# Book Review: To Explain the World

"To Explain the World" is a great book by Steven Weinberg. Every page goes down smooth, even the technical notes. Part of what makes it work is Weinberg's clear prose, granting an unobscured view into a mind well the equal of its words. Nothing is made obscure or complex, including technical ideas. It also helps that Weinberg has an appendeix of technical notes to illustrate what's going on, with plentiful figures. Another part is the multi-layered narrative. At a small scale, ideas are placed in the context of the lives of scientists, for whom Weinberg gives a mini-biographies. At a large scale, we progress through time from Ancient Greece, Hellenistic Greece, the Islamic Caliphates, the Renaissance and England on the eve of the Industrial Revolution. Finally, there's Weinberg's dry wit, which had me laughing throughout the book.

Weinberg takes a working scientist's approach to history, and judges the ideas of the past as we would the ideas of today: by how well they fit the data at the time, and how fine-tuned or ugly they are. He points out many failures and successes of the models, and compares them with each other. I don't think I could caught these without thoroughly studying the models. Heck, some of these errors went uncaught for ages. Like Aristotle's homocentric model of the celestial spheres, which predicted several planets crossed the sky multiple times a day. 

Weinberg also evaluates the contributions of some figures. Which, incidentally, is the sort of evaluation that Robin Hanson was describing in his proposal for predicting the long-term value of research by setting up prediction markets on the evaluations of far-future historians. 

Some of Weinberg's evaluations greatly differ from public and intellectual consensus . Like Descartes, Weinberg said contributed little of value to science and or the scientific method, though he did contribute to mathematics. Or the doctor of miracles, and noted futurist, Roger Bacon, who guessed at the possibility of many marvelous machines like automotives but did no significant science himself. Nor did his admittedly interesting ideas on how to do science have significant influence. 

These divergent evaluations on big figures sugest there might not be enough consensus on the value of past work to support prediction markets like Hanson describes. Even if you stipulate evaluation by relevant, like Weinberg's, it seems tricky to decide who're the relevant experts so far ahead of time. Many ancients would have thought that philosophers would be the experts on physics. 

Weinberg's historical stance means the focus of the book is on theory, data, and measurements. He does devote some time to how social conditions support and inhibit science, what philosophical stances one should take, the philosophical basis of science, what makes for a good theory and so on. But they're the minority of the book.  

Moreover, the book is mainly focused on *astronomy* and some physics. There is a little mention of mathematics, biology, medicine and chemistry. But again, it's in the minority. And the book focuses solelyon the West and the Middle-East, to the exclusion of all other research. The only exceptions I can think of some mentions of Arab scientists translating Hindu mathematics. 

And again, there is little in the book on the topic of how we came to develop concepts like the idea of laws of the universe, space and time, experimentation, accounting for errors etc. There is some. Weinberg talks about the debate on abolute vs relative space between Newton and Leibnitz. Or how we learnt the heavens are composed of the same stuff as the Earth through Galileo's observations. But it's not a thread that's developed throughout the book. Which is what I hoped for. 

So, while it isn't what I hoped for, "To Explain the World" is still a worth-while read. 

Some of what I learnt from the book: 
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First, Alexendria in Hellenistic times is where most of the scientific action happened, not Athens. Alexandria was home to a great many proto-scientists doing quantitative, where Athens was more focused on verbal ideas, if I recall correctly.

Second, the greatest discoveries of the ancient world happened in Alexandria. Aristarchus, or "The Mathematician" to his contemporaries, discovered figured out how to estimate the size of the sun and moon in terms of earth-radii from simple geometry, and observations of eclipses. He saw the sizes went: sun, earth, moon, in descending order and thought that since the sun was larger, the earth should be orbiting it, instead. Aristotle pointed out this implies the stars should move, which we don't observe, scuppering the idea for him. 

Third, the Mathematician, like all pre-moderns, didn't account for errors in his figures. He could've got robust lower bounds, but instead used faulty point-estimate observations as inputs to his rigorous geometric derivations. This lead to estimates that were off by many orders of magnitude. But he got the qualitative aspects right, which is what the Greeks mainly cared about. (Even Newton didn't know to care about errors.)

Fourth, Plato was a horrid influence on astronomy, inflicting on us his strange tastes in celestial. "Plato lay down the principle that the heavenly bodies' motion is circular, uniform, and constantly regular." Because of him, for about 2000 years astronomers were fixated on the idea of planets moving in circles. Why? A mix of authority, dogma, and perhaps aesthetics. Circles were the most perfect shape, and the heavens must be perfect. Observations didn't match the obvious way to do this (geocentrically). Plato proposed we figure out how to do so anyway. I think he was influenced by the mystical mathematics of the Pythagoreans, who viewed the heavens are moving in circles, with their velocities forming pleasing ratios. Eudoxus, Callopus and then Aristotle respectively developed and refined a hilariously bad, horribly bad, and bad model of rotating crystal spheres in which the sun, moon, planets and stars were set. This had a bunch of problems, like the variable brightness of the planets as they move in their orbits, a failure to explain the seasons and several celestial bodies going across the skies many more times than observed. Aristotle screwed up. (Though he did contribute to astronomy by giving a reason for stuff to fall towards the centre of a spherical Earth.)

For 2000 years after that, unfortunately, Plato's ideas formed the basis of both the main theories of cosmology in Europe and the Middle East. The other was, of course, the epicycle model.

Everyone agreed the epicycle model fit observation better, like accounting for retrograde motion, but there were flaws e.g. excessive variation of the distance to Mars and the Moon. But it was felt that this was "just a model" and didn't really explain the fundamental nature of the heavens. There were no crystal spheres to explain what kept the planets moving in circles, or what the heavens were composed of. I'm not even sure what to call this sort of reasoning.

Fifth, in spite of the above, there were those who actually attempted to improve the fit between theory and observation. The Alexandrians, Ptolemy in particular, refined the epicyclic model a great deal. He was perhaps the first to create a parametric model and vary the parameters to find the best fit to data. The Alexandrians got it to account for the motion of most of the planets, including various wobbles, but didn't quite manage to patch all the big-holes for unclear reasons. Tycho Brahe did. We'll get to him later.

Sixth, Astronomy was the closest we got to science for so long for several reasons: the motions of the planets are very regular over huge stretches of space and time, the motion of planets obeys simple laws, observations of the planets are not noisy, and predicting celestial motion was in demand for astrological, agricultural, chronological and way-finding purposes.  

Seventh, the Alexandrians were built different from the Athenians in a few ways: they were happy to keep religion out of research, they did not view knowledge for its own sake as far better than knowledge for practical ends, even commoners could become famous intellectuals, and they didn't focus on grand theories above piecemeal progress on specific phenomena. This let them make great strides in astronomy, optics, hydrostatics and more which were not matched until the 1600s. An example: Hero of Alexandria (perhaps the best name of a person in the book aside from 'Simplicius') argued that mirrors reflect light because light travels the shortest distance between two points in mediums of constant refractive index, echoing Hyugen's discovery of the principle of least time. Or Archimedes rudimentary methods of infinitesimals, used to calculate the volumes of simple 3d shapes. Archimedes was most proud of his proof that a sphere circumscribed within a cylinder occupies two thirds of its volume.

  
Eighth, religion was plausibly the downfall of Alexandrian science and of Islamic science. Christianity took over Rome, and provided a way to success for young, clever men apart from philosophy, medicine etc. Moreover, there was a sense that pagan science was a distraction from what truly mattered: religion. Finally, there were contradictions between scripture and pagan science. This surprised me. I expected this to be a modern phenomenon. But it not only happened in the Alexandrian world, it happened in the Islamic. In the 11th century, Al-Ghazzali would argue against reasoning about the world, not only because material causes limit God's power, but also because it is a distraction. Like wine, reason strengthens the mind but incites it to the wrong pursuits. This heralded the decline of the Islamic golden age of science.

Ninth, the Islamic golden age lasted from about the 7th century to the 13th, which was when the Abbasid caliphate fell, though the decline began about the 11th. They made numerous advances in astronomy, medicine and optics, though the impression I got was they didn't significantly surpass the Alexandrians.

Tenth, after that, the flame of science moved Westwards. Funnily enough, religious institutions contributed to kick-starting things by funding schools, translations of Arabic and Greek works etc.

Eleventh, Galileo was one of the true greats in the history of science. His invention of the telescope, discovery and measurements of craters and mountains on the moon, proof of change in the outer heavens by observation of supernovae, and analysis of how objects fall under gravity all represented major breakthroughs. He was also a bit of a hot-head, and wrote a dialogue with a character called Simplicus who was portrayed as a moron. And who happened to repeat views somewhat similar to that of the Popes, conveyed to Galileo in private conversations where the Pope tried to smooth out Galileo's snafoos with the Inquisition, some of which Galileo hid. Needless to say, the Pope wasn't pleased.

Twelfth, Tycho Brahe compiled a huge amount of high quality observations and used them to make a geocentric epicycle model which was better fit for observation than Copernicus' Heliocentric model. Of course, you could swap between the models via a shift in perspective, but this wasn't understood at the time. So Brahe's better model was viewed as a reason to discount Copernicus' model.

Thirteenth, Kepler made better observations yet and used them to grind out his laws. Which, incidentally, overturned the Copernican model that assumed celestial orbits were circular.  

There were more things I learnt, but the minute-hand of my clock is too close to midnight to allow me to convey them.