Steven Dutch, Natural and Applied Sciences, Universityof Wisconsin - Green Bay
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The ancient Greeks weren't trying to be us. They didn't know our sort of world was possible. In many cases they were trying to answer the big questions: what is motion? What is cause and effect? It wasn't at all clear that meticulous observations of commonplace natural phenomena would lead anyplace. Add to that the pervasive disdain for manual labor that permeated the intellectual community pretty much up till the time of James Watt, and it's not hard to see why they didn't develop science as we know it. But the clearest exposition of the fatal conceptual errors the Greeks made is probably in Aristotle's On the Heavens. Quotes are from The Internet Classics Archive.
A magnitude if divisibleone way is a line, if two ways a surface, and if three a body. Beyondthese there is no other magnitude, because the three dimensions areall that there are, and that which is divisible in three directions is divisible in all. ... We cannot passbeyond body to a further kind, as we passed from length to surface,and from surface to body. For if we could, it would cease to be truethat body is complete magnitude.
We're not off to a very promising start. Aristotle can certainly be forgiven for assuming there are only three spatial dimensions. Even modern scientists and mathematicians have trouble thinking about higher spatial dimensions, even though we can do the mathematics perfectly well. Aristotle could have taken three dimensions as given, or he could have tried to work out the implications of more dimensions and then argued that we don't observe those phenomena.
Instead, he commits an elementary fallacy - a circular argument. There is nothing else beyond body (three dimensional solid) because if there were, then there would be something else beyond body.
It's in Part 2 that we may find the clearest exposition of how ancient science went wrong.
The question as to the nature of the whole, whether it is infinitein size or limited in its total mass, is a matter for subsequent inquiry.
Good move. An impossibly turgid discussion of this topic makes up much of the early part of his Physics.
We will now speak of those parts of the whole which are specificallydistinct. Let us take this as our starting-point. All natural bodiesand magnitudes we hold to be, as such, capable of locomotion; fornature, we say, is their principle of movement.
I guess there's no harm in assuming everything is capable of motion, but there is also no deep conclusion to be drawn, either. By linking motion to a "principle," that is something inherently linked to matter, Aristotle has waded knee deep into a morass.
But all movement thatis in place, all locomotion, as we term it, is either straight orcircular or a combination of these two, which are the only simplemovements. And the reason of this is that these two, the straightand the circular line, are the only simple magnitudes.
Now he's waist deep. Yes, you can describe all motion as a compound of linear and circular motion. For that matter, vectors treat all motion as combinations of linear motion. And it makes sense to do this kind of analysis because lines and circles are easy to analyze. But that's solely a matter of mathematical convenience to us. It says nothing at all about the kinds of motion that exist.
In his Physics, Aristotle devotes much effort to distinguishing properties that are "essential" from those that are "accidental." Having weight is essential to a stone, being red is accidental. The stone could just as easily have been gray or black. Aristotle's fundamental mistake here is failing to realize that the geometric description of motion is accidental, not essential. The shape of an object's path is wholly dictated by external forces. The motion itself has no other meaning. A stone in a sling moves in a circular path solely because the sling is the radius of a circle, and the motion itself has no other significance. In fact, all motion itself is accidental. A stone might be at rest on the ground, or in linear motion because you throw it, or in circular motion because you are slinging it.
We have now encountered the two chief fallacies that derailed Greek science, and the whole Western world, for that matter:
Now revolutionabout the centre is circular motion, while the upward and downwardmovements are in a straight line, 'upward' meaning motion away fromthe centre, and 'downward' motion towards it. All simple motion, then,must be motion either away from or towards or about the centre. Thisseems to be in exact accord with what we said above: as body foundits completion in three dimensions, so its movement completes itselfin three forms.
If "up" is away from the center, and "down" is toward the center, then Aristotle must have believed the earth is a sphere, right? Yet another demolition of the myth that people in ancient times thought the earth was flat.
And Aristotle comes this close to drawing the correct conclusion about motion in three dimensions. A rock has three dimensions because it has length in a vertical direction, from right to left, and from front to back. Motion has three dimensions because something can move in a vertical direction, from right to left, and from front to back. Instead, he falls back on numerological mumbo jumbo, classifying motion as circular, upward, or downward to get his mystical three. His failure to consider horizontal motions has enormous negative ramifications for science. Actually, he comes so agonizingly close. If circular motion is motion about the center, then motions parallel to the surface of the earth are actually circular, which means they must be the same as circular motions in the heavens. He could have avoided the false dichotomy between celestial and terrestrial that burdened science up to the time of Galileo, but he muffed it. Now he's chin deep in the swamp.
Bodies are either simple or compounded of such; and by simple bodiesI mean those which possess a principle of movement in their own nature,such as fire and earth with their kinds, and whatever is akin to them.
Now he's in over his head. We have come 777 words in the translation used here. It has taken Aristotle a mere 777 words to shunt science off onto a dead end that we won't extricate ourselves from for close to 2,000 years. He has assumed there is a fundamental link between matter and motion, he has assumed the geometry of motion has special properties, and now he's assuming that certain materials inherently possess motion as a property. All of it completely wrong.
Supposing, then,that there is such a thing as simple movement, and that circular movementis an instance of it, and that both movement of a simple body is simpleand simple movement is of a simple body (for if it is movement ofa compound it will be in virtue of a prevailing simple element), thenthere must necessarily be some simple body which revolves naturallyand in virtue of its own nature with a circular movement.
Rephrasing: Supposing, then,that there is such a thing as simple movement [there isn't], and that circular movementis an instance of it [it isn't], and that both movement of a simple body is simpleand simple movement is of a simple body [these don't even rise to the level of being false - they're simply meaningless. What he appears to mean is that if a motion is simple - linear or circular - then the body with that motion must be simple.] (for if it is movement ofa compound it will be in virtue of a prevailing simple element) [Except when the body isn't simple after all], thenthere must necessarily be some simple body which revolves naturallyand in virtue of its own nature with a circular movement [non-sequitur].
We can see the groundwork being laid for the geocentric picture of the Universe, with the heavenly bodies having inherently circular motion. All based on a grand non sequitur. Just because a type of motion can be said to exist doesn't mean there must be a body which possesses it.
By constraint,of course, it may be brought to move with the motion of somethingelse different from itself, but it cannot so move naturally, sincethere is one sort of movement natural to each of the simple bodies.
Talk about a missed opportunity. If, say, a stone in a sling has circular motion only by constraint, maybe all circular motion is by constraint? Maybe the planets move in circles only because they're constrained?
Again, if the unnatural movement is the contrary of the natural anda thing can have no more than one contrary, it will follow that circularmovement, being a simple motion, must be unnatural, if it is not natural,to the body moved.
Motion is unnatural unless it is natural. We can see why philosophy has been regarded as the pinnacle of human intellectual endeavor for thousands of years. And what says something can only have one contrary? Saying Milwaukee is the capital of Wisconsin is the contrary to saying Madison is the capital, but so is saying Green Bay, or Sheboygan, or Superior is the capital.
If then (1) the body, whose movement is circular,is fire or some other element, its natural motion must be the contraryof the circular motion. But a single thing has a single contrary;and upward and downward motion are the contraries of one another.If, on the other hand, (2) the body moving with this circular motionwhich is unnatural to it is something different from the elements,there will be some other motion which is natural to it. But this cannotbe. For if the natural motion is upward, it will be fire or air, andif downward, water or earth.
I bet Aristotle never went fishing. Everyone who's ever gone fishing has been confronted with a snarl where, the more you try, the worse it gets. The only cure is to cut the mess off and start over. Aristotle is hopelessly snarled here. He's way over his head in the morass and sunk deep into the mud on the bottom. Having already erroneously decided that he knows what kinds of motions exist, and what sorts of matter naturally possess what kinds of motion, he just keeps piling wrong conclusions one atop the other.
Further, this circular motion is necessarilyprimary. For the perfect is naturally prior to the imperfect, andthe circle is a perfect thing. This cannot be said of any straightline: not of an infinite line; for, if it were perfect, it would havea limit and an end: nor of any finite line; for in every case thereis something beyond it, since any finite line can be extended.
Even in Aristotle's day, this was simply nonsense. A circle and an infinite straight line are the only two simple forms that are self-similar, that is, any part is like any other. We now know of self-similar fractal forms, but we can forgive the ancient Greeks for not knowing. However, an infinite straight line has the property that every portion, whatever its size, is exactly like every other portion. You can't say this about circles. Any 10-degree arc of a given circle is like any other, but it's not like a 10-degree arc of a different sized circle, nor is it like a 20-degree arc of any other circle. A millimeter of an infinite straight line is exactly like a segment a light year long. Aristotle says an infinite line can't be perfect because it has no end, and a finite line can't be perfect because it has an end.
Clearly, Aristotle has some sort of mystical attachment to circles. And another golden opportunity goes by. Because if he'd decided straight lines were the perfect form, he might possibly have groped his way to the concept of momentum and Newtonian physics.
Here we go. Road map to the Middle Ages.
Andso, since the prior movement belongs to the body which is naturally prior,and circular movement is prior to straight, and movement in a straightline belongs to simple bodies-fire moving straight upward and earthybodies straight downward towards the centre-since this is so, it followsthat circular movement also must be the movement of some simple body.
For the movement of composite bodies is, as we said, determined bythat simple body which preponderates in the composition. These premisesclearly give the conclusion that there is in nature some bodily substanceother than the formations we know, prior to them all and more divinethan they.
Not a single premise in that paragraph is true and not a single statement follows from any other:
At any rate the evidence of all other cases goes to showthat it is the unnatural which quickest passes away. And so, if, assome say, the body so moved is fire, this movement is just as unnaturalto it as downward movement; for any one can see that fire moves ina straight line away from the centre. On all these grounds, therefore,we may infer with confidence that there is something beyond the bodiesthat are about us on this earth, different and separate from them;and that the superior glory of its nature is proportionate to itsdistance from this world of ours.
So there we are, locked to the notion that circular motion is inherently superior and that bodies that possess it must be inherently superior as well.
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