The Invisible Link Between Bad Math and Bad Theology

Another piece of junk that I received: “The Invisible Link
Between Mathematics and Theology”
, by a guy named “Ladislav Kvasz”,
published in a rag called “Perspectives on Science and Christian Faith”. (I’m
not going to quote much from this, because the way that the PDF is formatted,
it requires a huge amount of manually editing.) This is a virtual masterwork of
goofy clueless Christian arrogance – everything truly good must be Christian, so
the author had to find some way of saying that mathematics is intrinsically tied to Christianity.

This article actually reminds me rather a lot of George
Shollenberger
. His arguments are similar to George’s: that there’s some
intrinsic connection between the concept of infinity and the Christian god.
But Kvasz goes further: it’s the nature of monotheism in general, and
Christianity in particular, which gave us the idea of using
quantifiers in predicate logic. Because, you see, the idea of
quantifiers comes from the idea that existence is not a predicate, and the
idea that existence is not a predicate comes from a debate over an invalid
proof for the existence of god.

In fact, he comes up with a list of five different areas where he claims
that the influence of Christianity (or at least monotheism) allegedly fundamentally changed mathematics:

  1. Infinity. He claims that the modern concept of infinity is fundamentally
    different than the pre-Christian one, and that the reason for that is
    that the acceptance of an infinite god makes it more natural to accept
    the concept of an infinite number.
  2. Randomness. He claims that the modern concept of randomness is something
    new, because before Christianity, fate and chance were considered to be
    one and the same; but after Christianity, people see fate as the province
    of god, but things like gambling are governed by randomness.
  3. Unknowns. He claims that the concept of a symbolic representation
    of an unknown value as a variable in algebra is an intrinsically
    monotheistic notion. He can’t tie this one to christianity, because
    we know that the word algebra comes from the name of an Muslim scholar,
    so he drops back to monotheism.
  4. Space. He claims that prior to Christianity, the concept of “space” independent of the things that occupy it is an intrinsically Christian notion. This one he doesn’t even really try to defend in terms of Christianity; he really just asserts that it’s part of the same thing as the
    concept of infinity, and since infinity is Chistian, space must be as well.
  5. Motion. Again, the same deal as space. Without space, you can’t really have a mathematical study of motion; since the mathematical concept of space relies on the concept of the monotheistic god, that means that mathematical
    study of motion is therefore christian.

This stuff is frankly silly beyond words. I had to stop several times while reading the paper, because I simply burst out laughing at the sheer goofiness of it! I mean, take a look at this passage from page 114:

Now we come to the third common feature of the above-mentioned changes. Let
us first take the notion of infinity. While for the ancients apeiron was a
negative notion associated with going astray and losing the way, for the
medieval scholar, the road to infinity became the road to God. God is an
infinite being, but despite his infiniteness, he is absolutely perfect. As
soon as the notion of infinity was applied to God, it lost its obscurity and
ambiguity. Theology made the notion of infinity positive, luminous, and
unequivocal. All ambiguity and obscurity encountered in the notion of
infinity was interpreted as the consequence of human finitude and
imperfection alone. Infinity itself was interpreted as an absolutely clear
and sharp notion, and therefore an ideal subject of mathematical
investigation.

It’s hard to take this seriously. Pre-christian mathematicians didn’t
understand infinity, because they viewed it as an unknown with negative connotations, but because of their belief in god, the wonderful christian
mathematicians were able to see it as a definite positive but unknowable. Right, Ladislav. Just back away from the keyboard slowly, and go with these nice men in white monks robes, OK?

It gets worse when he starts talking about algebra. One of the really
dreadful things about this train-wreck of a paper is that it pretends that
mathematics started with the Greeks – so if the Greeks didn’t know it, then it
was unknown before monotheism. But much of the best of early math had nothing
to do with the Greeks. Algebra may have been introduced to the west by Muslim
scholars, but it was invented in India. Brahmagupta, who I wrote
about in my article about zero quite
definitely worked with the roots of what became known as algebra, roughly 1000
years before algebra was known in Europe. The Arabic scholars learned it when
the Caliph of the Arab empire invited one of the students of Brahmagupta to
come to Baghdad to teach Hindu astronomy sometime around 700AD. But our man
Ladislav doesn’t let little things like his own ignorance get in the way of a
nice piece of Christian propoganda.

This bit caused me to spray soda out through my nose. I can’t even comment
on it, it’s just too much.

A similar tension between the ontological definiteness (necessary for the
application of arithmetical operations) and epistemological indefiniteness is
characteristic in the notion of the unknown in algebra. The unknown is unknown
for us, finite beings. For God there are no unknowns at all. As soon as he
looks at the formulation of an algebraic problem, he immediately sees the
value of the unknown. He has no need to solve the equations, because due to
his omniscience, he immediately knows the solutions. Thus, in a way similar to
the case of the theory of probability, in algebra too, the ontological
ambiguity, which prevented the Greeks from mathematicizing this area, was
transformed into an epistemological ambiguity, having its space, and motion.

Whew, got past that one without any more soda on the keyboard.

0 thoughts on “The Invisible Link Between Bad Math and Bad Theology

  1. Ambitwistor

    On a similar note, check out this Usenet post summarizing various textbooks on “Christian mathematics” that have appeared over the years.
    I love this anti-New Math complaint: “Stresses absolutes, concrete facts, drill for training; `set theory has done to … mathematics what the theory of evolution has done to … science.'”

    Reply
  2. Blake Stacey

    MarkCC wrote:

    He claims that the modern concept of randomness is something new, because before Christianity, fate and chance were considered to be one and the same; but after Christianity, people see fate as the province of god, but things like gambling are governed by randomness.

    A cursory knowledge of Lucretius shows that this is fundamentally wrong. His De Rerum Natura explains that, as Democritus said, all matter is atoms in motion. Free will is made possible by slight random bounces this way or that, a small amount of stochasticity introduced into the otherwise deterministic Cosmos. Lucretius, so it happens, died half a century before Christ was born.
    Also:

    He claims that prior to Christianity, the concept of “space” independent of the things that occupy it is an intrinsically Christian notion. This one he doesn’t even really try to defend in terms of Christianity; he really just asserts that it’s part of the same thing as the concept of infinity, and since infinity is Chistian, space must be as well.

    It’s good that he doesn’t try to defend this, because it is also fundamentally wrong. Until well after the Reformation, the Catholic Church was committed to the Aristotelian idea that a vacuum could not exist, because a place can only be defined as the location in which an object exists. Aristotle held that the Universe must be a plenum, that is, filled with matter; the Church adopted this idea and said that God must be everywhere, filling all existence. A vacuum is impossible, because that would imply a place in which God is not — clearly absurd.
    This made the investigation of air pressure rather difficult.
    Near the end of his life, Galileo was asked to solve the problem which plagued the miners of his day: the fact that their pumps could not force water more than about ten meters up a tube. Galileo passed the problem on to his colleague Torricelli, who realized that the pumps worked by the weight of air pushing down on the water, forcing the water up the pipe. He decided that one could make a scale model using mercury, much heavier than water, to study the physics of the situation, but Italy was too close to the Pope to investigate the vacuum. . . . which is why the mercury barometer was first tested in France by Blaise Pascal, and why the first practical vacuum pump was invented in Germany.
    (Torricelli is also the reason why we have a “torr” as a unit of pressure.)
    So, “the concept of ‘space’ independent of the things that occupy it”, far from being a fundamentally Christian notion, was directly opposed to Christian dogma, and moreover this opposition actually impeded the advance of science.

    Reply
  3. Norm Breyfogle

    Combined with your profile’s photo, Mark, I now have a clear and persistent image of soda spraying out of your nose. (lol)
    For me, the chief irony in Kvasz’s pov is that if the concept of infinity as an attribute of “God” is thoroughly contemplated (not to mention omniscience and omnipotence), it wipes out the anthropmorphism that is arguably the most important aspect of the tradional, literalistic religious view of “God”!
    Kvasz’s thinking is just more confusion over the difference between metaphor, symbolism, mythology, and literal fact.

    Reply
  4. Coin

    `set theory has done to … mathematics what the theory of evolution has done to … science.'”
    Awesome. Let’s start going around calling all the mathemeticians we meet “Russellists”.

    Reply
  5. Rev. BigDumbChimp

    Mark. Old Georgie’s book has been out for about 8 months or so now and he hasn’t gotten a single review on Amazon about it. You should check out what his steadily decaying mind has come up for as a reason no one has commented. Check out entires at his blog and at Amazon especially.
    It’s really hilarious.

    Reply
  6. Daniel Martin

    Mark, are you seriously saying then that the modern conception of infinity, and of the idea of an infinite number of things wasn’t invented in Europe? Specifically, wasn’t invented in a Europe full of intellectuals willing to argue about things such as whether the number of angels able to stand on the head of a pin was infinite or finite? If not, where did this concept get imported from?
    The rest of his claims range from simply false to bizarre, but I think on infinity he may have something to stand on: it was invented in Europe by intellectuals in a Christian society. Of course, by that count he might as well also claim calculus, at least differential calculus, for the faith. (see: Newton) He has not (at least not in what you quoted) tied the development of the concept of infinity to some peculiarity of Christianity. He’s tried, but so far it seems a weak attempt.

    Reply
  7. Doub

    That guy should be put on a rocket to space, fitted in a space suit and released in infinite nothingness without anchor. I wonder if he will still find infinite so luminous and positive.

    Reply
  8. Mark C. Chu-Carroll

    Daniel:
    The concept of infinity definitely preceeds the European englightenment that Kvasz credits. Even his beloved Greeks had a solid idea of infinity; much of the western concept of infinity was came along the same lines as algebra. The only thing that the Europeans really added were things like Cantor’s transfinites and Leibnitz infinitessimals. But neither of those is necessary for the concept of infinity, and neither is a necessary part of modern math. They’re both interesting and useful, but far from necessary.

    Reply
  9. Blake Stacey

    There’s a good argument to be made that the Sanskrit Yajurveda (c. 1200–900 BCE) discusses infinity, using the word purna (“fullness”). Furthermore, Archimedes seems to have avoided the Aristotelian hang-up about “potential infinity”, and our friend Lucretius also had something to say:

    In the first century BC Lucretius wrote his poem De Rerum Natura in which he argued against a universe bounded in space. His argument is a simple one. Suppose the universe were finite so there had to be a boundary. Now if one approached that boundary and threw an object at it there could be nothing to stop it since anything which stopped it would lie beyond the boundary and nothing lies outside the universe by definition. We now know, of course, that Lucretius’s argument is false since space could be finite without having a boundary. However for many centuries the boundary argument dominated debate over whether space was finite.

    Given that after the fall of Rome, virtually all intellectual activity in Europe was conducted by Church people, I don’t think there’s very much content in saying “Christians were the only ones to think about infinity”. The history of medieval Christian thought is neatly bookended by Augustine, who sent everyone into drop-out mode with “life is a veil of tears” rhetoric; and Aquinas, who performed one of history’s great “save the appearances” performances, establishing a double standard for truth which plagues us to this day. Getting out of that death-trap was not easy, and Europe couldn’t do it without help. . . . I guess I just don’t have high regard for those taking censuses of angels on pinheads.

    Reply
  10. Jonathan Vos Post

    I’m pretty sure that Homer wasn’t Christian. Probably not Jewish, either.
    Following excerpt from
    http://etext.virginia.edu/cgi-local/DHI/dhi.cgi?id=dv2-67
    “The Old Testament exulted in the omnipotence of the Creator, but it did not initiate problems about the unboundedness of His power or the infinity of His creation. The Hebrew of the Bible did not have a word for ‘infinity’ in general. It only had words about particular aspects of infinity, and leading among these was the word ‘olam. It designated eternity, that is infinity in time, without reference to spatiality. Post-biblically, however, the word began to acquire traits of spatiality, ever more so, and it may have given to the present-day Arabic word ‘alam its meaning of ‘world,’ ‘cosmos,’ ‘universe'” (Encyclopedia of Islam, New Ed. [1960], 1, 349).
    “Greek literary works, in poetry and prose, were less theocratic than the Old Testament. But from the first there was in them an awareness of immensity and even
    unboundedness in the cosmos, and Greek rationality showed very early a disposition to examine the meaning of infinity in its complexity. The standard Greek word for infinity was apeiron (ἄπειρον ; probable etymology: a = non, peiras or peras = limit, bound). Close cognates to it occurred in Homer, and the word itself had a considerable literary cachet, in poetry and prose, letters and science. The word occurs in Hesiod and Pindar, in literal fragments of most pre-Socratic philosophers, and in reports about
    Pythagorean statements which seem verbally proximate to original utterances of theirs (Bochner, “The Size of the Universe…,” sec. II)…

    Reply
  11. shiva

    The Jaina philosophers in ancient India (4-200 BCE) had some interesting ideas about infinity http://tinyurl.com/24lq7k. This was a time when the philosophers from the later Hindu, early Buddhist, and Jaina – among others – may have debated ontology and epistemology; because the latter two schools came up with some new ideas. The historical context of these debates and much of what actually was discussed may never come to light, and all we have are some terse verses. This is around the time Kanada proposed an atomic theory of matter (and almost made it into the flavor of the month). As a rule all philosophies schools originating in India take the infinity of time and space as a given.

    Reply
  12. Bronze Dog

    So, “the concept of ‘space’ independent of the things that occupy it”, far from being a fundamentally Christian notion, was directly opposed to Christian dogma, and moreover this opposition actually impeded the advance of science.

    Learn a new thing every day. So things Christian fundies have tried to repress: Game Theory (all that rhetoric about the necessity of punishment to enforce altruism), simplicity building up to complexity, vaccines, religious freedom, the square root of 2, the dodecahedron, yadda yadda, and now: The concept of a vacuum and empty space.

    Reply
  13. mtraven

    I don’t quite understand the level of vituperation directed at this article. Whether his efforts to link the intellectual history of mathematics and Christian theology are valid or not, I can’t say, but it certainly seems plausible that various currents in the two fields of study influenced each other, and an interesting topic for speculation. He’s certainly not the first to propose that monotheism was an important and necessary precursor to the development of science.
    The excerpts you selectively quote give the wrong impression — he’s really not asserting statements about God as much as describing how a certain idea of God might give rise to certain ways of thinking.
    Maybe you are misreading it as some sort of effort to use mathematics to justify or validate a set of religious beliefs. That’s something which would deserve scorn, but I don’t think that’s what the article is about. He’s not proselytizing, and even if he’s got some of the history wrong he doesn’t deserve abuse.

    My aim is not to settle the question of the role of theology
    in the development of science and mathematics, but to
    propose an indirect method of its study. As Max Weber
    analyzed the role of Protestant ethics in the development
    of modern capitalism, in a similar way, it is possible to
    analyze the role of monotheistic theology in the development
    of modern science. Monotheistic theology, like
    Protestant ethics, did not directly influence its development.
    Rather, it helped to create conditions in which the
    development of modern science became possible.

    Reply
  14. Norm Breyfogle

    mtraven, I think you’ve got a point, one that I would’ve seen if I’d bothered to read Kvasz’ article first. After reading your post I did check out the article in question, and though I didn’t read it in detail, I perused it and found it less ideological than I expected it to be.
    Still, the ad at the end of the article for a Christian website and magazine does make me somewhat suspicious.

    Reply
  15. Thony C.

    “He can’t tie this one to christianity, because we know that the word algebra comes from the name of an Muslim scholar, so he drops back to monotheism.”
    Sorry to correct you on this one Mark but the word “algorithm”comes from Abu Ja’far Muhammad ibn Musa al-Khwarizmi’s name, the word “algebra” comes from the title of his book Hisab al-jabr w’al-muqabala. The arabic word al-jabr means to put together, which is why an algebraist in Spanish is not a mathematician but a bone setter!
    “But Kvasz goes further: it’s the nature of monotheism in general, and Christianity in particular, which gave us the idea of using quantifiers in predicate logic. Because, you see, the idea of quantifiers comes from the idea that existence is not a predicate, and the idea that existence is not a predicate comes from a debate over an invalid proof for the existence of god.”
    Frege who was the first person to explicitely use quantifiers would be very surprised by this explanation.
    On the subject of infinity and christianity the Greek philosophy of atomism was considered heretical in the early modern period exactly because it claimed that the universe had existed for infinitely which contradicted the christian concept of creation.

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  16. David Corfield

    mtraven surely has things right. I’ve met Kvasz on a number of occasions and have read some of his work. Some may say he allows the desire to find large historical patterns to swamp historical reality, but he’s not a proselytizer. That there is an important religious context in which the mathematics of the seventeenth century develops is hardly contentious, see e.g. the book mentioned here. How much you choose to take this context as determing the content of modern mathematics is another issue.

    Reply
  17. David Corfield

    On the subject of historical accuracy, the ‘angels on pinhead’ myth reared its ugly head in the comments. Try the second bullet point of this to convince yourself that it was just a piece of Protestant propaganda.

    Reply
  18. Michael Saelim

    If what this author says is true, mathematicians should be saints and math majors like me should at least be beatified or something. 🙂

    Reply
  19. Torbjörn Larsson

    He’s certainly not the first to propose that monotheism was an important and necessary precursor to the development of science.

    But is there anything that specifically is based on monotheism here, as apart from alleged christian religious influences in general?
    Link or influence, it still reads like apologetics.

    On the subject of historical accuracy, the ‘angels on pinhead’ myth reared its ugly head in the comments.

    But it is (at least, should be) understood to be an unfriendly allegory of a theological discussion. After all, “Aquinas does discuss “whether several angels can be in the same place at the same time””, which is actually a worse argument to do.

    Reply
  20. dogscratcher

    ” This is a virtual masterwork of goofy clueless Christian arrogance – everything truly good must be Christian, so the author had to find some way of saying that mathematics is intrinsically tied to Christianity.”
    It seems odd that any belief system that requires a person to believe that “1=3” could claim to be intrinsically tied to mathematics.

    Reply
  21. Mark C. Chu-Carroll

    mtraven, David:
    I’m forming my judgements solely on the contents of the paper. And the paper is, quite frankly, a wretched piece of work. It’s poorly researched, contains numerous historical errors, and sloppy reasoning. It is just another piece of apologetic nonsense.
    Anyone who publishes a paper arguing that the development of algebra is dependent on the concept of monotheism, but who didn’t bother to do enough research to know that algebra wasn’t developed by monotheists deserves to be mocked.
    And he makes errors like that throughout the paper. The concept of infinity is not a Christian invention. The reasons that he attributes to the greeks for not treating infinity mathematically are not an accurate representations of the Greek ideas about infinity. The concepts of space, motion, and probability are not Christian inventions, and he mischaracterizes the ideas of the Greeks about all of them, and completely ignores the pre-Christian history of mathematics everywhere except Greece.
    There are scrolls from ancient Egyptian temples that contain algebraic equations – with variables for unknowns. He ignores that. The Babylonians had concepts about infinity. He ignores that. A huge part of what grew into modern math was invented in India. He ignores that.
    It’s either a thoroughly dishonest piece of writing (if he chose to ignore the entire non-greek history of math), or more likely a dreadfully poorly researched ignorance-filled piece of junk (if he just didn’t know about the history of math outside of Greece, and didn’t bother to look any of it up).

    Reply
  22. ObsessiveMathsFreak

    Actually, there are some links between mathematics and religions, but nothing so invisible as the paper’s author invisioned. Rather, they are more mundane.
    Take for example the degrees in a circle. There are 360 of them. And each degree is divided up into 60 arc minutes. This goes back to the Babylonian sexigesimal( base 60) number system, which, if I remember correctly, was based on the fact that number of gods in the babylonian pantheon was 60.
    And don’t forget Pythagoras’s theorem! As it turns out Pythagoras and his followers were in fact a religious cult one of whos beliefs was that all numbers are rational, (i.e. All numbers are elements of Q). Anyone who thinks mathematicians are all logical and all secular beings should spare a thought for the fate of Hippasus, who proved that sqrt(2) was irrational, and was subsequently executed for heresy by the Paythagoreans.
    And don’t think that mathematicians have kept themselves out of religious debates either. Here’s a quote from St Augustine:

    “The good Christian should beware the mathematician 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.”

    Because as it turns out, back in his day, the main job of mathematicians in those days was as astronomy and predicting both the seasons and the weather for their agranian societies. And astronomy was never too far from the all too pagan astrology, which many “mathematicians” invariably dabbled in.
    But mathematics in the post Renaissance world is more generally a secular affair, and indeed gets a lot more done that way. But don’t think criticism of mathematics for being so secular is a new concept. When presented, by Laplace, with his magnum opus, “Méchanique céleste”, Napoleon asked why there was no mention of God in the entirety of the book. Laplace replied; “Je n’avais pas besoin de cette hypothèse-là.”(I did not need to make that hypothesis).
    As it turns out, mathematicians never do.

    Reply
  23. Mark C. Chu-Carroll

    OMF:
    I hate to be the one to break it to you, but that Augustine quote is a nasty mistranslation. It’s actually talking about
    astrologers :-(. See, for example: http://en.wikiquote.org/wiki/St._Augustine.
    A more accurate translation of that is: “Hence, a devout Christian must avoid astrologers and all impious soothsayers, especially when they tell the truth, for fear of leading his soul into error by consorting with demons and entangling himself with the bonds of such association.”
    I was terribly disappointed when I found out that translation was wrong. 🙂

    Reply
  24. Coin

    It seems odd that any belief system that requires a person to believe that “1=3” could claim to be intrinsically tied to mathematics.

    The finite field of order two?
    ^_^

    Reply
  25. Blake Stacey

    Actually, there’s a very mundane reason why the Sumerian (and later, the Babylonian) number system embraced 60 and 360. When you don’t like fractions, it’s good to use numbers which have lots of divisors. 60 is divided evenly by, let me see, 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30. Knowing nothing else, I’d say that 60 and 360 might spring up all over Babylonian myths just because they’re convenient, largish numbers. (Well, “large” if you’re talking about kings, gods, years, etc.)
    The seven-day week, also of Babylonian origin, comes from the fact that seven mobile celestial bodies were visible to the naked eye: Mercury, Venus, Mars, Jupiter and Saturn plus the Sun and Moon. Ever since, we’ve been stuck with the problem that 7 doesn’t go nicely into 365 which is not exactly 12 times 30. Combine the Babylonian penchant for nice numbers with the not-quite-even number of days in the year, and you get calendrical confusion which persists to this day.
    The following is quoted from George Sarton’s Ancient Science Through the Golden Age of Greece, page 71:

    Not only did the Sumerians use a positional notation (though without zero) and extend it to submultiples of the base as well as to multiples, but their number ssytem was closely connected with the subdivision of weights and measures. That is, they had devised a complete sexagesimal system before 2000 B.C.; in order to appreciate their genius it will suffice to recall that the extension of the same ideas to the decimal system was only conceived in 1585 (by the Fleming Simon Stevin), that its implementation was begun only during the French Revolution and is not yet completed today. The old Sumerians were more consistent than are many of our own contemporaries who persist in defending English metrology in a decimal world. Having realized that, it becomes a little difficult to consider the former as primitives or the latter as truly civilized.

    On the following page, Sarton says,

    The sexagesimal base was strangely reinforced in the course of time by the occurrence of another unit six times as large. The sumerians thought at first (like the earliest Egyptians) that there were 360 days in the year. They began by dividing the days into six watches (three day watches and three night ones, which were naturally of varying length), but they soon realized the impracticality of unequal time periods for astronomical work and divided the whole day (day and night, nychthemeron) into 12 equal hours of 30 gesh each. That is, their astronomical day was divided into 360 equal parts. There were 360 days in the year and 360 gesh in the day; the same division into 360 parts was applied later to parallels, and later still (in Achaemenian times, c. 558–330) to the ecliptic (zodiac, dodecatemories). We divide the circle into 360 degrees to this day, and subdivide the degrees on a sexagesimal basis, because of the Sumerian mathematicians who flourished more than two millennia before Christ.

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  26. Blake Stacey

    By the way, I heartily recommend George Sarton’s History of Science to everybody. Sarton, the grand old man of science history, writes with lucidity and erudition. He sounds like the prototype of the dry-witted professor. Carl Sagan read the History of Science; along with Bertrand Russell’s History of Western Philosophy, it is probably the source of the Plato-bashing in Cosmos.
    I looked up “infinity” in the index to Sarton’s Volume I, from which I quoted this morning. It directed me to page 502:

    Aristotle’s greatest service to mathematics lies in his cautious discussion of continuity and infinity. The latter, he remarked, exists only potentially, not in actuality. His views on those fundamental questions, as developed and illustrated by Archimedes and Apollonios, were the basis of the calculus invented in the seventeenth century by Fermat, John Wallis, Leibniz, and the two Isaacs, Barrow and Newton (as opposed to the lax handling of pseudo infinitesimals by Kepler and Cavalieri). This statement, which cannot be amplified in a book meant for nonmathematical readers, is very high priase indeed, but justice obliged us to make it, the more so because Plato is more famous as a mathematician than Aristotle, and that is exceedingly unfair. Aristotle was sound but dull; Plato was more attractive but as unsound as could be. Aristotle and his contemporaries built the best foundation for the magnificent achievements of Euclid, Archimedes, and Apollonios, while Plato’s seductive example encouraged all the follies of arithmology and gematria and induced other superstitions. Aristotle was the honest teacher, Plato the magician, the Pied Piper; it is not surprising that the followers of the latter were far more numerous than those of the former. But we should always remember with gratitude that many great mathematician s owed their vocation to Plato; they obtained from him the love of mathematics, but they did not otherwise follow him and their own genius was their salvation.

    Need it be said that the thread to Christianity runs through the early Church Fathers back to Plato, not to Aristotle (or, perish the thought, Empedocles or Democritus)? Indeed, when full copies of Aristotle’s books made the scene once more — thanks to the “Reconquest” of Arab Spain — the theologians of Europe rightly saw them as heresy. It took Thomas Aquinas’s synthesis, a.k.a. “saving the appearances”, to restore order. . . .

    Reply
  27. Shawn P Gell

    Hello my name is Shawn and I want to tell you about 311Music (a rock band). The members of the band have family names like Hexum, Nexum and Sexton.
    To the best of my knowledge they are Greek words associated with numbers. I am telling you this because I have found connections between me and the number 311. This is illustrated below.
    When I started doing this 311 was so prevalent that I began to wonder about the band. When I bought two of their CD’s I found the number 8904 connected to their web address and their mailing address in them. That is not the case now, but when I saw the number it led me to the discovery of a connection to the number 777 to me. this is illustrated below.
    311 has a song called Crack the Code a another one called amber. It starts “this phenomenon. I had to put it in a song and it goes like, woah amber is the color of your energy.” This song is one of their most popular.
    The song can be seen on one of their websites. You just type in 311music in your web search and one of the websites says amber on it. You can click on that and review the song.
    I am telling you this because over 3 years ago I met a girl named Amber Rachel Black. And I found parallel algorithms between us over the moment we met. this is illustrated below. There is also connections to the number 311 there too.
    I don’t know what 311(the band) is about or what they do, but I do think I am on to them. they must know a lot about Gematria and have some advanced way of calculating it.
    Gematria method
    A=1 J=10 S=100
    B=2 K=20 T=200
    C=3 L=30 U=300
    D=4 M=40 V=400
    E=5 N=50 W=500
    F=6 O=60 X=600
    G=7 P=70 Y=700
    H=8 Q=80 Z=800
    I=9 R=90
    What I do with this system is add up the numbers to the corresponding letters in names, words and phrases.
    My full name- (Shawn Phillip Gell) = 957
    957 = (Pure Jehovah)
    (Shawn is Oracle)
    (All is real) + (He is the oracle of God)
    (True) + (He is an oracle)
    (Is the oracle of real light)
    (He is a pure oracle) + (God)
    (God’s message) + (The real oracle)
    (Sacred and Divine gift)
    (He the Divine Light)
    (Is the good Lord of Light)
    (God considers pure)
    (Gematria is love)
    (Gematria Scientific Fact)
    (From the Divine God)
    (Is the perfection of God)
    (The son of the Lord God)
    (Christ the Messiah) + (God)
    (Sacred Sword)
    (God’s will for all)
    (The Peace Savior)
    (The good sacred Christ)
    (He is Messiah of God’s peace plans)
    (Is the Messiah) + (Is Messiah)
    (The Oracle has the name of God)
    (Is the one) + (Is the God of all)
    (777 is God)
    (311 is in spirit)
    (Is the message of 311)
    (Sacred Light) + (311 Oracle)
    2(Is 311) + 117
    (117 is Divine light)
    2(957) = (311 is with 777)
    (God’s will for the World) + (plan)
    777 + (Divine Savior)
    (777 Sacred Oracle) + (He is the Christ)
    (The Oracle is like Jesus Christ on Earth)
    (Judges the Divine truth)
    (The Divine Savior of Perfection)
    (He is the Divine 311 of power)
    2(777) + (God’s oracle)
    (The oracle of God’s Divine truth)
    (The 777 Devine Oracle message)
    (The Divine Oracle has the wisdom)
    1/7 = .142857142857…..
    1(142857) = 142857
    3(142857) = 428571
    2(142857) = 285714
    6(142857) = 857142
    4(142857) = 571428
    5(142857) = 714285
    7(142857) = 999999
    2857 + 14 = 3(957)
    8571 + 42 = 9(957)
    5714 + 28 = 6(957)
    (9999 + 99) – (7142 + 85) = 3(957)
    (9999 + 99) – (1428 + 57) = 9(957)
    (9999 + 99) – (4285 + 71) = 6(957)
    The number 132645 is taken from above as the consecutive multiples of 142857.
    132 + 645 = 777
    326 + 451 = 777
    264 + 513 = 777
    645 – 326 = 319
    451 – 132 = 319
    513 + 451 – 645 = 319
    3(319) = 957
    311 – 117 = 194
    326 – 132 = 194
    513 – 319 = 194
    645 – 451 = 194
    513 + 326 – 645 = 194
    My birthdate: 11-7-1982
    11-7-1982 = 365.25(1982) + 311 = 724237
    11-7-1982 is 724237 days in the A.D.
    11-7 is the 311th day of the year
    1982 = 2(777) + 311 + 117
    1982 = (The 777 oracle was born)
    1982 = (957 is the Sacred Oracle) + 311
    724237 = 851(851) + 6(6)
    (851 + 6)(851 + 6) – 724237 = 851(12)
    724237 – (851 – 6)(851 – 6) = 851(12)
    142857 – 132645 = 851(12)
    724237 – 851(2) = 957(755)
    724237 = 142857(5) + 311(32)
    142857 = 481(297)
    481 + 297 + 777 = 311(5)
    142857 = 117(1221)
    724237 = 1221(593) + 184
    184 + 593 = 777
    724 + 237 = 961
    184 + 777 = 961
    961 + 593 = 777(2)
    142857 = 593(220) + 537
    220 + 537 = 777
    142857 = 961(148) + 629
    148 + 629 = 777
    142857 = 957(148) + 1221
    1221 = 3(148) + 777
    1221 + 957 + 777(2) = 311(12)
    1221 + 957 = 1089(2)
    1089 + 9801 = 10890
    1089(2) = 2178
    2178 + 8712 = 10890
    1089(3) = 3267
    3267 + 7632 = 10890
    1089(4) = 4356
    4356 + 6534 = 10890
    1089(5) = 5445
    5445 + 5445 = 10890
    977 = 151 + 826
    142857 = 151(946) + 11
    946 + 11 = 957
    142857 = 826(172) + 785
    172 + 785 = 957
    977 = 331 = 646
    143857 = 331(430) = 527
    430 + 527 = 957
    142857 = 646(220) + 737
    220 + 737 = 957
    977 = 204 + 773
    142857 = 204(696) + 873
    (696 + 873) – 204(3) = 957
    142857 = 773(184) + 625
    773 + 184 = 957
    977(3) = 957 + 777 + 1197
    1197 = (311 is 777)
    My SSN: 592-16-6211
    592 + 16 + 6211 = 6819
    6819 = 977(6) + 957
    592 + 166 + 211 = 969
    6819 = 969 + 117(50)
    6819 = 969(2) + 957(4) + 117(9)
    6819 = 969(5) + 1197 + 777
    969(8) = 6819 + 311(3)
    969(10) = 6819 + 957(3)
    6819 = 957(3) + 777(2) + 1197(2)
    6819 = 1197 + 957 + 311(15)
    311(15) =1197 + (957 + 777)2
    6819 = 311(30) – 777(2) – 957
    777(2) + 957 = 1197(2) + 117
    6819 – 117 = 957(2) + 1197(4)
    6819 – 117(2) = 957(15) – 777(10)
    6819 – 117(3) = 1197(8) – 777(4)
    957(7) = 777(4) + 1197(3)
    957 + 1197 = 1077(2)
    6819 = 1077 + 957(6)
    724237 + 311 = 6819(106) + 957 + 777
    (Shawn) = 659
    (Phllip) = 226
    (Gell) =72
    659,226,072 – 592,166,211 = 957(70073)
    724237 + 70073 = 957(830)
    592166211 = 6279(94309)
    94309 – 70073 = 311 + 957(25)
    6279 = 1197(2) + 777(5)
    977(755) = 724237 + 957(14)
    977 + 755 = 866(2)
    866(866) + 6819 = 724237 + 957(34)
    977(3) – 755 = (311 + 777)2
    755(3) = 977(2) + 311
    117 + 311 + 957 + 1982 = 3367
    724237 = 3367(215) + 332
    215 + 117 = 332
    724237 = 1089(2)332 + 1141
    724237 = 311(7)332 + 1141 + 332
    1141 + 332 = 851 + 311(2)
    851 + 1141 = 332(6)
    1089(2) + 3367 = (777 + 332)5
    311 = (He is Oracle)
    (Lord of All)
    (God is good)
    (God’s dream)
    (God’s Child) + (King)
    (King of Peace) + (A change)
    (Of God’s change)
    (From One)
    (Credit)
    (God’s Logical)
    (Is in hope)
    777 = (He is a pure oracle)
    (Of the Perfection)
    (The Messiah of Israel)
    (Good Nature)
    (He is all divine 117)
    (The 117 Oracle message)
    (311 Sacred Messiah)
    777(2) = (The 957 Oracle is King)
    (Of the Divine Truth)
    (Is the Christ, is the Messiah) + (Of God’s)
    (Is like Divinity)
    (God is in 957’s message)
    (Is not evil or wicked)
    (Is the only Sacred Oracle)
    (He is righteous) + (God’s message is one)
    1197 = (311 is 777)
    (The one Divine Sacred Oracle)
    (Is in the true peace of God)
    (957 is good)
    (957 an oracle)
    (Divine) + (Important)
    (957 for peace)
    (The one Holy God)
    (A hope for the World)
    (Is the Divine Oracle of Hope)
    1197(2) = 3(Truth) = 3(Holy)
    (957 the Oracle of God’s Truth)
    (957 judges the truth)
    837 = (God’s Divine Oracle)
    (He is the one sacred Lord)
    (Is Christ and Messiah)
    (Is in God’s perfection)
    (The real perfection)
    1127 = (957 is all)
    (The 777 of God)
    (Messiah of truth)
    (King of Divine Perfection)
    (Sacred Oracle) + (He is the Messiah of God)
    (The only change)
    (The Divine One is King of all)
    (Is the true Son)
    (Real sacred truth)
    (He is true Christ)
    (Sacred Oracle of God’s Perfection)
    1359 = (957 the Oracle)
    (Holy Oracle is Messiah)
    (The true Messiah) + (Plan of God)
    (Sacred Oracle is true Messiah)
    (Holy Christ Plan)
    (The message is true Lord)
    (The Divine Gemaria oracle of All)
    (Holy Divine Peace)
    (He is the Divine Christ of God)
    (The Gematria Oracle is lord 311)
    1380 = (Judges for truth)
    (957 is right)
    (The Oracle is Holy God)
    (Of the Sacred Truths)
    2(The Divine)
    2100 = (957, 311 and 777)
    (777 is the Sacred Truth)
    (The 311 is the Divine 777)
    (957 is Righteousness)
    (The Sacred 777 is Holy)
    (The Holy Divine Prophet)
    (777 Divine oracle is Divine God)
    (The Most High God is Divine Truth)
    626 = (Good love)
    (Of the son of God)
    (The Oracle is One)
    (The Messiah of Peace)
    1255 = (957 is Oracle)
    (311 the Divine Light)
    (The Messiah of Wisdom)
    1623 = (957 Divine Oracle)
    (The Holy Prophet)
    (The Most High God is Holy)
    (Harmonized Integers)
    1785 = (957 is the Messianic Oracle)
    3(True)
    777 + (He is the Christ Messiah)
    (Holy Truth Oracle)
    (The true 311 Divine Oracle)
    (Is the Divine God of all) + (Is the sacred Messiah)
    (Divine God of All is the Divine Lord of All)
    987 = (Holy Oracle)
    (The Oracle is the Messiah)
    (True Sacred Oracle)
    (117 is 311) + (He is the one)
    977 = (Divine 311 Oracle)
    (Only of God)
    (The Sacred Oracle is Messiah)
    (True lord) + (God of all)
    1193 = (The Divine Prophet)
    (He is the true Messiah)
    (Is 957 of all)
    (The good Oracle) + (The Oracle message)
    (The peace Christ is an Oracle of God)
    (Is God’s Holy One)
    (The Sacred 777)
    713 = (The Messiah of God’s)
    (Wisdom)
    (Is an Oracle of the truth)
    (The 311 oracle)
    (Is the light of God)
    (God’s Gematria Oracle)
    713(2) = (Is an Oracle of truth)
    (The 777 Perfection Plan)
    (The Child of true Perfection)
    646 = (The Oracle is like God)
    (Nature)
    (311 is chosen)
    (He is the 311)
    (Sacred Oracle Light)
    1169 = (The Sacred Oracle of Perfection)
    (Most valuable)
    (777 sacred Oracle)
    (The Divine 311 is in)
    1137 = (957 is God)
    (The Divine Oracle Message)
    (The real truth)
    (The Oracle of God) + (He is the Messiah)
    (The oracle of God’s perfection)
    (Divine Savior)
    (Sacred Oracle) + (He is the Christ)
    (311 is with)
    (The 311 Oracle is all light)
    (Gods 777 Oracle)
    (311 is the lord of light)
    1137(2) = (957 is the Christ) + (Is the Messiah)
    1317 = (Is the Christ, is the Messiah)
    (957 God’s Oracle)
    (Is the all Sacred Divine Light)
    (God’s 777 oracle is God)
    897 = (Is true) + (He is God)
    (The Lord Messiah of God’s)
    (The God of all Is an Oracle of God)
    (God is with)
    (God is the Lord of Lords)
    (311 is Divine)
    (God’s Oracle is his Lord of All)
    735 = (Divine message)
    (Of God’s perfection)
    (The name of God’s Oracle)
    (Sacred and Divine)
    (He is the Messiah of God)
    (The Good Light of God)
    (Has good love)
    1217 = (Light of the World)
    (God’s Divine Will)
    (Oracle 957) + (God)
    (He is Gods Oracle of true change
    (To 957)
    (He is God’s child of correct thinking)
    (The logical truth of)
    (The power of the)
    (The pure Oracle of God)
    927 = (Yes he is)
    (He is the Divine One)
    (His eyes)
    (God’s perfection message)
    (King of Kings and Lord of Lords)
    (The Divine of God’s)
    1275 = (Divine Truth)
    (777 perfection)
    (The wisdom is an Oracle)
    (It is 957)
    (Thinking is of good judgment)
    1443 = (957 is an oracle of God)
    (The Sword of Christ)
    (There is only one God)
    (957 he is the plan)
    (The Divine Oracle of perfection)
    (Lord Oracle) + (He is the Messiah of God’s peace plan)
    (The true perfection of God)
    1254 = (Divine 777)
    (Is the Messiah’s will)
    2(Justice)
    (Justice for the good of all)
    (957 the peace)
    (Divine Oracle) + (The Divine Perfection)
    1570 = (True Divine Perfection)
    (I am the Alpha and the Omega) + (The Oracle has spoken)
    (957 is a prophet)
    (777 perfection) + (God is one)
    (The 777 of God) + (Oracle Light)
    (957 Sacred Christ)
    (957 the messiah of God)
    1138 = (957 is a God)
    (He is the Divine Oracle of God)
    (The Kingdom of God’s Perfection)
    (Three- Eleven is chosen)
    1001 = (The Divine 311)
    (Sacred truth)
    (The peace of logical perfection)
    (He is the Divine Oracle)
    755 = (The Gematria Oracle)
    1381 = (Divinity)
    (All True Power)
    807 = (Christ the Lord)
    717 = (The lord of light)
    899 = (He is 777)
    888 = (Is true Lord)
    886 = (Is 777)
    3051 = (957) + (Wisdom) + (Divinity)15
    477 = (Divine)
    (the all sacred)
    Now here some algorithms that show how the numbers listed above connect to each other.
    1570 + 1127 = 899(3)
    886 + 1127(2) = 1570(2)
    957 + 1197 = 1077(2)
    1570(3) = 1077 + (117 + 477)7
    1570(3) + (777 is Messiah) = 837(3)
    1570(2) = (Is the Gematria oracle) + 1138(2)
    1570(2) + 1138 = 713(6)
    1570 + 311 = 987 + 777 +117
    1570 + 311(4) + 777 = 1197(3)
    1570 + 117 + 311(4) = 777 + 957 + 1197
    1570 + 311 + 117(10) = 3051
    3051 = (957 is 311) + 1570
    1570 + 311(10) = 117(40)
    1197 + 777 = 957 + (3051)/3
    3051 + 837 = 957(2) + 777 + 1197
    3051 + 837(2) = 1197(2) + 777(3)
    3051 + 837(3) = 957(5) = 777
    3051 + 837(4) = 1197 + (957 + 777)3
    1127(6) = 1197(5) + 777
    3051 = 1137(2) + 777
    3051 = 897 + 1197 + 957
    3051 + 777 = 957(4)
    3051 + 957(3) = (1197 + 777)3
    1197 + 837 = 2(3051)/3
    897(5) = 837(3) + 1197 + 777
    897(5) = 899(3) + (777 +117)2
    (807 + 837)2 = 957 + 777(3)
    897(4) = 717 + 957(3)
    897(3) = 117(23)
    117(23) = 957(2) + 777
    837(7) = 1197 + 777(6)
    897(2) = 777 + 3051/3
    3051 + 807(2) = 311(15)
    897(7) = 1197(2) + 777(5)
    I have hundreds of these. I will share them with you later.
    Gematria method
    A=1 J=10 S=100
    B=2 K=20 T=200
    C=3 L=30 U=300
    D=4 M=40 V=400
    E=5 N=50 W=500
    F=6 O=60 X=600
    G=7 P=70 Y=700
    H=8 Q=80 Z=800
    I=9 R=90
    What I do with this system is add up the numbers to the corresponding letters in names, words and phrases.
    Here are some calculations with 8904
    957 = (Shawn Phillip Gell)
    8904 + 311 = (957 is 777)5
    8904 = 1127(4) + 1099(4)
    1127 = (The 777 of God)
    1099 = (Is the 777)
    8904 = 777 + 311 + 977(8)
    977 = (311 Divine Oracle)
    977 = (True lord) + (God of all)
    8904 + (Is 311) = 777(12)
    1982 + 957 + 311 +117 = 3367
    3367(3) = 777(13)
    3367(3) = 8904 + 1197
    1197 = (311 is 777)
    777 + 311 = 544(2)
    777(777) + 544 = (544(3) + 311)311
    8904 = (311 + 777)3 + 1138(4)
    O,K. now here is the story with Amber.
    I met this girl named Amber Rachel Black on March 27th, 2005 In a bar called Brass Monkey. I went home with her and stayed for the following week. We dated for about 8 months and broke up in December, 2005.
    Her birthdate is 8-26-1979 and I calculated it to be 723068 days in the A.D.
    My birthdate is 11-7-1982 and I calculated it to be 724237 days in the A.D.
    On the day we met she was 1168(8) days old and on the following day I was 1168(7) days old. The numerical value for the bar we met in (Brass Monkey) also was 1168
    I calculated the numerical value for her name to be 331 and mine is 957. The difference between these two numbers is 626 and the difference in our age is 1169 days.
    Subtract 626 from 723068 and you get 1169(618)
    Subtract 626 from 724237 and you get 1169(619)
    One week later she was 1169(8) days old and I was 1169(7) days old. That day was 1170(626) days in the A.D. We both attended church on that Sunday.
    On the day of 3-27-2005 she was 9345 days old and I was 8176 days old. One week later she was 9352 days old and I was 8183 days old. If you add 9345 to 8176 you get 626(28) and if you add 9352 to 8176 you get 626(28). Subtract 9345 from 724237 and you get 1142(626) and if you subtract 8176 from 723068 you get 1142(626). Now 1142 + 28 = 117(10) or 1170
    If I had married her and changed her name to Amber Rachel Gell the number for her name would be 347.
    I found that on her 26th birthday I was 347(24) days old and on my 23rd birthday she was 957(10) days old.
    347 and 957 are 652(2). 723068 is 652(1109)
    723068 = 365.25(40) + (1109 + 1169)311
    724237 = 652(1110) + 517
    517(365.25)4 = 724237 + 311(100)
    957(5) – 331(6) = 311(9)
    957(3) – 347(2) = 311(7)
    Now also bear in mind that both of our house addresses were 311 on two different streets at the time.
    I broke up with her on 12-04-2005 and on that day
    I was 1204(7) days old.
    I have some more on this and next time I will tell you about a girl I have recently met named Harmony.

    Reply
  28. Simon

    Hey, just stumbled on your hilarious blog!
    Actually, I’d say this instance is reducible to a narrow view: Look for in , and something roughly resembling infinity pops up.
    For example, look for sense in the world, you’ll find god. Look for a number in division by zero, you’ll find infinity. Look for structure in an economy, find the efficient markets hypothesis.
    That something doesn’t really exist doesn’t mean it isn’t a useful concept, but one should not assume it exists or can be realized. It may just live in your brain.

    Reply
  29. Simon

    HTML cleansing was too strict. That’s it:
    Look for “concept” in “field where concept doesn’t apply”, and something roughly resembling infinity pops up.

    Reply

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