Reflections, Reflections

I am slowly progressing through “The Dream of Reason,” by Anthony Gottlieb, a light and breezy history of Western philosophy. I’m still in ancient Greece and that’s where I came upon this fella Zeno. Zeno caught my initial sympathy because he was regarded by some simply as a philosophical troublemaker and that’s always nice. Although the book tells very little of the politics and individual lives of these early philosophers, what is interesting is that almost every one of them was persecuted for political trouble making (or the perception that this is what their philosophying was all about). At the same time, Zeno instigated some initial antipathies in me by seeming to be just another lazy guy that poses idiotic musings for other wealthy lazy bums to play with all day long. Some people drink beer and shoot darts, others drink beer and shoot inane synapses to pass the time.

Zeno became famous because he started playing around with paradoxes. As I read Gottlieb’s Zeno chapter, I decided to try to solve the paradox before going on to read the solution. So I came to the first motion paradox:

Suppose, for the sake of illustration, that Achilles intends to run a race at the Great Panathenaea. Zeno points out that before Achilles can reach the finishing post, he must get halfway there. And before he can get halfway, he must get a quarter of the way. And before he can get a quarter of the way, he must get one-eight of a way, and so on. Zeno persuades Achilles that he cannot therefore run any distance at all, because before he can cover that distance, he will have to cover half the distance, ad infinitum.

First thought that sprang in my mind: I am standing, I take my right foot and lift and place it quite ahead of the left foot. With just one step I’ve covered all the infinities of subdivisions in the distance of Zeno’s paradox and there is not paradox at all. It’s solved. Then you just take your other foot and cover more distance. Where is the paradox, I asked myself? What Zeno had done is to subdivide infinitely a finite distance and not to add infinite additional measures to a finite distance. When I imagined the repeating subdivisions of the distance of one step, that long forgotten calculus and tending to infinite math stuff vaguely came back. But since I’m not a mathematician, I’m interested in solving these paradoxes by intuitive logic, not by math formulas.

So I was very disappointed with this first paradox because it doesn’t have good logic to it, but thanks to wikipedia, I found a great definition for paradoxes:

A paradox is an apparently true statement or group of statements that seems to lead to a contradiction or to a situation that defies intuition, such as "This statement is false". Typically, either the statements in question do not really imply the contradiction; or the puzzling result is not really a contradiction; or the premises themselves are not all really true (or, cannot all be true together). The recognition of ambiguities, equivocations, and unstated assumptions underlying known paradoxes has often led to significant advances in science, philosophy and mathematics.

So, you see, it’s very easy to intuitively solve this paradox, you just lift your foot and place it down and you know you can cover the “infinite” distance. That’s why I was disappointed as if I were dealing with a problem that's really hard to solve.

For me, what was really interesting about this paradox is the thought that you can, with only one step, truly cover infinity. This is a beautiful thought if you keep it at the metaphorical level, a symbol for the paramount importance of taking certain first steps in life.

Gottlieb has also more interesting things to say about this paradox and how other people love to take it as a starting point to peg their lofty musings about infinity (admittedly an interesting subject).

Then I went on to Zeno’s arrow paradox. This paradox seeks to show that an arrow which is apparently in flight is in fact motionless, since at any given time moment of its flight it occupies a space that is exactly equal to itself. (From wikipedia :) At every moment in time, the arrow is located at a specific position. If the moment is just a single instant, then the arrow does not have time to move and is at rest during that instant. Now, during the following instances, it then must also be at rest for the same reason. The arrow is always at rest and cannot move: motion is impossible.

First thought: this is also not a paradox in the sense that what he stated is not true. It is true. My immediate solution to this paradox was the relativity of moving objects. If object A is moving in relation to object B, who is to say it is not object B that is moving in relation to object A, that is, everything in motion depends on your point of reference. So, if the arrow was at distance zero from a rock at instance A, and then at 12” to the right from the rock at instance B, who is to say that it was not the arrow that remained still and the rock which moved 12” to the left of the arrow? And so on for each subsequent instance?

The explanation given by Gogglieb to the paradox, however, is another. It’s the very simple reality that motion is dependent on a time interval. It’s truly nice how the paradox seemingly hides that from you at first. This is called the static theory of motion. And I thought, “Why wasn’t my solution a solution to the arrow paradox?” But it was, as Gottlieb then goes on to explain that other Zeno paradoxes highlight that “nothing can be said to move in itself, but only with respect to other things.”

And I thought, “Yessssssss! You go, girl! Is that supposed to make you feel like Einstein or what?” Right there, I had my 3 seconds of Einstein glory. Beautiful relativity thinking. My elation didn’t last long, however. I had gone to wikipedia to read more on the subject and what does it tell me:

Several of Zeno's eight surviving paradoxes (preserved in Aristotle's Physics and Simplicius's commentary thereon) are essentially equivalent to one another; and most of them were regarded, even in ancient times, as very easy to refute.

How is one supposed to go on living with this kind of blow? You mean to tell me I thought I had brilliantly solved a 2000 year old paradox in under 30 seconds only to find out morons throughout the ages have been doing the same? I don’t know if I can go on. My 3 seconds of Einstein glory shattered into thousands of little pieces and scattered on the floor. Maybe there is a Zeno Paradox Solvers Support Group I can join.

However, even after my rough paradox solving reality landing, I tried flying again. Before reaching the Zeno chapter, a few days ago, I had read about Heraclitus and a particular thought has stayed with me since. Heraclitus was the dude who tried to make an impossible conversion of two opposite ideas: flux is unchanging. Consider Heraclitus' river example, told by Gottlieb:

Heraclitus stated, “As they step into the same rivers, other and still other waters flow upon them.” Here Heraclitus is drawing attention to the fact that each river really consists of perpetually changing waters. Thus if I step into the Thames at one place today and at the same place again tomorrow, I shall be stepping into different water each time. […] Although a river is just one river, it consists of many waters. And although it consists of many waters, still it is only one river.

When I reflected about what Heraclitus said, I tried to experience it regarding time. If time is passing, just like the waters flowing in a river, could I experience time passing? It was as if I held my breath (figuratively) and tried to feel time passing, the actual passing itself. You try to feel one second and then... it’s gone. You concentrate on your experience and another second just passes by too. Like that instant in the river, the world will never be the same again. All the things in the universe will never be exactly the same like they were that one second that just passed.

These thoughts and experiments made me fly to Zeno’s mount again. If the arrow is not moving, neither is time. A moment, like the arrow, is frozen, it does not move. Therefore time does not move as well, because it is composed of non-moving moments.

I am happy to announce that Alessandra’s time paradox is born! Which led me to another question:

Why does time pass?

This is the first philosophical “why” question that I find profoundly intriguing. I find the obsession with all the other similar existential ones tremendously annoying and stupid. What is reality? How do you know your big nose is real? Am I not a Martian butterfly dreaming I am a man?

Please. These questions are ones where I just roll my eyes over and say, “Get over it.” You’re real enough, trust me. Instead of getting 100 thousand tenured dollars a year to ask if you are featherbrained butterfly’s lunacy, let’s just pay you the minimum salary and I will bet you will smarten up about just how real the world is very quickly.

However time is another matter altogether, although there are more important things to think about. But what is time?


Time is so very intriguing.


p.s. I know this is nothing new to people who have thought about the concept of time, however I don't know the famous names of other people, besides Einstein, who have asked time concept questions, so for now, this will be Alessandra's Time Paradox, make that Alessandra's Grand Time Paradox.

related entry: Cogito...

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