The Renaissance brought a rebellion against the knowledge-strangling restrictions imposed by Christian dogma and scholasticism. This was the time when Western Europe rediscovered Greek philosophy and free thinkers such as Galileo became emboldened to seek empirical knowledge. It was rediscovery of higher math, more than anything, which made the Renaissance possible. Interestingly, it was in art that the value of mathematical rediscoveries first became apparent, as painters reveled in a newfound ability to convey perspective.
In science Renaissance thinkers did not reject God (as far as we know; atheism was not a safe or respectable position to espouse), but they did reject the notion that individual received knowledge – whether from Church leaders or Aristotle – was immune to scrutiny. As the Age of Enlightenment progressed, rejection of the inviolability of scripture, then rejection of God and religion, became the norm. At the same time, many Christian prejudices remained unexamined. Astrology, psychic activity, magic, and many of the healing arts continued to be shunned by the new high priests. Empiricism was reaffirmed, but only in designated areas and only when dominated by men.
A physicist friend of mine once told me, as I tried to explain the aura to him, that the problem with adherents of metaphysics is that they try to use science in their explanations when they should avoid scientific language altogether, because science and metaphysics are two different things. He laid out his ideas in that imperious I’m-right-and-you’re-wrong voice (acquired already, at such a young age) that so terrifies women from pursuing the hard sciences. I tried to follow his advice for years, but I now believe that by putting a firewall between science and the occult what we have is bad science and bad magic, including flaws in the predictive sciences.
The study of numeric symbology, indispensable to the study of predictive signs, occasionally wanders into territory claimed by the high priests of math and science. Because we have been banished from mathematical frontiers for so long, we will doubtless make mistakes at times, which will be pounced upon with reprobation by those eager to see us fail. But the godless Christians of the modern era cannot defend their boundaries indefinitely against the heathen hordes. Math is Pagan. Numbers originate in the womb. Priestesses hold the keys to understanding the laws of the universe.
This is actually going to be a five, not a four, part series.
The most fertile and revolutionary place for math and science in the West was the city of Alexandria in the first centuries of the Common Era. This is where the demanding theoretical philosophy of the Greeks met the more practically minded math of the Egyptians. Scholars took the leap into theorems based on what would become the discipline of algebra, trusting in what had validity in solving problems in the real world. People enjoy the Fran Lebowitz joke that children are right to sleep through algebra because “In the real world, I assure you, there is no such thing as algebra,” but constructs are necessary for us to understand much of the real world.
Alexandria meant the breakdown of limitations imposed by Greek philosophy. The erasure of lines between pure and practical mathematics, pure and practical science, allowed both areas to flourish. Knowledge is furthered most by collaboration between cultures. Scholars who came together at Alexandria did, however, share a motivation to become closer to the gods through their understanding of math and science. With the tolerance characteristic of polytheistic religions, they were not bothered by the fact that they worshiped different gods, or they saw themselves as worshiping the same gods despite differences in ritual and mythology. By the end of the fourth century, scholars were probably on the cusp of discovering how the earth travels around the sun, an idea that had been proposed many centuries earlier yet had been rejected, despite its attractive simplicity, due to gaps in knowledge.
And then the Christians came. The destruction of the Library of Alexandria, the murder of the scholar Hypatia, and other atrocities against learning were a systematic attempt, ultimately unsuccessful, to destroy “heathen knowledge.” Science and mathematical philosophy were seen as pagan disciplines. The “heathen temples” which the Christians were so bent on eradicating were centers of education much like the monasteries of the Middle Ages, except the pagan temples were not constrained to make knowledge fit a highly developed dogma as the monasteries were.
Learned refugees from Alexandria escaped to the coast of Anatolia. Mathematical scholarship resumed in the Arab world, continued along the Indus River, and was tolerated to some degree by the Eastern Orthodox Church, but religious and political barriers discouraged widespread cultural exchange.
Greek mathematics was concerned with understanding underlying rules for numerical relationships and concentrated on geometric proofs. Math became a component of philosophy, a pursuit of the leisure class, and a way of discerning the laws of the gods. Mesopotamian practical applied math could not be disposed of because cities now required it to function, but the philosophical elite would not stoop to learn it.
The Greeks liked geometric proofs because they are tangible, irrefutably a part of the real world. There was a fear that if mathematics diverged from the concrete world it would become fantasy, and that the pursuit of this fantasy math would be a rejection of truth by the learned man.
The fear of deviating from truth meant that there were four important concepts, integral to the way we see the world today, that people were unable to accept in classical times. 1) Algebraic proofs (if you can’t draw it, is it real?) 2) Zero as a number, not just a placeholder (how do you define something that by definition does not exist?) 3) Irrational numbers (why would the gods create puzzles that have no solution?) 4) Negative numbers (again, they don’t exist)
Although mathematically speaking the Greeks had their limits, these obstacles were not germane to Greek philosophy. The point where mathematics moves into abstraction is a point of crisis for any society. There was a Hindu mathematician in the seventh century, Brahmagupta, who proposed using negative numbers for accounting purposes without finding many takers. How can you do accounting without negative numbers? It boggles the mind. Yet it was once hard for people to take numbers, the most irrefutable link to objective truth, into the world of make-believe.
Numerical symbolism was an abstraction the ancients had no problem with, or maybe it was a problem that was resolved in prehistory. Using a word to represent a number is itself a construct, as is all written language, mathematical or otherwise. Numerical symbolism as a predictive device, which was widely used, is complex, difficult and not entirely reliable. It was therefore not difficulty, complexity, or uncertainty that early mathematicians bulked at: it was the idea of consciously embracing something intrinsically unreal (negative numbers) or intrinsically imprecise (irrational numbers).
In Mesopotamia the first accounting systems arose out of the need to record and disperse temple commodities. Many of these early accounting scribes were women. As societies became more complex, arithmetical systems developed to accommodate trade, architecture, irrigation, and land division. Math and record-keeping were also necessary for the development of Mesopotamian astrology, which was the genesis for the Greek astrological system we use today. We’re not talking about grade school arithmetic at this point either: Mesopotamians had a base 60 counting system (it eased division), utilized square and cube root tables, calculated compound interest, and (by the later period) could calculate the time of an eclipse to within a few minutes. Both Mesopotamians and Egyptians understood triangular relationships long before Pythagoras, although the Greeks did provide the theorems.
The whole of the universe should be represented by the number zero rather than the number one. When I ran across this contention on the blog of a pagan queer theorist (a queerist?) I decided to ignore this incredible statement, once my head stopped exploding, because it is, er – not credible. But since this idea has actually been seriously entertained by a few other people, I’m going to address it. I will not link to the post, even though the author proudly took credit, because I’m embarrassed for zhir. In mathematics we use words and symbols to represent things that exist in the real world or to represent concepts that do not actually exist but help us to understand reality nonetheless. There is one cat in the picture to the left and two cats in the picture to the right. The numbers one and two have a physical, concrete basis in the real world. In the next picture, there are six images of cats, but taken as a whole this is one picture (or, as it is known in mathematics, one set). But what if there are no cats? We can designate a picture without cats in it as “no cats” or “zero cats,” with zero referring to cats that do not exist. Zero is is defined as having no existence. It is nothing, only a useful human construct for that which does not exist in the real world. Now let’s look at the whole of the universe, represented by this whole uncut apple pie. We have one (1) pie, and when we take a piece of out of it, say one-fifth, we have one divided by five (1 ÷ 5) or 1/5. But what if we start with a universe of nothing? In this picture of the whole of everything represented by nothing, not even any pies, we can take a fifth out of this nothingness and have 0 ÷ 5 or 0/5, which equals zero. Another way of saying this would be that something cannot exist within nothing, or you can’t get something out of nothing.We’re talking about numbers and math here, which involve definitions, so if you want to arbitrarily redefine things, you can call zero what used to be one and call one a purple rhinoceros and still be right within your personal made-up universe. The possibilities are endless in the realm of making stuff up. It stands to reason that this “zero is everything” idea should come out of the universe of queer theory, where queer includes all kinds of people who used to be straight but are now queer, along with all the queer people who used to be queer but are still queer. Queer means nothing anymore – in fact in postmodern queer theoryland everything means nothing anymore – so it stands to reason that nothing should now mean everything. It has a sort of balance. But maybe the source of the confusion comes from the symbol 0, which sortof looks like a pie. It’s the kind of mistake a child would make. You might infer, if you didn’t know any better, that the symbol 0 is defined as the number one, a word which has an O in it. Those of us who are not queerists pay attention in the first grade, at least one-fifth of the time, so we learn our numbers 1, 2, 3, 4, 5, etc., and we use the symbol 0 to designate nothing or as a place-holder. I recommend the first grade to everyone who still calls themselves “queer” and thinks it means something other than “I’m an idiot.” It might mean no longer embarrassing yourself, or zhir-self, or whOever zoo say zoo are.