Sunday, June 29, 2014

thought for the day/ Greek Astronomy

Image Credit & Copyright: Ken Crawford (this picture just happens to be called the Hercules galaxy cluster)

- Quote for the day,

"It will be proper to discuss this, in order that we may know whether the universe revolves and the earth stands still, or the universe stands still and the earth rotates. For there have been those who asserted that it is we whom the order of nature causes to move without our being aware of it, and that risings and settings do not occur by virtue of the motion of the heaven, but that we ourselves rise and set. The subject is worthy of consideration, in order that we may know in what conditions we live, whether the abode allotted to us is the most slowly or the mosty quickly moving, whether God moves everything around us, or ourselves instead." - Seneca(nat.quaest. vii.2.3 through Thomas Heath's Aristarchus of Samos, page 308)

When people think of the Greeks, they think of Plato, Aristotle, Athens and Sparta.  But, their history goes back to Minoans, Myceneans.  Really, the history there is still quite controversial.  The Greek history as the common man on the street would imagine it came about after a Greek 'dark ages.' Some modern scholars try to dismiss this 'dark ages' just like many try to dismiss the medieval 'dark ages.' But, when the Myceneans had arches in their architecture, and the classical Greeks did not, this must indicate lost knowledge/skills.  I'd like to say more about the era preceding the Greek age that brought deductive logic and mathematical astronomy to mankind for the first time.

- self interpolating, the arched Mycenaean tomb I mentioned above,

I've shown a youtube of this before; this one is a bit more informative.
One of the major archaeological mysteries of our time, as I'm writing this, still is what's called the "Aegean collapse".  This 'Aegean collapse' led to the end of the Minoan, Mycenean, Hittite, Babylonian world and was the last time the Egyptians were ever the most powerful nation in the western cultures. When the classical Greeks discovered mathematical knowledge like none before them, the Egyptians were ancient history.
Before this dark ages leading to the classical Greek period, the Egyptians, Hittites, Minoans, Babylonians were prospering.  Some fighting, but not that bad. The economies were temple economies.  Like the way the second half of the European medieval period were economies built around the horse, Bronze age cultures were based around temple building. What happened to them? I got interested in all this because maybe the coming iron age made them obsolete.  Iron can go through bronze age weapons like they were nothing. But, evidence seems to indicate that at least for the Greeks, the iron age didn't really become established till 1050 B.C. Well, this is a hundred and fifty or so years after the fall of the Bronze age civilizations. But, another possibility is plague. All the Bronze age cultures except the Egyptians burned their cities down - the Hittites, the Myceneans, and the Canaanite Levant(which later evolved into the Hebrews). Well, the Minoans did not, and neither did the Babylonians.  Every book I've read finds arguments against every theory of what happened. It's still one of the major unsolved archaeological mysteries, and I'm moving on!

- self interpolation, some recent argument about whether plague could have led to the Aegean collapse, and the recent conflicts between the U.S./Russia/Ukraine and really the U.S./Iraq and other such warfare has made me wonder if the Aegean collapse was due to war.  Wars destroy economies. The reason Russia/U.S. doesn't go to full all out war is because both sides know this. Back then, they probably didn't know this.  One should note also that as I say, they were temple economies.  They were economies that relied on slavery and acquisition of slavery.  They went to war with one another for each others slaves.  Their temple economies were inherently self-destructive.
Homer's epic poems, the Iliad and the Odyssey, were not strictly about scientific knowledge or even about rationality; but, there is mention here and there of scientific things.
Book 23 mentions a morning star, "But at the time when the morning star goes forth to tell that light is coming over the Earth . . ." When I first read this, I was confused.  I though it meant that the morning star goes down, then, the light of the sun comes up. This would mean the morning star is setting in the east, while the sun is rising in the west. I'm reading this with knowledge before hand. I know that Thomas Heath relates in his "Aristarchus of Samos" book that Pythagoras(or Pythagoreans who followed him) figured out that the morning star that rises at different years, and sets at other years is the same star!  The Greeks would later distinguish these star from the other stars as 'planets.' Well, I mentioned this to my father who brought out the latest Sky and Telescope sky chart and showed that Venus sets in some years at sunrise, and rises just before the sun rises at other years. Now, Homer doesn't know this.  He knows some stuff and not other things as well.
Homer mentions in book/chapter 18 of his Iliad, "Upon it he wrought the Earth, and the Sky, and the Sea, the untiring Sun and the full Moon, and all the Stars that encircle the sky- Pleides and Hyades, Orion the mighty hunter and the Bear(which mean also call the wain), which revolves in its place and watches Orion, . . ." The bear constellation is what's called today Ursa Major. I can't help bringing up the Nebra Sky disk again. I point this out and it's mythological significance in my Gospel of Truth(first post of this blog). In the Nebra Sky disk is the sun, the moon, and the Pleides.  Well, I suppose Homer knew a few more things than whoever made the Nebra Sky disk; but, maybe the Nebra sky disks maker just ran out of room on his disk! And that folks is pretty much all that Homer knew about astronomy, mathematics and so on. But, when learning of these things, I decided to read Homer's epics and see what else I could dig out of him.
I remember wanting to read Homer awhile ago and only making it halfway before getting tired of it.  I remember there was some curious nature-poetry, but not much else. When I learned of the above, I wanted to dig out all these nature-poetries.  I've done so for the most part.  It certainly got a little tiresome.  Some of it got a little repetitious, others were a bit trivial(maybe one sentence, maybe just a word phrase). In digging out these nature-poetries, I found some remarkable Jacob Bronowskian reasonings!
Jacob Bronowski, in his "Science and Human Values", mentions how Mount Everest hikers shows how perception works. Eric Shipton discovered new routes up Mount Everest even the locals didn't know about. He relates learning what the locals knew about Mount Everest,
"On the morning of the 27th we turned into the Lobujya Khola, the valley which contains the Khombu Glacier(which flows from the south and south-west side of Everest). As we climbed into the valley we saw at its head the line of the main watershed. I recognized immediately the peaks and saddles so familiar to us from the Rongbuk(the north side): Pumori, Lingtren, the Lho La, the North Peak and the west shoulder of Everest. It is curious that Angtarkey, who knew these features as well as I did from the other side and had spent many years of his boyhood grazing yaks in this valley, had never recognized them as the same; nor did he do so now until I pointed them out to him." - Eric Shipton(through Jacob Bronowski's "Science and Human Values", page 30)
Perception is like two complementary surfaces. Either the surfaces match, or they don't.  This is like the constituent relations stage of creative concept formation, as I mention in my Origins of mathematical knowledge(third post of this blog). Jacob Bronowski goes further . . .
Jacob Bronowski points out that true and false exists at the proposition level and not the formation of abstractions/concepts level(constituent relations level). Once the sense data is put into a concept form, then we ask what is true. "If this is really a mountain, we say, then the bearing of that landmark should be due east;"  I'd like to quote the Shakespear he also quotes as well,
"Is this a dagger, which I see before me, the Handle toward my Hand? Come, let me clutch thee-
      Come, let me clutch thee: I haue(have?) thee not, and yet I see thee still. Art thou not fatall Vision, sensible To feeling, as to sight? or art  thou but A dagger of the Minde, a false Creation?"
When I reread Jacob Bronowski, "Science and Human Values" up to these pages(not the whole short book), I found it remarkable that I was able to make connnections to his "Origins of Knowledge and Imagination".  I always considered his later book a later inspiration; it's certainly an elaboration, but to find that one can see the whole of Origins in his much earlier 1950's effort pleased me that his thought was consistent, although in a slightly different state of development. And of course, I point this out, because I found examples in Homer's Iliad!
I couldn't find an example of how perceptions work as complementary surfaces as Jacob Bronowski describes in my notes of Homer's Iliad; but, I did find the testing after the concept is made examples,
"There speaks Aineias, the wise councellor! Indeed yon man is exactly like Diomedes, if I may judge by the shield and the vizard, and I can see his horses. But I am not sure he is not really a god. If he is only a man, the clever son of Tydeus does not run mad like this without a god to back him. There must be some god beside him invisible, and he turned the shot aside even as it hit the man. For I have tried already, and I hit the right shoulder through the corselet-plate. I thought I should send him to hades, but yet I did not bring him down. It must be some angry god." - Pandaros(through Homer Iliad, chapter/book 5)
Homer's Iliad is about war.  It's even a little anti-war. Achilles refuses to get involved as long as possible. The question almost becomes "on who's side are the gods on?" Zeno uses the Achilles character in his paradoxe about how Achilles can never pass the tortoise because at each second, Achilles had to cross half the distance to the Tortoise.  Achilles can get close to the tortoise, but never pass the turtle. Zeno's paradoxes and really the Pythagorean discovery of the irrationality of the square root of two gave Greek mathematicians much trouble until Eudoxus made all his discoveries about proportions(in particular his definition of a real number, which is really just a definition in Euclid's Elements, book 5, definition 5). Getting back to the war themes of Homer . . . Homer uses lots of nature-poetry to describe all the experiences of war.  The Nature-poetry are observations of nature; they are the science of the times. The nature-poetry(always in connection with describing warfare), and the few mentions of astronomy suggests that the Greeks really came out of a 'dark ages' after the fall of the Bronze age cultures.  The Greeks got the knowledge of the twelve constellations from the Egyptians much later after Homer's time(remember the two constellations mentioned by Homer above - Orions belt and Ursa Major).
I'll mention a few examples of the nature poetry, and hopefully get around to posting lots more in the comments section.
"But as soon as Alexandros saw him come out in front, his heart sank and he slunk back into the ranks to save himself. He might have been some one walking through the woods who suddenly sees a snake, and jumps back all of a tremble pale with fear." (in book/chapter 3, near the beginning)
"Diomedes shuddered when he saw Ares. As a man after a long march stops helpless when he sees a furious river foaming and flowing along, and leaps back, so Diomedes leapt back, and cried out to his people:" (book/chapter 5)
Homer's astronomical knowledge is few and far in between, and his science is at the level of classification like what the early biologists did with his nature-poetry. Thomas Heath quotes a Plato dialogue Epinomis which says astronomy really began when mathematics was applied,
"the true astronomer will not be the man who cultivates astronomy in the manner of Hesiod(close but later contemporary of Homer) and many other writers of that type(Homer!), concerning himself only with such things as settings and risings, but the man who will investigate the seven revolutions in the eight revolutions and each describing the same circular orbit[i.e. the separate motions of the sun, moon, and the five planets combined with the eighth motion, that of the sphere of the fixed stars, or the daily rotation] which speculations can never be easily mastered by the ordinary person but demand extraordinary powers."
As it turns out, the Epinomis is of suspicious authorship.  It's probably not written by Plato, but a follower of Plato. Never the less, the point is that astronomy for the classical Greeks started when astronomy was mathematized to some degree(for them, it was at the level of circles within circles which the sun, the planets, and the stars are rotated on). From my 20/20 vision of reading this after reading the modern scholarly work on Greek astronomy, the author of the Epinomis also messes up by saying the astronomers who just observed risings and settings did not do astronomy mathematically spoke rashly!  Euclid wrote many other works besides his monumental Elements(which unifies in a deductive/axiomatic way all knowledge from the Babylonians to the Greeks up to Euclid's time).  He wrote on Optics, Mirrors, and some other works.  In his spherical geometry book, he derives the sphericity of the Earth and the Heaven's by risings, settings, and great circles.
Great circles are when their radius/diameter goes through the center.  Because of this property, all great circles bisect one another.  Euclid observed, or got from someone else not said, that because of the way the zodiacal constellations are divided into six at a time and other such astronomical observations about risings and settings, that various circular patterns in the sky are great circles; hence, the Earth and the circle the stars rotate on must be circular!
Getting back to the Epinomis quote, if astronomy starts with mathematics, then we should start with the first mathematician, Thales. Well, Thales was much greater as a mathematician than an astronomer, even with his prediction of a solar eclipse; Thales, if he did predict it, did so on Babylonian data.
Thales cosmology was actually similar to what's found in book/chapter 1 of the Hebrew bible's Genesis book. The sky is blue and so is the water, therefore, the sky is somehow water as well, and the Earth was created by the splitting of these waters. Besides inspiring Pythagoras to travel to Babylonia and Egypt as he did, he other colleague was Anaximander.
I've mentioned Anaximander's interesting insight that led him to think of evolution from non-life in a previous post of this blog. Anaximander innovated an arbitrary substance to create everything in the universe - instead of earth, fire, water, and air. He also thought this substance and the universe must be infinit; how else can everything keep going? The quote is "in order that the process of coming into being might not suffer any check." He introduced the Gnomon into Greece.  The Gnomon would be used as a sundial; in fact, he set up the first sundial in Sparta, a land more known for its military state. The Greek mathematicians would make much use of the Gnomon - for relating the infinit series of triangular and square numbers, and for geometric algebra. Carl Sagan likes Democritus as an especially insightful Greek even if the insights are not exactly proven mathematicaly; I do to, but Anaximander clearly to me seem to be on the level of Democritus as well!
Pythagoras innovated the idea that the Earth was a sphere. Nobody knows how.  Carl Sagan suspects that he observed that as a ship goes down beyond the horizon, then the Earth's surface is curved; if it's curved, then the curve could go all the way to a sphere. - self-interpolation, Aristotle mentions the evidence that because a boat can be seen dipping below the horizon, the Earth must be a sphere.

Self-interpolation - Iamblichus, who lived from 245 to 325 A.D, describes a story about how Pythagoras discovered musical scales.  He was passing by iron blacksmiths who were banging on the metal and creating tones. Pythagoras experimented with different weight hammers and found that hammers of simple ratios, of their weight generated harmonious sounds. He then generalized this to strings.  So, Pythagorases musical discoveries were inspired 1) by someone with a mathematical perspective, and 2) by the recent iron age revolution.
 Pythagoras also thought of the 'music of the spheres.' This thought allowed the Pythagoreans to find some of the order of the Planets. The Babylonians knew of the planets apart from the stars and even their retrograde motion, but the order of the planets was beyond them. As far as they knew, there was no order. Of course, the 'Music of the Spheres' is a wrong idea. Outside of Pythagorases mathematics, his idea that the Earth was a sphere is his important contribution.
The idea of the sphericity of the Earth suggested it could rotate.  Some Pythagoreans, Philolaus in particular, came close to the Heliocentric hypothesis that Copernicus is so famous for. Part of his reasoning had to do with explaining the phases of the moon. To explain the Moon's phases(and even solar eclipses), Philolaus innovated a counter earth that sometimes comes between us and the Sun and sometimes in between the moon as well. The issue of how the eclipse works influenced whether the Greeks believed in a Heliocentric or a Earth centered universe.  It should also be noted that this whole Greek heliocentric/Earth centered universe drama speaks to the fact that people really did believe the Earth and the Universe was flat. If they were discussing whether the universe and the Earth was round or not, then they and others before them thought the Earth/Universe was flat!
A couple of great ideas/discoveries before we get back to the solar system astronomy. Empedicles astronomy was pretty weak; he thought the universe was powered by love/hate relationships.  But, beyond that, he thought of air as a substance for the first time. Carl Sagan makes this famous in his Cosmos episode/chapter 7 about the Greeks. Empedicles took a spherical object that had two holes in it. One could put your thumb on one hole and put the sphere in a bucket of water, and the water won't go in. Or, one could put the sphere in the water without closing one of the holes and the water would go in. If you cover one of the holes with the water in and take the sphere out, the water doesn't come out! Empedicles discovered the invisible. Democrites would later be the first to suggest the universe is made of invisible atoms that combine in various ways. Getting back to astronomy . . .
Parmenides is generally credited with saying the moon shown by the light of the sun.  Anaxagoras, who lived around 510 to 428 B.C. made the connection between this Parmenides idea and the phases of the moon and how eclipses work.  Anaxagoras was jailed for his idea: this theory "fritter away the deity into unreasoning causes, blind forces, and necessary properties." Anaxagorases great connection is also like what Jacob Bronowski is talking about in his "Science and Human Values", about how the experience of Mt Everest hikers(both explorers and natives) as described above!
The Greeks were close to the heliocentric hypothesis. But, Hanno, a carthegenian, sailed to the edge of the Mediterraenean, a little past the rock of Gibraltar(which they'd of called the twin pillars of Hercules), and a little out into the Atlantic ocean and reported no counter Earth!  Likewise, other Greeks travelled to India and reported no counter earth; so, the Greeks stuck to the Earth centered theorizing!
This fact of the Greeks explorations led them to false conclusions(although disproving a false theory of the counter-earth; it was still a little bit of a setback) led them to continue developing the Eudoxus concentric spheres theory.  Eudoxus came up with it before the Hanno sea explorations; but, they didn't conclude one way or another between these theories. The Eudoxus concentric spheres theory is interesting for mathematical reasons.
Eudoxus as I've noted a recent previous post was taught by an Archytas. Archytas came up with a really elaborate intersection of various surfaces to solve a duplication of the cube problem. I didn't see any Greek reference for this idea, so I'm going to credit Thomas Heath for saying this . . . that Eudoxus was influenced to make his concentric spheres theory based on Archytas intersection of various surfaces. Thomas Heath, in his "Aristarchas of Samos" and his "Greek Astronomy" book goes to great lengths to explain Eudoxuses theory. Well, he shows some and a modern spherical trigonometric interpretation of it. If you see this, you'll gain a certain amount of appreciation for Eudoxus! Eudoxus creates an intersection of concentric spheres that makes for a figure eight as the resultant curve of the intersection of spherical surfaces. The sheres rotate in different ways, one for various phenomenon like the ecliptic, the rotation of the Earth and so on. He manages to come up with an approximation to the retrograde motion of the inner planets I do believe.  HIs concentric sphere's manages to simulate the observed motions to amazing accuracy!  But, unfortunately his theory is pretty inaccurate for the outer planets.

- self-interpolation, Cleomedes was a follower of Eudoxus.  He improved the Eudoxus system a little bit, but he appears to have made a greater discovery - atmospheric refraction. Cleomedes notes that earlier astronomers noticed some odd lunar eclipses.  Some of them occurred while the sun was still up.  How can this be? Cleomedes answer - atmospheric refraction. It takes the application of language to what we're seeing to note this.  This isn't something that one can just say 'an observation is an observational fact.'  In other words, this shows that an observational fact is not some unit devoid of reason. If we had just observed the fact, we never would have reasoned out the existence of atmospheric refraction, at least in this case.
After Eudoxuses time, Heraclides observed that mercury and venus follow the sun, while Mars, Jupiter, and Saturn do not. Once again, the Greeks were close to discovering the heliocentric hypothesis.  In fact, one Greek did put all these clues from Anaxagoras to Heraclides together and said the Sun is the center of the universe. Unfortunately for him and humanity really, Archimedes laughed him off the stage.  One of the few mentions of Aristarchuses heliocentric is in Archimedes Sandreckoner.  He says, "if Aristarchuses theory were true, the Stars would have to be ridiculously far away!"(my paraphrase; it's a few paragraphs long).

The only extant work we have from Aristarchus is about the sizes and distance of the sun and moon, which he gets pretty as wrong as any Greek before him. The mathematics is a bit involved. Unfortunately, the majority of it is results from previous people whom we don't know. It's one hypothesis after another including Anaxagorases about how eclipses work. A Greek named Posidonius calculated the size of the sun and its distance to far greater sizes, but even those calculations miss the mark by wide margins - almost ten thousand times the radius of the Earth, which makes the Sun 3 million stades(or stadium; a stade is various in ancient times from 157 feet to six hundred feet) in length.
Like Homer's nature-poetry, I hope to mention more Greek astronomy in the comments section that I didn't fit in the write-up.


  1. Oliver Dickinson, in his 'The Aegean from Bronze age to Iron age', beginning of the fifth chapter, mentions that the practice of chipped flint was still in use into the early Iron age!

    That is that stone age technology that goes back four millions years ago . . . the start of all technology, with the Australopithacines!

  2. What connections between ancient mathematics of the Greeks to the Calculus and then to all of Analyses? The theory of Proportion; differential calculus is proportions taken to a limit.

    As for integrals, that's just going from finding the area of straight line figures to curved geometric objects. All this of course leads to the mathematics of real numbers, and then to the continuum and George Cantor transfinite numbers and so on . . . see my post about the finite and infinit . . .

  3. Greek Astronomers knew the Ptolemaic(and Eudoxus and Aristotle crystal spheres) were artificial fictions, just for mathematical purposes. See Timothy Ferris "Come of Age in the Milky Way", page 30.

    "Proclus noted, "These circles exist only in thought . . . They account for natural movements by means of things which have no existence in nature."

  4. Hi there! This post couldn't be written any
    better! Looking at this article reminds me
    of my previous roommate! He continually kept talking about this.
    I most certainly will forward this information to him.
    Pretty sure he'll have a very good read. Thanks for sharing!

    1. I enjoyed rereading this. I remember thinking I need to come back to this and re-write it. Perhaps I do; but, it's not so bad!

      I'm glad you like this, and I hope your friend finds it interesting!