Tag Archives: science

We are MacApes, O’Monkeys, and Ben-Reptiles

1764-1777

A couple years back, Jonathan Marx and Jerry Coyne had an online spat on the question “Are humans apes?” (Marx says noCoyne says yes; see also John Hawks, who says no.) I offer my own solution below, after talking about Linnaeus (1707-1778) and biological categorization.

There’s a branch of cultural anthropology that studies “folk biology,” also known as “ethnobiology,” which is (among other things) about how different groups classify living things. Folk biological categories don’t vary randomly across cultures; there are some general principles at work. A quick summary: the basic level of categorization is roughly the genus. American folk genera include oakcrow, and fox (although a lot of Americans today are really bad at folk biology, maybe using that part of the brain for Pokemon.) Many peoples, and most hunter-gatherers, only take categorization down to the genus level. Others (especially horticulturalists) take it down to the species level, often with two part names (red oak, silver fox). Going toward more inclusive groups, genera are lumped together in larger, intermediate-sized, non-overlapping categories (palmhawk), which belong in turn to the more inclusive level of “life forms”: (bird, snake, fish, tree, grass/herb).

From an anthropological perspective, Linnaeus’s famous scheme of classification is an elaboration of these universal principles, with more species and more taxonomic levels (the famous Kingdom, Phylum, Class, Order, Family, Genus, Species).

A version of Linnaeus’s scheme served evolutionary biologist well for centuries. But starting in the later twentieth century, many biologists turned to another approach that was claimed to be a better fit for evolutionary principles: According to cladists, the classification of living things should be based on clades: groups containing all and only the descendants of an ancestor. This requires overturning or revising many familiar categories. For example, monkeys are not a clade, since Old World monkeys are more closely related to apes (including humans) than to New World monkeys. Reptiles are not a clade, since crocodiles are more closely related to birds than to lizards and snakes. Fish are not a clade, since lungfish are more closely related to amphibians and reptiles than to most other fish.

After some bitter disputes. cladists seems to have won the battle among scientists. But cladism has made less headway among non-scientists. In Naming Nature: The Clash Between Instinct and Science, Carol Yoon argues that cladistics is just too much at variance with the way the human mind understands biological categories. Most people are never going to take to cladistics any more than they’re going to take to twelve-tone music, or Loglan. So different answers to the question “Are humans apes?” reflect disagreement about how far we can or should bring folk categories in line with the austere logic of cladism. Apes, including humans, are a clade. Apes, not including humans, are not (since chimpanzees are more closely related – but not really more similar – to humans than to gorillas).

I suggest a compromise. Folk categories like ape, monkey, reptile, and fish, defined by shared ancestral traits, are useful, even if they aren’t clades, defined by shared derived traits. But the concept of a clade is also important one for biologists. So maybe when we want to talk about the clades associated with folk categories, why don’t we use a prefix – the Scottish Mac, Irish O’, or Hebrew/Arabic ben/bin. (Any of these will serve.) So human beings are not apes, monkeys, reptiles, or fish. But we are MacApes, O’Monkeys, Ben Reptiles, and/or Bin Fish.

(For other We Are posts see We Are Upside Down Bugs and We are Stardust.)

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Steam engine time

1714-1730

The steam engine was a child of seventeenth century science; the Scientific Revolution gave birth to the Industrial Revolution. That’s not at all the conventional story, but David Wooton’s recent book The Invention of Science: A New History of the Scientific Revolution makes the case.

According to the conventional story, the steam engine resulted from the work of generations of inspired tinkerers, ingenious craftsmen with no particular scientific training and no great scientific knowledge. Indeed, according to one historian, “Science owes more to the stream engines than the steam engine owes to science.” (After all, the steam engine did inspire Carnot’s thermodynamic theory.)

But Wooton traces a path from scientific theory to practical application, beginning with the seventeenth century science of vacuum, air and steam pressure. The pioneering scientists here were not just theorists. They built (or at least designed) a number of devices for making use of differences in gas pressures, including an air gun (Boyle), a steam pressure pump (della Porta), and a vacuum-powered piston (von Guericke). Huygens took up the last idea, using an explosion to empty air from a cylinder, through a valve, and then using the partial vacuum to move a piston. This in turn was taken up by Denis Papin, a French Protestant medical doctor and mathematician, who worked as an assistant to Huygens, and then to Boyle. Papin combined scientific knowledge and engineering experience to design several steam engines. None of these was very practical – sadly Papin ended his life in failure and poverty. But the first of them was very similar to the first commercially viable steam engine, produced by Newcomen in 1712 – so similar that many historians have been convinced that Newcomen must have been familiar with Papin’s design.

Up to recently there’s been no convincing account of how Newcomen could have learned of Papin. But now Wooton has discovered the likeliest link, a book by Papin with the unpromising title A Continuation of the New Digester of Bones. The book has been neglected by historians, not surprisingly, but sold well in its own day. It gives plans for a pressure cooker (hence the title). But it also contains detailed descriptions both of vacuum powered piston, and of the use of steam condensation to produce a vacuum: just what Newcomen needed to put together to build his first engine. Wooton writes:

Newcomen’s steam engine is a bit like a locked-room plot in a detective story. Here is a dead body in a locked room: How did the murderer get in and out, and what did he use as a weapon? … We cannot exclude the possibility that Newcomen went to London and met Papin in 1687 … But we do not need to imagine such a meeting. With a copy of the Continuation in his hands, Newcomen would have known almost everything that Papin knew about how to harness atmospheric pressure to build an engine. … From this unintended encounter, I believe, the steam engine was born.

He concludes:

Historians have long debated the extent to which science contributed to the Industrial Revolution. The answer is: far more than they have been prepared to acknowledge. Papin had worked with two of the greatest scientists of the day, Huygens and Boyle. He was a Fellow of the Royal Society and a professor of mathematics. … Newcomen picked up … where Papin began. In doing so he inherited some of the most advanced theories and some of the most sophisticated technology produced in the seventeenth century. … First came the science, then came the technology.

The last of the magicians

1676-1694

If I have seen further than others, it is by standing upon the shoulders of giants.

I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.

These familiar quotations from Newton are sometimes presented as expressions of his humility (a quality not otherwise much in evidence). In fact, though, it became clear in the course of the twentieth century that they are really an expression of Newton being not just a great scientist – the greatest ever – but also a great kook. Here’s a less familiar quotation from Newton about the intellectual origins of heliocentrism

It was the opinion of not a few, in the earliest ages of philosophy … that under the fixed stars the planets were carried about the sun; that the earth, as one of the planets, described an annual course about the sun, while by a diurnal motion it was in time revolved about its own axis. … This was the philosophy taught of old by Philolaus, Aristarchus of Samos, Plato, … and of that wise king of the Romans, Numa Pompilius, who, as a symbol of the figure of the world, erected a round temple … and ordained perpetual fire to be kept in the middle of it.

The Egyptians were early observers of the heavens; and from them, probably, this philosophy was spread abroad among other nations … It was their way to deliver their mysteries, that is, their philosophy of things above the common way of thinking, under the veil of religious rites and hieroglyphic symbols.

The Renaissance was committed to recovering the ancient past. This led not only to the recovery of ancient art, literature and science, but also to the recovery of a whole body of ancient magic and pseudoscience. For example, many Renaissance thinkers, and Newton, were fascinated by the mystical writings of Hermes Trismegistus (Thrice Great Hermes, hence “hermeticism”), an alleged Egyptian sage. By Newton’s time it had already been demonstrated that these writings were “pseudepigraphia,” a nice scholarly term for “fakes”; Hermes Trismegistus never existed. Nevertheless, Newton was convinced that there was an esoteric tradition preserved by the ancient Egyptians, passed on to Moses, Pythagoras, and Plato, and hidden away in the Bible. Read the Bible or stories of Pythagoras closely enough and you could recover the inverse square law of gravitation. Newton spent huge amounts of time throughout his life trying to recover further scientific secrets from the Bible.

John Maynard Keynes, who got hold of some of Newton’s papers wrote

In the eighteenth century and since, Newton came to be thought of as the first and greatest of the modern age of scientists, a rationalist, one who taught us to think on the lines of cold and untinctured reason.

I do not see him in this light. I do not think that any one who has pored over the contents of that box which he packed up when he finally left Cambridge in 1696 and which, though partly dispersed, have come down to us, can see him like that. Newton was not the first of the age of reason. He was the last of the magicians, the last of the Babylonians and Sumerians, the last great mind which looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance rather less than 10,000 years ago.

After Newton, it became clear that modern science had surpassed anything achieved by the ancient world, and natural science and the humanities went their separate ways. Reverence for the secret wisdom of the ancients would survive in the novels of Dan Brown and in the weird Masonic pyramid on the back of the US one dollar bill.dollar-bill-eye

Copernicus versus the scientific method

1532-1558

I have to confess that for a long time I didn’t really “get” Copernicus. That is to say, while I knew that Copernicus is right and Ptolemy is wrong, I wasn’t clear on just why Copernicus had a better scientific theory, partly because I didn’t bother understanding Ptolemy. So here’s a brief summary of the two. (Howard Margolis’s book helped me out.) There’s a larger point here: what makes Copernicus’s theory better doesn’t quite fit with a lot of pronouncements about “the Scientific Method.”

First, a diagram that illustrates Ptolemy’s model.

ptolemy

To account for the motion of the planets, Ptolemy needed to assume that the five planets (not counting the sun and moon) have both cycles (the big circles) and epicycles (the little circles). If you’re going to put Earth at the center of the system, then you have to have epicycles to account for the motions of the planets, like the retrograde motions where planets seem to go backwards.

Here’s something to note about this diagram: some of the cycles and epicycles vary independently, while others are exactly tied to the motions of the sun. For Mercury and Venus, the epicycles vary independently, taking different periods of time (88 days, 225 days) to complete a circuit. Their cycles, by contrast, take exactly one Earth year to complete a circuit. Furthermore, the deferent, the point at center of each epicycle, is always exactly in line with the sun. For Mars, Jupiter and Saturn on the other hand, the cycles vary independently (1.88, 11.86, and 29.46 years to make a complete circuit). But the epicycles take exactly one Earth year to complete a circuit. Furthermore, in each case the line from deferent to planet is exactly parallel to the line from Earth to Sun. Note that it’s hard to see any reason why the epicycle for Jupiter, say, couldn’t take 3.14 years to complete a circuit. But instead somehow, mysteriously, it’s connected with the sun’s motion around the earth.

(A large fraction of diagrams on the web purporting to illustrate Ptolemaic astronomy get this crucial point wrong! They show higgledy-piggledy non-parallel deferent/planet lines, pointing any which way. This makes it impossible to understand why Copernicus had a better theory. So I’m not the only person not to get Ptolemy.)

Copernicus’s model, by contrast, doesn’t just replace five circles (the cycles for Mercury and Venus, and the epicycles for Mars, Jupiter and Saturn) with one (for the Earth going around the Sun). It also automatically explains why the five superfluous cycles show an otherwise unexplained synchronic parallelism.

copernic

People who read Copernicus 1543 book carefully (not many at first) could see he had a real explanation for something that’s just a mysterious coincidence in Ptolemy. But contrary to what you may have heard, and what students get taught, about the Scientific Method, Copernicus did not formulate a hypothesis and then collect data to test his hypothesis, and show that it made the right predictions. Ptolemy and Copernicus make the same predictions about where the planets will appear in the sky. (Both are slightly off because they assume circular rather than elliptical orbits.) Eventually other scientists would gather data in support of Copernicus – Galileo’s observation of the phases of Venus was the real clincher – but the explanatory economy of his theory was a very strong reason for believing in it even before that.

Fortunately, there is a modern theory of how induction works – Solomonoff induction – that can explain why Copernicanism is a better theory. According Ray Solomonoff, induction has two parts. First there is Bayes’ Rule. Bayes’ Rule is an application of probability theory that tells you how you should revise probability estimates in the face of new evidence. Eliezer Yudkowsky gives one of the best introductions around to a counter-intuitive approach that has become enormously influential in recent years. (It’s fun to read too).

But Bayes’ Rule is only part of the story. The rule assumes that you have already assigned some prior probabilities to events before you look at the evidence. And where do scientists get their prior probabilities? Yudkowsky gives one answer: “There’s a small cluttered antique shop in a back alley of San Francisco’s Chinatown. Don’t ask about the bronze rat,” i.e. “Don’t ask.” Solomonoff offers a different answer. He argues that we can use the theory of algorithmic complexity, as developed by Kolmogorov, to assign prior probabilities. Roughly, if your theory were turned into a computer program, how long would the program be? The longer the program, the lower the prior probability. (Probabilities fall off exponentially with length of program, and are weighted to sum to one.) Suppose I give you a sequence of numbers corresponding to the first 1000 decimal digits of π. A computer program to calculate the first 1000 digits of π is going to be a lot shorter than just a list of the first 1000 digits, so the theory that I generated the list by calculating π is astronomically more likely than the theory that I generated the list at random. This is a formalization of Occam’s Rule, that simple explanations with fewer working parts are better.

So collecting evidence in support of a theory is part of good induction. But proposing more economical theories, accounting for more data with fewer working parts, is another part. Sometimes a new theory is so much better than the alternatives that we can assign it a much higher likelihood even before we collect more evidence. With Copernicus, explaining some striking coincidences which were otherwise unexplained, this was the first act in the modern Scientific Revolution.

This isn’t just a matter of historical interest. Physicists now, as they close in (hopefully) on a final theory of fundamental physics find themselves in a similar situation to Copernicus. Our best looking theory – some version of string theory – provides immense explanatory economy (or so we’re told), but just now is difficult or impossible to test. Here’s an article on the conundrums this poses for philosophy of science and the “scientific method.”

Brave New World

1503-1531

Columbus’s discoveries overthrew the Medieval conception of Earth’s place in the cosmos. No, he did not discover that the Earth was round. Educated Greeks had known that two millennia earlier. But he also did more than just discover new lands.

The standard, educated medieval view of the cosmos was a synthesis of Aristotle and Christian theology. The universe consisted of larger and larger spheres of more and more rarefied elements: a sphere of earth, a sphere of water, a sphere of air, a sphere of fire (the sublunary sphere, home of meteors), and successive quintessential spheres for the planets, the fixed stars, and heaven beyond. The first two spheres were not concentric, obviously – otherwise the earthly sphere would have been underwater. Instead, Providence had set the earthly sphere sufficiently off-center that some of it – including the whole inhabited world – stuck above the water.

to-map

Here’s a representation of the old view, still surviving just after Columbus (from David Wooton’s fine recent book The Invention of Science: A New History of the Scientific Revolution). At the very center of the chart, inside the wavy lines representing the sphere of water, is a funny shape: a T-and-O map of the inhabited world. The East, and Asia, are the white area above the horizontal crossbar of the T. The vertical bar of the T is the Mediterranean, with two further horizontal black lines separating Iberian, Italian and Balkan peninsulas to the North (left). Africa is South (right) of the Mediterranean. Not shown on this map, at the very crux of the T, is the holy city of Jerusalem, site of the Crucifixion and Resurrection. T-and-O maps aren’t much use for navigation, but they were popular for a long time because they showed a Higher Truth.

It’s hard to square this conception of the universe with the discovery of a whole New World sticking up on the opposite side of the watery sphere. Columbus tried out various theories. At first he imagined that he had reached the (East) Indies. Later, he started thinking that the earthly “sphere” might be pear-shaped (shaped like a woman’s breast, he put it) rather than strictly spherical, and you could reach the site of earthly Paradise (the nipple) by sailing up the Orinoco.

The generation following Columbus, beginning with Amerigo Vespucci, abandoned the nested spheres idea, at least as far as earth and water were concerned. When Medieval writers wrote about “the Earth” they almost always meant just the earthly sphere, minus the Ocean. After Columbus, “the Earth” would come to refer to the whole terraqueous globe.

waldseemuller

The Waldseeemüller map (1507) is one of the first to show the Old World and the New. Copernicus almost certainly saw a copy of the map. It spurred him to imagine that the Earthly globe – land and water – could revolve around its own axis, and – even more radically – might revolve around the sun.

Back to the future with Renaissance Man

1439-1471

The Renaissance walked backward into the future, with eyes fixed on the past, scorning the Middle Ages for Antiquity. The Renaissance was not the first or last epoch to be blinded by “the glory that was Greece and the grandeur that was Rome,” but the Renaissance, at the beginning of the modern age, caught a particularly bad case of nostalgia. This period is famous for recovering a sense of history. (Donald Brown argues that this has to do with Italians – and then urban Westerners in general – moving from a closed to an open class system; this in turn has to do with the decline of serfdom and the rise of cities in the West.) The Renaissance also coincided with the beginning of the modern scientific revolution. Not coincidentally, the pioneers of the scientific revolution, all the way up to Newton, considered that they were doing intellectual archaeology, recovering the Lost Wisdom of the Ancients.

vitruvian-man

Leonardo da Vinci – not quite a scientist, but equally fascinated by art and technology – is an early example, from the time when the Two Cultures were one. Lucio Russo, who argues that the Hellenistic age produced a Forgotten Revolution in science, puts it this way:

The oft-heard comment that Leonardo’s genius managed to transcend the culture of his time is amply justified. But his was not a science-fiction voyage into the future so much as a plunge into a distant past. Leonardo’s drawings often show objects that could not have been built in his time because the relevant technology did not exist. This is not due to a special genius for divining the future, but to the mundane fact that behind those drawings there were older drawings from a time when technology was far more advanced.

The forgotten revolution

257-132 BCE

103,049

Here’s where this number comes from: Take a sequence of symbols, (a b c d e f g h i j), say. Construct as many groups as you want by sticking parentheses around any two or more symbols or groups. For example, ((a b) c d (e (f g)) h i j). Or (a (b (c (d e f g) h) i) j). Or (a (b (c d e)) f g (h i j)). There are 103,049 ways of doing this with ten symbols, so 103,049 is the tenth Schröder number, named after the man who published this result in 1870. But it turns out that the same number is given in Plutarch – attributed to Hipparchus (190-120 BCE) – as the number of “affirmative compound propositions” that can be made from ten simple propositions. It is only in 1994 that somebody connected the dots, and realized that Schröder numbers had been discovered 2000 years before Schröder.

This is just one example of the very high level of mathematical, scientific, and technical accomplishment attained within the Hellenistic world — the world of Greek culture after Alexander. Lucio Russo calls Hellenistic science The Forgotten Revolution. A couple more examples from his book:

Everybody knows that Aristotle – and thus “the Greeks” – thought that heavy objects fall faster than light ones. Supposedly it took Galileo to prove him wrong. But in fact there is a clear statement in Lucretius (De Rerum Natura II:225-239) that objects of different weight fall at the same speed, unless air resistance kicks in; Russo argues that circumstantial evidence points to Hipparchus as the source.

Russo also argues that Hellenistic thinkers understood that gravity could account for the spherical shapes of the earth and planets, and that the balance between gravity and linear velocity could account for circular orbits. He shows that some strange passages in Vitruvius and Pliny about the sun making planets go around by shooting out triangular rays make sense if you assume the authors were looking at, but not understanding, vector diagrams of successive straight line motions bent into a circle by a centripetal thrust.

Russo argues that scientific progress largely came to an end by 150 BCE, and the Roman period saw an actual decline in scientific understanding. Later writers like Ptolemy and Galen, often taken to represent the height of Classical learning, were derivative, and didn’t really understand their predecessors: a stark reminder that a civilization may avoid collapse, and even maintain a decent level of prosperity, but regress intellectually.