Zeno, a disciple of Parmenides, is famous for his paradoxes that seem to defy common sense. Some of the examples are quoted below from Wolfram Mathworld and other sources on the internet:

Dichotomy paradox: Before an object can travel a given distance d, it must travel a distance d/2. In order to travel d/2, it must travel d/4, etc. Since this sequence goes on forever, it therefore appears that the distance d cannot be traveled.

That which is in locomotion must arrive at the half-way stage before it arrives at the goal. Suppose Atalanta wishes to walk to the end of a path. Before she can get there, she must get halfway there. Before she can get halfway there, she must get a quarter of the way there. Before traveling a quarter, she must travel one-eighth; before an eighth, one-sixteenth; and so on. This description requires one to complete an infinite number of tasks, which Zeno maintains is an impossibility.

“This sequence also presents a second problem in that it contains no first distance to run, for any possible (finite) first distance could be divided in half, and hence would not be first after all. Hence, the trip cannot even begin. The paradoxical conclusion then would be that travel over any finite distance can be neither completed nor begun, and so all motion must be an illusion.” This argument is called the “Dichotomy” because it constantly breaks space into two.

Achilles and the tortoise: A fleet-of-foot Achilles is unable to catch a plodding tortoise which has been given a head start, since during the time it takes Achilles to catch up to a given position, the tortoise has moved forward some distance. In a race, the quickest runner can never over­take the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.

“In the paradox of Achilles and the tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 meters, for example. Suppose that each racer starts running at some constant speed, one faster than the other. After some finite time, Achilles will have run 100 meters, bringing him to the tortoise’s starting point. During this time, the tortoise has run a much shorter distance, say 2 meters. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles arrives somewhere the tortoise has been, he still has some distance to go before he can even reach the tortoise.”

Arrow paradox: An arrow in flight has an instantaneous position at a given instant of time. At that instant, however, it is indistinguishable from a motionless arrow in the same position, so how is the motion of the arrow perceived?

Zeno states that for motion to occur, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one (duration-less) instant of time, the arrow is neither moving to where it is, nor to where it is not. It cannot move to where it is not, because no time elapses for it to move there; it cannot move to where it is, because it is already there. In other words, at every instant of time there is no motion occurring. If everything is motionless at every instant, and time is entirely composed of instants, then motion is impossible.

Whereas the first two paradoxes divide space, this paradox starts by dividing time—and not into segments, but into points.

Now the Indian solutions. It is curious that the fertile Indian world-view gives various resolutions to these conundrums of space and time. Let us look at these:

1)            The Concept of Kaala: Time as understood by Indian mathematics and physics is inseparable from action. So is space. These are not separate objects lying out there, that can be picked up and split. Satkaryavada says that Kaala is the unfolding of potential, i.e., the effect is already present in the cause, like a seed sprouting, growing and branching into a tree. At no point in time can the tree be split from the seed. Or in more physical terms, the kinetic energy cannot be split from the potential by infinitesimal piecing.

2)            Anvik Theory: Space and time, as all objects, are formed of infinitesimal entities which are called anu. These are not physical atoms but concepts or abstracts. Space and time are not physical objects that can be picked up and made granular or looked under a microscope. It is as if one picked up the river and started slicing it into cross-sections. A different calculus , it seems, was divined by our rishis long before Newton or Leibnitz.

3)            Sankhya Theory: Space is a tanmatras, a rudimentary or subtle element, an essence. The tanmatra is so fine that it may not be divided or held back from movement. For Prakriti cannot be made immobile or carved; it exceeds our instruments as their cause. Thus, what Zeno is proposing is an impossibility. If we were to adopt a paradigm from Quantum Physics we would say that when space is split to sub-atomic levels, all Newtonian laws collapse, thus invalidating the whole argument.

4)            Vedanta Theory: Vivartavada maintains that all movement is modification of one Reality from one manifestation to another, each equally That. What seems to be change is eternally one, the Sole, the Causeless and the Endless. Perhaps this is what Zeno was trying to show us by perplexing our minds. But for that he would have had to be born in Kashi or meditate in the Himalayas. 

I attempted these solutions more for fun than serious academic debates. But in doing so I realized how advanced Indian physics and metaphysics is. Perhaps if we could start looking at the world with our own eyes someday, we can begin fixing it.

DISCLAIMER: The author is solely responsible for the views expressed in this article. The author carries the responsibility for citing and/or licensing of images utilized within the text.