Last week, I was given the
opportunity to interview one of the most influential and
noteworthy individuals in the history of mathematics. This
man, called Zeno of Elea, is widely known for his pronounced
doubt in mathematics. He has achieved the bulk of his fame
through his work with paradoxes; arguments dealing with reality
that are known for their illogicality. Although not
considered a mathematician by established standards, it is safe
to say that the world would not be as it is today were it not for
Zeno's contributions to the field. And now, readers, here
is the account of my talk with Zeno of Elea. I think that
you will find it as interesting and intriguing as I have, so
without further ado, I now present to you the aforesaid
conversation.Q: How about you start out by telling me a little about your background, Zeno?
A: Well, I was born in 495 B.C., in Elea, Italy. I grew up there, and I also lived in Athens, Greece for some time as well. My teacher in Elea was Parmenides, a great philosopher. That was how I wound up in Athens- I had accompanied him on a trip there. It was quite a memorable one too, for I had the pleasure of meeting Socrates and Plato, the latter of which was generous enough to include me as a character in one of his books.
Q: I understand you became quite accomplished in the affairs at Elea.
A: Yes, that is correct. I was politically involved in the city; I had a role in the government. I was also involved in education there. I met my teacher, Parmenides, at the Eleactic School, which focused on philosophy. The school was established by Parmenides and fellow philosopher Xenophanes, and as I was taught by them, I was also working on a project of my own. It is known as dialectic, a type of debate, you could say. It uses the process of reductio ad absurdum, the reduction of an idea to absurdity by an opposing speaker. In practice, this invention of mine has been utilized by arguers who have taken their adversaries' statements and have broken them down to form two contradictory conclusions, thus proving them ridiculous. The dialectic method has been and will probably continue to be taught at the Eleactic School.
Q: Very impressive. Very impressive, indeed. But while you did invent dialectic, you earned more fame from your paradoxes. Can you tell me about that?
A: Yes. As you know, a paradox is an argument that challenges the realness of something. Some of the things I have argued against are motion and time. While it seems apparent that motion and time do readily exist, I have come up with arguments that dispute that fact. People may think that it is absurd, but I believe that time, motion, and change are all illusions. And while some people do not believe in what I am saying, I can still support my views.
At this point, as Zeno told me that his paradoxes were openly opposed by many, and that he faced wide criticism, I saw how passionate he was about his work and I realized that he is extremely stubborn, yet admirably persevering, with an independent personality that allowed him to get this far in life without him being disconcerted by the extensive skepticism surrounding him and his works. I could tell he had a noble character, and this feature was even further accentuated by the graceful manner in which he handled himself. I went on to ask him more about his work.
Q: Can you give me an example of one of your paradoxes?
A: Well, I have many that argue over motion, but to pick one example, I'll tell you about The Achilles. Basically, this paradox says that the slower will never be overtaken by the quicker, contrary to popular beliefs. In a race where a slow tortoise has a head start, the faster-running Achilles will never win. He must first reach the point from where the tortoise first began. And by the time he has reached that point, the tortoise will have reached another point, point b. In the time it will take Achilles to then move to point b, the tortoise will have already gone to point c, and so on. So there you have it, in a race between the slower and the faster, if the slower has been given a head start, the faster can never win because the slower will always be some distance ahead.
Q: Wow. What you're saying really does make sense, although, as you pointed out, it does seem natural that it would be possible for the Achilles to overtake the tortoise… it really is a paradox! How about an example of a paradox concerning something other than motion?
A: Okay. Here is one regarding multiplicity: It is paradoxical that a line segment is limited and unlimited in number of points. It must be limited because the segment is just as many points as it is, no less and no more. It is thus compiled of a definite, or limited, number of points. However, the line segment must also be unlimited in number of points, because assuming that a line segment is composed of a multiplicity of points, then we can always bisect it. Once that segment is bisected, we can always bisect it again, and so every bisection leaves us with a line segment that can itself be bisected. This process of bisecting never ends, and since we never come to a stopping point, a line segment cannot be composed of a multiplicity of points. So you see, although it seems quite obvious that multiplicity, motion, and time, just to name a few, do exist, it really is quite simple to prove them illogical thoughts.
Q: Once again, that is very impressive. It is obvious that you have put a lot of thought and effort into your work.
A: Why, thank you. It is always nice to hear a compliment once in a while, aside from all the criticism I have received.
Q: You're welcome. I understand that you supported your teacher, Parmenides', views? Is that correct?
A: Yes, that is an accurate statement. He believed that reality was immutable, that it was set in its ways and immune to change. He also faced much opposition from the people for his beliefs. As his student, I picked up some of the things he believed in, I guess you could say he rubbed off on me because I too, began to publicize my views just as he did. I supported him just as I do now, and I am still trying to get people to see what we do. I am trying to further develop Parmenides' principles and his philosophies, while refuting the nonsensical ideas that some of our opponents throw at us. I even wrote one book on this, Epicheiremata, which defended Parmenides' ideas and demonstrated how others' views cannot be true. So yes, I do support him and I look up to him because of all he has done for me and how he has influenced my life and my beliefs.
Q: As you said before, there are people who tell you that your beliefs are incorrect. How do you feel about that?
A: Well, as anyone would be, I was first offended, discouraged, that people would say such things to me. But then as I watched and learned from Parmenides, if you mold yourself to please others, you will not get where you want to be. So now, when people tell me that my work is ridiculous, I simply ignore them and continue on with my life.
Q: I see. You should be a model for others to look at when they are in despair about public rejection of their ideas or beliefs. Well, I'm afraid our time has run out, but I truly enjoyed talking with you, Zeno. This has been a very educational and interesting experience for me. Thank you for meeting with me.
Zeno and I said our parting goodbyes, and then he left to return home where he will continue working on his book of time and motion arguments.
So, as you have now seen, Zeno has been a very busy man. A doubter of mathematics, he has introduced the world to new and unfamiliar ideas- that reality is unchanging and without plurality. He has certainly influenced society, and although his views are widely disputed and are looked down upon, the impact Zeno has made on life will always remain, no matter how trivial and absurd his paradoxes seem.
