘O’Neill, Tim. ‘“Agora” and Hypatia – Hollywood Strikes Again‘. Armarium Magnum blog, Wed May 20, 2009

Zielinski, Sarah. ‘Hypatia, Ancient Alexandria’s Great Female Scholar‘. Smithsonianmag.com, Mar 14, 2010.

…and about Neoplatonism

Wildberg, Christian, “Neoplatonism“, The Stanford Encyclopedia of Philosophy (Spring 2016 Edition), Edward N. Zalta (ed.)

* ‘What If Trump Wins?’ by Jeet Heer in New Republic, Nov 24, 2015

** in reference to the quote ‘Extremism in the defense of liberty is no vice’ from Barry Goldwater’s 1964 presidential nomination acceptance speech