“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.”
—Aristotle, Physics VI:9, 239b15
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 metres. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 metres, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 metres. 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 reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise.
An apple of discord is a reference to the Golden Apple of Discord (Greek: μήλον της Έριδος) which, according to Greek mythology, the goddess Eris (Gr. Ερις, "Strife") said that she would give "to the fairest" at the wedding of Peleus and Thetis, sparking a vanity-fueled dispute between Hera, Athena and Aphrodite that eventually led to the Trojan War1. Thus, "apple of discord" became a euphemism for the core, kernel, or crux of an argument, or for a small matter that could lead to a bigger dispute. The Ancient Greek word "μῆλον" also means sheep or goat.. Homer in his Odyssey describes how Odysseus sacrificed two goats (μήλα) when he reaches the underworld.
In 1977, physicists E. C. G. Sudarshan and B. Misra studying quantum mechanics discovered that the dynamical evolution (motion) of a quantum system can be hindered (or even inhibited) through observation of the system. This effect is usually called the "quantum Zeno effect" as it is strongly reminiscent of Zeno's arrow paradox.
This effect was first theorized in 1958.