Considering Time II - Zeno

                Zeno of Elea was one of those ancient philosophers who greatly impacted classical thought, yet was survived by none of his works. This, it seems, was a common theme in those days, when students ardently scribbling notes saved the legacies of their teachers. In this case, Zeno’s legacy was preserved by Aristotle and Simplicius. (Cajori, 1920)  While Zeno had many interesting theories and teachings, the ones on which I am focusing today is his concept of instants and motion as is illustrated in his “Dichotomy Paradox” and “Paradox of Achilles and the Tortoise”.

         It was on an overcast, slightly rainy afternoon much like this current one, when I was first introduced to what, at the time, was merely stated as “Zeno’s Paradox” (I had little idea at the time that there were even more paradoxes).  On that afternoon, I had chosen to remain indoors during recess on a typical midweek day in high school. As others headed outside to throw the football, I had accepted an invitation to play chess from my math teacher. I can’t think of anyone who would really want to spend recess with their math teacher, but there was something different about this one.  First of all, I am not entirely sure that he was genuinely a teacher of mathematics, but rather someone who understood it and had a passion for it, and was both willing and eager to convey that knowledge to unruly young men.  He was a peculiar man, short and slight of frame with an asymmetrical face and a slightly warped hand from an accident earlier in life.  I recall his jackets and sweaters being perpetually coating in chalk dust and, often, he would become so engrossed in the topic he was scrawling on the blackboard, that he would be unaware of the derision of his students behind him.  But I found something fascinating about what he had to share – he mentioned names of philosophers that were uncommon, and occasionally verboten, in the halls of the Catholic school; there was something quite nearly Jesuit in his attitude, despite being a layman.  So it was that we sat, moving our pawns cautiously when he distracted me with a nod at the door behind me.

         “Zeno would say that your classmate just achieved the impossible, walking out the door like that.” He smiled and I watched his scarred thumb grip a plastic chess piece (the best and most prudent material for chess boards in service at a boys’ school).

         “Who?” I was perplexed.

         “Zeno, the Greek philosopher.” It was then that he explained Zeno's “Dichotomy Paradox”, while simultaneously derailing the momentum of my pawns seizing the center of the board (which I would later understand as the "Italian Game” opening”). This would also be a memorable enough conversation for me to remember twenty-three years later on a quiet mid-week afternoon.

         The “Dichotomy Paradox” is as simple as it is profound:  

         If something is not in motion, it must be at rest.

         If something is at rest, it cannot be coming to a rest.

         Everything naturally capable of motion or lack thereof will be in motion or at rest.

         Anything in motion must occupy a period of time.

        

         Everything which moves, therefore, must necessarily initiate movement across an infinite number of distance measurements (movement which also occupies an infinite number of split moments).  Zeno refers to the initial split moment, the one in which an object initiates movement or comes to rest, as the “primary time”. (Aristotle, 2009)  As demonstrated in the picture, the figurine must break through that wall of perpetually moving the first increment of distance/time in order to travel the indicated 28 increments. 

         “The Paradox of Achilles and the Tortoise” is related to the Dichotomy Paradox except that the goal (the tortoise which Achilles is chasing) is provided a head start and a constant rate of movement lower than Achilles. Zeno reasons that Achilles will be forever caught in a cycle of catching up to the tortoise’s last position, although one can imagine that at a certain point Achilles would simply have to reach out his arm to catch it.

         Certainly, this seems absurd to someone who is casually introduced to it. One can imagine Aristotle thought as much as evidenced by his response in Physics:         

         “Zeno's reasoning, however, is fallacious, when he says that if everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless. This is false, for time is not composed of indivisible moments any more than any other magnitude is composed of indivisibles.  Zeno's arguments about motion… cause so much disquietude to those who try to solve the problems that they present…” (Aristotle, 2009) 

         Aristotle’s critique is exactly what most sane people would likely consider when taking the time to examine Zeno’s paradoxes.  After all, why would anyone view time in slices or portions as Zeno has done?  But what is remarkable is that modern science may actually support Zeno’s theory.  We perceive reality around us based upon light hitting our photoreceptors via the cornea. (BrainFacts/SfN, 2012)  This, in turn, contributes to a follow-on process involving our primary visual cortex which relays the information onward – resulting in us perceiving our surroundings.  But the reality we perceive is not quite in real-time, demonstrated by the “flash jump illusion” from the University of Wisconsin: https://www.salk.edu/images/video/Reynolds_video.html.  This illusion demonstrates that the brain is trying to compensate for a delay of up to 70 milliseconds for the brain to process a stimulus. (Salk Institute, 2006) 

         Ok, before we go down the neurology rabbit hole, let’s get back to Zeno.  There’s a delay in processing information. But we process it nonetheless. We process photons of light that reach our eyes.  Would this knowledge, if possessed by Aristotle, cause him to view Zeno’s paradoxes differently? After all, Aristotle had his own questionable and hotly debated theories on sensual perception. (Shields, 2016) 

         We can probably all agree that Zeno’s paradoxes are demonstrably untrue, in the context of “never being able to take that first step” or “Achilles never surpassing the tortoise”.  But there’s something else.  The concept of something at rest not occupying a period of time. What truth can we find to this?  What demonstrations?  What is something motionless yet conscious?

         In many cultures and religions, meditation is used to focus on the present. Such focus, when executed properly can achieve a sense of timelessness – the here and now, nothing more. This is something, I presume, which is central to the Buddhist concept of Dhamma (Bhikkhu, 2013) as well as western philosophies, such as Stoicism.  While I can only speak to the latter, of which I am a practitioner (or prokopton), the key point here is that Zeno may have been on to something – our perception of movement, and therefore of time.  After all, if we just cease sensual observation, do any of Zeno’s paradoxes matter? If we induce a heightened or controlled sensory state, through meditation; or if we begin a conditioning system of repetitive events (whether a prison sentence, a COVID quarantine, or deployment to a warzone), can we start to see a warp to our perception of time? I would assume so.

         I’ve got to wrap this up. I don’t know how long blog posts are supposed to be, but this might be pushing it. At least for the early stages of this blog.

         But let’s close with this because it’s all I remember of that Mann-induced paper in college: there is more than one type of time.  One of those types is what I have discussed in this post – a sort of sensory perception of time-based upon movement or rest.  I recall there were three others I had written about in my bourbon induced scrawling that may have been equally as influenced by Kant as it was Old Crow.  We’ll get to Kant, and hopefully via a path free of puns.

         It’s taken me several weeks to get this post done. Time slipped away from me. I wasn’t even aware of it. I suspect it’s that way for most of us in the current global health situation.  Perhaps it’s because we are at rest, and it seems to not be moving.  But what are we also observing?  Flowers have bloomed, fledgling sparrows are plopping into the grass outside of their nests.  My children have grown taller.  The sun warms a different pattern on my floor every morning at the same time while I must crane my neck to see the moon from my window at night. There’s another time at play. Something that doesn’t wait for that student to walk out the cafeteria door, something that ages Achilles as he attempts to surpass the tortoise.

         It is Natural Time. And that will likely be our next discussion on the matter.

 

 

 

References

Aristotle. (2009). Physics. Retrieved May 2020, from The Internet Classics Archive: http://classics.mit.edu/Aristotle/physics.6.vi.html

Bhikkhu, T. (2013). Barre Center for Buddhist Studies. Retrieved from The Essence of Dhama: https://www.buddhistinquiry.org/article/the-essence-of-dhamma/

BrainFacts/SfN. (2012, April 1). www.brainfacts.org. Retrieved from Vision: Processing Information: https://www.brainfacts.org/thinking-sensing-and-behaving/vision/2012/vision-processing-information

Cajori, F. (1920). The Purpose of Zeno's Arguments on Motion. Isis , 3(1), 7-20.

Salk Institute. (2006, February 1). www.salk.edu. Retrieved from We live in the past and our brain makes up for it: https://www.salk.edu/news-release/we-live-in-the-past-and-our-brain-makes-up-for-it/

            Shields, C. (2016). Controversies Surrounding Aristotle's Theory of Perception. (E. N. Zalta, Editor, & Metaphysics Research Lab, Stanford University) Retrieved from Stanford Encyclopedia of Philosophy: https://plato.stanford.edu/cgi-bin/encyclopedia/archinfo.cgi?entry=aristotle-psychology