From various etymological sources in my upper level athenæum where various word and name references are stored, along with a good sized collection of entaxidermied civets, genets, binturungs, and so on, a miniature model of the Ptolemaic Universe which plays a haunting melody when one turns the crank with which the various planetary epicycles are empowered, as well as a quite stunningly and accidentally achieved collection of spiders and bats who maintain an uneasy hegemony regarding the mass consumption of the variegated insects who delight in ancient book fibers and embalmed vivveridæ, I have that the word paradox comes from the Latinate "paradoxum," meaning a statement which is seemingly absurd but actually true, which itself stems from the Greek phonemes "para" meaning contrary to and "doxa" meaning opinion. If we are to take this as our definition of the term, then in modern parlance this word has been molested and mis-used to stunning degree unrealized by few words other than the unfortunate ironic. Far be it from me to berate anyone for the rampant mis-understanding of words, the challenge of correcting word usage en masse is a sport fit only for elderly men with leather elbow patches on their tweed sport coats and the young and arrogant. My opinion has always been that it is best to leave the will-fully ignorant in their blissful states. Ah yes, but back to the supposed paradox at hand, attributed to Zeno in his solipsistic attempts to prove that motion and change were but mere illusions1:"That which is in locomotion must arrive at the half-way stage before it arrives at the goal." The fundamental mis-understanding inherent in this supposed para-doxa is that a finite length can only be sub-divided into finite portions, a statement that anyone with glancing familiarity with the Real number system (quite frankly even the Rationals will do in this case) knows is an assumption fit for laughter and jeers. While I shall not force you to endure a construction of the Real number system from the basic axioms of set theory (today, that is), I shall offer a quite concise animated example of the phenomena at hand, the Koch Snowflake. It is a shape with infinite perimeter yet finite area2
Entrancing, no?
1The Dean of a prominent university invited the head of the physics department in to berate him for his department's constant budget over-runs. He cites as a positive example the mathematics department, who's budget consists only of allowances for paper and wastebaskets, or even better, the philosophy department, who's budget consists only of allowances for paper.
2One constructs the Koch Snowflake by first constructing an equilateral triangle, then affixing equilateral triangles to the midpoints of each side, and then so forth
