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 Evil Mathematicians

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nordmann
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PostSubject: Evil Mathematicians   Sat 09 Feb 2013, 09:17

"The good Christian should beware of mathematicians, and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell."

Original: "Quapropter bono christiano, sive mathematici, sive quilibet impie divinantium, maxime dicentes vera, cavendi sunt, ne consortio daemoniorum animam deceptam, pacto quodam societatis irretiant."


St Augustine filling out his tax returns without a calculator

Saint Augustine was actually having a go at astrologers (numerology was something of which he had been once been a great fan, now in later life he had turned against its practitioners with a vengeance) and for that he must be congratulated. However in Augustine's time and place as he spoke, the crumbling Western Roman Empire's North African territories during the early 6th century CE, the distinction between pseudo-scientific astrology and actual science and mathematics had become very blurred indeed, not least due to Augustine's own church having effectively begun suppressing anything of the latter from entering the public domain lest it encourage the faithful to deviate from their main responsibility - to worship and wonder at the Christian god's enigmatic incomprehensibility (at least to the great unwashed - "illuminati" like Augustine reckoned they had an inside line). To have expressed an interest in mathematics at the time therefore would have been a very dodgy proposition socially - using numbers for anything other than simple counting automatically placing you directly in the church's line of doctrinal fire and often with rather severe personal repercussions.

But the sentiment, if not the rather liberal translation of Augustine's latin, got me thinking. Given that his condemnation did indeed cover what we would now call "legitimate" or "bona fide" mathematicians, especially those who, god forbid - literally - attempted to advance their science, had he a point? Is there actually a category of mathematician in which practitioners of the skill might be construed as "evil"?

The definitions of evil in most dictionaries effectively centre on one elementary semantic concept - a tendency to work against one's fellows' welfare, be it expressed in philosophical, moralistic or didactically absolutist terms. This allows great scope for subjective application of the concept, which in turn allows us to retrospectively consider its application to prominent thinkers in our history. Are there in fact people in this broad historical group whose contributions to our welfare have, as it has turned out, been largely negative - even catastrophically so?

In this day and age we tend to learn early and accept as natural that we be uncritically grateful for the fact that our species has produced, often against the odds, illuminaries like Copernicus, Einstein, Newton and Oppenheimer, to name but a few of the most renowned practitioners of mathematical theory. I threw Oppenheimer in as he is probably the one about whom, in modern times, a degree of critical assessment of his immediate impact is actually encouraged. But in the modern age he is almost a unique example of the mathematician of whom, as Augustine implied, one should be wary before glibly praising for his or her skill.

Are there others who, on balance, have advanced our understanding at the possible or even manifest expense of our communal welfare?

My own view is that scientific knowledge of any sort is innately beneficial to our species but that its application has huge scope for evil in its execution. If, as Aristotle once averred, the faciltators of evil must be considered therefore a part of it, which mathematicians - and indeed scientists - over the years could well fall foul of such accusation, despite whatever contemporary kudos we pay them, and even despite a possibly genuine philantropical motive for their work?
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PostSubject: Re: Evil Mathematicians   Sat 09 Feb 2013, 09:55

I can't help but think of Albert Einstein's dismay over some directions that the practical uses of his theoretical work took. But should he be held responsible for the way in which others have abused his work? I say not, as it was never his intention, plus there has been great benefit in the implementation of his work in other areas, which balances the books in a way.
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PostSubject: Re: Evil Mathematicians   Sat 09 Feb 2013, 10:26

That the book requires to be balanced automatically admits his contribution to evil deeds, however remote from them he was in terms of intent, begging the question; is mere dismay enough to exonerate him from a share in the guilt? But I agree that Einstein represents a borderline case - one can argue both for and against him, even within Aristotle's philosophical strictures regarding responsibility. Oppenheimer on the other hand takes the disambiguation of evil to a whole other level in terms of our lack of certitude.

Kurt Prüfer, not a name known to most, presents a similar challenge. As a young man he followed the latest developments in thermodynamic theory with great understanding and interest, and then made a career from applying this theory to practical use in the manufacture of incinerators for organic material which eliminated unwanted noxious emissions in the process. His groundbreaking innovation is still utilised to our enormous benefit in several industrial applications - recycling and funereal cremation being just two of them. It was in the latter field however that his skills were most infamously employed. As chief designer for Topf & Sons his ovens, originally adapted for disposing of typhoid victims in Buchenwald concentration camp in 1939, were improved by his firm and deployed throughout the death camps run by the Nazis over the next five years.

For the Soviets there was no ambiguity about Prüfer's Aristotelean share of the guilt. Interrogated and released by the Americans he was then arrested by the Russians and spent the rest of his life in a gulag, dying in 1952. Prüfer published academically until his arrest, his commentaries on and contributions to thermodynamic theory still providing valuable instruction and insight for those studying the subject today.
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PostSubject: Re: Evil Mathematicians   Sat 09 Feb 2013, 10:34

Quote :
which mathematicians - and indeed scientists - over the years could well fall foul of such accusation,

It might be more difficult to try to think of those who couldn't., given the human tendency to take morally neutral knowledge and pervert it to less than admirable ends. I am reminded of the NRA dictum 'Guns don't kill, people kill' which although risible in their context, is in some sense true.

The opposite is also true: that knowledge gained in the pursuit of what might be defined as evil purposes, and the Manhattan project is one example, can be deployed for the general good. At a stretch even Newton's research was driven by the desire to explicate God's presence in creation, not a motive of which I would approve (that's a highly personal and situated viewpoint but all these judgements are) but has been unquestionably beneficial.

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PostSubject: Re: Evil Mathematicians   Sat 09 Feb 2013, 10:44

Aristotle would entirely agree with both your points - essentially two aspects to the same point - and then throw it back as a philosophical conundrum. How neutral can neutral be in a moralistic sense? Moral ambivalence can suggest neutrality but it can equally suggest amorality and ignorance on the part of the person who presents such neutral facts for consumption by others - to do with as they will. However if the pursuit of knowledge precludes addressing the knowledge of what then may well be done with one's discoveries in pursuit of evil policies, how incomplete could this pursuit be said to be, not least in terms of knowledge itself?
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PostSubject: Re: Evil Mathematicians   Sat 09 Feb 2013, 11:29

So then, the researcher, in any field, must consider all possible applications of that work before disseminating her results? I'm sure I have a vague recollection of something of that nature happening but I can't remember when or who; no doubt you will, assuming it's not my imagination.

That degree of prescience is usually impossible, I assume Newton did not foresee the use of his calculations in the prediction of the performance of an ICBM, or desirable. As in everyday life, the unfortunate outcome of one's actions can only be held against one if that outcome was predictable.

As to whether or not the search for knowledge should be curtailed by its possible bad outcomes, there isn't really a choice is there? Not unless we, as a species, renounce that quality which defines us? Like it lump it, the Golden Road is the only one we can take.

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PostSubject: Re: Evil Mathematicians   Sat 09 Feb 2013, 12:03

So you can see why the early church seized upon Aristotle as an originator of morality as they saw it - with Oppenheimer, for example, the outcome of the research was not "possible", it was predetermined from the word go and in fact formed the major reason for it being done at all.

However this is exactly where the dilemma arises with regard to responsibility. Meitner, Hahn and Frisch cannot not have been in doubt about the employment of nuclear fission as a weapon, the largely anonymous researchers still perfecting nuclear fusion capabilities even less so. This means that they and others in their situation on the "Golden Road" are actually faced with a stark choice in moral terms. They can either refuse to contemplate it at all or opt to defer responsibility for subsequent actions completely onto those who take them. Aristotle would have said that in purposefully ignoring the likelihood of personal guilt or in actively assigning it completely to others then they in fact acknowledge that guilt by association exists. This, in other words, whether they like it or not, is therefore part of their knowledge - something they have learnt and understood through the pursuit of scientific knowledge and with no less potential for impact on their fellow man for their moral stance as they do with the results of their scientific research.
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PostSubject: Re: Evil Mathematicians   Mon 11 Feb 2013, 12:12

I'm back in the library, limited time on a borrowed machine, and with other work to do, so please forgive random thoughts intruding on the elegantly reasoned exchanges above. These are the thoughts and questions which immediately came to my mind when I saw this thread.

i) Were other early thinkers (pre-Christian) suspicious of mathematics? How did Greek and Roman commentators respond to Euclid's "pricks and lines" and to the work of Pythagoras? Was any disquiet expressed? (Do hope that's not too a daft question.)

ii) "Thrice -greatest" Hermes Trismegistus - I can't remember - was he an Egyptian? Was he a mathematician as well as a mystic philosopher? Did he actually exist? How did the early Church view his writings? With absolute horror? Trismegistic thought was of great interest to Renaissance humanists, I think - via Bruno? Didn't the Inquisition get him in the end?

iii) The School of Night - Ralegh, Harry Percy, the "Wizard Earl" and the great Doctor Dee and others - all passionately interested in mathematics? Dee, I know was a great fan of Trismegistic thought. Was being a serious mathematician towards the end of the 16th century more or less synonymous with being an atheist? Yet the subject was taught at Oxford and Cambridge; indeed I've read recently in a biography of William Cecil that the Fellows of St. John's College were fascinated by mathematics and that they lectured on "the related subjects of arithmetic, geometry and perspective - Cecil would have read Euclid geometry." So Maths was not heresy - it was a respectable subject up to a point?

iv) Brings me to thoughts of Marlowe and Faustus. It was known that maths gone wrong could corrupt the unwary and lead to all manner of evil! Two scholars at King's College crossed the boundary when they progressed "from mathematics and applied themselves to demonic arts"! Wizards combined geometrical inscriptions (lines and crcles), signs, letters and alphabetic letters (plus a few zodiac symbols thrown in for good measure) to produce the weird formulae which enabled them to communicate directy with demons. Heady stuff of course for your adventurous M.A. student!
"Divinity adieu!
These necromatic books are heavenly:
Lines, circles, scenes, letters and characters:
Ay, these are those that Faustus most desires."
The mathematician/magician means to wield godlike powers - "All things that move between the quiet poles/Shall be at my command" - or so he thinks.

As Hermes put it: "Man takes on himself the attributes of a god, as though he were himself a god..."
Or a devil? Faustus with unwittting irony also decides he rather likes hell. He declares: "O, might I see hell, and return again, how happy were I then."
Which leads me to the not so happy Oppenheimer and his famous quotation from the Bhagavad Gita: "Now I am become Death, the Destroyer of worlds."
I'm all for mathematicians with their "pricks and lines" - but I'm also all for a bit of humility before the gods.
PS Not very happy with this, but will send it. My new computer is being set up on Wednesday, so I should be back to normal then, thank goodness.
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PostSubject: Re: Evil Mathematicians   Mon 11 Feb 2013, 13:43

I'm not aware of any organised or systemic opposition to the development or publication (in an ancient sense) of mathematical theory in Greece. The opposite in fact - it was so tightly enmeshed with philosophical thinking that I don't think it could even have been regarded as a separate study to be criticised anyway. However it is important to remember that what we know about the Greeks and mathematics is what others later recorded, not themselves. Its survival can be attributed to a contemporary lack of enemies as such, however the attribution that it lacked enemies could equally have been assigned simply because it survived through the agency of others. There is nothing certain there.

We do know that the Romans tended to dismiss mathematical theory that did not readily lend itself to practical application. But then there was also much that the Greeks had developed as mathematical theory that the Romans respected on purely philosophical grounds. Aristotle pointing out the difference between the indecomposable and the decomposable is representable using Euclid's "pricks and lines" and is in fact an extension of the same theory. Likewise his famous division of argument into axioms and postulates is also one rooted in mathematical theory. The Romans, and later the church, have always treated these theories as "purely" philosophical assertions which were then applied to rhetoric by Marcus Aurelius and theology by his Christian successors. It has taken until the modern era of quantum theory however to reincorporate them vigorously into mathematical thinking.

The Hermetic canon is not attributed to any one person any more, I don't think. It is a hotch-potch of various cherry-picked Stoic and Platonic platitudes, often completely out of context, employed to add a veneer of intellectuality to what is really just gibberish by and large. The alchemy and astrology of which it is mostly comprised may have caught the imagination in the Renaissance, but by the late 16th century it was increasingly being dismissed as the rubbish it is. Although it had pretensions to being ancient Egyptian on the part of its authors and its fans it appears to have actually originated in around the 2nd or 3rd centuries CE somewhere in the wider Hellenic world (probably Egypt even, though that is not relevant), and when this could be conclusively indicated the bottom fell out of the Hermetic business (they had probably forgotten to Hermetically seal it).

Your quote re Faustus is especially revealing, isn't it? It shows that a deep suspicion of mathematics was not something that necessarily lessened with the advent of institutionalised learning and increased access to knowledge. In fact in some places this only seems to have deepened it further. And I wonder whether there are any of us who, after struggling through Hawking's "Brief History ...", have not privately entertained the notion that we are in the presence of someone who - while not demonic - is most definitely not governed by the same base logic and thinking which constrains the rest of us. So who knows what morality prevails in that mind?
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PostSubject: Re: Evil Mathematicians   Tue 12 Feb 2013, 19:27

Yet by the next century, Aubrey writes this in his "Minutes of Lives" ("Brief Lives"). He is referring to Thomas Allen, one of the Wizard Earl's followers:


"In those dark times, astrologer, mathematician and conjuror were accounted the same things, and the vulgar did verily believe him to be a conjuror. He had a great many mathematical instruments and glasses in his chamber, which did also confirm the ignorant in their opinion, and his servitor (to impose on freshmen and simple people) would tell them that sometimes he should meet the spirits, coming up his stairs like bees."

So, the end of the 16th century was, to Aubrey writing around 1680(?), "those dark times" and those who saw the mathematician as a magician were "the vulgar", "the ignorant" and "simple people"! How quickly things change!

Checked out Hermes Trismegistus in MacCulloch's "History of Christianity". Nordmann, you were right, surprise, surprise:

"Among the flood of new and strange material from the ancient world, which might or might not be valuable if put to use, was a set of writings about religion and philosophy purporting to have been written by a divine figure from ancient Egypt, Hermes Trismegistus. In fact they had been compiled in the first to third centuries CE, at much the same time as early Christianity was emerging."


A maths undergraduate, Cambridge, circa 1590.

The Arabs were great mathematicians, I believe. Were Islamic religious leaders/teachers also wary of the subject?
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PostSubject: Re: Evil Mathematicians   Sun 08 Nov 2015, 15:26

@Temperance wrote:
The Arabs were great mathematicians, I believe. Were Islamic religious leaders/teachers also wary of the subject?

Good question Temp. And I'm glad you've made the distinction between 'Arab' and 'Islamic'. It's one of those lazy conflations we hear all too often in the mass media.

The 'Golden Age of Islamic Science' (c. 8th Century - 13th Century) was strongly represented by Persian and Moorish elements as well as Arab. The language of writing, however, was generally Arabic and the public culture was undoubtedly Islamic. Considering that this culture extended from Iberia to India then alternative names such as 'Arab Science' or 'Eastern Science' are problematic. Somewhat counter-intuitively, therefore, the term 'Islamic Science' would seem to fit best.

As to whether or not there was a basic conflict between religious leaders and scientists (and specifically mathematicians) then this is a moot point. As in other cultures, academia was often beholden to powerful patrons. Needless to say that the attitudes of patrons towards scholarship could vary from era to era. In this respect the golden age of mathematics in Baghdad was relatively short lived. It enjoyed great patronage for about 100 years in the 8th and 9th Centuries before falling out of favour with later generations of Islamic rulers.
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Temperance
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PostSubject: Re: Evil Mathematicians   Sun 08 Nov 2015, 19:14

@Vizzer wrote:
Good question Temp.



Actually, it was rather, wasn't it? See, I'm not as stupid as I look.


Smile
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PostSubject: Re: Evil Mathematicians   Sun 08 Nov 2015, 19:25

@Vizzer wrote:
@Temperance wrote:
The Arabs were great mathematicians, I believe. Were Islamic religious leaders/teachers also wary of the subject?

Good question Temp. And I'm glad you've made the distinction between 'Arab' and 'Islamic'. It's one of those lazy conflations we hear all too often in the mass media.

The 'Golden Age of Islamic Science' (c. 8th Century - 13th Century) was strongly represented by Persian and Moorish elements as well as Arab. The language of writing, however, was generally Arabic and the public culture was undoubtedly Islamic. Considering that this culture extended from Iberia to India then alternative names such as 'Arab Science' or 'Eastern Science' are problematic. Somewhat counter-intuitively, therefore, the term 'Islamic Science' would seem to fit best.

As to whether or not there was a basic conflict between religious leaders and scientists (and specifically mathematicians) then this is a moot point. As in other cultures, academia was often beholden to powerful patrons. Needless to say that the attitudes of patrons towards scholarship could vary from era to era. In this respect the golden age of mathematics in Baghdad was relatively short lived. It enjoyed great patronage for about 100 years in the 8th and 9th Centuries before falling out of favour with later generations of Islamic rulers.
Vizzer and Temperance,


Vizzer in answer to Temp's question I did in the time on a French and even our BBC forum some research in the heat of the French Goughenheim discussion: No Renaissance without Islam? You had the French rightist camp and the French leftist/muslim camp with a lot of insults in the papers...

I remember to have written about the tension between the Greek philosophy and the revealed religions as in the Latin Middle-Ages, the Byzantine and the Islam. For the Islam even in the period that you mentioned, the hightime of the Islamic science in Bagdad with the House of Wisdom...
http://www.empereurperdu.com/tribunehistoire/viewtopic.php?f=6&t=321&start=15

And overthere the article of the Greek rooted American:

http://archaeology.kiev.ua/pub/vryonis.htm
And from this article:
"What of philosophy? Was this practical? Here the answer is not clear cut. First, the writings of Aristotle covered a huge epistemological horizon, from the sciences of the heavens, the earth, and the waters. The horizon covered more abstract matters, such as the process of reasoning and logic, etc. We should also recall that the Galenic system of medicine, which had made such an incursion into Islamic civilization, contained a very important philosophical component, as we see in Galen's famous treatise entitled, "On the fact that the best physician is also a philosopher." Whatever the causes, the influx of Aristotle and other philosophical writings created a serious problem and constituted a grave threat to a civilization based on a revelational religion which gave priority to the truth of revelation over human logic. The unchecked introduction of Greek philosophy and philosophers threatened to undermine the bases and overthrow the nature of the Islamic faith. Here the revelational demands of Islam prevailed, and the roles of philosophy and logic were limited, at best, to the obligational support of the veracity of the faith. In short, Islamic civilization relegated philosophy and logic to the role of the handmaiden of theology, as occurred also in the Latin West and in Byzantium."

Kind regards, Paul.
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PostSubject: Re: Evil Mathematicians   Sun 08 Nov 2015, 19:28

Temperance,

our posts crossed while I was "constructing" my message...
Glad to see you, I already thought that...

Kind regards from your friend Paul.
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PostSubject: Re: Evil Mathematicians   Mon 09 Nov 2015, 15:29

I wish they'd told the nuns at my convent schools that maths were evil all those years ago.  Maths never were my strong suit though I did't work that hard at them it's true.  One teacher (a lay teacher not a nun incidentally) moaned about my work being untidy - to be fair she may have had some cause.  So one night I made the effort to do my working out neatly AND the teacher accused me of cheating and having someone else do my homework for me!  I kind of lost interest after that.
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PostSubject: Re: Evil Mathematicians   Mon 09 Nov 2015, 21:38



Mathematician with absolutely no redeeming features - Sigismund Arbuthnot.
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