Gerald Rottman: The Geometry of Light: Galileo’s Telescope, Kepler’s Optics

Guest Review by Kit Bradley

The United Nations and the International Astronomical Union have declared 2009 to be the International Year of Astronomy, commemorating the 400th anniversary of Galileo’s use of a telescope to study the skies, and Kepler’s publication of Astronomia Nova. Through my membership in the Eugene Astronomical Society, I learned of a book self-published by Gerald Rottman, The Geometry of Light: Galileo’s Telescope, Kepler’s Optics, and I ordered a copy. This is a good year to learn about optics as Galileo and Kepler understood it in 1609.


Kepler published his work on optics in a short book titled Dioptrice. Rottman’s book presents the ideas in Dioptrice in a form accessable to us today. He explains refraction, convex lenses, concave lenses, what happens as we look through a lens, and how to put it together to make a telescope that magnifies objects.

Early on, Rottman recommends we read the Appendices first if we’re rusty on high school geometry. I am, and I did. I appreciate his including the math refresher.

It is interesting tracing rays of light through a lens and understanding the refraction that occurs. This all made sense to me until I got to the section that explains what happens when your eye is in the picture. Now you have to deal with the aperture of the eye (pupil), an internal lens, and focusing on the retina. I read one paragraph three or four times, gave up, and read the rest of the chapter. At the end of the chapter Rottman tells us to pick up any lens we have lying around (huh? oh yes, a magnifying glass), and he has us prove to ourselves that things work as he described. I went back to that paragraph, and this time it made sense!

We’re now ready to learn how to put two lenses together to make a telescope. It’s straightforward to understand how to magnify objects, but keeping the objects in focus requires more thought (at least for me). Galileo used a convex lens for the objective (the star end of the telescope) and a concave lens for the ocular (the eye end of the telescope). This works pretty well, but it has a very narrow field of view, that is, you see only a tiny section of the sky through the telescope. Kepler came up with a better design that uses convex lenses at both ends and has a much wider field of view. But it turns the images upside down (which is not much of a problem when looking at things up in space).

I went to a local star party last night, right after I finished reading this book, and coincidentally someone brought his homemade Galilean telescope. It was not much more than a cardboard tube and two lenses he had lying around. And indeed, the field of view was tiny – we could see only about half of the moon at a time through the telescope. And the edges were sometimes colorful (more on that in a moment).

Today I came across an International Year of Astronomy project that is producing an educational and very low cost “Galileoscope,” which can be configured for either the Galileo design or the Kepler design. Only $15 plus shipping! I ordered one (www.galileoscope.org).

I had to read The Geometry of Light very carefully to learn what was there for me to learn, and I’m glad I did. Rottman achieved his goal of explaining Kepler’s understanding of optics. Perhaps beyond the scope of this goal, however, there are three additional areas I would have liked to see discussed.

First, I wondered the whole time I was reading how things have changed since Kepler’s time. Is the information in the book still relevant today? Rottman partially answers this in the last section of the last chapter, where he shows the difference between Kepler’s approximation and the math used today to calculate the angle of refraction. They’re close.

Second, I wondered if Kepler had any understanding of chromatic aberration, in which a simple lens acts like a prism and refracts the different colors contained in white light by different amounts, which results in extraneous colors around the edges of objects. This wasn’t discussed in the book.

Third, I wondered if Galileo and Kepler understood the importance of the size of the objective lens for gathering light—the bigger the lens, the more light gathered, and the better the image. This wasn’t discussed in the book.

Given the limited mathematics of the day and the limited technologies for forming clear glass and grinding it smoothly, these three topics might have been beyond Kepler’s capabilities to address.

I had fun mastering this little book, and it will lead me into more explorations. It’s available from Gerald Rottman at his web site, www.thegeometryoflight.com.

Professor S. James Gates, Jr: Superstring Theory: The DNA of Reality

Guest Review by Kit Bradley
March 2, 2009

I recently finished an astronomy course that re-ignited my interest in physics, and so I decided to learn about something that wasn’t taught in physics way back when I was in college – string theory. I went to The Teaching Company and ordered their course Superstring Theory: The DNA of Reality, by Professor James Gates. The course contains 24 half hour lectures on DVDs.

Einstein’s general theory of relativity does a pretty good job of explaining what we see on a macro astronomical scale. And quantum physics explains what we see and deduce in the smallest micro scales. But apparently these two theories are incompatible, at least mathematically. The proponents of string theory claim it unifies these two theories, finally achieving what Einstein spent the second half of his life trying to do.

One of the first things Professor Gates tells us is that string theory is a very complex mathematical construction, and that nothing in string theory has been proven in experimental physics. It’s just math and theory! He then makes the commitment to teach this course about string theory without resorting to complex math and equations. But if it’s all mathematics, what’s left to teach? Professor Gates intends that his various graphics and animations will make things clear to us non-mathematicians and non-physicists.

The course starts with an overview of the quantum world and the “denizens” that inhabit it. We learn about a lot of subatomic particles that are smaller than the more familiar electrons, neutrons, and protons in atoms – like quarks and leptons and photons and gravitons and many more. All the particles have corresponding anti-particles. And later in the course all the particles are paired with superpartners.

Until the superpartners came up, I enjoyed getting to know all these particles, most of which can be seen or deduced in lab experiments, so they seem real, even if rather small – around 10^-16 meters. But then we learn that the strings that underlie these particles (visualized as little vibrating loops or wiggly strings) are only 10^-33 or so meters. I would be okay with strings that are a few orders of magnitude smaller than quarks, but not 17 orders of magnitude. Surely there must be something in between!

The course now proceeds through a detailed history of the development of the initial string theory in 1968, and on to the first, second, and third string revolutions, where the older theories are updated with newer mathematics that solve various problems, which ultimately leads us to M-theory. (M could well stand for Magic.) And we learn many new names along the way – superstrings, supersymmetry, supergravity, and much, much more.

One of the unsettling facts about this sequence of string theories is that the mathematics only works well when it describes many more than the four dimensions in our universe (three in space and one time). Eventually we get down to ten dimensions. That was in 2005. I suspect string theory has evolved since then.

My major learning from this course is that string theory is extremely complicated. Professor Gates describes a few dozen particles, the contributions of a few dozen physicists with their few dozen theories, accompanied with zero lab-proven results. As he says repeatedly, this is mathematics, not physics. Physics requires both theory and experimental validation.

I now know a few more terms and a little about a few particles, but I’m a long way from understanding string theory. I believe that a lot more of this material will stick if I listen to the lectures a second time. But first I’m going to read a book that both Professor Gates and my daughter (a physics major) recommend to me, The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory, by Brian Greene. But it doesn’t look like an easy read either.

Ellen Morris Bishop: In Search of Ancient Oregon

Guest Review by Kit Bradley
October 6, 2008

The last book I reviewed was Oregon’s Greatest Natural Disasters, which, if you think about it for a moment, is a geology book. So it is not surprising that I would be attracted to Ellen Morris Bishop’s In Search of Ancient Oregon: A Geological and Natural History, which is a much more detailed geology book, but still targeted at the interested layman.

I came upon this book in an unusual way. I was swimming in a pool with my mother-in-law in an adult trailer park, when I looked out the window and saw the local library bookmobile drive up. I dried off, got dressed, and went to see what they had. Almost immediately I picked up In Search of Ancient Oregon, and the pictures fascinated me. Every geological formation or event was illustrated with a picture of a place in Oregon. (The author took all of the pictures.) It is fascinating that many of the pictures are of places I have seen in my travels, and the rest I could easily see if I made the effort. This ability to see with my own eyes the evidence of the many geologic events that formed today’s Oregon is captivating.

So I went home and bought the book from Amazon. And a couple weeks later I met Ellen Bishop at a lecture and got a belated autograph.

In Search of Ancient Oregon has a chapter for each of the major geologic eras and epochs from about 400 million years ago through to today. A lot happens in ten million years, and a lot disappears in ten million years. It is very interesting to read how geologists follow the most obscure and unlikely of clues to reconstruct the history behind the terrains and rocks we can all see. And it’s all far more complicated than anything I can summarize here.

The oldest rocks in Oregon are limestone created during the Devonian epoch, roughly 400 million years ago, but the rocks weren’t in Oregon at the time. It’s a story of plate tectonics. Subduction zones in the middle of what is now the Pacific Ocean created arcs of volcanic islands (like the Hawaiian islands). In the course of a lot of time the Pacific plate containing these islands moved eastward and eventually ran into the North American plate. The ensuing subduction scraped off random sections that ended up as “exotic terranes,” large masses of rock that have no relationship to the land surrounding them. These 400 million year old rocks are found today in the Blue Mountains in northeastern Oregon.

There is a lot to be learned from fossils, and each chapter of Ancient Oregon includes a section on the flora and fauna of the period. The climate impacts the flora and fauna, and thus the fossils tell a lot about the climate. But something happened 248 million years ago that killed 96% of all living species—the Permian extinction that ended the Paleozoic era.

We now enter the Mesozoic era, the time of the dinosaurs. The island volcanoes were still active and were starting to drift into the Oregon coast, and by 100 million years ago Oregon was firmly joined with the Blue Mountain island arc. The formations we see today are varied and jumbled, and many of the early volcanic rocks are not on mountaintops, but are buried and only visible where exposed, as in Hells Canyon.

This was the era of dinosaurs, but apparently none lived in Oregon. One duck-billed dinosaur was found in southern Oregon, but it turns out it was a migrant from California (the first of many Californians to come)—when the bedrock containing its remains faulted and drifted into Oregon. The Mesozoic era ended abruptly 65 million years ago when a meteor (probably) caused the extinction of 70% of all species, including the dinosaurs.

Now comes the Cenozoic era, where the mammals we know today appeared. Oregon’s first “native” volcanoes erupted and grew around 50 million years ago. Around 30 million years ago the first grasses appeared. (Who would guess grass wasn’t part of the originally evolved flora?) And this enabled early horses to evolve from brush eaters to grazers, and to live in herds on open prairies.

15 million years ago, eastern Oregon sat over a hot spot in the earth’s mantle (which today is under Yellowstone National Park), and this caused extensive basaltic lava flows that covered a vast area of Oregon, reaching all the way to the Pacific Ocean. And over the next 10 million years much more volcanic activity and faulting and moving of plates occurred, forming the Oregon of today.

Finally 1.8 million years ago we entered the great Ice Age, and this is also when the high Cascade volcanoes we can see today were formed. This was a time of battle in Oregon—between the volcano building forces and the glaciers’ destructive forces. Only a few volcanoes (like Mt Hood and the South Sister) won—by erupting again after the last glaciers receded.

It has been hard to summarize this 288-page book, since there are so many interesting and complex events that formed today’s Oregon. I apologize to any geologists reading this for all my inaccuracies and over simplifications. To get it straight, read the book! It contains a minimum of technical jargon, and every geological term is defined in the glossary—which I referred to very frequently!

William L Sullivan: Oregon’s Greatest Natural Disasters

Guest Review by Kit Bradley
August 2, 2008

The Cascadia subduction zone lies a few miles off the Oregon coast. Every three to six hundred years the Pacific Plate and Juan de Fuca Plate slide, and Oregon gets a magnitude 9.0 earthquake and resulting tsunami. The last event was in 1700, so we’re due any time now for the next. Unfortunately, those beautiful 1930’s coast river bridges I mentioned in an earlier review are not likely to survive. Advice for Oregonians: Don’t live in a brick building, and on the coast don’t live farther than a ten-minute walk to high ground.

I chatted with Bill Sullivan at the Maude Kerns Art and the Vineyard festival a few weeks ago, where I was helping my wife, Sue, sell things at her fused glass art booth. After he told me the story above, I couldn’t resist buying the book.

Oregon’s Greatest Natural Disasters is a little history, a little science, a little politics, and a little advice. It describes a whole spectrum of natural events starting with the ice age floods, and then on to tsunamis, earthquakes, volcanoes, floods, windstorms, landslides, and forest fires. To a non-Oregonian this would likely be dry reading. To an Oregonian it is pretty interesting, since we’ve all heard stories of the major natural events that occurred here—before our time, or when we were young, or even five years ago. There is no plot to keep us engaged, but Sullivan works in personal stories of people impacted by many of the disasters. He describes the events in some depth, giving us both a technical understanding of what happened and a personal sense of its impacts.

I was interested in learning about the Vanport flood of 1948, since we later bought a house that had been recovered from the flood. And the Columbus Day storm of 1962, since my wife has told me stories of living through it. And the ice age floods that possibly lapped at our farm in the hills at the south end of the Willamette Valley. And the Tillamook Burns in the 1930’s and 40’s, which was still evident when I moved to Oregon in 1971. And even the Biscuit Fire of 2002, which led to challenges to conventional wisdom on how to manage a forest after a major fire. “Post-wildfire logging hinders regeneration and increases fire risk.”

Each chapter includes some historical data, like the chart showing the history of eruptions of each of Oregon’s major peaks. And the chapters contain predictions for future events and suggestions for surviving them. Interestingly, after reading this book I don’t feel terribly threatened. But I don’t live at the coast, near a volcano, downhill from a clear-cut, or in a floodplain. I do live adjacent to a forest that is pretty dry in August.

The book includes some surprises about the impacts of the works of man on natural disasters. Damming all of Oregon’s major rivers was supposed to reduce flooding, but has it? In a 1975 survey of 245 landslides that occurred in one coastal forest district, 91% were in clear cuts or road cuts. Wow!

P.W. Atkins: The Periodic Kingdom

Anyone who assumes that a book about the periodic table of chemical elements would be boring seems pretty rational. But they also have probably not been exposed to The Science Masters Series.

The Periodic Kingdom: A Journey into the Land of the Chemical Elements by P.W. Atkins is from that series. It is a delightful little book (149 pages) written by an expert, for non-chemists. Not only does Atkins explain why the periodic table is arranged the way it is, he explains why the elements act with one another the way they do. And while he is at it, he describes some history of how different elements were discovered. We learn about electrical charges and sharing electrons. We learn why some elements join into useful molecules and others seem to avoid each other.

I recently re-read this book when my daughter started asking me some questions from her college chemistry class. Although I never took chemistry in college, I am after all, a father, and expected to know a multitude of things. Atkins helped me appear more knowledgeable than I really am. What more can you ask of an author?

So The Periodic Kingdom is an easy read, and can teach you something. I like that. In fact, I’ve enjoyed anything I’ve read from The Science Masters Series.

Guest Review by Kit Bradley
March 13, 2008

I was browsing Nate’s blog a few weeks ago, and I came across his review of The Periodic Kingdom, by P. W. Atkins. In contrast to Nate, I did take chemistry, both in high school and college, but as with many other things in life, I don’t remember much of it. There is something about forming molecules with electron-related chemical bonds that works in a very rational way, but I couldn’t remember the details.

So I went out to Amazon and bought a used copy of The Periodic Kingdom for $0.33 plus shipping (no risk there!), and I put the book high on my read list – and now I’ve read it.

This book is all I hoped for! I now recall the Periodic Table of the Elements, I understand something about the shells of electrons around the atomic cores, I understand how incomplete shells leave atoms ready to acquire or give up a few electrons, and that leads to a rudimentary understanding of how molecules are formed. And the history of how we got to this understanding is interesting too.

Hmm. Am I being nerdy here or what? I really found it interesting to refresh my understanding of this basic foundation of chemistry. The book served its purpose well, but I do have a couple critiques.

Atkins, a well-respected chemistry author, builds the book around a simple analogy. The Periodic Table of the Elements is referred to, obviously, as a kingdom. The kingdom has many regions, each corresponding to an element. As the narrative unfolds the kingdom and regions are treated as geographical locales, with eastern and western shores and varying elevations. Using this imaginary physical world, Atkins maps out a number of atomic properties such as atomic number, atomic weight, and size of atoms, where increasing and decreasing trends are shown with varying elevations for the regions. However…

As I read the book I frequently wondered if the analogy was useful. Could I not learn just as easily if Atkins called “regions” “elements” and “kingdom” “table”? I don’t know, but I won’t complain much, after all I did learn what I hoped to learn.

My other critique comes in the latter part of the book. After giving us the needed background, Atkins proceeds to describe the allocation of increasing numbers of electrons to s-, p-, d-, and f-orbitals as the atomic number of an element increases, something that is influenced by certain quantum effects. But as we move up the table, the order of filling orbitals gets confusing. I think Atkins could have taken us a little deeper into the quantum mechanics controlling all this. On the other hand, it’s obvious that a short book is not going to introduce us to all the complexities of such an important concept as the periodic table. I accepted the orbital assignments as described and moved on to improve my understanding of chemical bonds.

This book worked well for me, a good (if nerdy) read!