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Posts Tagged ‘Copernicus’

Moon Observer's Guide by Peter GregoPhilip’s Moon Observer’s Guide, Peter Grego (Philip’s 2015)

If you ask someone to name the most important inventions in history, two will often be overlooked: the microscope and the telescope. You could say that one lowered the floor of the universe and the other raised the ceiling: we suddenly became aware of wonders that had previously been too small or too far away for us to see.

Practically speaking, the microscope might seem by far the more important, because it’s taught us so much about life on earth, not least our own. But the continued existence of humanity may actually depend on the telescope. Geologists have discovered that the earth has repeatedly been struck by asteroids; astronomers may be able to spot the next one before it hits. Otherwise we may follow the dinosaurs, trilobites, eurypterids and countless other once-flourishing groups into extinction.

If you want to see what asteroids and other large rocks can do to a celestial body, Mother Nature has kindly provided us with a giant memento mori: the Moon. The biggest scars there are visible with the naked eye, but it took the telescope to reveal quite what they looked like and quite how pock-marked the lunar surface is. As Peter Grego writes:

All the Moon’s ringed basins, ‘walled plains’ and the overwhelming majority of craters visible through the telescope were formed by asteroidal impact. […] Copernicus was blasted out of the lunar crust about 800 million years ago by an asteroid measuring up to 10 km across. The 29 km diameter crater Kepler, 500 km to the west of Copernicus, was formed at around the same time. (“Lunar geology and the Moon’s features”, pp. 13-4)

Grego knows a lot about the Moon and this book is the fruit of more than thirty years of selenoscopy, dating back to his first “systematic observations” in 1982:

Since that time, through patient observing and recording, the lunar landscape has become to me a broadly familiar place, yet always full of wonder. Today only a sliver of moon is visible, and the eastern lunar seas and their surrounding craters provide a visual delight until the Moon sinks into the haze above the city and its image dims, shimmers and degrades. (pg. 5)

The city was Birmingham back in 2002. Cities aren’t just noisy, dirty and harmful to wildlife. They also deprive us of one of the greatest sights in nature: the night sky. Light pollution is silent, tasteless and physically harmless, but it deserves much more attention from conservationists. The Moon can be big enough and bright enough not to be wholly drowned by it, but it’s lèse-majesté against the Queen of the Night all the same.

It also makes life much harder for amateur astronomers. Then again, perhaps that increases the rewards. And the Moon isn’t confined to the night sky, of course: you can observe it in full daylight using nothing more than binoculars. Serious observation demands a telescope, however, and Grego devotes a full section to what’s available. Inter alia, he himself has a “150mm f/8 achromatic refractor with digital camcorder setup with a zoom eyepiece for afocal video photography” (ch. 5, “Recording Your Observations”, pg. 144). Digital imaging and enhancement are now routine: modern technology can get “startling results from a seemingly mediocre video sequence” (pg. 146), sharpening and focusing blurred images.

But Grego and his fellow selenographers are still doing what Galileo, Thomas Harriot and other early astronomers did centuries ago: drawing and sketching the Moon. There’s a good practical reason to do this, as recent science-news has confirmed: “drawing pictures of information that needs to be remembered is a strong and reliable strategy to enhance memory”. There is a lot of detail to learn on the Moon. It’s a fractal place: there are craters at every scale, from the microscopic to hundreds-of-kilometres wide and “it is estimated that the Moon’s surface is studded with more than 3 trillion (3,000,000,000,000) craters larger than a metre in diameter” (pg. 9).

So learning your way around the Moon is a fractal process: first you learn to recognize the giant features, like Copernicus, Kepler and the maria (seas), montes (mountains) and valles (valleys), then you begin to fill in the gaps, then the gaps between the gaps, then the gaps between those. Grego supplies maps and commentary to help you on your way:

The polygonal crater Timaeus (33 km) perches on W. Bond’s south-western wall and surveys across the plains of Mare Frigoris across to the Montes Alpes, 175 km to the south. Archytas (32 km) and Protagoras (21) are two sharp-rimmed but somewhat misshapen craters whose dark shadow-filled eyes keep watch over the northern approaches of Mare Frigoris. (ch. 4, “Moonwatching”, Day seven, pg. 87)

He’s never finished learning about the Moon, however, and neither will anyone else. It’s a life-long adventure and although the Moon might seem cold and unchanging, at least over a human life-span, there are rare events called TLP, or “Transient Lunar Phenomena”, to look out for. These are “apparent obscurations, glows or flashes on the Moon’s surface” that don’t have definitive explanations. Are rocks collapsing? Is sublunar gas leaking out? Might there even be life there after all?

Life is highly doubtful, but Grego notes that “lunar topography is virtually neglected by professional astronomers” (pg. 6), so amateurs still have the chance to make important discoveries. This book might help someone to do that, but the rewards of selenoscopy don’t depend on advancing science or using clever technology. Grego opens the book by asking “Why Observe the Moon?”, then quotes an excellent answer to that question from the French astronomer Camille Flammarion and his book Astronomy for Amateurs (1903). What Flammarion said more than a century ago is still true today:

From all time the Moon has had the privilege of charming the gaze, and attracting the particular attention of mortals. What thoughts have not risen to her pale, yet luminous disk? Orb of mystery and of solitude, brooding over our silent nights, this celestial luminary is at once sad and splendid in her glacial purity, and her limpid rays provoke a reverie full of charm and melancholy. (“Why Observe the Moon?”, pg. 4)

In fact, you could say that the Moon is a touchstone of human nature. Chimpanzees and gorillas may be almost identical to us in their genes, but they don’t talk, make art or gaze at the Moon in wonder. We still do and although we don’t usually worship the Moon any more, we may owe it our very existence. How important have the tides been in the evolution of life on earth? They provided a zone of transition for the emergence of plants and animals from the sea, and perhaps a Moon-less Earth would also be a Man-less Earth.

But the Earth could have Moon without Man if it’s struck by an asteroid of sufficient size. The scars on the Moon’s surface should be constant reminders of the vigilance that’s necessary and the technology that we still need to develop. But the Moon is memento mori in more ways than one. Asteroid strikes are pinpricks by comparison with what may have happened to the Earth in the remote past:

Now widely accepted to be the most likely origin of the Moon is the giant impact or ‘big splash’ theory. This theory suggests that a Mars-sized planet (around half the size of the Earth) smashed into the young Earth, disintegrating the impactor and the Earth’s mantle at the site of impact. A cloud of debris was splashed into near-Earth orbit, and the outer rings of this temporary ring of material coalesced to form the Moon. (ch. 1, pg. 21)

As Sir Arthur Conan Doyle’s great character Professor Challenger pointed out in 1913: there are “many reasons why we should watch with a very close and interested attention every indication of change in those cosmic surroundings upon which our own ultimate fate may depend”. The Moon should frighten as well as awe and enchant us, or we might not survive to be awed and enchanted. This book will help you understand all these aspects of the Queen of the Night.

I also hope that Grego will write a sequel to it one day: Moon Tourist’s Guide. We’re still on schedule for at least some of the future envisaged by Arthur C. Clarke in his novel A Fall of Moondust (1961), which was set in the mid-twenty-first century. A moon-cruiser called Selene may not be sailing in a basin of dust as “fine as talcum-powder” by then, but there may still be lunar tourism. If so, selenographers like Peter Grego will be able to see close-up what they’ve long surveyed from afar.

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Infinitesimal by Alexander AmirInfinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World, Amir Alexander (Oneworld 2014)

Infinitesimal is an entertaining read on a fascinating topic: the pioneers of a new form of mathematics and those who opposed them. Amir Alexander claims that “the ultimate victory of the infinitely small helped open the way to a new and dynamic science, to religious toleration, and to political freedoms unknown in human history” (Introduction, pg. 14).

It’s an extraordinary claim and I don’t think he manages to provide extraordinary proof for it. In fact, he probably gets cause-and-effect reversed. Is it likelier that new mathematics opened minds, dynamized science and transformed politics or that open minds created new forms of mathematics, science and politics? I’d suggest that support for the new mathematics was a symptom, not a cause, of a new psychology. But Alexander makes a good case for his thesis and there is no doubt that the world was changed by the willingness of mathematicians to use infinitesimals. Calculus was one result, after all. The book begins in Italy and ends in England, because the pioneers lost in Italy:

For nearly two centuries, Italy had been home to perhaps the liveliest mathematical community in Europe. … But when the Jesuits triumphed over the advocates of the infinitely small, this brilliant tradition died a quick death. With Angeli silenced, and Viviani and Ricci keeping their mathematical views to themselves, there was no mathematician left in Italy to carry on the torch. The Jesuits, now in charge, insisted on adhering close to the methods of antiquity, so that the leadership in mathematical innovation now shifted decisively, moving beyond the Alps, to Germany, England, France and Switzerland. (ch. 5, “The Battle of the Mathematicians”, pg. 178)

Why were the Jesuits involved in an esoteric mathematical dispute? You might say that de minimis curat Loyola – Ignatius Loyola (1491-1556), founder of the Jesuits, cared about anything, no matter how small, that might undermine the authority of the Church. In the view of his successors, the doctrine of indivisibles did precisely that: “in its simplest form, the doctrine states that every line is composed of a string of points, or ‘indivisibles’, which are the line’s building blocks, and which cannot themselves be divided” (Introduction, pg. 9).

Indivisibles must be infinitesimally small, or they wouldn’t be indivisible, but then how does an infinitesimal point differ from nothing at all? And if it isn’t nothing, why can’t it be divided? These paradoxes were familiar to the ancient Greeks, which is why they rejected infinitesimals and laid the foundations of mathematics on what seemed to them to be solider ground. In the fourth century before Christ, Euclid used axioms and rigorous logic to create a mathematical temple for the ages. He proved things about infinity, like the inexhaustibility of the primes, but he didn’t use infinitesimals. When Archimedes broke with Greek tradition and used infinitesimals to make new discoveries, “he went back and proved every one of them by conventional geometrical means, avoiding any use of the infinitely small” (Introduction, pg. 11).

So even Archimedes regarded them as dubious. Aristotle rejected them altogether and Aristotle became the most important pre-Christian influence on Thomas Aquinas and Catholic philosophy. Accordingly, when mathematicians began to look at infinitesimals again, the strictest Catholics opposed the new development. Revolutionaries like Galileo were opposed by reactionaries like Urban VIII.

But the story is complicated: Urban had been friendly to Galileo until “the publication of Galileo’s Dialogue on the Copernican system and some unfavourable political developments” (pg. 301). So I don’t think the mathematics was driving events in the way that Alexander suggests. Copernicus didn’t use them and the implications of his heliocentrism were much more obvious to many more people than the implications of infinitesimals could ever have been. That’s why Copernicus was frightened of publishing his ideas and why Galileo faced the Inquisition for his astronomy, not his mathematics.

But Amir’s thesis makes an even more interesting story: the tiniest possible things had the largest possible consequences, creating a new world of science, politics and art. In Italy, two of the chief antagonists were Galileo and Urban; in England, two were the mathematician John Wallis (1616-1703) and the philosopher Thomas Hobbes (1588-1679). Alexander discusses Wallis and Hobbes in Part II of the book, “Leviathan and the Infinitesimal”. Hobbes thought that de minimis curat rex – “the king cares about tiny things”. Unless authority was absolute and the foundations of knowledge certain, life would be “nasty, brutish and short”.

However, there was a big problem with his reasoning: he thought he’d achieved certainty when he hadn’t. Hobbes repeatedly claimed to have solved the ancient problem of the “quadrature of the circle” – that is, creating a square equal in size to a given circle using only a compass and an unmarked ruler. Wallis demolished his claims, made Hobbes look foolish, and strengthened the case for religious toleration and political freedom. But I don’t think this new liberalism depended on new mathematics. Instead, both were products of a new psychology. Genetics will shed more light on the Jesuits and their opponents than polemics and geometry textbooks from the period. Alexander’s theory is fun but flawed.

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Discovering the UniverseDiscovering the Universe: The Story of Astronomy, Paul Murdin (Andre Deutsch 2014)

First published in 2011 as Mapping the Universe, this is a well-written, well-illustrated history of astronomy that begins in the Stone Age and ends with the Hubble Space Telescope and Large Hadron Collider. The photographs will stimulate your eyes as the text stimulates your mind. The universe is a big place and big things happen there, like gamma-ray bursts (GRBs):

Until 1997, astronomers didn’t know whether GRBs originated in some sort of explosions on the edge of our solar system, around our Galaxy, or far away. Two examples proved that the explosions occur the edge of the observable Universe. For their duration of a few seconds, the bursts had been over a million times brighter than their parent galaxy, the biggest bangs since the Big Bang. (ch. 17, “Exploding Stars”, pg. 87)

Ptolemy, Galileo and Newton would all be astonished by the technology that allows modern astronomers to study phenomena like gamma-ray bursts, but one thing has remained constant: the importance of mathematics and measurement in studying the sky. The story of astronomy is not just about seeing further and clearer, but also of measuring better and mathematizing more powerfully. Ptolemy’s geocentric universe entailed the arbitrary complexity of epicycles on epicycles, to explain how the planets sometimes seemed to move backwards against the stars. Then Copernicus resurrected the ancient Greek hypothesis of a heliocentric universe.

Back cover

Back cover


Planetary retrogression became easier to explain. Other hypotheses, like the steady state universe and Kepler’s planetary Platonic solids, haven’t proved successful, but data don’t explain themselves and astronomers have to be adventurous in mind, if not usually in body. This book contains the big names, the big sights and the big mysteries that are still awaiting explanation. More big names, sights and mysteries are on their way.

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