Are we really in a Cave?

Is justice simply following the laws laid down by those in power? Or is justice defined by God or Gods? Or does justice eminate from some underlying principles of the universe (like the laws of geometry or physics)?

In Plato’s The Republic, Socrates discusses this issue with some friends on a balmy afternoon two and a half thousand years ago.  As the discussion unfolds Socrates comes to the conclusion that one cannot simply rely on examples of justice in practice because there will be good and bad examples that succeed or fail for the wrong reasons. Therefore, Socrates argued,  we need to look at the principles behind the forms of justice that we see. Socrates then expounded on his allegory of “the cave”. Without light we cannot see anything. But light does two things, it illuminates solid forms, but those forms also cast shadows. What happens if people mistake the shadows for the forms? Socrates goes into quite some detail to explain how people might mistake forms and shadows, and that there are forms for everything, including the ideal form of justice. Since there is an ideal form for justice, it also has a shadows, the imperfect execution of the ideal form of justice.

What if we are all like prisoners, said Socrates, and we are chained to a cave wall facing away from the opening of the cave and there are forms outside the cave that we can’t see? The light would enter the cave  from behind us and we can only see the shadows of the forms outside the cave. We will almost certainly mistake the shadows for the actual forms. But what if a man were to break free from the wall and climb outside and into the bright light and see what was out there. He would initially be blinded by the light, but as his eyes adjusted to the brightness he would start to understand what is really going on, the objects outside are casting shadows into the cave and he now sees quite clearly how what he thought was reality turns out to be only a small part of the real world. Excited about his discovery this man rushes into the cave to tell the others. But two things happen. His eyesight will still be adapted to the bright light and inside the cave will appear to be pitch black and he will stumble around. The other thing that will happen is that his cave-friends will scoff and jeer at him and they accuse him of being drunk or insane.

So why was Plato, through the character of Socrates, talking about caves and shadows and forms? Well back then they saw it as the job of the leaders to become educated about the ideal forms and lead the population out of the metaphorical cave, and that is why they discussed this in The Republic. In its ancient form this allegory may seem a little strange to us today. Perhaps it meant something more to the ancient mind, and today it has lost something in the translation. But there are historical examples that we may find that might make the allegory clearer for us.

So let us fast-forward by 2000 years to the 1500s. Galileo has been looking through his telescope and he sees that the Moon has large mountains  and huge flat areas that look like seas. He turns his telescope towards Venus and sees it has phases just like the Moon, and he looks at Jupiter and he sees that it has  its own moons orbiting around it.  Over the months and years that he spends looking through the telescope he starts to for a rather strange picture in his mind of what the universe is like. Perhaps the Earth goes around the Sun just like Jupiter has moons that orbit it? Perhaps the Moon and the other planets are whole worlds, just like the Earth, and not just points of light? Wow!!! If you were on Jupiter and you looked out through your telescope towards the Earth you would see the Earth as we see Jupiter. From Jupiter you would see the Earth as a crescent illuminated by the Sun with one moon going around it! Wow!! It is as if he had clambered out of the cave that everybody else was in and been exposed to a bright light. He could never return to that small Earth-centered view that everyone held back then, he had been exposed to where we really are in the universe.

But Galileo realized that there were many problems with his new-found perspective. For example, if we are on a planet that moves like the other planets and the other moons, why don’t we feel that motion? To argue that we orbit the Sun would only draw arguments from his peers and the public that we feel no motion. But worse, why don’t these other worlds come crashing down on us?  All that Galileo’s raw observations had done was to raise more questions than it answered. Observations were clearly not sufficient to convince anyone, the new perspective needed new knowledge that would enable people to make sense of what had been discovered by looking through the telescope.  Unfortunately for Galileo, the issues relating to the principles of  gravity would not be resolved satisfactorily until Newton came along a hundred year later.

However, Galileo started thinking about gravity and was somewhat troubled as he did. For example, everyone can see that heavy things fall faster than light things, right? Just drop a feather and a hammer and see which falls fastest….it’s clear…isn’t it? But Galileo knew that things are not always as they seem and he pondered this question further. So here is a simplified version of Galileo’s thought experiment about gravity.

Imagine a bowling ball. Bowling balls are pretty heavy. If you were to climb up a tower and drop a bowling ball you could use your stop-watch to measure the time it took for the bowling ball to fall to the ground.  Now you go to the bottom of the tower and pick up the bowling ball you just dropped and take it to your work-shop and saw it into two pieces, say into  2/3rds and 1/3rd.  Now climb up the tower and drop the two pieces of the bowling ball one after the other and time the time they take to reach the ground with your stopwatch again. What would you expect if heavy things fall faster than light things?  Well both pieces should take longer to fall to the ground than the whole bowling ball, right? In fact, you would expect that the whole bowling ball would take the least time to fall to the ground, the 1/3rd piece would take the most time to reach the ground and the 2/3rd piece would be somewhere in the middle. Right?

Ok so now you pick up both pieces and go to the top of the tower again. Now what you are going to do is tie both pieces of the bowling ball together by a piece of cotton thread. You hold the two pieces of bowling ball next to each other and drop them together. What does your theory predict?

If heavier things fall faster that light things, you would expect that the 2/3rd piece will fall slower than the whole bowling ball, but faster than the 1/3rd piece. At some point during the fall the cotton thread might become taught. Your theory now predicts that there will be a tug of war between the two pieces of the balling ball as the 1/3rd piece tries to tug the 2/3rds piece upward and the 2/3rds piece tries to tug the 1/3rd piece downward. Presumably the two pieces will fall at some average speed of each of the two separate pieces. In fact, your theory predicts that the speed of the two pieces attached by a cotton thread will reach the ground some time-interval less than the 1/3 rd piece but greater than the 2/3rd piece.

But what if we made the cotton thread shorter and shorter over a number of repetitions of the experiment, until the pieces of the bowling ball were tied together so close that they may as well have been the whole bowling ball. Should the two pieces fall at the same rate as the whole ball? Or slower, as if attached by the thread? And why should the length of the cotton thread make a difference? Clearly this is nonsensical!

So if we start out with an assumption and follow a good logical process and find that we reach a nonsensical result, we must go back and re-examine our original assumption. In this case the assumption was that heavy things fall faster than light things! But if we discard the assumption that heavy things fall faster than light things, what are we left with? No matter how counter-intuitive it seems, we are left with a starting assumption that all things must fall at the same rates!! And this is why Galileo went out dropping heavy objects from towers, to test the result of his thought experiment–that all things fall at the same rate.

Notice that what Galileo was doing was putting logic first and experimentation second. Experiments were at the service of logic. That is, Galileo spent considerable effort examining the underlying principles of the universe first and then checking the outcomes of his thoughts with actual experiments to make sure that his starting assumptions were valid. In modern philosophical terms we might say that Galileo’s thought experiment was deductive, and his experiments were inductive. Deductive meaning thinking abstractly and looking for general principles from which we could understand specific phenomenon. While his experiments were inductive, because the specific trials were used to point at the more general principles. Modern science has been built on Galileo’s method of using deduction and induction together to build up our knowledge.

And Galileo was building on Plato’s idea of forms, that you must look for the underlying principles (the forms illuminated by the light) and not be seduced into leaping straight into believing what you see (confusing the shadows of the forms with the forms themselves).

So what did Plato predict would happen when Galileo went out enthusiastically pronouncing his discoveries?  Indeed those in power at the time, it happened to be the Pope and the church back then, thought Galileo was insane. So fearful were they of what they considered to be  Galileo’s flawed logic that they locked him up to keep him from harming others minds and in an attempt to silence him they accused his writings of being heretical and banned them.

What did Galileo say about all that? “Wisdom is written in that great book–I mean the universe–which stands continually open to our gaze, but we cannot understand it unless we first learn the language in which it is written. This book is written in the language of mathematics, and the symbols are triangles, circles and other geometrical figures, without which it is impossible to comprehend a single word of it. Without this language one is wandering about in a dark labyrinth”. (Quote attributed to Galileo from The Assayer, 1623, Thomas Salusbury) Doesn’t that sound like Plato’s allegory of The Cave?

Perhaps Galileo had read  Plato’s The Republic, or perhaps he hadn’t,  we can’t be sure. Even so, Galileo’s method for acquiring knowledge was predicted as being sound by Plato. So to, unfortunately, Plato had predicted the public’s reaction to ground-breaking knowledge–Plato’ prediction is not good, but perhaps if we take heed of the lessons in history we may do it better in the future.