Sagittarius is the Zodiac sign for those born between November 22 and December 21. The symbol for Sagittarius is centaur (half-man, half-horse) with a bow and arrow.
The model for Sagittarius is the wisest and most intelligent centaur, Chiron. Although most centaurs are known to be aggressive beasts only interested in women and alcohol, Chiron was different in that he was culture and civilised. He was interested in gathering knowledge and learning philosophy, especially medical knowledge. Chiron is also famous for being the teacher and master of many famous heroes and gods. Among his students are: the god of medicine, Asclepius; the Trojan War hero, Achilles; leader of the Argonauts, Jason; and the famous hero, Hercules. One day, Hercules ended up in a fight with some centaurs, which resulted in a bloody battle. Hercules used arrows coated with the poison of the Hydra (which he obtained during his twelve labours), swiftly killing many centaurs. Chiron saw this battle and galloped there to try and stop everyone from hurting each other. But Hercules did not see his master and accidentally shot him with a poison arrow. Although Chiron was given the gift of immortality by the gods, the Hydra’s poison still caused excruciating pain. Even though he was one of the best medical professions of his time, he could not alleviate the pain and begged Zeus to put him out of his misery. Zeus accepted this and raised him into the heavens to become a constellation as a sign of respect.
In 450 BC, a Greek philosopher named Zeno thought of the following paradox. Let us imagine that Achilles and a tortoise were to have a footrace. Achilles, obvious being faster than the tortoise, allows the tortoise to have a head start of 100 metres. Once the race starts, Achilles will quickly catch up to the tortoise. However, within the time he took to cover the distance, the tortoise would have travelled some distance as well (say 10 metres). When Achilles runs the 10m to catch up again, the tortoise has once again toddled on another metre. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Because there are an infinite number of points Achilles must reach where the tortoise has already been, theoretically the tortoise will be ahead of Achilles for eternity.
According to this thought experiment, motion is paradoxical and theoretically impossible. However, we know for a fact that motion happens. So how can we break Zeno’s paradox?
The main flaw of Zeno’s paradox is that he uses the concept of “eternity”. If we record the story mathematically, the time taken for Achilles to run the footrace is (if it took him 10 seconds to run 100m): 10 + 1 + 0.1 + 0.01 + 0.001… = 11.111… Ergo, the tortoise is only ahead of Achilles for less than 11.2 seconds (rounded). After 11.2 seconds pass, the time passed exceeds the sum of the infinite series and the paradox no longer applies.
Although it is a flawed paradox, the story of Achilles and the tortoise teaches the concept of geometric series – that something finite can be divided an infinite amount of times. For example, 1 = ½ + ¼ + 1/8 + 1/16… ad infinitum. This principle is a crucial part of mathematics and has significant implications in the field of economics. For example, it can be used to calculate the value of money in the future, which is necessary for working out mortgage payments and investment returns. Perhaps it is because of this mathematical principle that it seemingly takes an infinite amount of time to pay off a mortgage.
Zeno’s paradox teaches us that one should not take the concept of infinity for granted.