Monthly Archives: April 2016

Epictetus on suicide: the open door policy

Let me commend Massimo Pigliucci’s “How to be a stoic” series, from which this is reblogged, to all of my friends who choose to ponder what it is to live well. One excerpt will give the flavour: “I love the image of life as a festival, to be enjoyed, but also from which one eventually has to take leave, either when the party comes to a natural end, or when the circumstances are such that the occasion is no longer worth one’s time and effort.”

How to Be a Stoic

Epictetus“And what does it matter to you by what way you descend to Hades? All roads are equal. But, if you want to hear the truth, the one that a tyrant sends you along is shorter. No tyrant ever took six months to cut someone’s throat, but a fatal fever often lasts a year.”

So says Epictetus in Discourses II.6.17-19, while discussing the kind of death that one does not choose, but is imposed by external events. (The reference to Hades is a concession to then popular culture of the time, since the Stoics did not believe in an afterlife.) Because death is a (dispreferred) “indifferent,” Epictetus is arguing that it doesn’t matter, really, deeply, how one dies. What makes us fearful of the event is the (inaccurate) judgment that it is a bad thing that one’s consciousness cease existing.

View original post 1,628 more words

Science in the World of Islam, 1: The Syllable Al-

As in Alcatraz; Alcove; Alfalfa; Alcohol; Alkali; Alizarin; Almanac; Alchemy; Alembic; Algol; Almagest; Algebra; Algorithm; Alhambra

The syllable Al- is Arabic for “The”, and is attached to the beginning of the word to which it applies.

Like English today, or Latin in Renaissance Europe, the dominant language of learned discourse for several centuries was Arabic. Arabic-speaking scholars translated the great works of the Greek philosophers and scientists, as well as studying them in the original, did likewise for the texts of Indian mathematics (from which we derive our modern “Arabic” numbering system), and made important discoveries of their own. Spain was where the worlds of Islam and of Western Christianity met, fought, and mingled for more than seven hundred years, and it is mainly through Spanish that Arabic words have entered the English language.


Prison block, Alcatraz (now a museum)

Alcatraz, an island in California famous for its prison (left), was named by the Spanish explorers for the pelican (Arabic al-qadus, the water carrier), which they wrongly believed to carry water in its bill. In a further misapplication, the word has passed into English as the name for a completely different bird, the “Albatross”. Alcove (al-qubbah, the arch) reminds us of the glories of Moorish architecture, as in the Alhambra (or the red house) in Granada. This building was decorated with abstract designs (Arabesques) of great intricacy, whose patterns show so subtle a use of geometry and symmetry that they are studied by mathematicians even today. Alfalfa (from the Arabic name for the plant) is grown for hay in dry climates, such as that of Spain. The syllable al also occurs in numerous place names. The Algarve to us is the south of Portugal; to the Iberian Arabs, it was al-Gharb, the West. A very common combination is with wadi, valley, as in Guadalquivir (al-wad al-kebir, the Mighty River, the island of Guadalcanal in the Pacific (named after a town in Spain, wad-al-Kanat, valley of merchant stalls), Guadalajara (wad-al-Hajara or valley of stones) in Spain and Mexico. There are even a few Arabic-Spanish or Arabic-Latin hybrid names, such as Alicante (al– tacked onto the Roman name Lucentum, or City of Light) or Guadalupe (wad-al-lupus, valley of the wolf) But most of the Arabic al- words in common English use refer to the Arabic achievements in science and mathematics.


Decorated arch, Alhambra (click to enlarge)

Alchemy, algebra, and Arabic numerals

Historically, the West has failed to give anything like due credit to the Arabic contribution to knowledge. A century ago, the justly renowned physicist, philosopher, and historian Pierre Duhem described the “wise men of Mohammedanism” as “destitute of all originality”.[1] I myself, somewhat more recently, was taught at school that the Renaissance was brought about by Byzantine scholars who alone had been guarding the flame of knowledge kindled in classical times, and who, after the fall of Constantinople to the Turks in 1453, were dispersed throughout Europe. This account is as unhistorical as it is patronising. We can trace the golden age of Arabic science to the eighth century translation project, centred on Baghdad, which made the thought and knowledge of the Greece (and Persia and India) available in Arabic. And we must in turn acknowledge, as among the events leading up to the Renaissance and what we call “the” Scientific Revolution, the translation project centred on Toledo, that four centuries later was to translate the work of Arabic into Latin.

Our system of writing numbers was invented in India, from where Persian scholars brought it to the Arabic world. By the tenth century it had spread from there, through Spain, to the rest of Europe, so that we still refer to Arabic (as opposed to Roman) numerals. (The shapes of the actual numerals that we use follow those of the western part of the Islamic world, and have a clear family relationship to those from the eastern part, which are the ones used in Arabic writing today.)  The word algorithm originally meant calculation with Arabic numerals. The word preserves the name of the Persian mathematician and polymath al-Khwarizmi,[2] who had by around 825 CE worked out the procedures for doing arithmetic as we do, using zero, and positional notation for powers of ten. (If you think this was only a minor advance; just try doing long multiplication using Roman numerals. Masochists are invited to try long division.) The word “algorithm” has now acquired an interesting new meaning, as a procedure or set of rules for calculating an answer, and much of computing science is devoted to finding the best algorithm for a given class of problem.

AL-Khwarismi statue

Statue of al-Khwarismi, Uzbekistan

Al-Khwarismi’s writings also give us the name, and the concept, of algebra (al-jebr, sometimes translated as “balancing” or “completing”), including the rules for solving quadratic equations by completing the square. One other possible meaning of the word is “uniting” or “joining”, and in sixteenth century England it also meant “bone-setting”.

Mathematics finds practical application in astronomy. This is a science of great utility for tracking the seasons, and also for navigation (the Arabs traded as far as Indonesia), and orientation (Moslem worshippers would need to know, as exactly as possible, the correct direction to Mecca). Here Arabic scholars were greatly helped by their access to the work of the Greek astronomers of Alexandria. The Greek theory of planetary motions placed the Earth at the center, with the other heavenly bodies following epicycles, or wheels within wheels. This theory was fully developed by the astronomer Ptolemy in a work still referred to by the name of its translation into Arabic, the Almagest (Arabic al-, the; Greek megisti, greatest). However, Arabic astronomers made original discoveries in both observational and theoretical astronomy. They followed their Hindu precursors in anticipating Copernicus’ shift of the center of the revolutions from the Earth to the Sun, and developed the sophisticated mathematics required to handle the implications of such a shift. When they discovered that a star in the constellation Perseus showed varying intensity over time, they called it Algol, the ghoul (yes; ghoul is also Arabic), because it went against Aristotle’s view that everything above the moon was perfect and unchanging. The predicted motions of the moon (important in Islamic religious observance) and planets, together with a list of dates for planting, can of course be found in an almanac (al-manakh, the calendar).

The language of chemistry in particular shows evidence of its origins in the Arabic science of alchemy (al-Khemiya; from Greek chimeia, art of refining metals). If today we think of alchemy as a benighted precursor to the true science of chemistry, that is just a trick of historical perspective, and indeed the two terms were used more or less interchangeably, both in the Arabic-speaking world and in Europe, until relatively recent times.[3] While greatly discredited by its later practitioners in Europe, alchemy was the first serious attempt to relate observed chemical changes to an underlying theory of elemental composition. One piece of apparatus much used by the alchemists was the alembic (al-anbiq, the vessel, from greek ambix). Arabic craftsmen also developed the practical aspects of the subject, extracting the red dye alizarin (al-asarah, the juice) from the madder plant and developing the process for binding it to cotton. They also extracted potassium carbonate from the alkali (al-qali, the ash) made by burning seaweed, and this process was the main source of alkali for soap making and other purposes until the 19th century. The ladies of the Middle East used al-kohl (the powdered antimony) in eye makeup, a practice mentioned by the Prophet Ezekiel, who did not approve. This, strangely, is the origin of our word alcohol. Over time, this word has changed its meaning completely, from powdered antimony, to any fine powder, to a distilled essence used to suspend the powder, to the intoxicating substance ethyl alcohol (strictly forbidden to Moslems), and finally, in modern scientific usage, to any substance containing a similar carbon-oxygen-hydrogen grouping.


Phases and eclipse of the Moon, from al-Biruni’s Kitab al-Tafhim (Elements of Astrology}

Science, as I have mentioned, was pushed forward by its practical applications. Observational and theoretical astronomy, essential to navigation at that time, were highly advanced. Anatomy and medicine were also well developed, and, more than three hundred years before William Harvey, the Egyptian physician al-Nafis worked out that blood circulates through the lungs. Optics was well advanced, with knowledge of refraction and lenses, the laws of reflection from a curved surface, the fact that in vision the eye focuses incoming light, and the cause of the rainbow, which involves two refractions and one reflection from a curved surface. These discoveries in optics involved both sophisticated calculations (sine, cosine, and tangent functions were known and used), and true experiments involving water-filled bowls and light passing through slits. Arabic alchemists also conducted true experiments, and realized that sulfur and mercury were fundamental “principles” (we would say elements), although they failed to free themselves from the Aristotelian doctrine that the different metals were interconvertible.

While consciously and conscientiously built on classical achievements, Arabic science at its best was original, adventurous, and (especially in astronomy and geography) supported by meticulous observation. One of the greatest of Arabic astronomers and polymaths was al-Biruni, 973 -1048 (in 1970, the crater Al-Biruni on the Moon was named after him). He contributed to the development of observational instruments and numerical and geometric techniques, and recognised that the earth rotated daily on its axis, but was neutral on principle regarding whether the earth went round the Sun once a year, or vice versa, on the grounds that these two were observationally equivalent. He also very clearly distinguished astronomy from astrology, which, as he explained, had been concocted by astronomers to satisfy the popular demand for practical benefit from their science.[4] His other achievements include the recognition of the nature of fossils as petrified plant and animal remains, the realisation that valleys are formed by erosion, and the inference from the nature of the soil and the gradation in size of buried stones, that the plain of the Indus had been formed from river-borne sediments.

Al-Biruni’s contemporaries included Ibn al-Haytham (Alhazen), 965-1039, and Ibn Sina (Avicenna), 980-1037.  Ibn-Sina and al-Buruni agreed on the nature of fossils, the formation of river valleys and alluvial plains, and the implied antiquity of the Earth. Ibn-Sina’s greatest achievements, however, were in the area of medicine. These made his name familiar even in late mediaeval Europe, and he is referred to as an authority on poisons in Chaucer’sCanterbury Tales. Ibn al-Haytham was employed by the notoriously eccentric Egyptian Caliph al-Hakim to supervise engineering works intended to regulate the Nile floods. This proving impossible, he fell from favour, and it is said that he found it prudent to pretend madness. He was placed under house arrest, and his Book of Optics ranks, along with John Bunyan’s Pilgrim’s Progress, Adolf Hitler’s Mein Kampf, and Bertrand Russell’s Introduction to Mathematical Philosophy, among notable works written in prison.

Much Islamic art was highly mathematical. It involved a knowledge of all the ways in which the two-dimensional space of a wall could be symmetrically divided by tiling,[5] and anticipated in its practice even such twentieth century developments as color symmetry and five-fold pseudosymmetry.


Tiling, Alhambra, exhibiting colour symmetry (click to enlarge)

I have carefully referred to “Arabic” scholars and artisans, rather than to “Arabs.” “Islamic” might seem more accurate, for a culture that included Persia (Iran) and much of Central Asia, but the culture we are discussing borrowed freely from pre-Islamic sources, and many of the participants were not themselves Muslims. Throughout its greatest period, from the eighth to the thirteenth centuries, it was a multicultural society, with Zoroastrian, Jewish, and Christian scholars and craftsmen all contributing to its rich intellectual life. Ali ben Isa, the most noted Arabic oculist, was a Christian. Saladin’s family physician, Moses ben Maimon (Maimonides), was a Jew. The Persian mathematician Omar Khayyam, who systematized the solutions of cubic equations (as well as writing the lyric verse for which he is now best remembered in the West) was a free-thinking skeptic.[6] The mathematician al-Khwarizmi, whom we have already met, worked in Baghdad at the heart of the Arab world but borrowed freely from Hindu sources; both he and al-Biruni hailed originally from Central Asia, and Ibn-Sina was Persian.

Islam itself was far from being a single rigid structure. The doctrinal divisions between and within Sunni and Shi’a branches were (and are) as profound as those in Christianity between Catholic and Protestant, and in Sufism (which continues to flourish; you can now download Sufi music online) Islam has a mystical tradition that transcends all orthodoxies.

Arabic science and mathematics formed the bridge between the achievements of the ancient Greeks, and the emergence of modern science in Europe in the sixteenth and seventeenth centuries. By this I do not mean to imply that it was merely a passive vehicle, but rather that all of these should be seen as part of the same ongoing activity. To the enlightened, science was not regarded as hostile to religion; on the contrary, the visible world was seen as testifying to its invisible Creator. When the Arabs first over-ran the Hellenized eastern Mediterranean, a deliberate decision was made to translate the Greek texts available there into Arabic, and it was by way of these Arabic translations, in the multi-cultural societies of late medieval Spain, that this ancient knowledge was restored to pre-Renaissance Europe.

1] Physics, history of; Catholic Encyclopaedia, 11:48 (1911).

2] Or, to give him his full name, Abu-Jafar Mohammed ibn-Musa al-Khwarizmi, “Father of Jafar, Mohammed son of Moses, the man from Khiva (now in the central Asian republic of Uzbekistan)”

3] For this observation, among others here, I am indebted to Jim Al-Khalili’s Pathfinders, Allen Lane, 2010.

4] S. Pines, Isis, 55(3), 343, 1964

5] Technically, the two-dimensional space groups

6] We consider him part of this same cultural community, although, individual in this as in so many other things, he wrote in Persian

Alcatraz prison, (c) David Corby 2006 via Wikipedia; Creative Commons license. Statue of al-Khwarismi, Uzbekistan, Image by © Melvyn Longhurst/Corbis via the blog Missed in History. Alhambra architecture and tiling, photos by author; click to enlarge.

This piece originally appeared in 3 Quarks Daily

New theory explains mystery of excess of matter in our Universe

It’s being hailed as the most significant breakthrough since Hoyle proposed the Big Bang theory.


Horsehead Nebula in Orion (representative-colour image by NASA from the Canada-France-Hawaii Telescope in Hawaii)

Symmetry would require the production of exactly equal numbers of particles and their corresponding antiparticles in the earliest instants of the Big Bang, when radiation and particle-antiparticle pairs existed in equilibrium. However, these pairs would have irreversibly annihilated each other as our Universe cooled, eventually leaving nothing behind except the Cosmic Microwave Background. The persistence of matter is only one of several disturbing asymmetries; another such is the violation of parity in beta-decay, for predicting which Lee and Yang received the Nobel Prize in Physics in 1957.


Horsehead Nebula in U’ (calculated by the author)

Today, however, Dr Bubba Majntser, of Mierda de Toros University, has announced his Even Bigger Bang theory, according to which the formation of our Universe (from nothing, as so eloquently described by Krauss) was, of necessity, accompanied by the formation of an anti-Universe. The excess matter in our Universe U is then precisely balanced by an equivalent excess of antimatter, while the anti-Universe U’ must, according to the well-known properties of antimatter, be proceeding backwards in time. This ensures that U and U’ can never come into contact with each other, which is as well, since if they were to do so the result would be complete mutual annihilation. Moreover, each particle in our Universe is quantum mechanically entangled with its corresponding particle in the anti-Universe, so that if the descriptor of our universe violates some symmetry law, that law is nonetheless rigidly obeyed by the direct product U x U’ of the descriptors of Universe and anti-Universe. Similar considerations will apply to every other Universe in the Multiverse. Majntser has christened this principle Bifurcated Symmetry, or BS.

HawkingBookBut his theory, for all its elegance, has already attracted criticism. The Vatican has condemned it on the grounds that it violates Free Will; if a person in the anti-Universe is necessarily constrained by entanglement to behave in exactly the same way as the corresponding person in our Universe, they cannot both be functioning as autonomous agents. Shakespeareans have pointed out that the theory violates the fundamental maxim that “What’s done cannot be undone,” since according to BS, whatever is done in U is being undone in U’, and vice versa, and this happens all the time. There is also disagreement as to whether the expression U x U’ should be replaced by U* x U’, to cover cases where time is complex, or even under some circumstances, as suggested by Hawking, purely imaginary. Strict Occamists denounce the theory as involving unnecessary SevenDaysduplication of entities, while Richard Dawkins has already tweeted his opinion that it is insufficiently critical of religion. The Oxford theologian John Lennox, on the other hand, denounces the theory as undermining his attempts to reconcile science with Genesis, since it requires either 12 (6 + 6) or 0 (6 + [-6]) Days of Creation, whereas the correct number is, of course, 7.

The most serious criticism, however, comes from the UK’s National Union of Students, who are demanding that the author of this post be no-platformed for cultural imperialism, micro-aggression by ridiculing a non-Anglophone University, and using sexist and ageist language.

Hoyle himself could not immediately be reached for comment.


%d bloggers like this: