A photo of parhelion


Driving from Zagreb to the island of Krk on Friday afternoon, 16th of September 2011, somewhere in the region of Gorski Kotar, I spotted an instance of the atmospheric phenomenon known as “mock sun”, “sun dog” or, more scientifically, “parhelion“. It is a reflection of the sun in tiny ice crystals that constitute high altitude cirrus clouds. A perhelion looks like another, smaller and dimmer sun on either or both sides of the sun, at the same level and not very far from it (exactly 22 degrees away from it). Here is a picture that I asked my wife to make with my mobile phone.

The parhelion is indicated here:

There is a late doxographic account in Aetius which informs us that the reputable presocratic philosopher Anaxagoras of Clazomenae “explains the so-called parhelia” in a similar fashion in which explains the rainbow, which he takes to be “a reflection of the sun’s radiance from a thick cloud” (Aet. III.5.11= 59 A 86 Diels). A more detailed account is found in Aristotle’s Meteorology and I invite the reader to check the accuracy of this account at the picture above:

Parhelia and sun-rods always appear beside the sun,  and not either above or below it or opposite to it; nor of course do they appear at night, but always in the neighbourhood of the sun and either when it is rising or setting, and mostly towards sunset. They rarely if ever occur when the sun is high, though this did happen once in the Bosporus, where two mock suns rose with the sun and continued all day till sunset. (Meteor. III.2 372a12-16, tr. Lee, slightly modified)

I suppose that the curiosity of the Bosporus parhelion was not that it was double – that occurs relatively often – but rather (i) that it lasted the whole day, including (ii) when the sun was high in the sky. A bit later, in Meteor. III.6 377b28-a12, Aristotle gives his detailed explanation for the characteristic appearance of parhelia, notably why they “occur at sunset and sunrise, and neither above nor below the sun, but beside it, neither very close to the sun, nor very far off”. No need to go into his obscure explanation here, though.

What Causes Change of Seasons?


In the academic year 2010/11, I conducted a poll among 74 students at the Faculty of Humanities and Social Sciences in Zagreb, examining their knowledge of basic scientific facts. A half of the population were freshers, the other half were students of the second, third, fourth and fifth years of their studies, with about an equal distribution within that group. One of the questions was this:

Change of seasons is caused by:

(a) variation in the angle of the Sun’s radiation due to the tilt of the Earth’s axis of rotation

(b) variation of distance of the Earth from the Sun due to the elliptical orbit of the Earth

(c) periodic variations in Solar activity

59% of the students did not know that (a) is the correct answer. A large majority of them (55% of the total population) thought that (b) was the correct answer. To many, (b) may seem an obvious answer. Of course, people who hold that belief, and who live in the Northern hemisphere, are regularly surprised to learn that Earth is closest to the Sun (perihelion) in early January, when they typically experience winter cold. Also, they immediately see that their belief is contrary to the fact that winter cold in the Northern hemisphere coincides with summer warmth in the Southern hemisphere. For if the proximity to the Sun were the cause of summer warmth, it would be so on the whole plant.

In the formulation of answer (b) I added a hint about the elliptical orbit of the Earth because I supposed that the common knowledge of the ellipticity of planetary orbits (Kepler’s First Law) would suggest an explanation for variations in the Earth’s distance from the Sun, and thus subtly endorse the false answer. However, the supposition of the ellipticity of planetary orbits is not necessary for the false belief that the change of seasons is caused by variation in distance between the Earth and the Sun.

Here is an example from Aristotle:

For this reason it is not the primary locomotion which is the cause of generation and corruption, but that in the inclined circle. For in this latter there is both continuity and being moved with two movements; for, if there is always to be continuous generation and corruption, there has always to be, on the one hand, something being moved so that these changes may not fail, and, on the other hand, two movements, to prevent there being only one of the two results. So the locomotion of the whole is the cause of the continuity, whilst the inclination is the cause of the approach and retreat. For this results in its coming to be further away at one time and nearer at another, and since the distance is unequal the movement will be irregular. So, if it generates by approaching and being near, this same thing destroys by retreating and coming to be further away. (De generatione et corruptione II.10 336a31-b7; tr. Williams)

In other words, the Sun’s annual motion along the ecliptic, which is inclined, is the cause of the Sun’s approaching and retreating from the Earth, thereby causing the seasons, in particular spring and summer, which bring about heat conducive to generation of living beings, and then also autumn and winter, which bring about cold conducive to destruction of living beings. This is very clear from another passage:

The efficient, controlling and first cause is the circle of the Sun’s revolution. For it is evident that as it approaches or recedes the Sun produces dissolution and composition and is thus the cause of generation and destruction. (Meteorologica I.9 346b22-24; tr. Lee)

Now this is puzzling for two reasons. First, Aristotle did not think that the Sun is made of fire or that it produces any heat by itself. Rather, he thought that it is the friction between the uppermost sublunary (fiery) layer and the lowermost superlunary (ethereal) layer that generates heat, but that was a subject of controversy even in the Peripatetic school, so we may put that aside.

Second, Aristotle subscribed to a Eudoxan theory of the heavens, which involves a number of nested concentric spheres with the Earth in the middle. But if the Earth is in the middle, and the Sun is carried by several concentric spheres (3 according to Eudoxus, 5 according to Callipus, 9 according to Aristotle; cf. Metaph. XII.8), how can he account for the supposed variation in the distance between the Sun and the Earth, that is for the Sun’s ‘approach’ and ‘retreat’?

One may try to solve this problem by supposing that by ‘approach’ (prosienai) and ‘retreat’ (apienai) he means merely approach to it highest point at summer solstice and retreat to its lowest point at winter solstice. But that won’t do, since Aristotle in the first passage above explicitly connects ‘approaching’ with ‘being near’ (engus) and ‘generating’ (presumably, through heat), and on the other hand ‘retreating’ with ‘being farther away’ (porrō) and ‘destroying’ (presumably, through cold). How can he have variation in ‘being near’ and ‘being farther away’ if the Sun is carried by a set of concentric spheres? The suggestions that the spheres are not perfectly regular, or that the Earth is not in the centre of these spheres, can be rejected straight away in light of Aristotle’s statements in the De caelo.

I am not aware that this problem has been raised in scholaraly literature (though my search hasn’t been thorough at all), and at the moment I do not have an answer to it. But I would welcome any hints and suggestions.

Double rainbow


In his work Meteorologica (III.2, 371b33-372a3), Aristote wrote:

Not more than two rainbows occur at the same time. Of two such simultaneous rainbows each is three-coloured, the colours being the same in each and equal in number, but (i) dimmer in the outer bow and (ii) placed in the reverse order.

On 31 August 2010 Zagreb saw some drammatic weather, including heavy nimbostratus clouds which started to tear apart on the western horizon at the sunset. Here are two photographs I made from the window of my study, facing east, which verify Aristotle’s points (i) and(ii). I became aware of these two facts only after reading the quoted passage.

Unchanging heavens


It is well-know that the Aristotelian conception of the universe, adopted with some adaptations in the Middle Ages, divided the universe in two essentially different parts: the sublunar world of the four elements with their natural places – thus forming the layers of earth, water, air and fire – and the supralunar world of the fifth element, aither. The four elements have different natural motions (earth and water naturally go down, fire and air up), and objects made of them in various mixtures undergo all forms of change, including generation and destruction. The fifth element’s natural motion is circular, and objects made of it – the celestial spheres and stars attached to them – undergo only one sort of change, and that is change of place, or more precisely circular locomotion. Because they are made of the fifth element, the heavens and the stars are completely unchangeable.

In De caelo I.3, 270b12-16, Aristotle wrote: “Throughout all past time, according to the records handed down from generation to generation, nothing is observed to have changed either in the whole of the outermost heaven <viz. the sphere of the fixed stars> or in any of its proper parts.”

Simplicius (6th century AD) comments on this sentence that, according to his knowledge, astronomical records of the Egyptians go back 630.000 years, of and the Babylonians 1.440.000 years. This is surely a gross overstatement, but their records were certainly older than the Greeks’ for several hundred years. “In all that time since the records have been passed on,” writes Simplicius, “there is no mention of anything being different in the heavens than today, either concerning (i) the number of stars, or (ii) their sizes, or (iii) their colours, or (iv) their regular motions” (117.27-30 Heiberg) 

Ad (i): The exact number of stars has been proverbial in antiquity as beyond human cognition. In fact, however, there are only some six thousand stars visible to the naked eye in a typical dark night.

One way for the number of stars to change, of course, would be if a new star appears in the sky. It is well-know that Tycho Brahe observed a new star in November 1572 (SN 1572) and he described it in his 1573 treatise De stella nova. He argued that it showed no daily parallax against the background of the fixed stars, which means that it cannot be a sublunar phenomenon. Tycho concluded that the traditional view of the heavens as unchangeable cannot be correct. This observation was instrumental in overthrowing the traditional view in early modern age.

Before Tycho, we have records of two more new star observations in the West, both made by Islamic astronomers: in 1054 (SN 1054) and in 1006 (SN 1006). Weren’t there any observable supernovas in antiquity? The earliest positively recorded supernova was in 185 AD (SN 185), viewed by Chinese astronomers in the southern sky. Other than that, we have a report that Hipparchus, the greatest observational astronomer of antiquity, saw a “new star” in 134 BC. Pliny wrote in his monumental work Natural History, Book II.95: “Hipparchus before-mentioned, who can never be sufficiently praised, no one having done more to prove that man is related to the stars and that our souls are a part of heaven, detected a new star that came into existence during his lifetime; the movement of this star in its line of radiance led him to wonder whether this was a frequent occurrence, whether the stars that we think to be fixed are also in motion; and consequently he did a bold thing, that would be reprehensible even for God – he dared to schedule the stars for posterity, and tick off the heavenly bodies by name in a list, devising machinery by means of which to indicate their several positions and magnitudes, in order that from that time onward it might be possible easily to discern not only whether stars perish and are born, but whether some are in transit and in motion, and also whether they increase and decrease in magnitude.”  However, the stella nova observed by Hipparchus seems to have been a comet, given that Hipparchus  mentions its proper motion, and comets were deemed to be sublunar phenomena in Aristotle’s theory (cf. J. K. Fotheringham). This explains Simplicius’ confident claim that there has been no record of change in the number of stars. In any case, much like Charles Messier eighteen hundred years later, with his catalogue of nebulae not to be confused with comets, Hipparchus made a star atlas so that any new stars or proper motions of stars can be more easily detected.

Ad (ii):  The size (megethos) of stars must refer to their brightness. And what is truly striking is that ancient and medieval astronomers failed to observe variable stars, that is stars of changing brightness. There are tens of stars in the northern sky whose variations are easily detectable with the naked eye. Of course, one needs to know where to look, but more importantly – one needs to be open to the idea that variations are possible, and that seems to be something that ancient and medieval astronomers lacked. Even if they did observe a variation in brightness, they would probably dismiss it as a result of atmoshperic changes. This is a nice example of theory not only guiding observation, but also obstructing it.

Ad (iii): The ancients were well aware of different colours of stars and planets, but there is no record – to my knowledge – that they ever observed variation in their colour. However, it would be extremely difficult to observe such a variation without a spectrograph.

Ad (iv): Famously, Hipparchus discovered the precession of the equinoxes, the slow movement of the equinoctial points from east to west among the stars along the ecliptic, which we know today is due to the wobble of the Earth’s axis. Would that not be a counterexample to Simplicius’ claim that there has been no record of any change in the regular motion of stars? Perhaps not, if the precession of the equinoxes can be explained as another regular motion. However, this could only be a regular motion of the sphere of the fixed stars, and I am not aware that anyone in antiquity entertained the idea that the sphere of the fixed stars undergoes any other than the diurnal motion.

Perhaps someone can help me with this. (1) How did ancient astronomers and philosophers explain the precession of the equinoxes? (2) How come that Simplicius could affirm point (iv) in the light of Hipparchus’ discovery of the precession? Needless to say, other comments are most welcome.

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