Shadowy Man

Shake:

Eratosthenes of Cyrene measured the Earth's radius, and Aristotle proved the earth was round by observing lunar eclipses.

lpetrich

Geocentrism was the universal view before modern times. However, they discovered that the Earth was approximately spherical; Aristotle was the first to clearly state it.

But there were a few who advocated heliocentrism, notably Aristarchus of Samos.

The early Xians were not very interested in science; Lactantius ridiculed the roundness of the Earth as implying that all the stuff on the other side would be upside down. In fairness, however, flat-earthism did not become an official dogma.

But people could express skepticism about their society's religion that they could never do for centuries after Constantine. Plato suggested that his society's sacred books be banned from his ideal city on the ground that they presented such bad examples as heroes lamenting their dead friends and gods laughing. Xenophanes suggested that people make deities in their own likeness, the Epicureans believed that the Gods do not meddle in human affairs, etc.

And there were a lot of skeptic-type theories that were popular, like euhemerism, the theory that the Gods were originally human heroes, and the theory that religion can be socially useful without being true.

But the persecutions Bede mentions were peanuts compared to what would happen after Xianity became the Empire's official state religion. Theologians would have vicious fights over such theological issues as homoousia vs. homoiousia (do the Father and the Son have the same essence or similar essences?), whether or not the Three Persons of the Trinity are coequal, and whether to call the Virgin Mary the Mother of God or the Mother of Christ.

And half a millennium ago was the witch-hunt mania -- large number of people, mostly women, were accused of malicious sorcery that caused bad weather, sick cattle, impotence, etc., not to mention sex with devils. The orthodox were the biggest supporters; they'd suggest that witchcraft skeptics were not only infidels, but atheists. And one mark of being a skeptic was being skeptical about witchcraft.

This overlapped with the Wars of Religion, in which Catholics and Protestants viciously fought each other; which sect people followed was often the sect that the current ruler followed.

Such ideals as secularism and tolerance of different religions were a byproduct of those wars and their inconclusive outcome -- some people got the bright idea that it is best for governments to avoid taking sides in disputes over religion.

Modern science was an outgrowth of the rediscovery of the Greco-Roman classics; how much was derived from medieval philosophy is an interesting question, because at the time that modern science seriously got started, that philosophy had ossified into scholasticism and Aristotle-thumping. Was it more ancient works coming over? Was it greater economic development?

[ October 25, 2002: Message edited by: lpetrich ]</p>

Friar Bellows

That's not true. For example, they invented algebra. That is a big improvement over the Greeks. Here, from the best web site on the 'net for the history of mathematics, is an interesting essay on Arabic contributions to mathematics:

<a href="http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Arabic_mathematics.html" target="_blank">Arabic Mathematics</a>

There are plenty of good references, too.

Marduk

According to the book "The History of Zero" it was the Sumerians who came up with idea, they used it as a place holder. In India it was first used in computation.

This zero discovering business always puzzelled me. Why this took so long, what did a merchant do before when he was all out of stuff to sell or ran out of money? I had 2 left but now I have...uh uh uh (smoke starts pouring from ears)

lpetrich

I'm not aware of the Sumerians having invented any such thing.

And the idea of the number zero raises the question of "how can nothing be a number?"

Here is <a href="http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Zero.html" target="_blank">a nice short history of zero</a>.

One has to distinguish between the number zero and a zero digit in a positional number system; the zero digit came long before the number zero.

Positional number-representation systems and the zero digit were invented in several places, notably Babylon, Greece, India, and Central America.

However, zero as a standalone number was first described in India by some mathematicians around 650. And though Europeans would learn of the Hindu-Arabic number-representation system in 1200, it took until the 1600's before they would accept the reality of the number zero.

Ancient Greek mathematicians had also failed to recognize the existence of negative numbers; here again, those Indian mathematicians were ahead of them, and here again also, European ones took some centuries to catch up with them.

However, some early follower of Pythagoras had discovered irrational numbers -- which the Pythagoreans had considered Satanic Verses.

Amen-Moses

This is hardly surprising as they don't acually "exist" in any real world way. Just like 0 and imaginary numbers they are useful tools used to carry out particular math but they don't really "exist" as in I have minus two apples in my hand.

Zero is an easier concept but even then you can imagine the arguments against it; "Don't be silly, it isn't zero apples it's just a lack of any apples!".

Amen-Moses

lpetrich

Actually, positive numbers can be imagined as assets and negative numbers as debts.

And representing numbers as points on a line makes it easy to visualize negative numbers -- which makes me wonder why no ancient Greek mathematician ever thought of that, especially since they had been so geometrically oriented. Also, a line segment with coincident endpoints can be thought of as a zero-length segment.

Heathen Dawn

Ah yes, I forgot that delightful part of my schoolyears called algebra...

The Qur'an is very much like the Bible in its naive cosmological assumptions. The sun and moon are lamps as in the Bible. There is one verse (in chapter 82) suggesting a flat earth: "...and of the earth, how it was spread...". Interesting is that the standard commentary of that verse says: "showing that the earth is flat, and upon this all the men of religious law agree - not a ball as the laymen say". Still, you can, as in the Bible, point to other verses which would seem to suggest a round earth, vaguely.

Best to do as the Greeks did and rely on observation instead of sacred books...

Bede

If I remember, double entry book keeping was developed in Christian Europe too...

B

echidna

Wasn’t that so Vatican bishops needed to keep track of money paid by people buying indulgences ?