Greek Philosopher Zeno has an interesting Archilles paradox. I would paraphrase it here. [You can google for the original version].
There are two runners, Archilles (great hero of Greek mythology) and tortoise. We assume Archilles was running at a speed of 5Km/hr and tortoise at 0.5km/hr (Archilles is 10times faster than the tortoise). Now there was a race and race field is 10km. Archilles started the race at the starting point and tortoise at the mid-point of the track. Now if we calculate mathematically, Archilles would take just 2 hours to finish the race and tortoise would take 10 hours. There should be no problem. Now I will state the formulation of the paradox.
By the time, Archilles have reached the midpoint of the race, tortoise would have left the midpoint and reached a point A. By the time, Archilles reach the point A, tortoise would have reached a point called B. And this trend goes on. Surely the distance between the tortoise and Archilles is reducing, but never equal to zero. We require infinite such attempts for Archilles to cross tortoise. [Some would say this is a trick, definitely this is tricky. In real life, we know Archilles would overtake tortoise. There are some attempted solutions, the one based on calculus is something I like]
Now I would like to bring an understanding of time based on philosopher Bersgon(my own understanding of him based on a book). According to him, there could be two understandings of time, scientific time or real time (duration). Scientific time is what is used by us in our day to day understanding. Time is infinitely divided and could be separated. Time is divided into past, present and future. We have only access to the present. Deleuze would say time is treated like the space or time is spacialized.
The abstract, divisible, homogenous representations of time are not real representations of real time. But some would say, because of the Platonic inspiration (for Plato, forms of the ideal world are more real than things out here; praying for souls is more real than helping the poor), we consider the abstract representation of time (which is available through clocks) as more real than the real time itself. Bergson completely disagree with this trend. For him, past and present are interpenetrated. It is indivisible. Time is one continuous whole. By division, something is definitely lost.
Movement (of runners or any other) is similar to the understanding of real time (not scientific time). We can’t construct the movement by a series of immobile states (which happens when we divide). The essence of the movement is lost in the division. Thus paradox is the result of an analysis of movement by dividing into several parts.
[I am not saying that scientific understanding of time is not useful. But it has certain limitations too]. I would put down some philosophical implications..
- Language and concepts finds it extremely difficult (I don’t wish to say impossible as poets, artists and thinkers do it to some extend) to capture the mobility/dynamism of an idea/movement and they do so by making it immobile/static.
- As much as possible, reduce classification, segregation and labelling as it fails to capture the dynamism and creativity of people, things and matter. (it is impossible to be free of them completely).
- Even our understandings of God, human person, morality are not decided once and for all. The dynamism of the evolution of our understanding shouldn’t be stifled. Some would immediately equate this to ‘anything goes’ or ‘anything is ok’ principle. I don’t think that is warranted or necessitated.
[I know the article might have been a little technical (philosophical words)for some. Sorry for that. I am indebted to a book on Bergson by Leszek Kolakowski for many ideas].