Galileo Discusses the Size of the Universe and the Seasons
Galileo's Dialogue, Day 3, Part 4
As I wrote in a recent post, I intend to write posts for each of the four days in the Dialogue Comparing the Ptolemaic and Copernican Systems1, the book that got Galileo in trouble with Rome. This is the fourth post about Day Three in the Dialogue. Here are the previous posts:
Day One: Galileo Dismantles Aristotle's Separation of Earth from the Heavens.
Day Two, Part 1: Galileo Attacks Aristotle’s Followers.
Day Two, Part 2: Galileo Insists the Earth is Spinning on its Axis.
Day Two, Part 3: Galileo on the Acceleration of Falling Bodies.
Day Two, Part 4: Galileo Channels Plato.
Day Three, Part 1: Galileo Calls Out Chiaramonti’s Manipulation of Data.
Day Three, Part 2: Galileo Praises Aristarchus and Copernicus.
Day Three, Part 3: Why the Apparent Motion of the Sunspots Supports the Copernican Model.
Once it has been clarified that the earth’s revolution around the sun simply explains the apparent retrograde motion of the outer planets, and the apparent curved motion of the sunspots on the sun’s surface, the discussion of Day Three moves on to Peripatetic objections to the idea of this revolution.
Simplicio begins to read from Locher’s book2 a number of theological arguments, which Salviati refuses to address. Simplicio continues:
[H]e deduces with very precise calculations that if the orbit in which Copernicus makes the earth travel around the sun in a year were scarcely perceptible with respect to the immensity of the stellar sphere, as Copernicus says must be assumed, then one would have to declare and maintain that the fixed stars were at an inconceivable distance from us, and that the smallest of them would be much larger than this whole orbit, while others would be larger than the orbit of Saturn. Yet such bulks are truly too vast, and are incomprehensible and unbelievable. [p.358]
Salviati’s responds with an initial salvo:
Here the adversaries of this opinion rise up, and take what Copernicus has called “imperceptible” as having been assumed by him to be really and absolutely nonexistent. [p.359]
Salviati first addresses the idea that the fixed stars would have to be enormous in the Copernican model. He does some quick calculations and comes up with an estimate that a sixth-order star would be of a similar size to the sun, and not of the size of the earth’s orbit. He then states that no astronomer has focussed on this topic:
To speak quite frankly, I thoroughly believe that none of them — not even Tycho himself, accurate as he was handling astronomical instruments and despite his having built such large and accurate ones without a thought for their enormous expense — ever set himself to determine and measure the apparent diameter of any star except the sun and moon. [p.361]
Salviati then explains a little experiment for measuring the size of a star. It consists of hanging a rope in front of the star, and moving back and forth until the rope completely covers the star, but no more. The distance from the eye’s focal center to the rope is then measured, and the angle between the two rays from the eye to each of the two sides of the rope can then be calculated. It turns out that the hanging rope is effective at making the halo around distant shiny objects disappear:
[F]or the string, by covering the body of the star, takes away the halo belonging not to it but to our eyes; of this it is deprived the moment the true disc is hidden. […]
By this very precise operation I find that the apparent diameter of a star of the first magnitude (commonly believed to be two minutes, and even put at three by Tycho in his Astronomical Letters, p.167) is no more than five seconds, which is one twenty-fourth or one thirty-sixth of what they thought. Now you see what a serious mistake their doctrine is based upon. [p.362]
The discussion then moves on to the distance of the fixed stars from the earth. Simplicio begins:
[I]t still remains true that the earth's orbit would necessarily cause changes and variations in the stellar sphere similar to the observable changes produced by the earth's radius in regards to the sun. No such changes, or even smaller ones, being observed among the fixed stars, it appears to me that by this fact the annual movement of the earth is rendered untenable and is overthrown. [pp.364-365]
Salviati takes up the gauntlet and immediately responds, explaining that the Ptolemaics think that the supposed immense size of the Copernican universe makes it untenable:
[N]othing prevents our supposing that the distance of the fixed stars is still much greater than has been assumed. You yourself, and anyone else there may be who does not want to disparage the propositions accepted by Ptolemy's followers, must find it a very convenient thing to suppose the stellar sphere to be enormously larger than we have said it must be considered thus far. [p.365]
Salviati continues, insisting on the immensity of the universe:
Simplicio, I wish you could for a moment put aside your affection for the followers of your doctrines and tell me frankly whether you believe that they comprehend in their own minds this magnitude which they subsequently decide cannot be ascribed to the universe because of its immensity. I myself believe that they do no not. It seems to me that here the situation is just as it is with the grasp of numbers when one gets up into the thousands of millions, and the imagination becomes confused and can form no concept. The same thing happens in comprehending the magnitudes of immense distances; there comes into our reasoning an effect similar to that which occurs to the senses on a serene night, when I look at the stars and judge by sight that their distance is but a few miles, or that the fixed stars are not a bit farther off than Jupiter, Saturn, or even the moon. [p.366]
Salviati continues by insisting that few understand size in terms of the different scales of discussion:
But aside from all this, consider those previous disputes between the astronomers and the Peripatetic philosophers about the reasoning as to the distance of the new stars in Cassiopeia and Sagittarius, the astronomers placing these among the fixed stars and the philosophers believing them to be closer than the moon. How powerless are our senses to distinguish large distances from extremely large ones, even when the latter are in fact many thousands of times the larger!
And finally I ask you, O foolish man: Does your imagination first comprehend some magnitude for the universe, which you then judge to be too vast? If it does, do you like imagining that your comprehension extends beyond the Divine power? Would you like to imagine to yourself things greater than God can accomplish? And it it does not comprehend this, then why do you pass judgment upon things you do not understand? [p.367]
When Simplicio complains that from the point of view of humanity, created by God, what would the point of such vastness, Salviati responds that it is not for humans to restrict what is in the mind of God:
I am certain that Divine Providence omits none of the things which look to the government of human affairs, but I cannot bring myself to believe that there may not be other things in the universe dependent upon the infinity of its wisdom, at least so far as my reason informs me; yet if the facts were otherwise, I should not resist believing in reasoning which I had borrowed from a higher understanding. Meanwhile, when I am told that an immense space interposed between the planetary orbits and the starry sphere would be useless and vain, being idle and devoid of stars, and that any immensity for holding the fixed stars, I say that it is brash for our feebleness to attempt to judge the reason for God's actions, and to call everything in the universe vain and superfluous which does not serve us. [p.368]
Salviati returns to the technical, insisting that all adjectives pertaining to size are relative:
Returning to our natural and human reason, I say that these terms “large,” “small,” “immense,” “minute,” etc. are not absolute, but relative; the same thing in comparison with others may be called at one time “immense” and at another “imperceptible,” let alone “small.” Such being the case, I ask: In relation to what can the stellar sphere of Copernicus be called too vast? So far as I can see, it cannot be compared or said to be too vast except in relation to some other thing of the same kind. [p.369]
Salviati even posits the possibility of an infinite universe in which the stellar sphere that we perceive is just one luminous point:
Now if the whole stellar sphere were one single blazing body, who is there that does not understand that in an infinite space there could be assigned a distance so great that, from there, such a brilliant sphere would appear so great that, from there, such a brilliant sphere would appear as small as or even smaller than a fixed star now appears to us from the earth? So from such a point we should judge as small the very things which we now call immeasurably huge. [p.370]
Of course, this passage, channeling Giordano Bruno, is carefully written using the subjunctive mood. Galileo was quite aware of what happened to Bruno.
The final discussion of Locher’s work has Sagredo, in his brash style, make this outburst:
To me, a great ineptitude exists on the part of those who would have made it that God made the universe more in proportion to the small capacity of their reason than to His immense, His infinite, power.
Finally, Salviati himself concludes that Locher really has no idea of what he is talking about:
From the questions this fellow asks, it seems to me that one may deduce that if only the sky, the stars, and their distances were permitted to keep the sizes and magnitudes which he has believed in up to this point (though he has surely never imagined for them any comprehensible magnitudes), then he would completely understand and be satisfied about the benefits which would proceed from them to the earth, which itself would no longer be such a trifling thing. Nor would these stars any longer be so remote as to seem quite minute, but large enough to be able to act upon the earth. And the distance between then and Saturn would be in good proportion, and he would have very probable reasons for everything, which I should very much like to have heard. But seeing how confused and contradictory he is in these few words leads me to believe that he is very thrifty with or else hard up for these probable reasons, and that what he calls reasons are more likely fallacies, even shadows of foolish fantasies. [pp.370-371]
With Locher duly dispensed, Salviati moves on the question of whether the revolution of the earth around the sun should lead to any kind of apparent changes among the stars:
Now it might be that there is a variation, but that it is not looked for; or that because of its smallness, or through lack of accurate instruments, it was not known by Copernicus. This would not be the first thing that he failed to know, either for lack of instruments or from some other deficiency. Yet, grounded upon most solid theories, he affirmed what seemed to be contradicted by things he did not understand. For as already said, without a telescope it cannot be comprehended that Mars does increase sixty times and Venus forty times in one position as against another, and their differences appeared to be much less than the true ones. Yet since that time it has become certain that such variations are, to a hair, just what the Copernican system required. Hence it would be a good thing to investigate with the greatest possible precision whether one could really observe such a variation as ought to be perceived in the fixed stars, assuming an annual motion of the earth. [pp.372-373, emphasis mine]
Salviati considers the different possibilities:
I have indeed found authors writing in general terms that the annual motion of the earth should not be admitted because it is improbable that visible changes would not then be seen in the fixed stars. Not having heard anyone go on to say what, in particular, these visible changes ought to be, and in what stars, I think it quite reasonable to suppose that those who say generally that the fixed stars remain unchanged have not understood (and perhaps have not even tried to find out) the nature of these alterations, or what it is that they mean ought to be seen. In making this judgment I have been influenced by knowing that the annual movement attributed to the earth by Copernicus, if made perceptible in the stellar sphere, would not produce visible alterations equally among all the stars, but would necessarily make great changes in some, less in others, still less in yet others, and finally none in some stars, however great the size of the circle assumed for this annual motion. The alterations which should be seen, then, are of two sorts; one is an apparent change in size of these stars, and the other is a variation in their altitudes at the meridian, which implies as a consequence the varying of places of rising and setting, of distances from the zenith, etc. [pp.377-378, emphasis mine]
The technical discussion continues, and Salviati gets Sagredo to recognize that it is not possible to see if there is any retrograde motion of the fixed stars. This is because the retrograde motion of the outer planets is detected by comparing their motion with that of the fixed stars, while for the latter, there is no other fixed reference frame for comparison purposes. Sagredo summarizes the discussion:
It seems to me that you have explained to us two sorts of differing appearances as being those which because of the annual motion of the earth we might observe in the fixed stars. One is their variation in apparent size as we, carried by the earth, approach them or recede from them; the other (which likewise depends upon this same approach and retreat) is their appearing to us to be now more elevated and now less so on the same meridian. Besides this you tell us (and I thoroughly understand) that these two alterations do not occur equally in all stars, but to a greater extent in some, to a lesser in others, and not at all in still others. The approach and retreat by which the same star ought to appear larger at one time and smaller at another is imperceptible and practically nonexistent for stars which are close to the pole of the ecliptic, but it is great for the stars placed in the ecliptic itself, being intermediate for those in between. The reverse is true of the other alteration; that is, the elevation or lowering is nil for stars along the ecliptic and large for those encircling the pole of the ecliptic, being intermediate for those in the middle.
Furthermore, both these alterations are more perceptible in the closest stars, less sensible in those more distant, and would ultimately vanish for those extremely remote. [p.385]
The discussion then moves on to the apparent motion of the sun between the Tropics of Capricorn and Cancer over the year, the varying number of hours per day, and the seasons on earth. It is essentially the explanation that any good school teacher might give to their class. The earth’s axis is tilted at a fixed angle of 23.5º with respect to the ecliptic. This tilt, combined with the 24-hour diurnal rotation on this axis, and the annual revolution around the sun, explains both the apparent rise and fall of the sun of 47º over the year, as well as the seasons, with the lengthening and shortening of the day throughout the year, with extreme northern and southern latitudes not getting any sun for part of the year, nor night in the opposite part of the year.
How does Simplicio respond to this discourse, so obvious to a modern reader?
If I must tell you frankly how it looks to me, these appear to be some of those geometrical subtleties which Aristotle reprehended in Plato when he accused him of departing from sound philosophy by too much study of geometry. I have known some very great Peripatetic philosophers, and heard them advise their pupils against the study of mathematics as something which makes the intellect sophistical and inept for true philosophizing; a doctrine diametrically opposed to that of Plato, who would admit no one into philosophy who had not first mastered geometry. [p.397]
Salviati responds sarcastically:
I endorse the policy of these Peripatetics of yours in dissuading their disciples from the study of geometry, since there is no art better suited for the disclosure of their fallacies. You see how different they are from the mathematical philosophers, who much prefer dealing with those who are well informed about the general Peripatetic philosophy than with those who lack such information and because of that deficiency are unable to make comparisons between one doctrine and the other. [p.397]
An exchange between Simplicio and Salviati follows. Simplicio complains that the Copernican model requires the earth to have four contrary motions, namely downwards (towards the center of the universe), rotation about its axis, revolution around the sun, and “another whirling about its own center, completed in a year, and opposite to the previously mentioned twenty-four-hour motion.” The fourth is the third motion that Copernicus gives to the earth. Salviati explains that the first motion had already been previously dispensed of, and that the fourth simply does not exist. As for the other two, he had previously explained how they were completely complementary and explained all phenomena.
The last discussion of Day Three begins with speculation by Salviati that the fixed tilt of the axis might be a magnetic attraction of the earth to a particular part of the firmament:
But what will Simplicio say if, to this independence of any coöperating cause, we add a remarkable force inhering in the terrestrial globe and making it point with definite parts of itself toward definite parts of the firmament? I am speaking of magnetic force, in which every piece of lodestone constantly participates. And if every tiny particle of such stone has in it such a force, who can doubt that the same force resides to a still higher degree within the whole of this terrene globe, which abounds in this material? Or that perhaps the globe itself is, as to its internal and primary substance, nothing but an immense mass of lodestone3? [pp.399-400]
This discussion will be the topic of the next post.
If you wish to donate to support my work, please use the Buy Me a Coffee app.
Galileo Galilei. Dialogue concerning the two chief world systems — Ptolemaic and Copernican. Translated by Stillman Drake, foreword by Albert Einstein. University of California Press, 2nd ed., 1967.
Johann Georg Locher, Disquisitiones mathematicae de controversiis ac novitatibus astronomicis (Mathematical discussions about astronomical controversies and innovations). Ingolstadt, 1614.
It seems to me gravity alone cannot explain the earth circling the sun. That is an unstable model. Any minor deviation and the earth would spiral into the sun or sail off into space.
I expect there is a force that pushes earth away from the sun. The earth's orbit would be the point where this force balances gravity. Looking forward to the discussion about magnetic forces!