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Drowned at SeaSeason 2, Episode 3Complete Transcript : Brian Frye is a law professor at the University of Kentucky Law School. He's an expert in copyright law and he gets a call from someone who graduated from the law school years ago.BF: there's a divorce case in Illinois this seventh-day adventists televangelist named Danny Shelton is I believe like the most well known seventh-day adventists type figure had at some point written up a brief manuscript relaying, in a very kind of folksy fashion, his iteration of seventh-day adventists theology interspersed with some of his own observations.Barry: Danny gave his manuscript to a woman named Shelly Quinn who started revising it and they ended up co-authoring it togetherBF: and it was a massive big seller and started generating a lot of profitBarry: at the same time they were putting the book together Danny was getting a divorceBF: the ex-wife wanted a cut of the profit from this very successful book and argued that it was a derivative work of the manuscript that Shelton had prepared while they were still marriedBarry: and so Brian's job was to read the original manuscript study it, read the best-selling book study it, and make a kind of expert legal judgment as to whether the content of the book was derived from the content of the manuscript. Anyhow, Brian's testimony was ultimately that the book was different enough from the manuscript that it wasn't derivative. That's not the part of the story that was interesting to me. It was what was in the book.BF: I always thought that seventh-day Adventism was basically just like Protestants who went to church on Saturday instead of Sunday, boy was I wrong. (Laugh)Barry: could you read the title of the book and describe the cover for me?BF: the title of the book is “The Antichrist Agenda: Ten Commandments twice removed,” and it shows a photograph of the Chrysler Building I'm not sure exactly why as well as a bunch of conspiracy type documents at the bottom labeled “my agenda to control the world.” They refer to the vision of Daniel and the fourth beast which rises up with the iron teeth and ten horns there's ten feet and ten toes of the statue that stands in for the Antichrist, “look the Roman Empire was dissolved into ten kingdoms.” SO each one of those kingdoms is one of the toes of the statue.Barry: and so the number ten is important, it's the number of Commandments, the number of kingdoms hostile to Israel, the number of plagues in Egypt. It's up there with the number seven in terms of significance to biblical numerologists, there are a lot of sevens in the Book of Revelations: seven churches, seven seals, seven trumpets.BF: the Bible foretold that Constantine the Great, Napoleon, Kaiser Wilhelm and Hitler would all loseBarry: and of course seventh-day adventists have a number right in the name of their sect. These numbers are trying to tell us something, some essential truths that for some reason God decided to do with numerical code. Could you tell me what your take was as to the endgame? What are they trying to convince people of in a book like this?BF: it's kind of a like an apocalyptic type take with the Catholic Church and Sunday church observance as the first step toward the apocalypse, so like Satan's using that as his wedge because the churches are not enforcing that one of the Ten Commandments then God's law is no longer present and that's gonna be a big problem when the apocalypse comes.Barry: Wow so it sounds like it's simultaneously a huge deal it's about the end times, but also a small deal in that it's about changing something you do from a Sunday to a Saturday.BF: that's why the Catholic Church is basically SatanBarry: from Vassar College you're listening to Hi-Phi Nation, a show about philosophy that turns stories into ideas. I'm Barry Lam. What is it about numbers? Why do we think that God is communicating something to us through numbers? Here we have a book that's already supposed to be the most complete record of what you need to know in life, but somehow God also wanted to tell us about the rise and fall of Hitler, and decided to do it through repeated patterns of the number ten. This obsession with the secrets of the universe revealed through numbers it's hardly unique to seventh-day adventists. You could say it's the foundation of modern science. Well today on the show we're going to look into one of the deepest mysteries of the universe, and that's why do numbers and mathematics seem to describe it so well? It’s show about numbers and religious cults and vegetarianism and legumes, yes beans. For some reason these things all go together. We’ll look at a small religious cult in southern Italy twenty-five hundred years ago that looked eerily like seventh-day Adventism, but instead gave rise to almost all of Western philosophy science mathematics even music to this day this cult informs how we think about using numbers to describe the universe.GR: I'm Gideon Rosen I'm the Stuart professor of philosophy at Princeton University. Mathematics is just monumentally useful. If we were just making it up it would be a mystery, why it should be so useful, so fruitful, in describing the manifestly real world of physical objects in space and time. The fact that it is so useful gives us reason to believe, and this is something that Plato took very seriously and that Platonists down through the ages emphasized, that not only is there a subject matter for mathematics that's not made up by us, it is somehow connected to the real physical world, and that explains why the one is so useful in helping us think about the other. Barry: There's no rulebook that tells you how math is connected to reality, that's why you have everything from quantum physics to biblical numerology. There's an ancient story about the uneasy connection between math and reality, it's become a legend, lots of people have heard it, I probably heard it in middle school. There was a religious cult in southern Italy, they had a spiritual leader Pythagoras who advocated the worship of numbers. He was Jesus-like, had disciples, surprising teachings, advocated a disciplined lifestyle. After he died there was a split in the cult: two factions formed. One of the factions was led by a man named Hippasus. Here’s filmmaker Errol Morris, friend of the show, who studied and wrote about the story.EM: the way it's often told is Hippasus, who was a Pythagorean, part of the Pythagorean number cult, came up with this proof that the square root of two or if you like, the diagonal of a unit square could not be expressed as a rational fraction, as a fraction of two whole numbers. What happened to Hippasus, is he was thrown overboard by angry pythagoreans and drowned.MJ: my name is Monty Johnson I teach philosophy at the University of California in San Diego. Pythagoras wrote nothing and so we can only attribute tenets to him on the basis of later testimonies and a sort of reconstruction of his influence on others especially Plato.Barry: he had two ideas that influence Plato the first was-MJ: the immortality of the soul and metempsychosis or the transmigration of the soul at death into a new body. The other idea is a mathematical conception of the cosmos.Barry: and in particular the idea that everything in the universe was a whole number. This is how the idea came about: the pythagoreans are credited with discovering the relationship between musical harmonies and numbers. If you think about it, when people first started singing or playing an instrument, there's no reason to think that what was coming out had to be mathematical, that numbers were a way of describing which two notes harmonize. But as it turned out, if you had a string and plucked it then divided it in half and plucked it again you end up playing the same note an octave apart. In fact all of the notes in a scale are related according to ratios of whole numbers or fractions. You can write out the entirety of any piece of music using nothing but whole numbers and fractions. In fact Hippasus, the man who drowned, had a major role in this discovery.MJ: Hippasus is the earliest person for whom we have evidence that he could have actually demonstrated these facts experimentally. He did this by making bronze discs of equal diameter but of unequal thickness, and a musical conchord such as an octave could be produced by sounding two desks in the relevant ratio of thickness. We could actually credit him with being the first to demonstrate a mathematical law inherent in physical phenomena, an extremely important moment for science.Barry:You can understand why this discovery would amaze you if you didn't expect ahead of time that whole numbers and ratios could explain the beauty of music. And you could see how you might then think that the whole universe might be constructed according to such whole numbers. And so pythagorean's are attributed to believing that-MJ: everything is number, but they may have actually determined that numbers exist in the cosmos as actual physical entities. A lot of the earlier and even later Pythagorean material comes across to us now is what we would call numerology, for example saying that marriage is the number six or that the Sun corresponds to the one, and we can identify different processes that happen in nature according to mathematical ratios or formulas.Barry: it wasn't just numerology that was a central feature of pythagoreanism, it was also a lifestyle.MJ: the idea seems to be that one's behavior in this life can affect the form in which one is reincarnated in another life, and therefore certain kinds of purification are necessary in this life in order to prepare the soul for death in its transmigration. The importance of temperance and self-control and developing habits of controlling sexual appetite, appetite for food, and appetite for drink. For Pythagoras it apparently involved the prohibition on eating animals or even possibly eating beans.Barry: Beans might have been thought to be too close to the appearance of human gonads or fetuses. Another suggestion is that flatulence disturb the tranquility of the mind to contemplate mathematical issues. Incidentally the controversy about beans in austere diets tied to religious cults survives to this day. It's either a panacea or an evil.Blue Zone: if you're eating a couple of beans a day it's probably adding three or four years to your life expectancyBarry: on the one hand we have the Blue Zone diet tied to Seventh-Day Adventists, the healthiest people in America with a vegetarian lifestyle and long life expectancy. And then you have the Paleo cult:Paleo: are legumes paleo? In general, no, legumes are not paleo. They're hard to digest, legumes are not particularly nutritious.MJ: I think the thing about beans is mostly a way of mocking pythagoreanism, but it must go back to some prohibition that they originally had.Barry: there's a reason why there's been so much speculation about Pythagoras. About a thousand years after he died a group of pagans were seeking to stem the rise of Christianity and they too sought some kind of semi-mystical guru figure who had disciples, advocated an alternative lifestyle, and was martyred for it. They settled on Pythagoras, who they reported to have a golden thigh, performed miracles, and had an angry mob set fire to his house. Some say he died in that fire, another legend says he tried to escape but refused to run through a field of beans and was killed. One legend says he starved himself to death in response to his persecution. So what happened to the cult after he died?MJ: we're told in a fragment of a work by Aristotle that the Pythagoreans eventually divided into two groups, the so-called acousmatici and on the other hand the mathematicii. The acousmatici practiced the way of life and precepts of pythagoreanism, but did not participate in the mathematical or cosmological speculations. The mathematici, however, possess both the instructions and the explanations for them, and Hippasus is supposed to have led one or the other of these, probably he was a more mathematical pythagorean.Barry: Hippasus according to the ancient sources did not construct a unit length square to prove the existence of irrational numbers. Instead the cult drowned him at sea for constructing or showing or somehow exhibiting a secret revealed through a dodecahedron.MJ: Dodecahedron’s we know are important cult objects going back to prehistory. Some of these were used in the process of divination, used as dice and so forth. In fact dodecahedra are still used to this day in dice and the game Dungeons & Dragons you roll a dodecahedron.Barry: here's what you need to know about the dodecahedron, every face of it is a pentagon. If you connect all the points of a Pentagon you'll get a pentagram, the five sided star, another famous occult symbol. If you look in the middle of a pentagram you'll see yet another Pentagon upside-down. This is the source of Hippasus supposed proof of the existence of irrational numbers. If you study a Pentagon with an inscribed pentagram and recognize that you can go on to infinity inscribing smaller and smaller Pentagon's and pentagrams inside, you will be led by simple arithmetic and geometry to the conclusion that there are no whole numbers that describe the ratio of a side of the pentagon and a side of the pentagram. MJ: but if the pythagorean's held that everything is number they were referring to these-Barry: whole numbersMJ: -then the existence of irrational numbers would be a big metaphysical problem for them.Barry: The metaphysical problem is precisely how you connect mathematical reality with perceivable reality. If whole numbers were all you have and you can easily connect each whole number to something in reality, two to one is an octave, one is the Sun, then there's only one reality to contend with. But if irrational numbers can be proven to exist in mathematical reality and there was nothing even remotely appearing to be an irrational number in the world, you no longer have a nice neat connection between numbers and the perceivable world. So which is it? If nothing in your perception fits the existence of a certain kind of number, does that number not exist or does it still exist it just doesn't matter whether it fits your perception or not? Numbers don't have to be in the world. This is the central problem that Plato inherited from the Pythagoreans. Gideon Rosen: Mathematics is a peculiar subject in two ways. On the one hand we have absolutely perfectly certain knowledge, mathematical knowledge is not subject to the kind of doubt that ordinary scientific knowledge and everyday knowledge are subject to, and on the other hand its source is mysterious. We don't arrive at this kind of mathematical knowledge by making observations and doing experiments and making measurements and so on. All of that can be helpful, but our generalization that every triangle has internal angles that add up to one hundred eighty degrees isn't a sort of statistical inference from careful measurements of lots of real triangles. Do we invent the theory of numbers or were the numbers out there already waiting for us to describe them and discover them? Plato thought it was obvious that the kind of superlative knowledge that we arrive at in mathematics is the discovery of a world that's already there. That's the age-old conundrum in the philosophy of mathematics how is it that we confined to our armchairs in the physical world managed to get perfectly certain knowledge of things that we cannot observe?Barry: Without the constraints of modern science, Plato had more leeway to speculate about the answer to this problem. Plato solution was to identify numbers in geometrical shapes as things that inhabit an invisible world, a perfect world. This is the world that our imperfect visible world is striving to become, but falling short. The way we can have knowledge of this invisible perfect world is that our immortal souls once lived there. Using Pythagorean ideas, Plato could all at once explain why the visible world had the appearance of mathematical properties, it was trying to be like the invisible world. And he could explain how we can have perfect knowledge of mathematics, Plato's theory gave him a model to think about everything else in the world.Gideon Rosen: The social world that we see is an imperfect approximation to something perfect. Somehow we know looking around that the social world we live in is not just. How do we know that? We must have some conception of what a perfectly just society would be so that we can compare that idea of perfect justice with what we see when we look around us. So in all of these cases you get an invisible non-empirical perfect world that we can compare to the world we actually see around us in order to identify imperfections. So that's one deep analogy between mathematics and political theory and moral theory.Barry: and so we get the origins of philosophy in the Western tradition, with questions like what is justice? What is good? Since then a lot of Western philosophy has been influenced by this idea of Plato, which takes mathematical knowledge to be the model for philosophical knowledge. Which brings us to today, the cult that drowned Hippasus turned out to be wrong there are irrational numbers all over the place square root of two, pi, the golden ratio, they all appear in a countless number of applications from architecture and design, to calculating the speed of trains and this just kept happening. There's the famous Fibonacci series 0 1 1 2 3 5 it's just what you get when you start adding two numbers in a series to get the next number. Centuries after Fibonacci we keep seeing this series in nature, the structure of the human body, DNA, flower petals, pine cones.GR: for some reason the theory of complex numbers which was invented for pure mathematical reasons having to do with the solutions to cubic equations turned out to be exactly the mathematics that you needed for 20th century physics, a mathematical object called Hilbert space, that was invented by David Hilbert the early years of the 20th century for reasons having to do with pure mathematics. It so happened that Hilbert space was exactly the mathematical object that you needed for describing the very strange physics that was uncovered twenty-five, thirty years later. The mathematical structures that you need for Einstein's physics, the tools that you need for studying what we now call curved space-time, many of them were discovered by mathematicians for purely mathematical reasons toward the end of the 19th century, all of that stuff was waiting on the shelf for Einstein and subsequent physicists, and that can look like a bit of a miracle. No one knows why those thingsBarry: No one knows why no one has a hypothesis as to why? I mean like people aren't speculating about this?GR: I don't think anyone is tempted by the kind of speculation that might have tempted Plato, the kind of speculation that says the complex numbers exist in a mind dependent realm and somehow impinge on our thinking, somehow affect our reasoning so that when the time comes they come to mind and we bring them to bear in our theorizing about nature. That sort of genuinely mystical view on which the numbers reach out from the abstract realm affect our brains and bring us into contact with mathematical features of reality, no one believes that.Barry: in our centuries long development of science and mathematics, we've come to give up invisible realms and immortal souls but at the same time we found more and more of the universe to be explicable using numbers functions and n-dimensional spaces and now we're left with-GR: an absolutely striking and mystifying fact no one has a particularly good explanation for the usefulness of mathematics.Barry: We found our way back to Plato and Pythagoras and Hippasus over 2,000 years ago only now we can't help ourselves to mysticism or numerology, no more immortal souls, no more invisible worlds, and so we're left with trying to explain mathematical knowledge as maybe some elaborate invention and construction of humans, rather than discoveries about a visible or invisible realm.GR: We construct these objects by constructing theories of them. So we choose the axioms, for say elementary arithmetic. Once we've chosen them we can talk about the objects that exist according to those axioms, the numbers that you've studied, but those numbers didn't exist prior to our adoption of the language of mathematics, and all we're doing when we study the objects of mathematics is studying the consequences of a stipulation that we collectively somehow engaged in. So that view goes under many names it's sometimes called constructivism.Barry: If you're a kind of constructivist then mathematical discoveries are kind of like discoveries in works of fiction. Is Harry Potter taller than Bilbo Baggins? Yeah you can be pretty certain of that you just have to study these invented stories closely enough. But in constructivism like in fiction, any resemblance to events in the real world is purely coincidental. There are some cases where you invent the math to describe the world, calculus is an example, but again and again the stories came first. We only saw that they describe the world much later. Are there views that numbers and even the complex numbers, even the things of pure mathematics, are in some sense in the world and causally interacting with us, are there views like that? GR: There are. Philosophers who were independently committed to philosophical naturalism, the idea that the natural world is all there is, but who didn't want to dismiss mathematics as a mere useful fiction, started looking around for things in the natural world that could be the objects of mathematics.Barry: These things aren't going to be the Sun or the moon like it was for Pythagoreans, they're going to be things like collections or structures, sets, things the naturalist takes to be in the world, wherever individual objects are also, and these are the kinds of things that using the mathematics of sets you can then show to have all the same properties as the numbers you use in the rest of math. GR: The problem for views like that is that for all we know there are only finitely many objects in nature, there are a lot of them, but there might only be finitely many, and if there are only finitely many, then the biggest collection out there in nature has only finitely many things in it, and the biggest number property in nature is I don't know the number twenty seven billion or something like that, and none of that's enough for mathematics, because mathematics assures us that there are infinitely many numbers. So, the big problems for views like that is first of all explaining why mathematical assumptions of infinity are justifiable, and second of all explaining the connection between those things that are allegedly in nature and ordinary mathematical practice, which is still an armchair business. It's not as if mathematicians have to go out and inspect these natural things in order to do their work, they're going to sit at their desks with their pencils and paper.Barry: We don't drown people who come up with mathematical discoveries today, we give them tenure, and we're at a point where we're running out of things that can't be described mathematically. I just saw an equation with six terms in it that's supposed to predict human happiness over a lifetime. This doesn't come from a numerologist, it came from scientists. In many ways Pythagoreanism is alive and well. Every time we worry about the proper ratio of fat, protein, and carbs, or use a phone that has GPS, or trying to describe the world economy with an equation, we're being Pythagoreans, actually we're being mathematici, we're following Hippasus. And yet today we have a paradox: the more we discover the deeper the mystery. Hippasus drowned because they feared he discovered numbers that couldn't possibly be part of the physical world. Now the world seems to be pretty much waiting for new math to describe it. We used to be able to explain this, but if our souls don't come from some perfect invisible world of Hilbert’s paces complex numbers and goodness and justice, and the real world isn't just striving to become mathematical perfection then why does it appear so much like it does? ................
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