On this page, observations of various kinds will appear that are related to big history teaching, as well as to big history
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.
OVERSTATE THE MAGNIFICATION OF HIS TELESCOPE 16 TIMES? OBSERVING THE MOON AND JUPITER WITH A TELESCOPE
March 28, 2015 (with
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 Herald of the Stars,' 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
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
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.
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.
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
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
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
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.
was a very smart suggestion. As soon as I found time I checked it. And indeed, all the evidence that I could find, including Galileo's
description of his telescope's magnification in Sidereus Nuncius, indicates that Belmonte is right. Clearly, I had not recognized
that the definition of magnification had changed in the meantime.
As a result, my suspicions about Galileo possibly trying
to keep the competition at a distance were not correct, either, although I am not completely sure about that. His stated magnification
of 900 to 1000 times sounds much more impressive, and thus possibly a little daunting, than if he had only stated the
enlargement of the diameter of a celestial object, about 30 times (which he did mention, too, which should have put me on the correct
However, I still very much stand by my personal observations in biochemistry about such practices, and also about what
other scientists said about these things during the time that I spent in the Leiden university laboratories in the 1970s.
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 my earlier observations.
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?
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.
In April of 2018 I found by sheer coincidence
that my suspicions concerning Galileo were not entirely unfounded. There have indeed been moments during which the great scholar did try
to put the competition at a distance. As the US philosopher of science Ernan McMullin described in his fascinating article ‘Openness
and Secrecy in Science: Some Notes on Early History’ (in: Science, Technology, & Human Values Vol. 10, No. 2, 1985, p.18):
months after the appearance of the Sidereus Nuncius (1610), Galileo observed what looked like bulges on the side of Saturn. Not surprisingly,
he took these to be moons. Instead of announcing them right away, he sent an anagram to the Florentine ambassador in Prague, who he
knew would pass it on to Kepler, the Imperial Mathematician. In that message, the news of his discovery was concealed in a meaningless
jumble of letters.
The aim was to enable him to claim priority of discovery while he further checked the observations. The effect
on Kepler, a simpler and more unworldly man than Galileo, can be imagined. He wasted days trying to decipher the anagram. When the
Emperor asked Galileo some months later for a solution to the anagram, Galileo was happy to comply; he was gradually becoming convinced
that the bulges were moons and that they were unmoving.’
In the article, Ernan McMullin provides more examples of Galileo engaging
in such efforts. This reinforces my earlier suspicion that the stated magnification of his telescope of 1000 times in Sidereus Nuncius may
have served a similar purpose.