Showing posts with label mathematics. Show all posts
Showing posts with label mathematics. Show all posts

Tuesday, November 20, 2018

The Ascent of Jacob Bronowski


I just finished reading a pre-publication copy of Timothy Sandefur’s upcoming The Ascent of Jacob Bronowski. If even I, a reader of many popular science books, have barely heard of Jacob Bronowski, you can bet that most people have forgotten him. But before there was Neil DeGrasse Tyson, before Stephen Jay Gould, before Carl Sagan, there was Jacob Bronowski (1908-1974) whose passion was to open up the minds of non-scientists to the power and beauty of science.


Bronowski’s work was based on a fundamental assertion of faith that I share, but which I sometimes question. It is that most people are smart enough to understand science, at least in its basic outlines, and smart enough to use the scientific mode of thought. This is the basis of my book, to be released in December, ScientificallyThinking. Bronowski’s gospel was to get scientists to speak clearly and simply to non-scientists and open their eyes to science. I believe that most people are smart enough to do this, but relatively few people really want to. Most people would rather sit in their backwater of ignorance and listen only to things that reinforce their lazy prejudices.

Bronowski (known to his friends as Bruno) was the perfect example of a Renaissance Man, that is, someone who is interested in everything. I first learned this term back about 1977 when a friend called me a Renaissance Man. I was a biology major who wrote novels, wrote orchestra music, and studied history and languages. Perhaps only a Renaissance Man (or woman) can make the connections necessary to bring people from all different modes of thought together. This was certainly Bronowski. An English child of eastern European immigrants, he started off as a poet. But he was also interested in mathematics, which led to statistics. (Statistics differs from pure mathematics because pure math deals with the certainties of deduction, while statistics tries to understand the messy reality of the world through induction. At least, that’s my summary of it.) His mathematical expertise got him involved in the effort for the Allies to win World War II, and later to make industrial production more efficient.

This mathematical work did not always lead Bronowski where he might have expected. Yes, he helped the Allies win World War II, but like many other scientists he was deeply disturbed by the effects of atomic bombs. He traveled in Japan after the bombs, and knew that the new power we had unleashed from the atom was completely disproportionate to any legitimate military goals even the best of countries might have. Also, his dedication to industrial efficiency led him on the ultimately quixotic quest to produce Bronowski Bricks from coal dust, sort of a fossil fuel version of charcoal briquets. The briquets reduced coal waste, to be sure, but they were very expensive to produce, and, according to Prince Philip, they looked like turds.

But Bruno’s wide knowledge, and being at the right place at the right time, threw him into the public spotlight in radio and television broadcasting. He produced, one after another, important science documentaries, culminating in his still-famous The Ascent of Man. He dabbled in lots of things at which he was not really skilled, such as writing a light opera libretto that was not very good (the music was by Peter Racine Fricker, who was on the music faculty when I entered the University of California at Santa Barbara). But he tried!

Science and art, said Bronowski, were both creative. Take, for example, Copernicus, who did some of the earliest work that proved the sun to be the center of the solar system, rather than Earth being the center of the universe. Copernicus had to imagine what the planets would do if he were at a central solar vantage point, but as an artist has to imagine what the final work would look like. Both scientists and artists test concepts: scientists, how well the concept explains the natural world, and poets, how well the poem expands our experience.

Another idea he had was that animals need intelligence in order to have free will. You have to be able to visualize possible futures before you can choose among them. Only humans can do this. I do not know if Bronowski actually solved the problem of free will, but he clarified it, at least for non-philosophers like me. He helped lay the foundation for the study of language acquisition. He said that only humans can make a sentence out of separate words, and then isolate one word and generalize about that one concept.

When he helped to start the Salk Institute, Bronowski moved to La Jolla, California. He would host scholars for discussions in his living room (where he also filed the final episode of Ascent). He was an inspiring partner for dialogue. While he knew everything about everything, he could make you feel brilliant even when he was saying you were wrong, according to more than one of his acquaintances.

Jacob Bronowski inspired us to think big, to see all human thought as a single fabric rather than as a collage of specialties. And he was an early inspiration for what we now call citizen science. They didn’t have the internet back then, but on his televised shows he encouraged viewers to send in postcards with their own scientific thoughts on them.

You can get a taste for the kind of spellbinding quality Bruno had by seeing this short YouTube clip from one of the Ascent episodes. Apparently when the BBC was filming this segment, they did not expect Bruno to walk out into the pond; this was extemporized.

I have a lot of different kinds of creative and intellectual output. I am not equally good at all of them, and am not world-class at any of them, as far as I can tell. But I can still do a lot of good with them. Bruno is my guiding light in this respect.

Friday, April 20, 2018

Hypatia, You Are Not Forgotten


The movie Agora, starring Rachel Weisz, is one of the few fictional movies ever to be reviewed in Science magazine. I have now seen it three times and have come to understand it. It is one of the few essential movies that you need to see to understand the meaning of science in the human mind. You’d better see it at least once.



Hypatia of Alexandria (Egypt), in the fourth century of the Christian Era, was a philosopher and teacher. She accepted students of diverse faiths, including a Roman pagan and a Christian. She taught them that if two things are equal to a third, then all are equal, and she insisted that this applies to herself and to her students: she the (we would say today) atheist, and her pagan and Christian students, were all equal.

Hypatia’s faith was different from those of any of her students. They believed that truths were revealed by one or more gods, while she believed that the highest pursuit of the human spirit was to understand the universe itself, to decipher what it is telling us. In particular, she wanted to understand why the planets did not move in a perfect circle around the Earth. Ptolemy had said that the planets and sun traced their own little circles as they orbited the Earth, but this seemed whimsical: if the universe is perfect, why should these little epicycles be necessary? Then she found out that the philosopher Aristarchus, centuries previously, had suggested that the planets, including Earth, went around the sun. But if the universe was built on perfect circles, then the Earth must describe a perfect circle around the sun, which it does not: sometimes the sun was smaller (more distant) and dimmer than at other times. Then she figured out that the Earth travels in an ellipse around the sun. After she died, and her writings were lost, it took another 1,200 years until Johannes Kepler rediscovered this truth. To Hypatia, the universe had to have mathematical perfection, and it was our job to understand it. This remains the fundamental belief of scientists, although we now recognize that a great deal of historical contingency, what we might call messiness (for example, the Big Bang created globs of galaxies, not perfectly spaced ones) that Hypatia might have found unacceptable.



Alexandria was going through successive waves of turmoil all during this time. Unlike Hypatia and her students, the adherents of religions all hated each other. The Egyptian pagans attacked the Christians, then the Christians attacked the Egyptians and destroyed the library of Alexandria, the most famous condensation of knowledge in all of history, gleefully rejoicing in the burning of scientific books. Then the Christians turned on the Jews. The Romans couldn’t do much; they were the nominal rulers, but the Empire was in decline and the Roman soldiers couldn’t do much. Hypatia’s Roman student became the Consul of Alexandria, and he very publicly loved Hypatia. Her Christian student became a famous bishop. They tried to keep violence from getting out of hand, but the majority of Christians did not listen to the peaceful bishop; instead they followed the radicals who called upon Christians, in the name of Jesus, to stone to death everyone who did not agree with them, and this eventually included Hypatia. The charges leveled against Hypatia were that Scripture forbade a woman to teach in public. They should just stay home and, if they should happen to venture out in public, keep their damned mouths shut. Hypatia spoke in public and was a scholar. This was plenty of reason for the Christians to push her to the altar, strip her, stone her, and drag her mutilated body through the streets. A young Christian man, who had been Hypatia’s slave but whom she liberated even though he sexually assaulted her, tried to save her, but not very hard.



In this image, Hypatia tries to save scrolls from the Library of Alexandria as it is being pillaged and burnt.

All of the religions that were concentrated together in Alexandria were guilty of killing people of other religions. But in Alexandria during Hypatia’s time, it was clearly the Christians who carried out the most and the worst violence, and who eventually became the leaders of the western world. The leaders of this violence became saints, such as Saint Cyril.

Hypatia was troubled by the fact that the events on the Earth were so messy and random, while all around the Earth, the heavens were perfect, though in an elliptical rather than a circular way. The recurring imagery of the movie is the ellipse—such as the circular opening in the library vault, seen from the side—and a view of Earth from outer space, focusing down onto Alexandria, and then receding again into the indifferent stars.

Today, most of the American opponents of scientific truth are evangelical Christians, and they are closer to using violence against scientists than we usually think. American evangelical Christians do not even want to question whether the proclamations of their preachers and of Donald Trump are consistent with the Bible, much less with scientific and historical truth. At other times and in other places, there are other enemies of truth: Stalin killed geneticists, and Islamic terrorists don’t want anybody to disagree with them about anything. But for me, here in America and now, it is the evangelical Christians whom I consider the most dangerous, just as they were to Hypatia of Alexandria. The violent Christians (that is, most of them) set science back a millennium. Many of them appear to want to do so again.

Whether the tragedy of Hypatia is repeated again, or not, we should not forget her or the power of a woman’s mind.

Friday, September 23, 2011

Are We the Inevitable Products of Mathematical Equations?

I have just finished reading Martin Nowak’s Super Cooperators, a book written with Roger Highfield. Nowak is a biomathematician at Harvard. He has spent a career designing mathematical models that demonstrate the conditions under which altruism can evolve. Altruism is when one animal is nice to another animal of the same species.

Nowak’s view of the world resonates with my spirit. He sees the natural world as full of cooperation. Cooperation is at least as important as the “survival of the fittest,” which Darwinism is often portrayed to be. I find his viewpoint inspiring just like the viewpoint of Lynn Margulis (whom Nowak hardly mentions). The fact that Nowak is a fellow devotee of the music of Gustav Mahler doesn’t hurt any either.

And some important results have emerged from Nowak’s mathematical models. I cannot summarize all of them, but one that I remember is the following. In simple, direct interactions, when a cooperator and a defector come in contact, the defector always wins. That is, the cooperator becomes a sucker for offering help that is not reciprocated. In large populations in which all the animals are equally likely to come in contact, altruism doesn’t have a chance. But in populations in which small groups can form, where animals can choose their friends, so to speak, altruistic groups can emerge. And when they do, they can beat out the pathetic defectors every time, at least temporarily. This is particularly the case in animal societies where the animals know the reputations of other animals, which is something they can do within small groups. This is, in fact, probably the most important way in which altruism evolved. It is an example of multi-level selection: selection among groups within a larger population.

However, in one sense, I consider Nowak’s work to be unrealistic. He begins the book by expressing his feeling that all of truth can be expressed precisely by mathematics. Toward the end of the book, he claims that his equations would be true anywhere in the universe. He admits that his conclusions are not too different from beliefs, such as the Golden Rule, found in traditional religions. But he still thinks he has made a monumental universal discovery. “Now, for the first time, aspects of these powerful ideas [from religion] have been quantified in experiments, captured in equations, and enshrined in science.” He seems to mean that ideas such as the Golden Rule are really true for the first time in the history of the universe as a result of his mathematical simulations.

Nowak’s mathematical approach is unrealistic because it omits all historical contingency. In Nowak’s models, animals are cooperators or defectors for logical reasons. So maybe his equations would work reliably on the planet Vulcan. But they cannot be relied upon for human behavior. The equations mirror many, but not all, aspects of human behavior. The primary historical contingency is religion. The memes of religion have parasitized the human mind to such an extent that, throughout human history, many people have considered it a religious duty, absent any benefit, and more important than life itself, to bring death and destruction to others. Nowak’s models do not include the thirst for evil that is so common in human motivation, in which loss is reward because it ensures eternal life in a heaven.