The Dark Ages Myth

masmpg said:

If we look to the reformation, which was the protestors of the catholic church oppression and inquisition we will find how long the dark ages lasted.

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The Dark ages only lasted until the High Middle Ages, AD 1000

Quid est Veritas? said:

It does not mean Hindu-Arabic numerals are necessarily superior to Roman numerals nor that Roman Numerals somehow kept Europe back.

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The arrival of Arabic numerals in Europe around 1200 included the number zero -- that fact alone made it infinitely superior.

Open Heart said:

The arrival of Arabic numerals in Europe around 1200 included the number zero -- that fact alone made it infinitely superior.

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"The nine Indian figures are 9 8 7 6 5 4 3 2 1. With these nine figures, and with the sign 0 which the Arabs call zephir any number whatsoever is written..." -- Leonardo of Pisa (Fibonacci), Liber Abaci, 1202

The decimal place-value system makes the calculation algorithms work, and it removes limits on the size of representable numbers. It was an enormous advance. The only downside was the ease of falsifying financial records (changing a 3 to an 8, for example, or sneaking in a 1 where there's space to do so).

Radagast said:

Medieval Europeans developed a better understand of domes, culminating in Brunelleschi's work in Florence.

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Brunelleschi was a great genius, but his innovative design for the dome of the Duomo was rooted in Gothic architecture, more than in classical ideas. His dome survived the earthquakes of 1510, 1675, and 1895.

A dome was long understood as being a rotated arch; in the case of the Duomo, it was a rotated Gothic arch (modified by the impact of a heavy weight at the apex, which was planned early on). This was very different from (and superior to) the hemispherical dome of, say, the Pantheon. The interior ribs of Brunelleschi's dome are influenced by the Gothic flying buttress. As with the earlier Gothic cathedrals, the key idea is that, if you plan carefully how the static loads will be transmitted, the amount of stone used can be reduced substantially. That's the same principle that gave us this structure, which is indeed the complete opposite of "dark":

masmpg said:

Are you going to give me some sort of catholic dictionary definition of what the dark ages was? I try to be as polite as possible on here. I appreciate all comments, but...

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I've alredy told you what "Dark Ages" means. It's not a Catholic definition, it's the accepted-by-historians-encyclopedia-defined definition https://en.wikipedia.org/wiki/Dark_Ages_(historiography)

ViaCrucis said:

Thirdly, Lutherans don't follow Martin Luther.

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Really? Huh. TIL.

Radagast said:

Brunelleschi was a great genius, but his innovative design for the dome of the Duomo was rooted in Gothic architecture, more than in classical ideas. His dome survived the earthquakes of 1510, 1675, and 1895.

A dome was long understood as being a rotated arch; in the case of the Duomo, it was a rotated Gothic arch (modified by the impact of a heavy weight at the apex, which was planned early on). This was very different from (and superior to) the hemispherical dome of, say, the Pantheon. The interior ribs of Brunelleschi's dome are influenced by the Gothic flying buttress. As with the earlier Gothic cathedrals, the key idea is that, if you plan carefully how the static loads will be transmitted, the amount of stone used can be reduced substantially. That's the same principle that gave us this structure, which is indeed the complete opposite of "dark":

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I agree, but Brunellesschi based his dome on more than Gothic Architecture. It is a product of the Renaissance, not just mediaeval architectural norms. Domes are rare in Gothic Architecture itself, but Gothic Architecture did influence later domes. Brunellesschi spent a lot of time examining Roman ruins as well. To try and ignore this and insist it was a product solely of mediaeval forms is mistaken.

http://www.italian-renaissance-art.com/Brunelleschi.html

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Open Heart said:

The arrival of Arabic numerals in Europe around 1200 included the number zero -- that fact alone made it infinitely superior.

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No one is denying that Algebra with Hindu-Arabic numerals is superior to previous forms of equation solving. The fact is though that the numeral system itself is not superior. Roman fractures based on a base of 12 are actually much better than our 10 based ones, for instance.
If Mediaeval Europeans had invented Algebra they would have created a similar thing to our zero out of necessity.

Roman numerals in use in the middle ages had a symbol for zero. It was called a Nulla, 'N'. This can be seen in the works of Bede when he explains how to calculate Easter for instance.
Similarly Mathematics already utilised a sign meaning nothing for centuries. In the Syntaxis Mathematica of Ptolemy (130 AD), it was used in a sexagesimal numeral system and presented as a circle with a crossbar (later versions as an omicron). This book, also called the Almagest, was very common in educated Western European circles throughout the early Middle Ages.

It was an advance to adopt this sign for nothing as a placeholder though. This is in fact what Muhammad al-Kwarizmi and colleagues did when they synthesised Greek Mathematics and Hindu Numerals and invented Algebra.Their zero, called sifr, was a direct descendant of the Greek sign mentioned above.

The Zero is merely further evidence that Algebra was created using Hindu-Arabic numerals, not that they are therefore innately superior to Roman or Greek numerical systems.

1) al-Khwarizmi didn't "invent" algebra. It would be more true to say that algebra was invented by Diophantus (c. 210 - c. 290).

2) the superiority of Hindu-Arabic numerals relates, not to algebra, but to arithmetic algorithms (such as "long multiplication" and "addition with carry") and to the representation of very large numbers.

3) it's the place-value system with zero (which Fibonacci calls zephir) as a placeholder that makes Hindu-Arabic numerals superior.

Radagast said:

1) al-Khwarizmi didn't "invent" algebra. It would be more true to say that algebra was invented by Diophantus (c. 210 - c. 290).

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I already adressed this in my previous post. There was no systematic system to solve equations, no Algebra, before the 8th century. Diophantus used ad hoc geometric formulations to solve problems, but these cannot be applied universally and are only specific to the case they were designed for.
Therefore the branch of Mathematics called Algebra only came into existence in the 8th century and all modern Algebra is descended of it.

While Diophantus has been called the 'father of Algebra' by 19th century Eurocentric historians, this is no longer considered the case by modern scholarship, nor is any of our modern Algebra in any way related to Diophantes's computations.

2) the superiority of Hindu-Arabic numerals relates, not to algebra, but to arithmetic algorithms (such as "long multiplication" and "addition with carry") and to the representation of very large numbers.

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This is a modern misconception as we have forgotten how to use Roman numerals. We are taught the basic values, but not how to use them properly.
Large numbers can be easily represented using underscores or brackets to represent 1000s or 500s as I explained in depth earlier in this thread.
Likewise, if one uses basic abacus technique then multiplication etc. is really not difficult with Roman numerals either.

Just because we are now used to and instructed in a specific method, it does not make it necessarily better.
This is like the redneck saying English is a superior language to say French because he can understand it and perhaps only knows one or two french words.
If properly instructed in the use of Roman Numerals then they aren't bad for basic mathematics, hence it took centuries for Hindu-Arabic numerals to replace them in such uses.

3) it's the place-value system with zero (which Fibonacci calls zephir) as a placeholder that makes Hindu-Arabic numerals superior.

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Which is related to the creation of Algebra and its modification of Hindu-Arabic numerals when they created numerical tables, not innate to Hindu-Arabic numerals.
If an Algebraic system had been constructed for Roman numerals, it is feasible a similar or like modification would likely have occurred.

1) Al-Khwarizmi did not have a "systematic system to solve equations" in the modern sense. He only considered quadratic equations, dividing them into different cases just as Diophantus had done. He solved the quadratic equations using the same geometrically-based methods as the ancient Babylonians. Al-Khwarizmi also used words instead of the symbols that we do. So, no, Algebra did not "come into existence in the 8th century." Al-Khwarizmi was merely one step along a chain of development.

2) Hindu-Arabic numerals really are better for large numbers. It would be hard to prove that 20,988,936,657,440,586,486,151,264,256,610,222,593,863,921 was prime using Roman numerals, for example.

3) Algebra and arithmetic are different things. I can do algebra with Roman numerals fine:

x^2 - VI x + IX = 0, therefore x = (VI +/- sqrt(VI^2 - IV * IX)) / II = VI / II = III

It's the associated arithmetic calculations like sqrt(VI^2 - IV * IX) that are easier with Hindu-Arabic numerals.

Armoured said:

Really? Huh. TIL.

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It's easy to imagine that Lutherans are "Luther-followers", but it's really not the case. There is a great deal of respect for Fr. Martin for his work as a theologian and biblical exegete. But it should be kept in mind that the term "Lutheran" was largely a term applied in order to suggest heresy. The early Lutherans called themselves Evangelicals (Evangelische in German). Luther's theological work is obviously very important, and Luther is obviously very important to and for Lutherans; but Luther isn't regarded as an infallible founding prophet or anything of the like; he was a tremendously flawed individual (and in many ways just plain contemptible) and just because Luther believed something, or had an opinion on something, doesn't make it Lutheran. Lutheranism, ultimately, is best defined by the Confessions (the Book of Concord), most important of these (aside from the Ecumenical Creeds) is the Augsburg Confession, which was written by Philip Melancthon. Only a handful of the confessional texts which define orthodox Lutheranism were penned by Luther (The Large & Small Catechisms and the Smalcald Articles). The Book of Concord largely came together because of "the other Martin", Martin Chemnitz, and in some ways Chemnitz is perhaps more important in this regard than even Luther.

An accurate view of Lutheranism is as an evangelical reform movement within Catholicism that resulted in a schism. For many Lutherans our identity as Catholics is quite important, because we aren't Catholics in spite of being Lutheran, we are Catholics because we are Lutheran. This, obviously, isn't going to be the perspective on Rome's side. But from a staunchly Lutheran POV, we never stopped being faithful sons and daughters of the Holy Catholic Church, and we confess faith in that Una Sancta; it is the very and same faith of the apostles, the holy fathers, and theologians of the One Church.

ViaCrucis said:

It's easy to imagine that Lutherans are "Luther-followers", but it's really not the case.

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In the same way, Calvinists are not followers of John Calvin.

Radagast said:

1) Al-Khwarizmi did not have a "systematic system to solve equations" in the modern sense. He only considered quadratic equations, dividing them into different cases just as Diophantus had done. He solved the quadratic equations using the same geometrically-based methods as the ancient Babylonians. Al-Khwarizmi also used words instead of the symbols that we do. So, no, Algebra did not "come into existence in the 8th century." Al-Khwarizmi was merely one step along a chain of development.

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Al-Kwarizmi wrote an exhaustive exposition on solving quadratic equations, supported by geometric proofs. He introduced reduction and the transposition of terms to the other side of an equation. While he used similar methods to Diophantes to prove the validity of his system, his was universal and Diophantes's specific to that case and the Persian Mathematicians were the first to treat Algebra as a division of Mathematics in its own right.
Besides, I never said al-Kwarizmi invented Algebra, I said he and his colleagues did so. His book just became the standard text.
Al-Kwarizmi studied equations for their own sake and gave an exposition from primitive terms which in combination acted as prototypes for all equations. This is in a nutshell Algebra, not the case-specific problem solving of Diophantes or the Babylonians.

This is like saying early artists mixing pigments invented Chemistry or Biblical injunctions on pure or impure animals constituted the invention of Biology. Before the 8th century there was no study of equations in mathematics, no true Algebra, even though 'problems' were solved on occasion.

2) Hindu-Arabic numerals really are better for large numbers. It would be hard to prove that 20,988,936,657,440,586,486,151,264,256,610,222,593,863,921 was prime using Roman numerals, for example.

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It would be hard to prove this was prime in Mediaeval times even with Hindu-Arabic numbers. You are making the mistake of anachronistically transposing modern mathematics backward.

3) Algebra and arithmetic are different things. I can do algebra with Roman numerals fine:

x^2 - VI x + IX = 0, therefore x = (VI +/- sqrt(VI^2 - IV * IX)) / II = VI / II = III

It's the associated arithmetic calculations like sqrt(VI^2 - IV * IX) that are easier with Hindu-Arabic numerals.

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I never equated Algebra and Arithmetic.
You are again making the error of transposing modern mathematics onto the ancients. This is modern notation which was designed for Hindu-Arabic numerals. While this developed out of mediaeval notation, it is substantially different. Roman numerals if we try to utilise long-division or such will likely be less effective, but this is to be expected. This is like trying to force a stiletto to act like a snowshoe. I can equally say that Hindu-Arabic numerals are inferior because it poorly represents the sexagesimal notation in the Almagest. This objection is a bit silly in my opinion.

Roman Numerals utilising its own notation with the use of an abacus on occasion, is more than equal to most arithmetical calculations.

I can only conclude that you are trying to obfuscate the argument with specious objections.

Root of Jesse said:

Well, that's not what the 'reformation' was, really. In fact, the 'reformation' was, in many ways, a step backward.



I understand that this may coincide with your opinion, but I have found no original source for the quote you provided, so I regard it as either false, or metaphorical.
Secondly, I don't believe youtube or any technology could show you extremely graphic tortures that were performed during the Inquistion. In fact, the Inquisition was a legal system used to keep law and order, very little more. Were there abuses? sure. As in any institutional system. Did they amount to the 'millions' quoted in the original link? Nope. In fact, the Inquisitions lasted more than 700 years, and there were only thousands actually put to death by the Inqusitions. Collectively.

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Modern historians have begun examining the records of the various inquisitions and their numbers are greatly inflated in the popular mind.

For instance the Spanish Inquisition had 44674 trials between 1540 and 1700 acoording to the records in the Spanish National Archives. Of these, 826 resulted in executions. These documents were examined by Henningsen and Contreras and although they aren't all Inquisition documentation extent, the other documents were excluded for methodologic reasons and the basic numbers are sound.

Therefore in 160 years the Spanish Inquisition likely killed less than 1000 people, although there were frequent convictions, penalties and fines for other offenses. The rates of executions were likely higher in the earlier days of the Inquisition, but the popular view of vast hordes burnt at the hands of bloodthirsty inquisitors is wrong (Kamen estimated that about 2000 executions were carried out prior to 1540).

If we look to the catholic tradition and their own documents the numbers of those murdered by them would definitely be underestimated to say the least. It was not only during the inquisitions that they murdered innocent people. While attending catholic school and catechism class I use to believe all that the good catholics of today believe and that would be only their documentation. BUT when I grew up and looked around and noticed who Martin Luther, John Huss, John Wycliffe, William Tyndale among thousands of others who were blowing the trumpet of truth against the oppressive ways of the church run state of the catholic church, I began doing research. I have been researching these things all my life.

You certainly can find very revealing videos on You Tube about the abuses of the RCC. Many documents have come to light about them, and they have been proven. Even on 60 minutes they mention how secretive the church is about the truth. Try reading some other sources like Fox's book or martyrs, of Wylies history of Protestantism http://www.reformedreader.org/history/wylie/protestantism.htm ,
or history of the reformation by J. H Merle d'AubigneÌ . These volumnous books are things the RCC wish were not in existence.

masmpg said:

If we look to the catholic tradition and their own documents the numbers of those murdered by them would definitely be underestimated to say the least. It was not only during the inquisitions that they murdered innocent people. While attending catholic school and catechism class I use to believe all that the good catholics of today believe and that would be only their documentation. BUT when I grew up and looked around and noticed who Martin Luther, John Huss, John Wycliffe, William Tyndale among thousands of others who were blowing the trumpet of truth against the oppressive ways of the church run state of the catholic church, I began doing research. I have been researching these things all my life.

You certainly can find very revealing videos on You Tube about the abuses of the RCC. Many documents have come to light about them, and they have been proven. Even on 60 minutes they mention how secretive the church is about the truth. Try reading some other sources like Fox's book or martyrs, of Wylies history of Protestantism http://www.reformedreader.org/history/wylie/protestantism.htm ,
or history of the reformation by J. H Merle d'AubigneÌ . These volumnous books are things the RCC wish were not in existence.

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As an example:

English records say about 300 were killed during the Marian Persecution of 1554-58. This was renowned for its ferocity and earned Mary I the sobriquet 'Bloody'.
This is the great and terrible persecution in Foxe's book with its emotive language which makes one prone to exaggerate these numbers. These are the numbers according to Protestant records, by the way.

Elizabeth I by contrast killed 5 for heresy in 44 years, but put to death 126 priests and quite a few recusant Catholics for treason. Her toll is probably between 200-400 killed on account of Catholicism or treason suspected due to it.

Mary was more to the extreme end of a typical monarch's execution headcount of the period, but Foxe certainly lays it on a bit thick. The Marian persecution was terrible, but not the thousands in popular memory being burnt in every town. The persecution was dying down as hardened Protestants fled or went underground. Even if we grant that it would have continued on with similar force if Mary had reigned the equivalent length of her sister, we would still only get about 3300 at most. This is far more than her sister, so 'bloody' is perhaps apt, but not as bad as one would think if we read Foxe and Protestant tracts of the period.