Friday, November 14, 2008

The West and Global Mathematics

The Fjordman Report

The noted blogger Fjordman is filing this report via Gates of Vienna.
For a complete Fjordman blogography, see The Fjordman Files. There is also a multi-index listing here.

This post is adapted from Fjordman’s comments on earlier posts here and here.

I’ve been reading Greek Thought, Arab Culture by Dimitri Gutas, which is a surprisingly boring book. Gutas treats the Arabic translation movement in Baghdad as a major achievement. It was an achievement in some ways, but he admits that they benefited greatly from the pre-established Zoroastrian Persian ideology of translation and libraries. He also admits that Muslims only translated scientific works, not the Homeric epics, for instance. He does briefly mention that they translated some Sanskrit and Persian works, but says almost nothing about the Indian ones. The Indian numeral system was important and should be mentioned, although the Greek texts were clearly the most important.

Muslims had access to Greek, Persian and Sanskrit works. Theoretically speaking, they could have explored the Indo-European linguistic tree. But they didn’t. Europeans did. It is true that Muslims made some worthwhile works in mathematics, but we should remember that the three most important mathematical traditions in the ancient world were the Greek, the Mesopotamian (which the Greeks head learned from, and which the Persian continued) and the Indian. This means that Middle Eastern Muslims had direct access to all of the most important mathematical traditions on Earth simultaneously. They did make some progress in algebra, but it would almost be surprising if they didn’t manage to produce any significant mathematical works.

One book on my reading list which I haven’t read so far is The Shape of Ancient Thought: Comparative Studies in Greek and Indian Philosophies by Thomas McEvilley. My impression from what I have read about it is that he places too much emphasis on the Indian influence on Greek culture. Everybody says nowadays that Greek culture was “really” invented somewhere else (think Black Athena). We do know that the Egyptians, Mesopotamians and Phoenicians influenced the Greeks, but the Greeks openly admitted this, and these cultures all belonged to the Eastern Mediterranean world whereas India was far away.

There is a school of thought which claims that Plato’s political system in The Republic mirrors the Hindu caste system, and that Greek atomism was imported from Indian atomism. I haven’t seen convincing evidence of this so far, and it’s difficult to see how this influence should have been transferred to Greece prior to Hellenistic times, but the question is worth exploring. We can find traces of a commonly shared Proto-Indo-European mythological heritage with India, however faint.
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The Chinese mathematical tradition was significant, but less influential than the Indian one. I would be tempted to say that China was a hardware civilization whereas India was a software civilization. The truth is that given the size of their economy and their population, the Chinese were surprisingly weak in mathematics and in the abstract sciences in general. This proves that although some minimum level of wealth is certainly a necessary cause for the growth of modern science (extremely poor people concentrate on surviving, not on inventing calculus or comparative linguistics), it is by no means a sufficient one. The Chinese believed the Earth was flat until the seventeenth century AD, and they only corrected this error after their astronomy had been virtually displaced by European astronomy. This was after European (Greek) astronomers had known that the Earth was spherical for more than two thousand years, a knowledge which, despite popular myths to the contrary, was never lost during medieval times.

Asian rockets weighed a couple of kilograms at most and were powered by gunpowder. None of them would have been able to challenge the Earth’s gravity, leave the atmosphere and explore the Solar System. In fact, Asians never coined the concept of “gravity” in the first place. Space travel is the invention of only one civilization, the Western one. None of the Asian nations ever came remotely close to achieving something similar on their own, not even the Japanese. In fact, without Europeans mankind might not have been able to explore the Solar System for many centuries yet.

From the fourteenth century AD, which is to say the Italian Renaissance, until the twentieth century, almost all important global advances in mathematics were European. I would be tempted to say that European leadership was stronger in mathematics than in any other scholarly discipline. Perhaps the simplest explanation for why the Scientific Revolution happened in Europe is because the language of nature is written in mathematics, and Europeans did more than any other civilization to develop — or discover — the vocabulary of this language.


thll said...
This comment has been removed by the author.
thll said...

The scientific revolution happened in Europe for the simple reason that it was an expression of the soul of European people. Only Western man is sufficiently objective to have developed technology to its current degree.

Czechmade said...

Mathematics: natures legal system?
Rule of law fully accepted?
Unstained product of universal harmony?
School of pure attention training?
School of self-restrain?

But even mathematics can develop different styles.

The Greeks created geometry watching Egyptians measuring their flooded lands doing their job for purely pragmatic reasons.

Geometry for the Greeks was more than science - it was knit with their religious thinking too.
A very light skeleton devoid of god=power pattern.

So the absence of floods in Greece turned their attention in a new direction. You can clearly elevate or debase anything you watch as a "reality".

Simone Weil treats these things in detail: "Sur la science" etc.

Linking science and religion was one of the tasks of the Czech exiled reformer Jan Amos Comenius (a contemporary and friend of Descartes). See Milada Blekastad

Menneskenes sak Om den tsjekkiske tenkeren Comenius

Gyldendal Norsk Forlag Oslo 1977

Funny: the Greeks enlarged their knowledge based on others, muslims reduced it...

Fjordman said...

Czechmade: It's well-established that Muslims made some advances in algebra, but their mathematics stagnated after the eleventh century, incidentally at about the same time as the once-majority non-Muslim population was shrinking at an accelerating pace due to harassment.

It is interesting to speculate what would have happened if we removed Europeans from world history. Would the world still have experienced the Scientific and Industrial Revolutions? My bet is no, at least not for many centuries to come. Nothing I have seen from the reconstructed scientific and technological histories of other nations and civilizations indicates that a similar breakthrough was about to occur elsewhere.

In the first half of the seventeenth century, leading Chinese scholars still believed the Earth was flat. In the second half of the same century, European scholars had already made scientific explanations for gravity and the movements of the bodies of the Solar System. By the late eighteenth century, European scholars had a reasonably accurate picture of the size of the Solar System and had made the first scientific measurements of the speed of light. As late as the sixteenth century, the Aztecs, living in the most scientifically sophisticated region of the pre-Columbian Americas, sacrificed thousands of people every year to ensure that the Sun would keep on shining. By the late nineteenth century, through the new science of spectroscopy, Europeans could investigate the chemical composition of the Sun and other stars. After the discovery of the world of subatomic particles and of radioactivity, they could also explain how stars generate energy. By the twentieth century, Western science and technology had reached the level of sophistication necessary to begin the first physical exploration of our Solar System.

The simple truth is that Western achievements in astronomy are so much greater than those even contemplated by any other civilization that it doesn't rank on the same scale. I'm sure the Japanese, the Chinese, the Koreans, the Indians and others will make many valuable contributions to our understanding of the universe in the twenty-first century, but that doesn't change the fact that they got modern astronomy and the very concept of space travel from us. And no, I've seen no indications that they were developing anything similar on their own.

Sagunto said...

Forget "Renaissance" and espec. the so-called "Enlightenment" as a starting point. European science started as a Medieval enterprise. European Universities took their recognizable form during the latter half of the twelfth century.
David Lindbergh (Beginnings of Western Science, 1992): "Scholars of the later Middle Ages created a broad intellectual tradition, in the absence of which subsequent progress in natural philosophy [the natural sciences, essentially] would have been inconceivable."

Moreover, European medieval scholars dared to challenge, and go beyond, the Great Aristotle - something Islamic copyists never really did.


Alcuin said...

More on Chinese Mathematics here, and the TV series, even though by the BBC, is presented by a Mathematician, Marcus Du Sautoy, and pretty balanced. The mythical "Muslim Renaissance" of Haroun al Rashid was mostly based on Assyrian, rather than Greek or Persian culture.

Both Assyrians and Persians were readers of the works of other cultures, and, until their enthusiasm was snuffed out by Islamic opression and orthodoxy, were both vibrant. In fact, according to Bernard Lewis, Muslims did not learn Kuffar languages, and there is no record of any Muslim learning a European language until the 18th Century - all the much hyped work of the likes of Avicenna were based on the work of Christians (Assyrian, Greeks) and Jews.

Indians might have developed a culture as advanced as Europe's, were it not for their opression by the Mughal tyrants. Indeed, it was only after the British removed the Mughal yoke, that India emerged from a long imposed slumber.

Czechmade said...

Some non-Arab background to be traced for development of sciences:

"What made the 'Abassid seizure of the caliphate unique was the heavy reliance on client Muslims, or mawali. The mawali were foreigners who had converted to Islam; because, however, they were foreigners they could not be incorporated into the kinship-based society of Arabs. They had to be voluntarily included into the protection of a clan, that is, they had to become "clients" of the clan (which is what the word mawali means). For the most part, they were second-class citizens even though they were Muslims.

The overwhelming majority of foreigners who rallied to the Hashimiyya cause were Iranian. Historians have argued that the 'Abassid caliphate represented a shift in Islam from Semitic to Iranian culture; other historians argue that there really no such shift. The truth probably lies somewhere in between. When the 'Abassids took power, the center of Islamic culture shifted from the Semitic world in Arabia and Syria to the Iranian or Persian world in Iraq. By shifting the capital from Damascus to Baghdad, the 'Abassids brought about a dynamic fusion of Persian and Semitic culture."

Remember Baghdad is a purely Persian name. Bagh - the pre-islamic god, means "gift of god".

Until panArab movement in fifties Iraqis described themselves as "cultural Persians" though speaking in Arabic. The poet al-Jawahiri was persecuted in Iraq for this and lived in Prague until ninties.

Google Iran-e-bozorg or IranZamin.
The whole concept becomes more clear.

Profitsbeard said...

Islam is doggedly irrationalistic, and would end up undermining anything scientific or culturally-liberating or any artistic endeavor that sought to progress beyond its paralyzed-in-the-7th century dogmatic strictures.

The headlock of Mohammadan iconoclasm ("an angel will not enter a house where there is a picture...") and the the sanctified nescience of the Koran ("the sun sets in a muddy lake") derail Muslim attempts to expand or humanize thought.

Mohammedans can temporarily steal the knowledge and achievements of a conquered people, and sometimes even expand on it ~if there is no specific Koranic religious injunction forbidding such activities~ but the Islamic deadening force of religious over-regulation will eventually reassert its numbing and blinding and pithing influence over the pilfered progress, and cause Muslims to regress back to the comforting darkness and silence and stillness of the "prophet"'s womb-like Koranic coma.

Islam is novocaine for the soul.

Conservative Swede said...

Fjordman wrote:
In the first half of the seventeenth century, leading Chinese scholars still believed the Earth was flat. In the second half of the same century, European scholars had already made scientific explanations for gravity and the movements of the bodies of the Solar System. By the late eighteenth century, European scholars had a reasonably accurate picture of the size of the Solar System and had made the first scientific measurements of the speed of light. As late as the sixteenth century, the Aztecs, living in the most scientifically sophisticated region of the pre-Columbian Americas, sacrificed thousands of people every year to ensure that the Sun would keep on shining.

That says it all, really.

Conservative Swede said...


Forget "Renaissance" and espec. the so-called "Enlightenment" as a starting point. European science started as a Medieval enterprise.

Yes thank you Sagunto, this is a very important observation. And it holds in general, not only for science. The Enlightenment was essentially just ideological: celebration of the failed cultures as mentioned in the Fjordman quote above; the birth of the many ideologies that killed millions of people and destroy our societies today.

People are made to believe that liberalism (and other Enlightenment products) is the source of success of our society. But the foundation had been built during the many centuries before.

People today seriously believe that the West is worth defending (against Islam), only for its democracy (another Enlightenment spin-off). Apparently they think its not at all worth defending if it does not comply with democratism. And apparently it was not worth defending back in the Medieval times according to them...

Altogether a sick brew for failure, destruction and suicide.

Western people find Russians strange and icky. Precisely because the Orthodox East never went through the Enlightenment. But this is only to their advantage. They got all the good stuff from the Medival era, all the stuff that build civilization, but was never hit with the poisonous brew known as the "Enlightenment".

Homophobic Horse said...

The long slow decline of the West can be attributed to the Catholic Church who erroneously taught that the logical syllogism is consistent with divine revelation. The Catholic church, being a Western church, has always contained that special feature of the Western mind: reliance on the logical syllogism. Having divinized human thought the decline was inevitable. In the scholastic Middle Ages, Christian theology became "systematised" and subordinated to logic. Logicalness becomes the first test of truth.

For this reason the Renaissance could only have happened in the West. Logic is a form of measurement performed by man, logically, man becomes the measure of all things, theology becomes "scientific method"; this follows to the "Enlightenment", with its profoundly naive optimism in the unlimited progress of man's reason. This logical "mechanicalness" also fired the ideas of mechanist thinkers like Newton and Descartes. Rationalism reached a dead end with Hume and Kant, who show that "pure reason" cannot exist by itself: all "truth" is subjective. Having dethroned God through the centuries and put reason in his place, Western man is now left with nothing--save himself. An infamous and disastrous attempt to regain order was attempted by Hegel, which Marx took and turned into "Dialectical Materialism" - a last attempt at trying to make the logical syllogism sympathetic with (material) objective reality-the "objective reality" that now serves as a God substitute (the divine true and beautiful higher future of humanity.). The pseudo-religiosity of Marxists, and the popularity of Marxism with lapsed Catholics (and vice versa) is well known and supports the above regard.

Ultimately we arrive at the nihilistic and irrational philosophies that have characterised the end of the 20th century. This subject is large so I shall concentrate only on the aspect of it that applies to the West's most immediate crisis - multiculturalism. Multiculturalism is predicated on a variety of Nihilism called Vitalism first espoused by Nietzsche in Beyond Good and Evil:

4. The falseness of an opinion is not for us any objection to it: it is here, perhaps, that our new language sounds most strangely. The question is, how far an opinion is life-furthering, life-preserving.

Here for the first time truth is eliminated as a criterion of action, and epistemology is reduced to what quite literally merely "feels good", truth is substituted for a new standard: the "life-giving," the "vital"; it is the final divorce of life from truth [Oprah says: God is a feeling]. This is dangerous because what feels good is not necessarily good. (As is clear to anyone who analyses the nature of Michael Foucaults "Iran Mistake". Michael Foucault did not want to condemn the Khomeinist revolution because he liked the idea of mixing religion with politics. Foucault believed that the religious often contained the "irrational well-spring of life" that the contemporary West did not have.) Vitalism is used a means for understanding man; he is a bundle of sublimated sexuality. This Vitalism is reflected in modern art. New and exotic sources and influences have been found in the art of Africa, the East, the South seas, prehistoric art, children, madmen, and occultism. When one ask's what any of it means one may be told that one should not impose standards on something that is "free" and "creative." The artist is a "creator," a "genius," he is inspired. His "vision" is transforming and sublime. Creation is, of course, irrational, surreal, miraculous.

The revolt against reason can be attributed to reason itself. The whole crisis could be read, as ConSwede might, as an attempt to reacquire the Christian god in one way or another.