Author's blog

On this page, observations of various kinds will appear that are related to big history teaching, as well as to big history in general.
Earlier blogs
- Big history and web site design
In-class observations
A few years ago, as part of teaching big history for small groups I started developing a series of observations that can be done by students in class. To my surprise, some of these observations turned out to be not only very helpful for teaching big history, but they also led to a few intriguing discoveries. This report is the first of a series of such observations with unexpected, exciting, results.
In March 2015, my son Louis and I set up a modest telescope (National Geographic 114/500 Compact Reflector Dobson Telescope). This instrument has a magnification ranging from 25x to 167x, depending on the eyepiece used. We connected it to our computer using a dedicated telescope camera (Orion StarShoot Solar System Color Imager IV) which yields a magnification of about 100x on the screen.
From the window of our home in Amsterdam we started observing the moon, and compared it with Galileo’s observations as reported in his publication Sidereus Nuncius, 'The Starry Herald,' of March 1610, which contains observations that changed the world.
In that booklet, Galileo explained that he had received news of the telescope's invention in Holland in 1609, and that he immediately proceeded to build several telescopes himself, each one with increasing magnification. As soon as possible he started his celestial observations and wrote them up. Already on “the first day of March 1610,” the booklet was ready and had received the clerical imprimatur.
Galileo made careful observations of, most notably, mountains on the moon as well as  of the hitherto unseen moons of Jupiter. All of this was worldshaking, because in Europe it was assumed at that time that the moon’s surface was perfectly smooth, while Jupiter tugging its moons along immediately suggested to Galileo that Earth could do the same with its single moon while circling the sun.
Interestingly, even though Sidereus Nuncius contained such potentially heretical views which were strongly condemned later, it had received the clerical imprimatur very speedily. I wonder why.
While it turned out to be relatively easy for us, using the computer, to take a reasonably sharp picture of the moon at about 100x magnification --even though the turbulent air over Amsterdam made the image move in and out of focus very quickly--, we were struck by how fast the moon moved off our screen as a result of Earth’s rotation around its axis. We were not using a motor-driven equatorial mount that would compensate for that movement, but instead kept it steady on a homemade mount on a tripod.
Because Galileo did not use an equatorial mount either but a simple tripod much like ours, this made us wonder how he had been able to make detailed drawings of the lunar surface. And this becomes even more intriguing, because Galileo claimed that in order to make his observations, a magnification of at least 400x was required (SN, p.6).
On the same page he claimed to have checked this magnification using circles of different sizes: one that he was looking at through the telescope, and one next to it with the naked eye. If they looked the same size, this showed the magnification of his telescope. A truly ingenious solution!
However, the dimensions of his telescope are known, even though the original eyepiece is lost. By using these data, it is possible to calculate its magnification, which turns out to be about 25x, so the lowest magnification that our telescope can achieve. This magnification yields an image of the moon that is consistent with Galileo’s drawings. It would also allow the moon’s image to stay within sight for a sufficient amount of time to draw it carefully.
Already at 100x magnification it proved impossible for us to view the moon as a whole, simply because higher magnification decreases the image range. As a result the moon’s image soon becomes bigger than the view in the eyepiece, or of the camera image on the screen.
If Galileo’s magnification had been 400x, he could not possibly have seen the moon as a whole the way he drew it in Sidereus Nuncius. He would also have had great trouble keeping it within his eyesight, because the moon moves across the sky as a result of Earth's rotation, as was noted above: the greater the magnification, the more quickly the moon moves through the field of vision, and the smaller the area becomes that can actually be observed. This is nicely explained on Making a Galilean Telescope.
On April 5, 2015, we were finally able to observe Jupiter and its four large satellites from our window. Much like observing the moon, it turned out that this could be done very well with a 25x to 50x magnification. Because our camera overexposed Jupiter and the resulting image did not show any of its moons (we still need to learn a lot), I recorded my observations much like Galileo had done before.
It was very exciting to watch all of that, and imagine how the great Italian scholar may have felt when he observed those moons for the first time, realizing full well what enormous consequences that would have for our world view as well as for his own career.
So clearly, Galileo’s magnification claims were way off. Instead of a 400x to 1000x magnification, he only reached about 25x. This is still a most impressive achievement. I am sure only very few of us would be able to construct such a telescope today at home, designing it and grinding our own lenses without detailed instructions.
Interestingly, I have not yet been able to trace any academic reports saying that Galileo overstated his magnification so much. They may well exist, and if they do, I would love to see them. One wonders why Galileo did so. He was otherwise a very careful observer.
As was noted earlier, Sidereus Nuncius was published within months after Galileo’s first observations. Clearly Galileo tried to capture the market with his claims to fame. Perhaps he tried to keep competitors at a distance by claiming technical expertise that would discourage others to try as well, which would allow him some time to further explore the heavens and report discoveries without being upstaged by the inevitable competition.
If so, this could be a potentially rich field for further exploration, not least because I experienced similar strategies, or at least suspicions of them, while doing biochemical research in the 1970s. So this may well be part of a more often used strategy in academia to keep competitors at a distance while claiming fame.
In addition, we learned that magnification becomes a relative term as soon as photographs are made, because the resulting pictures can be shrunk or enlarged at will, especially when they are digital. To some extent this also applies to earlier non-digital photos, and even to drawings.
As a result, what matters in such situations is not only the magnification reached by telescopes but even more the amount of light that they capture, which yields more detail as more light is captured. The amount of pixels that a camera captures is, of course, also of great importance.
In fact, telescopes are light buckets, similar to buckets that capture rain water. That is why water butts are connected with tubes to a roof, which collects all the rain water falling onto it. Roofs are simply the largest rain water capturing devices that are available in such situations.
Similarly, a telescope captures as much light as possible with its primary lens or mirror, while it subsequently concentrates and feeds it with lenses and sometimes also mirrors into the eyepiece or the camera, which acts as the water butt of a telescope. This is why astronomers want ever bigger telescopes, and why magnification is no longer stated, but rather the size of the main mirror.
All of these insights became clear to us while aiming our modest telescope at the moon. Furthermore, because we started our observations soon after the new moon, when only a small bright moon sickle could be seen, our first picture of it turned out to be exactly the area the Apollo 8 crew had in view  while shooting their world-shaking Earthrise picture. An amazing coincidence!
I have not yet used the telescope in class, mostly because good observations must take place at night and are hard to schedule, because they depend so much on the viewing conditions. But I may try it in the future.
On February 25, 2016, while explaining at Leiden University the seemingly hugely overstated magnification of Galileo’s telescope as reported in Sidereus Nuncius during the seminar  From Stone Age to Space Age, Spanish archeoastronomer Juan Antonio Belmonte Avilés suggested that Galileo may have been referring to the magnification per surface, while today, the magnification of telescopes (including Galileo's instrument) is measured in terms of the angle of view. While the angle of view magnification of Galileo's telecope is only about 25x, the resulting surface magnification is 625x, which corresponds well with what Galileo reported.
That was a very smart suggestion. As soon as I found time I checked it. And indeed, all the evidence that I could find indicates that Belmonte is right. As a result, my suspicions about Galileo possibly trying to keep the competition at a distance were also not correct.
However, I still very much stand by my personal observations in biochemistry about such practices, including what other scientists said about these things during the time that I spent in the Leiden university laboratories in the 1970s.
Furthermore, when I recently spoke with experimental scientists about these suspicions as part of Galileo’s possibly overstated magnification, many of them immediately recognized such practices as an issue that also they had encountered. So by getting it wrong about Galileo and talking about it, I unwittingly performed an enquiry into such experiences, which very much reinforced those impressions.
This misunderstanding about magnification raises the question of how those two different ways of defining magnification emerged. It seems as if Galileo had been the first to publish a method of measuring the magnification of a telescope. And his definition in terms of surface size actually corresponds better to what can actually be observed --which could be called 'a lay person's intuitive definition of magnification'-- than the current scientific definition in terms of angle of view. In the end, it is the size of the enlargement of the image that matters for what one is observing. But surface magnification is probably less easy to measure reliably, while angles can be more easily be measured. This may explain why such a switch was made.
When was that change effectuated and by whom, one wonders, after Galileo may have set the tone with his approach? How did the Dutchmen who had invented the telescope measure its magnification, one wonders, if they did so? And how and when did the approach of measuring magnification in terms of angles become accepted among telescope makers and astronomers? And how is magnification defined for digital cameras today, and are customers aware of that?
All intriguing questions, or so it seems to me. So even though I got it wrong (which I don't like, of course), my mistake may have resulted in a possibly fresh enquiry. That is what the scientific enterprise is all about: seeking to achieve the best possible images of reality, with ups and downs, while opening up new questions for research.
International Big History Association
Un. of Amsterdam big history
Cosmic Evolution
Big History Project
Book: Teaching Big History
Bill Bryson: Short History of Nearly Everything
Other useful stuff on the web
Other big history
How to use the book
Course models
Learning goals and objectives
Teaching tools
Assignments (little big histories)
Answers to FAQs by students
Questions by students and teachers that go beyond the book
Examination models
Teaching big history