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- Extraordinary claims, such as that UFOs have visited our planet or that aliens exist, require extraordinary evidence.
- Personal testimonies are simply insufficient to conclude that UFOs and aliens are real.
- Good luck having a rational conversation about it with anyone on Twitter.
If you were hoping, based on the title, that I was going to describe the time I saw strange lights moving at inexplicable speeds across the sky, then I am about to disappoint you. This column is actually about my experience in the public spotlight talking publicly about the connection between UFOs and extraterrestrial life. It was quite a ride.
Extraordinary claims require extraordinary evidence
On May 30, 2021, I wrote an op-ed in the New York Times titled "I'm a Physicist Who Studies Aliens. U.F.O's Don't Impress Me." I don't get to write titles for the op-ed pieces that I write for the Times — or most other places for that matter — but, as provocative as it was, I think it captured the essence of my point. As a scientist involved in the search for life and "techno-signatures" on exoplanets, I think a lot about what constitutes a good data set for that search. In other words, what kind of data would allow me to make the extraordinary claim that my colleagues and I have detected life and a civilization on another world?
The answer had better be "some really damn good data." By that, I mean we would need to take measurements that gave us strong and unambiguous evidence for the conclusion that a particular signal comes from a technologically advanced civilization. My main point in the op-ed was that no matter how intriguing those navy UFO sightings may be — and they are interesting — they don't provide the extraordinary evidence that we need to conclude that aliens are visiting us. My arguments are in the op-ed if you want to see them. What I want to focus on here is what happened after that argument appeared in the press.
The UFO brigade
Within an hour or so, my email and Twitter feed began to light up. By the end of the day, I was getting more messages about the piece than almost anything I had ever written before. Some of the messages affirmed the argument I was making. The majority, however, wanted me to know how wrong I was. These fell into two categories.
There was a fair amount of "the-government-knows-but-won't-tell-us" kind of narrative. Lots of these messages were pretty mean.
Some people wanted me to know that UFOs — or as the government calls them, Unidentified Aerial Phenomena (UAPs) — didn't need to be connected to aliens for them to be of interest. I had however made this exact point in my piece.
I have no problem with people wanting to have those navy sightings (and others) studied scientifically and openly. My colleagues on the NASA techno-signature grant made this point in an excellent Washington Post op-ed. I think the process of vetting those sightings would greatly help show the public exactly how science works. These days, we have a real problem with science denial, and anything that lets folks understand "what science knows and how it knows it" would be helpful.
Credit: IgorZh / 280582371 via Adobe Stock
But many folks (on Twitter and elsewhere) held that the connection between UFOs and aliens had already been made. I got floods of links to one video or website after another, the vast majority of which were people describing something they had seen in the sky. As I said in the op-ed, there really isn't much science you can do with personal testimony. One can't get accurate measurements of velocity or distance or mass or any of the other basic data that a physicist would need to tell if something really was moving in a way that's impossible for human technology.
Some folks reached out because they had seen a UFO themselves. I totally understand that these people would want someone to take their reports seriously. I would never tell them that they did not have their experiences. What I can say, however, is that there's nothing a scientist can do to transform the description of that experience into data that we would need to reach the extraordinary conclusion that they had seen evidence for extraterrestrial life.
The truth is out there
But a significant fraction of what I saw coming across Twitter and elsewhere was just pure vehemence. These folks were absolutely certain that UFOs were alien visitors. There was a fair amount of "the-government-knows-but-won't-tell-us" kind of narrative. Lots of these messages were pretty mean. I got the sense that, for these folks, no public investigation — no matter how open and transparent — would be satisfying unless it reached the conclusion that they already believed. This, of course, is the opposite of science.
So, it was an interesting week. My brief time in the UFO limelight (I did many interviews on places like CNN, BBC, etc.) showed me a lot about how people view the question. Since I am so deeply involved with techno-signature science, I felt it was important to try to explain how the science of life and the universe works as a science.
But I don't really want to spend a whole lot more time in that limelight. It was kind of exhausting, in large part because of the vehemence of the true believers. I will follow whatever happens after the government's report comes out with interest. But my bet (and every researcher makes a bet when they choose their research topics) is that the data I need to know about life elsewhere in the universe will come from telescopes, not jet fighters.
What happened before the Big Bang?
Asking science to determine what happened before time began is like asking, "Who were you before you were born?"
- Science can allow us to determine what happened trillionths of a second after the Big Bang.
- But it likely never will be possible to know what brought about the Big Bang.
- As frustrating as it might be, some things are entirely unknowable. And that's a good thing.
Let's face it: to think that the universe has a history that started with a kind of birthday some 13.8 billion years ago is weird. It resonates with many religious narratives that posit that the cosmos was created by divine intervention, although science has nothing to say about that.
What happened before time began?
If everything that happens can be attributed to a cause, what caused the universe? To deal with the very tough question of the First Cause, religious creation myths use what cultural anthropologists sometimes call a "Positive Being," a supernatural entity. Since time itself had a beginning at some point in the distant past, that First Cause had to be special: it had to be an uncaused cause, a cause that just happened, with nothing preceding it.
Attributing the beginning of everything to the Big Bang begs the question, "What happened before that?" That's a different question when we are dealing with eternal gods, as for them, timelessness is not an issue. They exist outside of time, but we don't. For us, there is no "before" time. Thus, if you ask what was going on before the Big Bang, the question is somewhat meaningless, even if we need it to make sense. Stephen Hawking once equated it with asking, "What's north of the North Pole?" Or, the way I like to phrase it, "Who were you before you were born?"
To ask from science to "explain" the First Cause is to ask science to explain its own structure. It's to ask for a scientific model that uses no precedents, no previous concepts to operate. And science can't do this, just as you can't think without a brain.
Saint Augustine posited that time and space emerged with creation. For him, it was an act of God, of course. But for science?
Scientifically, we try to figure out the way the universe was in its adolescence and infancy by going backward in time, trying to reconstruct what was happening. Somewhat like paleontologists, we identify "fossils" — material remnants of long-ago days — and use them to learn about the different physics that was prevalent then.
The premise is that we are confident that the universe is expanding now and has been for billions of years. "Expansion" here means that the distances between galaxies are increasing; galaxies are receding from one another at a rate that depends on what was inside the universe at different eras, that is, the kinds of stuff that fill up space.
The "Big Bang" was not an explosion
When we mention the Big Bang and expansion, it's hard not to think about an explosion that started everything. Especially since we call it the "Big Bang." But that's the wrong way to think about it. Galaxies move away from one another because they are literally carried by the stretch of space itself. Like an elastic fabric, space stretches out and the galaxies are carried along, like corks floating down a river. So, galaxies are not like pieces of shrapnel flying away from a central explosion. There is no central explosion. The universe expands in all directions and is perfectly democratic: every point is equally important. Someone in a faraway galaxy would see other galaxies moving away just like we do.
(Side note: For galaxies that are close enough to us, there are deviations from this cosmic flow, what's called "local motion." This is due to gravity, The Andromeda galaxy is moving toward us, for example.)
Going back in time
Credit: Andrea Danti / 98473600 via Adobe Stock
Playing the cosmic movie backward, we see matter getting squeezed more and more into a shrinking volume of space. Temperature rises, pressure rises, things break apart. Molecules get broken down into atoms, atoms into nuclei and electrons, atomic nuclei into protons and neutrons, and then protons and neutrons into their constituent quarks. This progressive dismantling of matter into its most basic constituents happens as the clock ticks backward toward the "bang" itself.
For example, hydrogen atoms dissociate at about 400,000 years after the Big Bang, atomic nuclei at about one minute, and protons and neutrons at about one-hundredth of a second. How do we know? We have found the radiation left over from when the first atoms formed (the cosmic microwave background radiation) and discovered how the first light atomic nuclei were made when the universe was merely a few minutes old. These are the cosmic fossils that show us the way backward.
Currently, our experiments can simulate conditions that happened when the universe was roughly one trillionth of a second old. That seems like a ridiculously small number for us, but for a photon — a particle of light — it's a long time, allowing it to travel the diameter of a proton a trillion times. When talking about the early universe, we must let go of our human standards and intuitions of time.
We want to keep going back as close to t = 0 as possible, of course. But eventually we hit a wall of ignorance, and all we can do is extrapolate our current theories, hoping that they will give us some hints of what was going on much earlier, at energies and temperatures we cannot test in the lab. One thing we do know for certain, that really close to t = 0, our current theory describing the properties of space and time, Einstein's general theory of relativity, breaks down.
This is the realm of quantum mechanics, where distances are so tiny that we must rethink space not as a continuous sheet but as a granular environment. Unfortunately, we don't have a good theory to describe this granularity of space or the physics of gravity at the quantum scale (known as quantum gravity). There are candidates, of course, like superstring theory and loop quantum gravity. But currently there is no evidence pointing toward either of the two as a viable description of physics.
Physics' greatest mystery: Michio Kaku explains the God Equation | Big Think www.youtube.com
Quantum cosmology doesn't answer the question
Still, our curiosity insists on pushing the boundaries toward t = 0. What can we say? In the 1980s, James Hartle and Stephen Hawking, Alex Vilenkin, and Andrei Linde separately came up with three models of quantum cosmology, where the whole universe is treated like an atom, with an equation similar to the one used in quantum mechanics. In this equation, the universe would be a wave of probability that essentially links a quantum realm with no time to a classical one with time — i.e., the universe we inhabit, now expanding. The transition from quantum to classical would be the literal emergence of the cosmos, what we call the Big Bang being an uncaused quantum fluctuation as random as radioactive decay: from no time to time.
If we assume that one of these simple models is correct, would that be the scientific explanation for the First Cause? Could we just do away with the need for a cause altogether using the probabilities of quantum physics?
Unfortunately, not. Sure, such a model would be an amazing intellectual feat. It would constitute a tremendous advance in understanding the origin of all things. But it's not good enough. Science can't happen in a vacuum. It needs a conceptual framework to operate, things like space, time, matter, energy, calculus, and conservation laws of quantities like energy and momentum. One can't build a skyscraper out of ideas, and one can't build models without concepts and laws. To ask from science to "explain" the First Cause is to ask science to explain its own structure. It's to ask for a scientific model that uses no precedents, no previous concepts to operate. And science can't do this, just as you can't think without a brain.
The mystery of the First Cause remains. You can choose religious faith as an answer, or you can choose to believe science will conquer it all. But you can also, like the Greek Skeptic Pyrrho, embrace the limits of our reach into the unknowable with humility, celebrating what we have accomplished and will surely keep on accomplishing, without the need to know all and understand all. It's okay to be left wondering.
Curiosity without mystery is blind, and mystery without curiosity is lame.
Greed and the philosophy of wealth
When does a healthy desire for wealth morph into greed? And how can we stop it?
- It's common wisdom that most things in life are best in moderation.
- Most of us agree that owning property is okay but are hard-pressed to say why and when it has gone too far.
- Greed dominates your life if the pursuit of wealth is a higher priority than charity, kindness, and solidarity with others.
The great Greek poet, Hesiod, wrote, "Observe due measure; moderation is best in all things." It's a wisdom that finds support across all ages, stages, and aspects of life. Drinking water is a good thing, but drinking too much is dangerous. A shot of vodka won't kill you, but a gallon probably will. Working hard is good, but burning yourself out is not. Being nice is great, but a sycophant is creepy. Moderation in all things.
But, it's not always easy to determine where that line falls, and a great example of this concerns property and wealth.
Most of us agree that owning things, or at least having the right to own things, is good. It's okay to buy a phone, to own a car, or to have your own clothes. But equally true is that most people feel uneasy about a world which has both billionaires in vast mansions as well as children dying malnourished. Greed, avarice, envy, and venality are considered vices. To be obsessively driven for material things is still, in the main, considered to be either misguided or, at its worst, utterly immoral. So, when does wealth become greed?
John Locke and the philosophy of property
Credit: Godfrey Kneller via Wikipedia / Public domain
It's hard to pinpoint exactly when humans first called a thing "mine," but the philosophy and law of property is much easier to track. One of the biggest names to consider the issue was the 17th century English philosopher John Locke.
Locke's political philosophy is famously cited as a major influence on the U.S. Declaration of Independence but also fed heavily into the French Revolution and the Great Reform movements of Britain. His work on property is perhaps one of his most important contributions.
Although subject to a fair bit of debate — what isn't in philosophy? — it's generally accepted that Locke adopted a "fair usage" view of property. He argued that one can hold any property that meets the following criteria:
- It can be used before it spoils (e.g., we don't have huge stores of food that just rots).
- It leaves "good and enough" for everyone else (e.g., one person cannot own all the land in a country).
- The property must come from your own work and effort or what he calls "mixing your labor" with that thing (e.g., if you farm a field, the field and its produce become yours).
If we were to follow these rules, it seems hard to envisage a world of greed and inequality. Everyone can have and get what they want, so long as enough is left for everyone else to get what they want, as well.
But, there's a lot of ambiguity in these rules, and money rather changes things. Money, especially modern money in the form of digital numbers on a screen, does not spoil. And, thanks to modern banking, there is no limit to the amount of money there could be — a bank can, and does, literally create money each time they give you a credit card or a loan (although, in practice, few countries allow this and place limits on money creation). So, no matter how many billions someone creates, there will always be "good and enough" money for others, too.
(Of course, in practice, constantly creating huge new pools of money will lead to hyperinflation, devaluing the money for everyone. Yet, even if we were to ban all new money creation today, a Lockean could argue that there's more than enough already for a generous distribution around the world.)
So, money changes things for Locke's account. It won't spoil and there will always be at least some money for everyone else. It's even been argued that Locke, far from advocating an equal and distributive philosophy, can easily support rampant capitalist accumulation of wealth. Locke wrote that, because of money, "Now one man could have… a disproportionate and unequal possession of the earth… and fairly possess more land than he himself can use."
It's the philosophy of greed.
Too much greed
The idea that greed is an essential part of being human (or at least an animal) goes back at least to Plato and has a rich philosophical history from there. Today, it often takes the form of evolutionary psychology or genetics, exemplified by Richard Dawkins' The Selfish Gene.
It's when we think of little else than increasing our experiences and material possessions. This is the point at which greed has come to dominate your life.
One thinker who has challenged this is Peter Singer. Singer acknowledges the fact that evolution does work on a certain competitiveness, that is, the fittest will pass on their genes. But he also believes that it's wrong to associate this wholly with greed or selfishness. Cooperation and productive relationships are just as vital to survival.
Singer argues that the desire to do good, to work hard, and to succeed are admirable parts of the human condition, but when they are taken to excess, they turn into greed. That line comes when the want of more — particularly, the desire for material wealth — becomes the sole focus of a life. It's when working late or constantly looking for that promotion is prioritized over family, friends, and common human compassion.
The fact is that, in the West, most people have enough. Even poor people generally have TVs, smartphones, and automobiles. The average person in the West lives far better than royalty did for millennia. Singer asks us to get a sense of perspective. We spend more on bottled water than some families in developing countries live off for a day. We're so fixated on our current day-to-day condition, that we lose sight of how much we really have.
Greed über alles
Singer's argument helps us identify the point at which drive and success insidiously morph into greed: It's when we are loath to spend our money and devote all of our waking lives to determinedly accumulating more and more at the expense of our relationships. It's when we think of little else than increasing our experiences and material possessions. This is the point at which greed has come to dominate your life.
But it's also when greed replaces our common sense of compassion. It's when property and wealth become virtues greater than charity, kindness, and solidarity with others. It's when dollar signs and fast cars matter more than people dying in the street. It's when getting a pay raise matters more than someone else getting fired.
Nobody likes to think of themselves as greedy, but if you examine yourself closely, you will probably find some aspects of your life that are at least tainted by greed. We should all check ourselves from time to time.
Jonny Thomson teaches philosophy in Oxford. He runs a popular Instagram account called Mini Philosophy (@philosophyminis). His first book is Mini Philosophy: A Small Book of Big Ideas.
Pyrrho and the Skeptical way of life: ignorance is bliss
Why saying, "I don't know," might be the best thing you can do.
- Skepticism is the philosophy that there's very little that we can actually know with any certainty.
- Pyrrho is considered the father of Skepticism, and he believed we ought to suspend our judgment on all those things to which we can never find an answer.
- By giving up the dogmatic pursuit of some kind of resolution, we can be at peace with ourselves and stop getting wound up so easily.
There's always someone, somewhere, who will disagree with you. There will always be a second opinion, a different perspective, or the sliver of a doubt. Sam thinks the war's right, Joe thinks it's wrong. Ella thinks it's warm in here, Toby thinks it's cold. Bob thinks all humans are equal, AJ thinks some are better than others.
There's two sides to everything, and life has no easy answers.
This is the central belief of Skepticism, and two of its greatest thinkers — the Greek, Pyrrho of Elis, and the Roman, Sextus Empiricus — believed that recognizing this is one of the best things that philosophy can give us.
Radical Skepticism
As we've seen with Cynicism, Stoicism, and Epicureanism, Greek philosophy can all too often be misrepresented. Words like "cynical" and "skeptic" have mutated over the years to become entirely new beasts. To be skeptical, today, means to be doubtful. It's to question, challenge, and be somewhat disbelieving of an idea or person. Yet in the ancient world, Skepticism was much more extreme.
According to Pyrrhonism, we waste so much time and effort seeking and demanding answers or resolution where there's only doubt and ambiguity, that we're destined to be unhappy.
Pyrrho is considered to be the first Skeptic philosopher. He began with the simple observation that there are two sides to everything and that we are all invariably bound to our own opinions and thoughts. Thus, we will always see the world differently than others.
It's highly likely that Pyrrho witnessed first hand, or at least had heard of, the Eastern religions that repeatedly made the claim that the world is illusory, knowledge is limited, and human intellect is an infantile, narrow thing. Pyrrho agreed. For him, there's no possible way to determine what's true or "actual."
And yet, we all stubbornly, angrily, and even violently insist that others are wrong and that we are right. According to Pyrrhonism, we waste so much time and effort seeking and demanding answers or resolution where there's only doubt and ambiguity, that we're destined to be unhappy. The key to living a fulfilled, happy, and flourishing life (which is called eudaimonia in Greek and was the end goal, too, of Cynicism, Epicureanism, and Stoicism) is simply to stop the pointless pursuit of resolution. Instead, we ought to adopt a position called epoché, which means "suspended judgment."
For Pyrrho, if someone asks you for your views on some controversial ethical issue, on the latest government spending bill, or what's the greatest movie of all time, you ought to simply demonstrate epoché and say, "I have only my opinion on the matter, as have you, so I shall say there is no answer." Of course, you can debate and happily chat until the cows come home, but Pyrrho's wisdom is just to recognize there will be no hope of a final, absolute, and neat end point to the discussion. Someone, somewhere will always think Dude, Where's My Car is fantastic.
Is everything ultimately an opinion?
Pyrrho himself took things a bit far. His students reportedly had to stop him from walking off deadly precipices or into busy streets because he said he couldn't entirely trust his senses. So, it took a few centuries for Skepticism to develop, and it found its voice again in the Roman, Sextus Empiricus.
Like Pyrrho, Sextus Empiricus didn't place much stock in human knowledge because he thought everything we might claim to know was always open to doubt or challenged. But, Sextus further added the idea that there could be no possible way to resolve such a challenge. For example, let's suppose there are two people who disagree about something. What justification is there for one view being better than the other? For Sextus, both are equally valid.
Credit: OLIVIER HOSLET via Getty Images
We might say, "But we can give reasons for our beliefs!" However, this only begs the question: why does a particular reason make a belief stronger? If I think stealing is wrong because it harms someone, I still need to explain why "causing harm" is important.
For Sextus Empiricus, we'll always reach the point of saying, "This is just what I think." At no point is there an ultimate answer. Why, indeed, is causing harm bad?
Into this world of murky ambiguity, Sextus' Skepticism argued that we should live only according to how things seem. This isn't the same as trusting our senses, since even these are open to disagreement. (However, there are no stories of him nearly falling from cliffs.) Some animals can see ultraviolet light, some people hear Laurel and others hear Yanny, and there are psychedelic drugs that can make us see anything at all.
We only have how things appear.
The consolation of Skepticism
For Sextus and Pyhrro, recognizing the very clear limits to our understanding brings great benefit. With the revelation that there are some things — well, maybe a lot of things — that we can never know is deeply comforting. We can give up trying to dogmatically defend views that we have no way to know for sure are correct. We can stop getting so heated in debates where neither party can possibly come to a resolution.
But, this is not to give up trying. "Skeptic" literally translates as "enquirer," and we can still aim for something, while also accepting we may never succeed. To be a Skeptic is to say, "I'll probably never know the answer to this, but I'll try to find out anyway." It's to give up the false hope for easy answers and to find peace in our own experiences, alone.
So, why not try Skepticism? All you've got to do is let out a deep breath, give your best Gallic shrug, and be at peace with how little you really know.
Jonny Thomson teaches philosophy in Oxford. He runs a popular Instagram account called Mini Philosophy (@philosophyminis). His first book is Mini Philosophy: A Small Book of Big Ideas.
Hidden philosophy of the Pythagorean theorem
Pythagoras may have believed that the entire cosmos was constructed out of right triangles.
- Ancient Greeks believed that fire, air, water, and earth were the four elements of the universe.
- Plato associated these four elements with 3D geometrical solids.
- Pythagoras may have believed that the right triangle formed the basis of all reality.
In Plato's dialogue, the Timaeus, we are presented with the theory that the cosmos is constructed out of right triangles.
This proposal Timaeus makes after reminding his audience [49Bff] that earlier theories that posited "water" (proposed by Thales), or "air" (proposed by Anaximenes), or "fire" (proposed by Heraclitus) as the original stuff from which the whole cosmos was created ran into an objection: if our world is full of these divergent appearances, how could we identify any one of these candidates as the basic stuff? For if there is fire at the stove, liquid in my cup, breathable invisible air, and temples made of hard stone — and they are all basically only one fundamental stuff — how are we to decide among them which is most basic?
A cosmos of geometry
However, if the basic underlying unity out of which the cosmos is made turns out to be right triangles, then proposing this underlying structure — i.e., the structure of fire, earth, air, and water — might overcome that objection. Here is what Timaeus proposes:
"In the first place, then, it is of course obvious to anyone, that fire, earth, water, and air are bodies; and all bodies have volume. Volume, moreover, must be bounded by surface, and every surface that is rectilinear is composed of triangles. Now all triangles are derived from two [i.e., scalene and isosceles], each having one right angle and the other angles acute… This we assume as the first beginning of fire and the other bodies, following the account that combines likelihood with necessity…" [Plato. Timaeus 53Cff]
A little later in that dialogue, Timaeus proposes further that from the right triangles, scalene and isosceles, the elements are built — we might call them molecules. If we place on a flat surface equilateral triangles, equilateral rectangles (i.e., squares), equilateral pentagons, and so on, and then determine which combinations "fold-up," Plato shows us the discovery of the five regular solids — sometimes called the Platonic solids.
Three, four, and five equilateral triangles will fold up, and so will three squares and three pentagons.
If the combination of figures around a point sum to four right angles or more, they will not fold up. For the time being, I will leave off the dodecahedron (or combination of three pentagons that makes the "whole" into which the elements fit) to focus on the four elements: tetrahedron (fire), octahedron (air), icosahedron (water), and hexahedron (earth).
Everything is a right triangle
Now, to elaborate on the argument [53C], I propose to show using diagrams how the right triangle is the fundamental geometrical figure.
All figures can be dissected into triangles. (This is known to contemporary mathematicians as tessellation, or tiling, with triangles.)
Inside every species of triangle — equilateral, isosceles, scalene — there are two right triangles. We can see this by dropping a perpendicular from the vertex to the opposite side.
Inside every right triangle — if you divide from the right angle — we discover two similar right triangles, ad infinitum. Triangles are similar when they are the same shape but different size.
And thus, we arrive at Timaeus' proposal that the right triangle is the fundamental geometrical figure, in its two species, scalene and isosceles, that contain within themselves an endless dissection into similar right triangles.
Now, no one can propose that the cosmos is made out of right triangles without a proof — a compelling line of reasoning — to show that the right triangle is the fundamental geometrical figure. Timaeus comes from Locri, southern Italy, a region where Pythagoras emigrated and Empedocles and Alcmaon lived. The Pythagoreans are a likely source of inspiration in this passage but not the other two. What proof known at this time showed that it was the right triangle? Could it have been the Pythagorean theorem?
Pythagorean theorem goes beyond squares
We now know that there are more than 400 different proofs of the famous theorem. Does one of them show that the right triangle is the basic geometrical figure? Be sure, it could not be a² + b² = c² because this is algebra, and the Greeks did not have algebra! A more promising source — the proof by similar right triangles — is the proof preserved at VI.31.
Notice that there are no figures at all on the sides of the right triangle. (In the above figure, the right angle is at "A.") What the diagram shows is that inside every right triangle are two similar right triangles, forever divided.
Today, the Pythagorean theorem is taught using squares.
But, the Pythagorean theorem has nothing to do with squares! Squares are only a special case. The theorem holds for all figures similar in shape and proportionately drawn.
So, why the emphasis on squares? Because in the ancient Greek world proportional-scaling was hard to produce exactly and hard to confirm, and the confirmation had to come empirically. But squares eliminate the question of proportional scaling.
Pythagoras and the philosophy of cosmology
We have an ancient report that upon his proof, Pythagoras made a great ritual sacrifice, perhaps one hundred oxen. What precisely was his discovery that merited such an enormous gesture?
Could this review help us to begin to understand the metaphysical meaning of the hypotenuse theorem — namely, that what was being celebrated was not merely the proof that the area of the square on the hypotenuse of a right triangle was equal to the sum of the areas of the squares on the other two sides, but moreover, was the proof that the fundamental figure out of which the whole cosmos was constructed was the right triangle?
Prof. Robert Hahn has broad interests in the history of ancient and modern astronomy and physics, ancient technologies, the contributions of ancient Egypt and monumental architecture to early Greek philosophy and cosmology, and ancient mathematics and geometry of Egypt and Greece. Every year, he gives "Ancient Legacies" traveling seminars to Greece, Turkey, and Egypt. His latest book is The Metaphysics of the Pythagorean Theorem.
Electric eels and gladiator blood: the curious beginnings of modern medicine
Hippocrates overturned conventional wisdom and invented modern medicine.
- Ancient "medicine" once consisted of sacrificial offerings and divine petition. Disease was a supernatural infliction; health was a gift.
- Hippocrates invented medical science, and his theory of the humors and holistic health dominated Western medical thought for more than two thousand years.
- Today, medicine is much more disease centred, and perhaps something has been lost from the Hippocratic doctor-patient relationship.
You're feeling sick — so sick you can barely walk — and so you visit a professional. You wait outside, feverish and exhausted, hoping they can help. Your name is called. You start to explain your symptoms but are interrupted before you can get going.
"Let me stop you there", he says, "it's obvious what's happened. You've been cursed by the god Hermes. You must sacrifice two young goats and pray to him every day. I hope he takes pity on you. NEXT!"
You leave, still sick.
The doctor will see you now
This was the standard medical model of the ancient world. Priests and prayer cured diseases. That is, until Hippocrates reinvented the entire practice and defined medicine as a profession.
All we know of Hippocrates comes from a series of writings from the library at Alexandria, collected around 250 BCE. It's a mishmash of collected wisdom, case notes, and philosophy, composed by multiple authors over many years. But Hippocrates is the master and name that binds it all.
Hippocrates argued that sickness and disease can be understood by rational enquiry and had natural explanations (as opposed to gods or the supernatural). Man was just as much part of nature as chickens or cows and could be treated or cured in much the same way.
Because the Greeks had strict rules against dissecting or cutting a dead body, Hippocrates and the early physicians knew very little about human physiology. Most anatomical learning had to come from the gruesome mess of the battlefield — people (literally) carrying their arms or returning with gaping puncture wounds in their stomach. The only other way was by drawing parallels with the animal world. For instance, the Hippocratics believed human pregnancy was similar to how a hen nurtured her eggs.
Man was just as much part of nature as chickens or cows and could be treated or cured in much the same way.
Without microscopes or medical experimentation, Greek physicians were much more limited and took a holistic view of the body. Today, medicine is pretty heavily disease centered, in that it focuses on pathology, such as dysfunctional organs or microbial infections. For Hippocrates, sickness was a whole body thing — caused only when the natural balance and equilibrium of the body was disturbed.
A sense of humor
The humors blood (red) and phlegm (blue) are depicted in this document at Raeapteek pharmacy in Tallinn, Estonia.Credit: Alex Berezow
Hippocrates believed that the body was made up of various fluids, called humors, and different organs were responsible for their creation and regulation.
There were four humors: blood, phlegm, yellow bile, and black bile. These all existed in the body, and when present in moderation or in balance with the other humors, a person was considered healthy. (It should be noted that black bile was often seen as being uniformly negative). It was believed disease resulted when one or more of the humors was overproduced or located in an incorrect part of the body. So, if you have too much phlegm, you will get a cough. Too much blood, and you would vomit. Too much black bile, and you would become depressed.
While we might find this ridiculous, you can see why the Hippocratics thought this way. Even today, we're often guilty of confusing symptoms with causes, and it's completely logical for someone to think that since the body is expelling phlegm during a cold, that must be the cause of the disease. Or how a nosebleed is caused by excessive blood. Or how diarrhea looks like yellow bile.
Of course, this sometimes meant that Hippocratic medicine offered some absurd treatments. It was thought, for instance, that epilepsy was caused by phlegm blocking the airways — the convulsing was an effort to open them — so warm dry climates were recommended. A regular prescription was for a patient being told to drink Gladiator blood for its potency. If you had a headache, it was suggested that you hold an electric eel to your head to force out the unwanted humors.
Has your doctor ever sniffed your stool?
It's hard to understate just how sick or infirm people would have been in ancient Greece. Thanks to modern medicine and public health, we're very rarely sick, and when we are, medicine is usually effective and easy to get. Antiquity, though, was a world of fever, food poisoning, water-borne infection, animal bites, and frequent, brutal warfare (and the ensuing infections). Today, being healthy is the norm. Back then, it was being sick.
It's not unfair to say that Hippocrates invented both prognosis and diagnosis. For the first time, a physician could say, "I know what's gone wrong, and I can tell you how it'll pan out."
As such, having an empirically minded (if misguided) physician class like the Hippocratics would have had huge success for the patient and physician alike. By seeing disease as an imbalance of the entire body, the Hippocratics took keen interest in their patients. They were frequently bedside and their examinations incredibly thorough. For instance, they would often taste urine or ear wax to check if it was okay. They would eat leg hair and sniff patient's stools. It's not unfair to say that Hippocrates invented both prognosis and diagnosis. For the first time, a physician could say, "I know what's gone wrong, and I can tell you how it'll pan out."
These physicians did not recommend drastic or intense interventions like surgery (not least because anything short of amputation would be fatal, anyway). They would prescribe lifestyle changes such as diet, exercise, hot baths, and sex (which was especially important for older patients). They would constantly ask how patients are doing. They would check that they were taking their medicine.
Though practically none of the Hippocratics' medicine was anywhere near accurate, their bedside manner was quite different from the modern doctor's: "What's wrong with you? Right, here are your drugs. Good luck. So long." Hippocratic medicine used every trick necessary to re-establish harmony to the whole body. The doctor-patient relationship was just that — a relationship, not a transaction.
Hippocrates' legacy
Credit: Anne-Louis Girodet de Roussy-Trioson via Wikipedia / Public domain
Hippocrates gave us two great gifts. First, he made medicine a scientific discipline in its own right. Second, he showed us how important it is to pay attention to the whole patient and respond to the totality of their sickness, including their mental state. Medical professionals worldwide still have to swear by the "Hippocratic Oath," which, among many other things, obliges doctors to "remember that I do not treat a fever chart, a cancerous growth, but a sick human being, whose illness may affect the person's family and economic stability."
Voltaire once said, "The art of medicine consists in amusing the patient, while nature cures the disease." This was no doubt true of Hippocrates. Surely, many of his patients recovered, but most often it was likely due less to his medical prowess and more to his patients enjoying a month-long spa with great food and lots of sleep.
Jonny Thomson teaches philosophy in Oxford. He runs a popular Instagram account called Mini Philosophy (@philosophyminis). His first book is Mini Philosophy: A Small Book of Big Ideas.
