Zeno's paradox - the fallacy of myopia.

"Well-being is attained little by little, and nevertheless is no little thing itself."



Western Philosophy dates back to around 585 BC, with Thales of Miletus. Such philosophy branched eventually into four distinct components: logic, epistemology, ontology, and ethics. For most, Western Philosophy is best known through figures such as Socrates, Plato, Aristotle, and their incredible works like The Republic, Apology for Socrates, Politics, and Physics (Socrates is not thought to have written down his ideas, but had great influence on the perspectives of the likes of Plato and Aristotle). In fact, during the same period of Plato and Aristotle, we saw the first work on economics as we know it today. Oeconomicus was written by Xenophon in 362 BC; it documented the science of household and agricultural management. Whilst Adam Smith in 1776 (AD) gave a richer view of the nature of economics and society, considering the relative complexity of society during both time periods, it is perhaps not too radical to suggest Xenophon is the true founding father of economics.

Zeno was born in around 495 BC. He was part of the Eleatic school of thought, founded in Elea, a part of modern-day Italy. They rejected many principles of epistemology, and instead pursued ideas of truth and logic. Zeno himself favoured the argument reductio ad absurdum, or Proof by Contradiction. This led Zeno to be able to cast aside superficially logical arguments, by turning their principles on their heads and framing them as illogical. Reductio can be traced back to Xenophanes (not Xenophon), and a satirical poem. However, Zeno is credited by many to be the first to develop an argument using reductio ad absurdum; it is, however, hard to prove given that Zeno recorded very little of his beliefs and mechanism of logic. A stalwart of Western Philosophy, it is likely that every Western Philosopher you know will have used this theory at some point in their writing and line of argument. Through the use of reductio ad absurdum, Zeno was able to create many paradoxical problems, and survived in the works of Aristotle (Physics) and Simplicius (Thereon). Arguably the most well known is Achilles and the Hair, a motion paradox using the same fundamental idea as will be duly discussed.

The paradox I want to focus on relates to a start destination, and a final goal. This is the linear model of a journey, either figurative or literal, and humans throughout history have relied on it. Commerce relies on the linearity of travel, as does any other activity involved in the transportation of goods or humans. You yourself may recognise this linear journey; we are ushered towards ‘SMART’ goals or targets in every facet of everyday life. In work and school we are set deadlines, with a clear definition as to how we should go about the business (Aside: this is known as the correspondence principle, a concept developed by Bowles and Gintis; 1976). However, Zeno challenges this linearity, and argues that in theory it is impossible to reach our final destination.

Let’s use the example of a journey to school. You’re environmentally conscious, and so decide to make the 2 kilometre voyage on foot, you ecological hero. To complete your journey you must travel half the length of the total. Then three quarters. Then four fifths. Then ten elevenths. The fraction continues to whittle down, until the fraction becomes infinitesimally small. In conclusion, you never reach your end destination, as you are forever having to traverse an increasingly small distance! Now of course, in the literal sense this is not a theory problematic to disprove. One of Zeno’s contemporaries is thought to have walked from one side of the room in a fit of logic-induced hysteria, presumably belittling poor Zeno with each step he took. What he did not consider is that Zeno’s paradox was completely logical. Using reductio ad absurdum you can make the following statement: Assume that you can complete your journey to school. Therefore, you can deduce that it is possible to travel within a finite amount of time. However, you can also deduce that you can not complete the journey in a finite time, as it takes an infinite amount of time to travel the infinite distance made up of increasingly smaller fractions of your journey. As a result, it must be impossible to complete your journey. Yes, in reality we know that we can arrive at school in the morning without falling into a timeless journey of soul searching. However, maybe it is not the literal meanings we should take from this, but rather the applications to figurative scenarios.

I think we have a lot to learn from Zeno of Elea. We should be looking at the principle of beginning an impossible journey, not worrying about making it to school tomorrow on time. As humans we tend to be geared towards short-term rewards; Rudolph Cardinal coined the term ‘instant gratification’, where we prefer the near future to yield results, even if they are smaller, than in the far future. We also seem to take shelter in certainty. If you definitely have an assignment due in the week, there is a much greater impetus to complete it than being offered the chance to submit any time you like for the rest of your life. Many criticise the ‘cuckoo’ goal of 2% economic growth per annum, some for the reason it is an unrealistic aspiration; society is liable to great changes in direction and ‘Black Swans’ (see Nassim Taleb: intellectual superhero). Economic goals provide a certain direction to head in, but is that really the way we should be going.

Using the principles championed by Zeno, our figurative journeys as a collective and as individuals should be non-linear. No clearly defined, scientific end goal. The curve should resemble a parabolic arc; something highlighted in Jordan Ellenburg’s book How Not to be Wrong, although in a different context. Trends do not carry on forever he explains, citing a scientific paper that if current trends continue, every single American citizen will be obese by 2040. This is the exact fundamental idea I wish to emphasise: society and people will not develop one day into complete and perfect bodies; we will reach points where each adjustment in behaviour is smaller, and not as seismic. This trend will increase until things are tantalisingly close, but will never be quite there.

To be precise, I am arguing that when we undergo a transformation of mindset, we should not set out clearly defined goals in our heads. After we reach a point, what happens? Do we suddenly become perfect beings? No, but we have improved. We have improved in the same way we have made it halfway to school in the morning. The idea of being “straight locally, curved globally’ is a good embodiment of this idea. Newton used this concept, albeit in different terms” to describe the shape of the Earth. To be able to adapt to the future requirements in sustaining and improving humanity, it is perhaps time to start thinking about the small increments that occur, and accepting that our development in some areas will diminish. This is not to say we should give up, but rather target other components of our being and become more complete as a person, a collective, a society, and as a human race.

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