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Plato’s Allegory of the Cave

Plato’s ‘Allegory of the Cave’ is a famous section from his Republic, an influential meditation on how human societies should be organized. This allegory is meant to provide support for the idea that the most worthy ruler of his republic would be someone who saw the truth most clearly: the philosopher king.

The Republic

By Plato

Written 360 B.C.E

Translated by Benjamin Jowett

Book VII

Socrates – GLAUCON

And now, I said, let me show in a figure how far our nature is enlightened or unenlightened: –Behold! human beings living in a underground den, which has a mouth open towards the light and reaching all along the den; here they have been from their childhood, and have their legs and necks chained so that they cannot move, and can only see before them, being prevented by the chains from turning round their heads. Above and behind them a fire is blazing at a distance, and between the fire and the prisoners there is a raised way; and you will see, if you look, a low wall built along the way, like the screen which marionette players have in front of them, over which they show the puppets.

I see.
And do you see, I said, men passing along the wall carrying all sorts of vessels, and statues and figures of animals made of wood and stone and various materials, which appear over the wall? Some of them are talking, others silent.

You have shown me a strange image, and they are strange prisoners.
Like ourselves, I replied; and they see only their own shadows, or the shadows of one another, which the fire throws on the opposite wall of the cave?

True, he said; how could they see anything but the shadows if they were never allowed to move their heads?

And of the objects which are being carried in like manner they would only see the shadows?

Yes, he said.
And if they were able to converse with one another, would they not suppose that they were naming what was actually before them?

Very true.
And suppose further that the prison had an echo which came from the other side, would they not be sure to fancy when one of the passers-by spoke that the voice which they heard came from the passing shadow?

No question, he replied.
To them, I said, the truth would be literally nothing but the shadows of the images.

That is certain.
And now look again, and see what will naturally follow it’ the prisoners are released and disabused of their error. At first, when any of them is liberated and compelled suddenly to stand up and turn his neck round and walk and look towards the light, he will suffer sharp pains; the glare will distress him, and he will be unable to see the realities of which in his former state he had seen the shadows; and then conceive some one saying to him, that what he saw before was an illusion, but that now, when he is approaching nearer to being and his eye is turned towards more real existence, he has a clearer vision, -what will be his reply? And you may further imagine that his instructor is pointing to the objects as they pass and requiring him to name them, -will he not be perplexed? Will he not fancy that the shadows which he formerly saw are truer than the objects which are now shown to him?

Far truer.
And if he is compelled to look straight at the light, will he not have a pain in his eyes which will make him turn away to take and take in the objects of vision which he can see, and which he will conceive to be in reality clearer than the things which are now being shown to him?

True, he now
And suppose once more, that he is reluctantly dragged up a steep and rugged ascent, and held fast until he ‘s forced into the presence of the sun himself, is he not likely to be pained and irritated? When he approaches the light his eyes will be dazzled, and he will not be able to see anything at all of what are now called realities.

Not all in a moment, he said.
He will require to grow accustomed to the sight of the upper world. And first he will see the shadows best, next the reflections of men and other objects in the water, and then the objects themselves; then he will gaze upon the light of the moon and the stars and the spangled heaven; and he will see the sky and the stars by night better than the sun or the light of the sun by day?

Certainly.
Last of he will be able to see the sun, and not mere reflections of him in the water, but he will see him in his own proper place, and not in another; and he will contemplate him as he is.

Certainly.
He will then proceed to argue that this is he who gives the season and the years, and is the guardian of all that is in the visible world, and in a certain way the cause of all things which he and his fellows have been accustomed to behold?

Clearly, he said, he would first see the sun and then reason about him.

And when he remembered his old habitation, and the wisdom of the den and his fellow-prisoners, do you not suppose that he would felicitate himself on the change, and pity them?

Certainly, he would.
And if they were in the habit of conferring honours among themselves on those who were quickest to observe the passing shadows and to remark which of them went before, and which followed after, and which were together; and who were therefore best able to draw conclusions as to the future, do you think that he would care for such honours and glories, or envy the possessors of them? Would he not say with Homer,

Better to be the poor servant of a poor master, and to endure anything, rather than think as they do and live after their manner?

Yes, he said, I think that he would rather suffer anything than entertain these false notions and live in this miserable manner.

Imagine once more, I said, such an one coming suddenly out of the sun to be replaced in his old situation; would he not be certain to have his eyes full of darkness?

To be sure, he said.
And if there were a contest, and he had to compete in measuring the shadows with the prisoners who had never moved out of the den, while his sight was still weak, and before his eyes had become steady (and the time which would be needed to acquire this new habit of sight might be very considerable) would he not be ridiculous? Men would say of him that up he went and down he came without his eyes; and that it was better not even to think of ascending; and if any one tried to loose another and lead him up to the light, let them only catch the offender, and they would put him to death.

No question, he said.
This entire allegory, I said, you may now append, dear Glaucon, to the previous argument; the prison-house is the world of sight, the light of the fire is the sun, and you will not misapprehend me if you interpret the journey upwards to be the ascent of the soul into the intellectual world according to my poor belief, which, at your desire, I have expressed whether rightly or wrongly God knows. But, whether true or false, my opinion is that in the world of knowledge the idea of good appears last of all, and is seen only with an effort; and, when seen, is also inferred to be the universal author of all things beautiful and right, parent of light and of the lord of light in this visible world, and the immediate source of reason and truth in the intellectual; and that this is the power upon which he who would act rationally, either in public or private life must have his eye fixed.

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Essays

Aristarchus and the distance to the Moon

Source: G Kalyakin. Wikimedia Commons.
Source: G Kalyakin. Wikimedia Commons

And some things that should not have been forgotten were lost. History became legend. Legend became myth. And for two and a half thousand years, the ring passed out of all knowledge. — JRR Tolkien, Lord of the Rings

The figure above is a sequence of images of a total lunar eclipse. Note the shape of the Earth’s shadow.

How do we measure distances in everyday life?

There are a variety of ways we judge distances as we navigate the world. Here is a short list (from Wikipedia):

  • Parallax (binocular vision)
  • Motion parallax (following moving objects across our field of view)
  • Depth from motion (change in apparent size)
  • Perspective (using knowledge of shapes)
  • Relative size (compared to a known object)
  • Luminance contrast (distant things appear hazy)
  • Occulomotor cues (you perceive how much your eye needs to distort to focus on the object)
  • Occlusion (near things occlude far things)
  • Texture gradients (details are discerned if close)

None of these will work for measuring the distances to astronomical objects, except for parallax, but even then only by using artificial means. The naked eye cannot judge distances to objects like the Moon or Sun.

How did Aristarchus estimate the distance to the Moon?

By measuring the time it took for a moon to cross the center of the Earth’s shadow during an eclipse. (We’ll use round numbers below for simplicity.)

  • The longest eclipses take about t = 3 hours = 1/8 day.
  • Assume the Earth’s shadow is a cylinder with the same diameter as the Earth, d=2 r. (This is a good approximation, if the Sun is much farther away than the Moon. It requires assuming that the Moon shines by reflected light from the Sun.)
  • The Moon travels around the circumference of its orbit in one month, T = 30 days. Assume the speed along the orbit is constant. Therefore, using ‘speed = distance traveled/time’ we have (2π R)/T = 2r/t.
  • Solve for R/r = T/(π t) = 30/(3/8) = 80. (Note: I have used π  = 3, which in technical mathematical terms is a ‘brutal’ approximation, keeping only the first significant digit.)

This means that the Moon is about 80 Earth radii away from us. The true value is closer to 60, but the order of magnitude is correct.

Naked eye observations of lunar eclipses easily reveal that the Earth’s shadow is curved, not a straight line. Lunar eclipses occur several times a year, so they are fairly common. Why wasn’t it obvious from simple observations like this that Earth was a sphere? Many ancient astronomers, like Aristarchus, understood what they were looking at, and were convinced the Earth was a sphere, but some later cultures did not. Discoveries can be forgotten.

Psychologists and cognitive scientists have found that when a sensory stimulation, an observation, or other piece of evidence, violates our intuition we sometimes don’t see it, or don’t process it. We can memorize a 200 word poem easier than 200 random words. Why? It has something to do with the poem having structures and patterns that help us to understand it (e.g. rhythm, rhyme, as well as imagery, and other aspects that help it to make ‘sense’ to us), where a random set of words does not. Memorizing chess pieces on a board is similar: if the pattern arises from a game, a chess master will do far better than an ordinary mortal at memorization. If the pattern of pieces does not arise from a game, they do no better than anyone else.

We are bombarded all day long with sensory input. If we did not organize this somehow into an internal theory of the world, we would not be able to function. Most of this becomes second nature to us as we grow up, so we stop thinking about it. This internal ‘world theory’ becomes a kind of filter on our experience. It allows us to function and thrive, yet it can also keep us from seeing things that are right in front of us.

One goal of a liberal arts education is to reawaken your sense of newness, to keep you alive to the fact that the way you see the world is not the only ‘right’ way, and to rekindle your sense of wonder so you stay open to new ideas and new ways of doing things.

The ancients were not stupid, or even ignorant in some ways, but they did have an intuition about how the world worked and this could make it difficult to see things right overhead that violated their intuition. This is not uncommon today. Psychologists have a term for this difficulty in integrating new information that runs counter to our intuition: cognitive dissonance.  What types of things are right under our nose that we overlook because it doesn’t fit our preconceived notion of how the world works? [1]

Here is one of my favorite literary quotes on this matter:

A pair of wings, a different respiratory system, which enabled us to travel through space, would in no way help us, for if we visited Mars or Venus while keeping the same senses, they would clothe everything we could see in the same aspect as the things of the Earth. The only true voyage, the only bath in the Fountain of Youth, would be not to visit strange lands but to possess other eyes, to see the universe through the eyes of another, of a hundred others, to see the hundred universes that each of them sees…

— Remembrance of things past, by Marcel Proust

The challenge is always to try and see the world anew, to be astonished by it, like a child. The best scientists are often a bit childlike, because they try to preserve this sense of wonder intentionally.

In sum: Aristarchus drew upon evidence that was open and available to everybody. It was above their heads, and available to anybody who was able to see with an open mind.

1] See, for example, “Anomaly and the Emergence of Scientific Discoveries,” Chapter VI of The Structure of Scientific Revolutions by Thomas S. Kuhn. Kuhn describes an experiment by the psychologists Bruner and Postman where test subjects were asked to identify playing cards, having been told they were being tested on how quickly they could correctly identify the card. In fact, some playing cards were anomalous (e.g. a red four of spades, or a black ace of diamonds). Most test subjects did not detect the anomalies, but assigned the cards to one of the familiar — expected — categories. Even when given quite a long time to view the cards, they reported having a sense that something was wrong, but couldn’t articulate what the problem was. Many reported that viewing these anomalous cards was unsettling.

Copyright © Eugene R. Tracy

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 No part of this essay may be reproduced in any form or by any electronic or mechanical means including information storage and retrieval systems, without permission in writing from the author.

 

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Robert Boyle and W&M

robert-boyle

Robert Boyle [1627-91], of ‘Boyle’s Law’ from chemistry, is connected to W&M through a gift he left upon his death. These funds went to establish ‘Indian Schools’, one at Harvard and one at W&M. The website in the previous link provides more information on this connection between the new College in Virginia, and the Old World and one of the leading figures of 17th century science and philosophy. There is even a W&M Boyle Society, a philanthropic group.

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Web sites

American Institute of Physics history of cosmology web portal

This is a good online resource for the history of astronomy and cosmology:

http://www.aip.org/history/cosmology/

 

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Web sites

UNESCO World Heritage Astronomy sites

UNESCO has a program to protect extent astronomical sites worldwide that are part of our shared cultural heritage. The main website is here, while the portal with an interactive map of the sites is here.