Philosophy
On Columbus Day, it is probably worth discussing the fact that contrary to the storybook version of history that is part of our contemporary mythology, it was well-known in classical times that the world was, in fact, round.
We should start with the fact that there was among Greek thinkers a non-evidentially based bias in favor of thinking of the world as spherical. Symmetry, in Greek thought, was a measure of perfection. An equilateral triangle is more perfect than a scalene triangle because of its symmetry. Similarly, a square is more perfect than a triangle, not because it has more sides, but because if you rotated it about its mid-point, there are four ways to bring it back to its original orientation, whereas, only three for an equilateral triangle. You need to turn the triangle through 120 degrees to get it back to its original orientation, whereas you only need to turn the square through 90 degrees. The circle, on the other hand, has an infinite number of symmetries. turn a circle any amount and you still have the circle. circularity is perfection in geometry and the sphere is a circle of circles. It was on these grounds that Pythagoras and the Pythagorean-influenced later Plato argued for the shape of the globe.
Of course, this did not come from nowhere. The phenomenon of a ship disappearing as it approached the horizon gave experimental reason to believe that the Earth was curved. On a flat surface, the ship would simply get smaller, but on a curved planet, the curvature would obscure from view parts of the ship as it went farther and farther around.
But it is with Aristotle's On the Heavens, though, we begin to see complex argumentation. Again, Aristotle had metaphysical reasons to prefer a roughly spherical Earth. Everything from the moon on out was made up of a perfect element aether and were shaped spherically and moved in circular orbits because that was the nature of aether being more perfect. The Earth sat at the center of it all and was imperfectly circular because the elements down here were not quite so perfect. But they were jockeying about to settle in their natural places which formed concentric rings.
In addition to this cosmological picture, however, Aristotle did make several quite remarkably insightful arguments for the roundness of the world. First, he looks at the movement of heavenly bodies that trace out equal distances in rising and setting, not moving across the sky the way one would expect if the Earth was flat.
So, now you know that it was false that to his contemporaries, Columbus' belief that the Earth was round sounded like Greek to them.
We going out on that joke? No, we do reprise of song, that help. But not much, no.
- Brian Cox - Mars Loops The Loop
Thanks mainly to Aristotle's teleological metaphysics and the ancient idea that the heavens are a realm of perfection, it was believed for millennia that the celestial bodies moved along a perfect sphere around the Earth. Then some odd observations...
- Nicholas Of Kues..."ahead Of His Time In The Field Of Science"
Nicholas of Kues 1401 to August 11th, 1464 Cardinal Nicholas of Cusa was a "German theologian, influential philosopher, mathematician, and scientist. His scientific ideas, shrouded in theological language, were his personal speculations. Before Copernicus...
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"Poor Pluto: Number Of Dwarf Planets Increases" April 26th, 2010 SPACE DAILY New research from the Australian National University has further reduced the status of Pluto by suggesting there are many more dwarf planets in the Solar System than previously...
- A Perspective...natalie Angier On Vasily Kandinsky
“Several Circles” Vasily Kandinsky 1926 "The Circular Logic of the Universe" by Natalie Angier December 8th, 2009 The New York Times CIRCLING my way not long ago through the Vasily Kandinsky show now on display in the suitably spiral setting of...
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A 400 year old document is still interesting to read. Steven Kreis wrote... About ten months ago a report reached my ears that a certain Fleming had constructed a spyglass by means of which visible objects, though very distant from the eye of the observer,...
Philosophy
It's a Round, Round World
On Columbus Day, it is probably worth discussing the fact that contrary to the storybook version of history that is part of our contemporary mythology, it was well-known in classical times that the world was, in fact, round.
We should start with the fact that there was among Greek thinkers a non-evidentially based bias in favor of thinking of the world as spherical. Symmetry, in Greek thought, was a measure of perfection. An equilateral triangle is more perfect than a scalene triangle because of its symmetry. Similarly, a square is more perfect than a triangle, not because it has more sides, but because if you rotated it about its mid-point, there are four ways to bring it back to its original orientation, whereas, only three for an equilateral triangle. You need to turn the triangle through 120 degrees to get it back to its original orientation, whereas you only need to turn the square through 90 degrees. The circle, on the other hand, has an infinite number of symmetries. turn a circle any amount and you still have the circle. circularity is perfection in geometry and the sphere is a circle of circles. It was on these grounds that Pythagoras and the Pythagorean-influenced later Plato argued for the shape of the globe.
Of course, this did not come from nowhere. The phenomenon of a ship disappearing as it approached the horizon gave experimental reason to believe that the Earth was curved. On a flat surface, the ship would simply get smaller, but on a curved planet, the curvature would obscure from view parts of the ship as it went farther and farther around.
But it is with Aristotle's On the Heavens, though, we begin to see complex argumentation. Again, Aristotle had metaphysical reasons to prefer a roughly spherical Earth. Everything from the moon on out was made up of a perfect element aether and were shaped spherically and moved in circular orbits because that was the nature of aether being more perfect. The Earth sat at the center of it all and was imperfectly circular because the elements down here were not quite so perfect. But they were jockeying about to settle in their natural places which formed concentric rings.
Its shape must necessarily be spherical. For every portion of earth has weight until it reaches the centre, and the jostling of parts greater and smaller would bring about not a waved surface, but rather compression and convergence of part and part until the centre is reached. The process should be conceived by supposing the earth to come into being in the way that some of the natural philosophers describe. Only they attribute the downward movement to constraint, and it is better to keep to the truth and say that the reason of this motion is that a thing which possesses weight is naturally endowed with a centripetal movement. When the mixture, then, was merely potential, the things that were separated off moved similarly from every side towards the centre. Whether the parts which came together at the centre were distributed at the extremities evenly, or in some other way, makes no difference.
In addition to this cosmological picture, however, Aristotle did make several quite remarkably insightful arguments for the roundness of the world. First, he looks at the movement of heavenly bodies that trace out equal distances in rising and setting, not moving across the sky the way one would expect if the Earth was flat.
But the spherical shape, necessitated by this argument, follows also from the fact that the motions of heavy bodies always make equal angles, and are not parallel. This would be the natural form of movement towards what is naturally spherical.Second, he argues that the shape of the Earth is given away by the shape of its shadow during an eclipse.
How else would eclipses of the moon show segments shaped as we see them? As it is, the shapes which the moon itself each month shows are of every kind straight, gibbous, and concave-but in eclipses the outline is always curved: and, since it is the interposition of the earth that makes the eclipse, the form of this line will be caused by the form of the earth?s surface, which is therefore spherical.Next, he argues that the stars seen in different places are different and this could only happen if the world was round.
Again, our observations of the stars make it evident, not only that the earth is circular, but also that it is a circle of no great size. For quite a small change of position to south or north causes a manifest alteration of the horizon. There is much change, I mean, in the stars which are overhead, and the stars seen are different, as one moves northward or southward. Indeed there are some stars seen in Egypt and in the neighbourhood of Cyprus which are not seen in the northerly regions; and stars, which in the north are never beyond the range of observation, in those regions rise and set. All of which goes to show not only that the earth is circular in shape, but also that it is a sphere of no great size: for otherwise the effect of so slight a change of place would not be quickly apparent. Hence one should not be too sure of the incredibility of the view of those who conceive that there is continuity between the parts about the pillars of Hercules and the parts about India, and that in this way the ocean is one.So, Aristotle knew it was circular based on these arguments from observable evidence. Following him by a couple of generations was Eratosthenes, writing from Alexandra, a city of learning established in the memory of Aristotle's pupil Alexander. Eratosthenes found that at noon on the summer solstice, the sun would be directly overhead in the town of Syene by seeing it reflected from the water at the bottom of a very deep well. As a result, at that moment, a vertical object would have no shadow. If the Earth was flat, then the same ought to be true of a vertical object in Alexandria, north of Syene, when the sun reached its highest point in the sky there. Turns out, it doesn't. Objects in Syene have no shadow, but objects in Alexandria do. This means that the Earth must be round. Not only that, but by the length of the shadow, he was able to determine the circumference of Earth which he did with amazing accuracy.
So, now you know that it was false that to his contemporaries, Columbus' belief that the Earth was round sounded like Greek to them.
We going out on that joke? No, we do reprise of song, that help. But not much, no.
- Brian Cox - Mars Loops The Loop
Thanks mainly to Aristotle's teleological metaphysics and the ancient idea that the heavens are a realm of perfection, it was believed for millennia that the celestial bodies moved along a perfect sphere around the Earth. Then some odd observations...
- Nicholas Of Kues..."ahead Of His Time In The Field Of Science"
Nicholas of Kues 1401 to August 11th, 1464 Cardinal Nicholas of Cusa was a "German theologian, influential philosopher, mathematician, and scientist. His scientific ideas, shrouded in theological language, were his personal speculations. Before Copernicus...
- Alas Poor Pluto, I Knew Him Well
"Poor Pluto: Number Of Dwarf Planets Increases" April 26th, 2010 SPACE DAILY New research from the Australian National University has further reduced the status of Pluto by suggesting there are many more dwarf planets in the Solar System than previously...
- A Perspective...natalie Angier On Vasily Kandinsky
“Several Circles” Vasily Kandinsky 1926 "The Circular Logic of the Universe" by Natalie Angier December 8th, 2009 The New York Times CIRCLING my way not long ago through the Vasily Kandinsky show now on display in the suitably spiral setting of...
- Galileo's "the Starry Messinger"
A 400 year old document is still interesting to read. Steven Kreis wrote... About ten months ago a report reached my ears that a certain Fleming had constructed a spyglass by means of which visible objects, though very distant from the eye of the observer,...