Telescopic observations of Venus provided evidence for the Copernican view of the solar system. But was Galileo the first to see this, as he claims? Or did he steal the idea from a colleague and lie about having made the observations months before?
Opinionated History of Mathematics
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Galileo and the phases of Venus: it’s a plot that mirrors that of a murder mystery. Some scholars accuse Galileo of a crime—of falsifying data. The circumstantial evidence is enough to make anyone suspicious. If he’s innocent, he had remarkably bad luck with the timing of certain events; the worst possible coincidences for him. But he has an alibi! Huh, conflicting evidence. It’s a head-scratcher. Most historians these days believe Galileo. They think he’s innocent. But let’s see if we can’t poke some holes in their story.
First some background. The planet Venus is our closest neighbour in the solar system. But what kind of thing is Venus actually? To the naked eye, all we see is a dot of light. Is it a fire? A big thing of metal or diamond maybe? Some kind of mirror? It doesn’t seem likely to be just a plain old rock. Rocks don’t sparkle like that, do they? It’s so bright, you’d think it would have to be its own light source. You could speculate all day long. All of that was anyone’s guess before the telescope.
Now let’s look at Venus through a telescope. Aha! It’s a rock after all! It actually doesn’t shine with its own light, only reflected light from the sun. It’s a big round thing, a sphere, and only half of it is bright at any given moment, namely the half facing the sun.
This says a lot about the geometry of the universe. It’s telling us the relative spatial position of Venus and the sun. Back in the old days there was no way you could tell just by looking which thing in the sky was closer than the other. But now you can. Is Venus on the far side of the sun or nearer to us? Just look at which way the bright half of it is pointing and you have the answer. If you look at Venus and it’s like a new moon—mostly dark but with a crescent sliver of light on one side—then the bright side of Venus is evidently facing away from us, and hence Venus is between us and the sun. Sometimes it’s the other way around. Venus is on the far side, and then the bright half of it is facing us, so we see it almost completely lit up, like a full moon.
Those are the phases of Venus. They are just like the phases of the moon. Just like you have new moon, half moon, full moon, so you have “half Venus,” “full Venus,” and so on.
This could never happen in the Ptolemaic, geocentric system of the cosmos. In that system, the orbit of Venus is enclosed within the orbit of the sun. But the phases of Venus show that Venus is sometime on our side of the sun and sometimes on the far side, interchangeably. That’s impossible in the old system. So the phases of Venus are a great argument for the new Copernican system. Although they are also consistent with the hybrid system of Tycho Brahe.
But now, Galileo. What was his role in this? Of course he tried to claim credit for all of this. But does he deserve any? Most scholars think: yes. But I’m going to challenge conventional wisdom on this point.
Here are the key facts, which are very intriguing. The phases of Venus were discovered in 1610. But look at the timeline, it raises a lot of questions.
The first documented record we have is from December 5th. It’s a letter from Castelli to Galileo. Castelli was Galileo’s former student and a close friend. Castelli’s letter explains perfectly clearly the idea of using the phases of Venus to confirm heliocentrism, just as I outlined above. If Copernicus was right and Ptolemy was wrong, then it should be possible to prove this by means of the phases of Venus. But Castelli is not making observations himself, he is suggesting that Galileo make them. Remember, the telescope is almost brand new. Telescopic astronomy is less than a year old at this point.
There is no record whatsoever that Galileo knew anything about the phases of Venus before being told about it by Castelli on December 5th. But look what happens next: on December 11th, less than one week later, Galileo suddenly announces his great discovery, the phases of Venus. Galileo’s own words are that this something “just observed by me which involves the outcome of the most important issue in astronomy and, in particular, contains in itself a strong argument for the … Copernican system.” “By me”: Galileo is unequivocally claiming credit for himself, even though the timing is super suspicious. Did Galileo in fact steal the idea from Castelli? Very possibly.
But it gets more complicated. On December 30th, so another three weeks later, Galileo gave for the first time an account of his observations of Venus. At this point he claims to have observed Venus for about three months, and gives an accurate and fairly detailed description of its appearance during this period. So either he’s telling the truth and he already knew about the very important phases of Venus and he was just sitting on it for a while and just happened to receive Castelli’s letter at just about the time he was about to go public anyway. Or else he’s lying and he secretly made up those observations to boost his case.
There’s another letter, from November 13th of the same year, where Galileo seems to state expressly that he had no new planetary discoveries to report, which implies that he did not yet know about the phases of Venus, contrary to his later assertions. His defenders have a way of explaining this. When Galileo says “I haven’t discovered anything new about the planets,” these modern scholars are saying: yes, but nothing new “about” the planets really means nothing new “around” the planets, which means no new moons. So even though Galileo had made a very important new discovery concerning the planets, namely the phases of Venus, that was not a discovery “about” the planets, you see. So it comes down to a point of Italian linguistics how tenable that interpretation is. I’m not sure about it.
But it would make sense for Galileo to be on the lookout for moons. He had found moons around Jupiter and Saturn, and that was a huge deal. But that’s all the more reason for him to miss Venus’ phases. At this time, during these fall and winter months, Venus was well over half full. Modern astronomers can calculate backwards and know exactly the state of the planets so we know what Galileo would have seen. The shape of Venus would not have been very remarkable at this time, at the time when Galileo says he started to observe it. Unless you were specifically paying attention to it you may well think is was just a round blob. Galileo could easily have missed it; he could have failed to see that the shape was a bit off from a perfect circle. Especially if he was too busy moon hunting and looking only “around” the planets.
Another thing we have to take into account here are postal service delivery times. Castelli signed his letter December 5th and Galileo’s letter announcing the same idea to various colleagues is dated six days later. Is that enough time? Historians have argued about it. According to Westfall, it is “easily possible” that Galileo could have received the letter before December 11, while Stillman Drake, on the other hand, finds the probability of this “vanishingly small.” I guess we will never know. It is also possible that Galileo would have postdated his latter by a day or two just in case. He obviously realised the urgency of being first with these kinds of things.
Now, what about the details of Galileo’s observational report? If Galileo had not observed the phases of Venus before Castelli’s letter, then how could he later give an accurate description of their appearance dating back two months before this letter? Of course he could have fabricated data and passed it off as actual observations. We know that he did on many occasions, as we have discussed before. That’s business as usual for Galileo. It’s a fact that nobody disputes that Galileo published fake data on several occasions.
And if there ever was a time to fake data it was now. Galileo was of course concerned to get the important pro-Copernican argument from the phases of Venus on the record as quickly as possible and claim it for himself. And for this purpose it would be important to have observed the “full” appearance of Venus in the fall. Toward the end of the year it is transitioning to a crescent phase, which is no good, because that’s consistent with Ptolemy. The next opportunity to observe it in its full phase would be months away.
So Galileo certainly had a strong motive to fabricate this data. Making observations throughout most of December, after receiving Castelli’s letter, would also have been enough to give him great confidence that the heliocentric explanation for the phases of Venus was right. So faking the data was not risky.
Galileo’s defenders have a counterargument to this. They claim that Galileo could not have fabricated the data in question even if he had wanted to. According to them, the changes in appearance of Venus during these months were so complex and “non-linear” that Galileo could never have given such an accurate account if he had not if fact made these observations. Specifically, Galileo correctly describes the fact that the transition from a full to semicircular phase is quite rapid, while a roughly semicircular phase lingers for a considerable time. Here is what Palmieri says in a rather recent paper:
“Castelli’s letter cannot have been the spark that ignited Galileo’s programme of observation of Venus. It was simply too late. If he only then had started observing Venus, he would have seen it already nearing the exact semicircular phase, thus completely missing the non-linear patterns of change. And he could not possibly have been able to calculate the duration of one month for the “lingering” phenomenon. In other words, Galileo cannot have predicted Venus’s non-linear patterns of behaviour by re-constructing them ‘backwards’. For a Copernican it might have been easy to predict that Venus should display phases. However, it is one thing to predict this type of behaviour qualitatively and quite another to predict the non-linear patterns of change of Venus’s phases. A quantitative analysis would have required of Galileo a sophisticated mathematical theory that he did not have. There remains only one possibility, namely, that Galileo really did observe Venus’s non-linear patterns of behaviour.”
I say: this is wrong. On the contrary, Galileo could easily have reconstructed these phenomena. He would not have needed any sophisticated mathematics as all. All he would have had to do would have been to simulate the appearance of Venus with a simple physical model. Just take a sphere and paint half of it black and half of it white, and then look at it from different vantage points corresponding to the Earth’s position relative to Venus. That way you can simulate looking at Venus through a telescope very well without any need for sophisticated calculations.
I carried out such a simulation myself, using very simple means. I went to IKEA and bought a white spherical lamp. That was my model Venus. Then I had some black masking tape that I used to cover half of the sphere, to represent the half not illuminated by the Sun. I went to the office on a weekend and built a solar system in an empty parking lot. I picked one point to represent the sun, and then I put my Venus model in a certain position and then for the earth I used a camera so that I could take pictures. So I positioned these things according to a simplistic Copernican theory, just like Galileo could have done. I assumed for simplicity that the orbits of Venus and the earth are perfect circles and that their orbital speeds are constant. Estimates for these distances and speeds were common knowledge in Galileo’s time. Venus was seen exactly semicircular on December 18, right before Galileo’s observational report, which is very convenient for calibrating the initial position of this setup. Then you can just calculate backwards from there and move Venus and the earth back however many degrees they would cover in one month, two months, and so on. Just put a protractor at the sun and mark off those degrees.
Galileo could easily have completed such a simulation from start to finish in just a few hours, just as I did. Galileo would not have needed much imagination to come up with this scheme. The idea of illustrating the phases of the moon by an illuminated or half-painted sphere had been commonplace since antiquity, of course. It is a very obvious idea.
The results of my simple simulation are very close to the true appearances. Modern astronomers have calculated these appearances with great precision. If you put their figures next to my photos from the parking lot and you see that it’s the same thing. And crucially, the simulation is easily sufficient to reproduce the allegedly so unpredictable “non-linear” phenomena that Galileo got right in his December 30 report. So the claim that it would have been impossible for Galileo to recreate these appearances after the fact is definitely false. It would have been very much possible, in fact easy, for Galileo to recreate these appearances that he had not actually observed.
Another article on this has argued that Galileo’s account has “the ring of a record of visual impressions rather than an account coloured by calculations” in that it “has a highly visual character.” That’s supposed to show that Galileo did make actual observations. But obviously these markers of actual visual experience are consistent with my simulation hypothesis just as well as with actual observations.
In fact, my hypothesis makes a lot of sense if we compare it with Galileo’s treatment of sunspots. If my hypothesis is correct, these two cases are strikingly similar in several key respects. We discussed sunspots before. The following are the key facts for now. Galileo realised that sunspots constituted an important pro-Copernican argument only quite late, based on the input of others. He needed to act fast in writing something about it without having the time for thorough observations. I suggest that this is an exact parallel of what happened also in the case of the phases of Venus.
This parallel undermines the common assumption that Castelli’s idea must already have been obvious to Galileo. One scholar, for example, thinks it “would be to dignify the idea beyond reasonable measure” to view Castelli’s suggestion as a significant insight; rather, “the thought that Venus might have phases was ‘in the air’” and hence Castelli’s contribution is to be considered quite trifling. Another historian argues along similar lines that Galileo had no need to be spurred to action by Castelli’s letter, only by news of others making advanced telescopic observations. Around a day or two before hearing from Castelli, Galileo had received another letter, reporting that Clavius and his assistants at Rome had observed the moons of Jupiter. So Galileo now had serious competitors in the realm of advanced telescopic observations, or so it would have seemed to him. Presumably they would turn to the other planets next, and perhaps anticipate the discovery of the phases of Venus, so that would explain Galileo’s sudden urgency. According to this scholar, “the problem was to have a good telescope, not to posses reasoning power that astronomers had never lacked.”
These two scholars are wrong. The sunspots case is a counterexample to their claim. If there was no shortage of “reasoning power,” as they maintain, then Galileo should have realised the potential importance of sunspots much earlier and not let himself be beaten to the punch about their curved appearance by his arch-rival Scheiner. The fact of the matter is that the sunspots argument for heliocentrism eluded Galileo for twenty years, despite the fact the was passionately committed to proving heliocentrism in novel ways, and despite the fact that he himself had written specifically and in detail about the very phenomenon at stake, and despite the fact that the argument is very simple.
By analogy, this suggests that Castelli’s idea about Venus could very well have been news to Galileo. If Galileo could somehow miss the sunspots argument for twenty years despite all of this, then he could certainly have failed to think of the Venus argument during his one initial frantic year of telescopic observations, when he had a myriad other novelties and issues to deal with all at once.
But perhaps the most interesting aspect of the parallel between the two cases is the possibility that they both involved the use of physical models to simulate celestial appearances. In Galileo’s Dialogue, one speaker reports regarding the appearances of the paths traced on the surface of the sun by sunspots as seen from the Earth that Galileo “assisted my understanding by representing the facts for me upon a material instrument, which was nothing but an astronomical sphere, making use of some of its circles—though a different use from that which they ordinarily serve.”
The same sentiment is repeated later in the Dialogue: the appearances of the sunspot paths “will become better fixed in my mind when I examine them by placing a globe at this tilt and then looking at it from various angles.” This is very closely analogous to the Venus simulation I outlined above, suggesting that the latter would have been quite natural to Galileo, and in keeping with his style of reasoning.
So, to sum up, the following are generally accepted facts about the sunspots case: Galileo claimed to have conducted careful observations when he had not; according to his own account, Galileo simulated observations by looking at a physical sphere from a variable vantage point corresponding to the position of the Earth; Galileo failed to see an important pro-Copernican argument for a long time, despite it being simple and very naturally connected to his own work. These things did happen in the sunspots case. That’s a fact. Which obviously suggests that they very well could have happened also in the Venus case.
In conclusion, if Galileo had wanted to fabricate or reconstruct Venus observations he had not made, he could easily have done so. His December 30 account, where he describes appearances of Venus going back to October, is perfectly consistent with the hypothesis that he only started serious observations after receiving Castelli’s letter in December and simulated earlier observations using a simple physical model. There are, as we have seen, furthermore a number of circumstantial indications that this would have been very much in keeping with his character and habits.