The Renaissance Mathematicus

The Prof says: Tycho was a scientist, not a blunderer and a darn good one too!


We have a novelty here at RM, a guest post. Renaissance Mathematicus Internet friend and historian of science Professor Christopher M Graney wrote asking the assistance of the HISTSCI HULK in demanding justice for the sixteenth century Danish astronomer Tycho Brahe, who had been accused of being a blunderer by a David P Barash in the “Chronicle of Higher Education”. The crew here at RM think the Prof has done a good job of defending the Dane’s honour so we are more than pleased to post his demolition of Mr Barash’s arguments officially endorsed by the HISTSCI HULK.

I recently stumbled upon an old piece in the Chronicle of Higher Education — David P. Barash’s January 3, 2003 “Why We Aren’t So Special”  about people’s tendency to see the world in terms of themselves.  It centered on Tycho Brahe, the great 16th-century Danish astronomer.  In it Barash used the term “Brahean solutions” in regard to “a widespread human tendency: Whenever possible, and however illogical, we retain a sense that we are so important that the cosmos must have been structured with us in mind.”  Barash wrote that “Brahe’s Blunder is one of those errors whose very wrongness can teach us quite a lot about ourselves, and about the seduction of species wide centrality.”  What was Brahe’s Blunder, according to what is apparently the Chronicle’s only published piece to ever mention Tycho Brahe?  It was to recognize the correctness of the Copernican idea that the planets circle the Sun, but to reject the idea that the Earth circles the Sun as well.  Thus Brahe argued that the Sun circles an immobile Earth, while the planets circle the Sun.  According to Barash, this solution was an ingenious kind of “strategic intellectual retreat and regrouping” that allowed Brahe to “accept what was irrefutably true, while clinging stubbornly to … what he wanted to be true”.

Tycho Brahe’s large mural quadrant at Uraniborg Source: Wikimedia Commons

That is just so wrong.  Tycho Brahe deserves some justice — he needs the HISTSCI_HULK to come to his aid!  Here is the real story of “Brahe’s Blunder”, and it has lessons to teach us, too:

Barash refers to Brahe as “an influential Danish star-charter” who “achieved remarkable accuracy in measuring the positions of planets as well as stars”.  He might as well describe Christopher Columbus, as a sailor who achieved remarkable success in finding some land Europeans didn’t know about.  Brahe was the leading astronomer of his era.  While other well-known astronomers like Copernicus or Galileo made their observations and published their results and ideas as individuals, Brahe ran a major observatory (“Uraniborg”) and research program on his island of Hven.  The cost of Brahe’s program to the Danish crown was proportionately comparable to the budget of NASA.  With access to the biggest and best available instruments, and with the most skilled assistants, Tycho Brahe could achieve awesome accuracy in his work:  Even though the telescope had not yet been invented in Brahe’s time, he could measure positions to an accuracy of the width of a U.S. quarter coin seen from a football field away; for certain sorts of measurements he could do substantially better.  Harvard astrophysicist and historian of astronomy Owen Gingerich often illustrates [for example, see February 19, 2009 – about 10 minutes in] Tycho’s incomparable contribution to the astronomy of his time by means of a thick book by one Albertus Curtius, published in 1666, on the history of astronomical work:  Gingerich notes this book contains some tens of pages of pre-Brahean observations, hundreds of pages of material from Brahe, and again tens of pages of post-Brahean observations.  Gingerich argues that astronomy would not see a surge in new data proportionately comparable to the one Brahe generated until today’s digital age.  He notes that Brahe’s quest for better observational accuracy “places him far more securely in the mainstream of modern astronomy than Copernicus himself”.

One would think such a scientific powerhouse as Brahe could do better than “Brahe’s Blunder”, and indeed he did.  Using his naked-eye instruments, Brahe measured the sizes of the planets as seen from Earth.  Anyone who is watching the stars this spring – with Venus and Jupiter dominating the sky after sunset while Mars, Mercury, and Saturn all make an appearance –  knows from experience that Venus looks a lot bigger and brighter to the eye than does Jupiter, which in turn looks a lot bigger and brighter than Saturn.  Using his measured apparent sizes, and the known relative distances of the planets, he calculated their relative physical sizes.  His results:  Saturn and Jupiter both dwarfed Earth; Mercury was a little larger than the Moon; Mars was larger than Mercury; Venus was larger than Mars but smaller than Earth; the Sun dwarfed all.  His results were off — Saturn and Jupiter are larger than even what Brahe calculated; Venus is nearly the Earth’s twin, size-wise; his distance to the Sun was off and so his Sun was too small — but he got the general picture right.

But Brahe did not measure only the planets.  Using his naked-eye instruments, Brahe also measured the sizes of stars as seen from Earth.  Anyone who is watching the stars knows from experience that Jupiter looks a lot bigger and brighter than the most prominent of stars, Sirius (the Dog star), which in turn looks a lot bigger and brighter than a lesser star like Procyon (the little Dog), which in turn looks a lot bigger and brighter than the faintest stars the eye can see.  Brahe measured Procyon to appear roughly the same size as Saturn.  If you go out and look at them both (they can both be seen around midnight for most of this March) you can make a rough check of Brahe’s work:  They indeed appear similar.

In the traditional geocentric model of the universe, stars lay a bit beyond Saturn, the most distant planet.  Assuming that to be the case, Procyon would be somewhat larger than Saturn, although still smaller than the Sun.  No problem.  But in the Copernican system, the stars had to be immensely far away.  This is because Earth moves in the Copernican system, and that motion should be reflected in the stars, but no such “annual parallax” effect was observed in the sixteenth century.  The Copernican explanation for this was that the stars are so far away that Earth’s movement around the Sun is negligible by comparison.  Well, Brahe knew his measurements were so good that, if the stars were any less than hundreds of times more distant than Saturn, he could detect Earth’s motion reflected in them.  And thus, were Procyon several hundred times more distant than Saturn while appearing roughly the same size as Saturn, then geometry would dictate Procyon to be several hundred times larger than Saturn, too.  Indeed, Procyon would dwarf even the mighty Sun, like a basketball dwarfs a tiny bead.  Sirius would be still more immense than Procyon!  Indeed, every single star, even the faintest ones, would dwarf the Sun.  The Sun would be the sole bead in a universe of basketballs, beach balls, volleyballs, soft balls, etc.

All the Copernicans could offer against this was something about how the Creator could make all big stars if the Creator so chose:  “Who cares how big the stars are?” wrote the Copernican Christoph Rothmann to Brahe, since an infinite Creator God is far bigger still.

To Tycho Brahe, a single bead solar system enveloped in a basketball universe was absurd.  Reasonably sized stars made much more sense.  To be reasonably sized they had to lie just beyond Saturn, and that required a fixed Earth.  Since planets circling the Sun seemed like such a good idea, the logical choice was what Barash has so unjustly termed Brahe’s Blunder — planets circling the Sun, the Sun circling the Earth.

 Tycho’s system of the world. Note the stars directly beyond Saturn

So why was Tycho wrong?  He was wrong because the sizes of stars are illusory.  Even a telescope, which will show the true appearance of planets (showing Venus’s phases, for example, as Galileo observed) or the Moon, fails with stars.  Two generations after Tycho, Giovanni Battista Riccioli (the Italian astronomer who, among other things, named the features on the Moon such as the Sea of Tranquility where Apollo 11 landed) would update Tycho’s argument using telescopic measurements of the “sizes” of stars.  A century after Riccioli, William Herschel (the English astronomer who discovered Uranus) would still speak of stars in terms of “sizes”, although by then he and most other astronomers knew those sizes to be illusory.  In the nineteenth century astronomers gained a full understanding of the illusory nature of the appearance of stars — that stars are truly points of light, with merely an appearance of size whose source is the intricate physics of the wave nature of light.  But the reasonableness of Brahe’s work was still in common memory.  The 1836 Penny Cyclopædia wrote:  “The stars [are] spheres of visible magnitude … nobody can deny it who looks at the heavens without a telescope; did Tycho reason wrong because he did not know a fact which could only be known by an instrument invented after his death?”  The blundering Tycho who illogically insisted on an unmoving Earth was a myth not yet invented.

And so this is yet another example of what the Renaissance Mathematicus is always pointing out about popular history of science — it is full of wonderful stories that seem to have something to teach us, but that turn out to be myths that we have created to tell us wonderful stories.  Tycho Brahe clinging stubbornly to the centrality of the Earth against the advance of science is a wonderful image.  Tycho Brahe, the finest scientist of his age, doing precisely what fine scientists do? Comparing rival models against the best available data?  That’s just nerdy, boring, and apparently absolutely forgettable.

Still, are we no less obliged than our nineteenth-century forebears to get the story right, and to put away the myth that Tycho Brahe blundered?  I wrote to the Chronicle about this.  They were not interested.  On one hand that is understandable.  After all, are they really going to devote space to me writing on minutiae in response to a decade-old piece on a long-dead scientist most people have never heard of, who was wrong?  I mean really — who cares?  On the other hand, the Chronicle of Higher Education is a journal for an educated audience, and they printed wrong information about a highly skilled scientist.  What I have written about Brahe is not widely known (what about Brahe is?) but it can be found in standard sources — for example, Victor Thoren’s Lord of Uraniborg (Cambridge University Press, 1990) has a full discussion, complete with a table of Brahe’s planet sizes on page 304.  Was there not an obligation to get the story right the first time, or correct it now?

I believe getting the story right is not just an academic matter.  Part of the problem science is having today with various “deniers” is rooted in that which turns Thony Christie into the HISTSCI_HULK.  In an article in the January issue of The Physics Teacher  I argue that the way history of science is commonly presented conveys an idea that answers in science are easy, and that the wrong answers come from human folly.  Thus Brahe becomes the blunderer who didn’t get the answer right because he wanted the Earth to be the center of the Universe.  The problem with such myths is that they hide the real difficulty in getting the right answer in science.  “Deniers” claim that the real answer is out there, but is being hidden by powerful forces — and they can wrap themselves in the mantle of science “history” with its stories of people who don’t want to see the real answer (like Brahe, supposedly), and who might persecute those who do (“Look what they did to Galileo!”).  So the real story, that the most accomplished astronomer of the day argued for an immobile Earth using a darned solid scientific argument, matters.  It shows that answers are not easy in science, and that good scientists follow the data, not what they want to be true.