Some say that mathematics is difficult, and the more proficient you become in it, rather like English, the more difficult it becomes to comprehend. When questions such as What is 1? are asked and you are told that One is -eiπ, you begin the grasp with credulity the ineffable complexity that is mathematics. You may then be told that Euler’s formula precisely defines all real numbers x by { eix = cos(x) + i sin(x) }. A mathematician somewhere will complain that having placed the equality within braces Coco thus invalidated what he had just proposed. Ah well, such is the world of the mathematician.
The word epic springs to mind when setting out on the voyage of discovery that is mathematics, but have you ever considered whether epic is the right word to use? Epic comes to us from the Greek. We speak of epic poetry. For the Greek that is a poem that tells a story. It may be a short story or it may be a long story such as that of Ulysses (Homer’s Odyssey).
In English we shorten the epic poem to the epic, and then start to corrupt its use to describe things that are not stories. It was an everyday word which simply meant story (ἐπικός) which necessarily requires the passage of time, so to use it to describe an extraordinary thing or brief event is quite incorrect. Of course when we read the epic poetry of Greece, and its equivalent in Rome, Scandinavia or even India, we realise that there is quite a great deal of poetic licence in use, and some of the events are entirely unreal, or as some would say imaginary, but they serve well in the purpose of the story.
Another strange, but wonderful thing, occurred to me whilst considering rotational motion. If we consider firstly a very long, inflexible rod (though it need not be very long, but the longer it is the easier it is to comprehend), which is fixed at one end but free at the other, such that it can spin but only around the fixed point, and secondly that nothing can travel faster that the speed of light (c), then we take space craft travelling at perhaps a little over half the speed of light (difficult but not implausible), which is pushing the rod just below its mid-point such that it swings round the fixed point, then the end of the rod must be travelling at a speed somewhat greater than c. Given that rotation is circular π must be involved somewhere in the calculation. There must be a fallacy in here, perhaps you will point it out, but at what speed does the end of the rod travel?
Returning to epic, Coco has already mentioned the use and inclusion of the imaginary in these epic poems, which indicates that they have something in common with mathematics, where real and imaginary numbers can co-exist side by side and even in combination to produce some quite extraordinary results such as the value of One, and also something in common with our rotational motion problem which suggests an entirely unreal, that is imaginary, result. This revelation led Coco to a most satisfactory conclusion concerning the speed at which the extreme end of the rod could be travelling, and an answer could be found.
Truly the answer is eπic.
MMXXV IV I