Gorgias the Nihilist

Existence and the coastline paradox

Image: https://iep.utm.edu/gorgias/

The road between Lviv and Kyiv, two cities in Ukraine, is 541 kilometres long and would take me, right now, six hours and forty minutes to drive. If I wanted to walk the distance between the self-same starting and finishing points, it would take me four days and ten hours. And, what’s more, the distance would no longer be 541 kilometres but 516 kilometres (or 516,000 metres). Ukraine’s M-06 trunk road, which also shares a road number familiar in Belgium, the E40, does not cross from west to east between the two cities in a perfectly straight line. Between Yaseniv and Zhytomyr, the road describes a huge arc to the north, before, 315 kilometres later, resuming the direct line—more or less—that the crow would have flown. The motorway is longer than the crow, but it’s faster—except you need to be in a car. If you walk, the direct line is shorter.

In 1990, as a prelude to Ukraine declaring its independence, the citizens of Lviv, Kyiv and, I assume, all points between the two towns, joined hands in a human chain linking the metropolises as a show of unity in defiance of the Soviet leadership in Moscow. The reports state that the chain contained 3,000,000 individuals.

If I stood with my two hands linked into the palms of two other individuals either side of me, my reach from palm to palm would be 1.25 metres. Five hundred and sixteen thousand metres divided by 1.25 metres gives the number of human links needed to span the distance between Lviv and Kyiv, which is: 412,800.

Impressive, but not quite three million. If, instead, we all stood comfortably next to one another, without crowding as if on some rush-hour metro train, I occupy a width of around 50 centimetres. Three million Ukrainians without outstretched hands but stood next to one another would occupy a distance of (3,000,000 x 0.5 =) 1,500,000 metres, or 1,500 kilometres, which is more than the distance between Lviv and Kyiv, and is actually just under three times that distance. Maybe there were three human chains, all parallel, like the lanes of a motorway.

I don’t dispute either of the figures of 516 kilometres or 3,000,000 participants because, even if they were a human chain, this was a festive act of defiance and I’m sure no one was setting up a theodolite. Challenging the figures is not the aim of these peregrinations. Rather it is this: do I exist?

Let us assume that, on that day in January 1990, there were indeed three million people linking hands between Lviv and Kyiv. Perhaps it is feasible that four million could have been there. Naturally, I myself on my own could not ever span the 516-kilometre gap between the two towns, so that the ideal number of participants to link the start and end points of this human chain and still have nobody superfluous or the chain broken through a lack of participants (call that figure U) can be determined as being greater than one and less than 3,000,000:

1 < U < 3,000,000

Actually, I can improve on this formula. If I myself certainly cannot span 516 kilometres, then I can fairly surely state that I cannot span one kilometre. And, if three million would almost form three human chains between Lviv and Kyiv, I can surely safely halve that figure. My new formula is therefore:

516 < U < 1,500,000

That’s much more accurate, isn’t it?

Well, no it isn’t. Neither of the formulae is more accurate than the other, because they simply express the value of a variable, U. If the second is correct, the first must be correct. But the first can be correct without the second being correct. Because the range of possible values of the second expression is entirely contained within the larger set of values of the first expression.

At this point, I put my thinking cap on and start being more realistic. I cannot possibly span even one-hundredth of a kilometre—ten metres—nor even five metres. In fact 2.5 metres would be pushing it. Surely, I can up the first figure by a factor of 400 (the number of times 2.5 metres goes into 1,000 metres), making the figure 516 x 400 = 206,400. The upper limit of 1,500,000 is still quite high, but I don’t want to third it, in case I drop below my multiple of 516. We’ll remove another 100,000:

206,400 < U < 1,400,000.

Now a question arises: how do I know that the distance between Lviv and Kyiv is really 516 kilometres? The app on the web tells me it is but I wonder how the distance was measured. Because if it was measured using a scale map, with a key at the side, and a point to point approximation between the starting and finishing points of the journey, that would be accurate as far as the crow flies, but not for a car, not even one driving the shorter, pedestrian route. One could take a yardstick, perhaps four or five metres long and use it to measure the distance from Lviv to Kyiv. But the coastline paradox as expounded by Lewis Fry Richardson tells us that, the shorter the unit that is used to measure the cumulative length of a non-straight topographical line, the longer the distance covered by that line becomes. And, unlike with a regular polygon drawn within a circle, which, as sides are added to it (and they therefore become smaller) tends to the finite circumference of the circle as its maximum dimension, the coastline paradox results in a tendency that knows no limiting factor: the distance tends to infinity.

Suddenly it becomes very feasible to have 3,000,000 people in this human chain. The line simply needs to wiggle a bit like an oscillation on a cathode ray tube and plenty more folk can be accommodated in the chain. That is not in and of itself dramatic. What is more dramatic is that, regardless of how small the measuring units can become, and therefore no matter how long the distance theoretically can become, we are, in the Ukrainian case, limited by the physical size of a human being. If we were to form the human chain using toy soldiers, then U would have a far wider range of possible values, simply because a toy soldier occupies only a centimetre or two in the chain of 51,600,000 centimetres. The more interesting question is how many people one could remove from the human chain and still have it fulfil its function of linking the towns of Lviv and Kyiv?

If we look back to my initial calculation, the human chain could have been formed by 412,800 individuals. That was all that was needed. The other 2,587,200 people who attended on that day wasted their time. They were superfluous to requirements. That is, they were superfluous if the requirement was to form a human chain between Lviv and Kyiv. And that’s the problem: what was the purpose of building the human chain?

Clearly, the purpose was to show solidarity and, on that score, if you favoured independence for Ukraine, it was important to have as big a turnout as possible and as few as possible if you didn’t. For independence-minded Ukrainians, the human chain that day was a people’s statement, and there was no upper limit on the chain.

What about a payroll? Are there upper limits on payrolls? In much the same way as fixing the ideal number U in the human chain example, a payroll also needs to be fixed at an ideal figure. Too many, and the line needs to wiggle a bit to fit everyone in. Too few, and people are stretching for each other’s fingertips to even build a semblance of a human chain.

Imagine enthusiastic Ukrainians rising early to get breakfasted and out to form their human chain on that day in January 1990. Imagine they see the throng of folk as they arrive at the designated spot. They get this thrill of belonging, of community and common purpose. And then a steward comes along and says, “Please, go home again. We want a human chain and we have enough for that already. We don’t need you. For us today, you may as well not exist.”

When the distance is measured not with five-metre sticks but with one-metre sticks, the distance increases according to the coastline paradox. But the number of people needed to make the chain doesn’t increase, because the time taken to walk from Lviv to Kyiv cannot be dependent on the length of the rod used to measure the distance.

Effectively, what large corporations do is reduce the measuring stick in order to create redundancy in the workforce. People who previously had a purpose are now no longer required, because the reduction of measurement units creates superfluity of payroll. When staff get laid off as a result, those who remain must stretch out their hands and fingers to be able to accommodate the lack of links in the chain, because the time taken to walk the distance remains the same, even if the coastline paradox will allow you to reduce staff numbers.

At an event like the 1990 Ukrainian human chain, those who retain a spirit that says no matter how many people turn up to the event, there is always space for them, because the purpose is not to build the chain but to be together and communal, adopt an approach that is more worker-centric than owner-centric. Corporate owners and corporate employees need each other, but they don’t need each other in the same measure all the time. Trouble is, if you send the keen but superfluous away and suddenly want to extend your human chain to Kharkiv; you can do it with 3 million, but not with 412,800. The obviously transactional nature of employment shows that large corporations place little to no importance in people, for all the word company means exactly that.

The Greek philosopher Gorgias propounded a philosophy that is hard to grasp, partly because of the terms in which it’s expressed and partly because so many of his writings have been lost. His philosophy was grounded in a sequence of four posits:

1. Nothing exists;

2. Even if something exists, nothing can be known about it; and

3. Even if something can be known about it, knowledge about it can’t be communicated to others;

4. Even if it can be communicated, it cannot be understood.

Originally from Sicily, Gorgias was at one point sent from Syracuse to Athens to plead for protection from the Syracusans; he ended up settling in the Attic peninsula and, one wonders how come: sent for help from Athens, he ends up just staying there. It’s almost as if Athens refused his request and he—somewhat pragmatically—decided that going back to Sicily to get whopped by flat-roofed Syracusans who can’t cook proper spaghetti, wasn’t a brilliant prospect, not without some Athenian heavies at his side. Smart guy. Maybe even very smart.

Because posit 1 is challenging, given that most of us are grounded in a belief in our own existence, let me quickly leap to conclusion no. 4, from where we will quickly trace our way back to no. 1. Inductively.

That which is communicated cannot be understood. Some months ago, I touched on this idea in the following article:

What I said there is that communication corrupts communication, the same way that being conscientious of a camera spoils a portrait photograph, and the popularity of a tourist destination eventually makes it a rotten tourist destination. Therefore, the mere endeavour of communicating something is predicated on expectations and conventions that may well be shared to some degree with the listener, but are never shared one hundred per cent. The manner of the communication distorts both what is communicated and how it’s understood, including with it being subjected to cultural overtones (“What a prig!”, “Oh, isn’t she beautiful?” ... ). So, Gorgias’s conclusion in posit no. 4 is, I believe, right: the chance of something that is communicated being understood is by far less than the chance of its being misunderstood.

To posit no. 3: knowledge can’t be communicated. Needs must, knowledge of something is communicated via words. A word is a construct made to fit a panoply of cases. No word is unique as a description of what it is. Not even the word Graham. And not even Graham Vincent; and even if the description were to assume a uniqueness making it instantly recognisable (so that, even if there were a thousand Abraham Lincolns, you’d know who I mean when I quote that name), such would be the aura of fame and legend surrounding it that it’s highly unlikely I could proclaim anything like true knowledge of the Abraham Lincoln. The need for a medium of communication in order to effect communication renders the communication of knowledge unfeasible. It more frequently allows the communication only of misinformation and imprecision.

To posit no. 2: even if something exists, nothing can be known about it. Quantum physics is just one area known to science that is teaching us strange concepts: that something does not exist unless it be observed. Likewise legal reasoning: a fact is that which is known, and there are no facts that are not known. Meanwhile objectivity in our universe is a series of convenient constructs, one for each of our multifarious purposes and filled with our multifarious assumptions and precepts. We use our objectivity more as an excuse to deny our own egotistical subjectivity. And then we argue endlessly about who’s right and who’s wrong, and end up passing laws justified by natural law and the rule of law, which turn the world and its nature upside down (Thomas More in A Man For All Seasons: Some men think the Earth is round, others think it flat; it is a matter capable of question. But if it is flat, will the King’s command make it round? And if it is round, will the King’s command flatten it?”; for that matter, will the King’s command make Rwanda a safe refugee haven ...?)

If we but knew it, upside-down is where the Earth has been the whole time, but that’s just an ocular trick. Nevertheless, if we could only eliminate our own brains from the process that turns the images in our iris into right-way-round sense in our minds, our judgment of what we see could be infinitely more objective. It is we ourselves who obstruct our own objectivity. As do our ideas of perfection, like democracy and proportionate use of force.

And so to no. 1: nothing exists. Now, let me think about this. Didn’t Descartes say I think therefore I am? Then if I am pondering posit no. 1, I must surely exist to do that?

Truth is, there are eight billion people on the Earth and only a handful of them have even heard of me. If I ceased to exist, what difference would it make? Here we are back at the coastline paradox, then: that one cannot measure the coastline of ... Norway. At a map scale of one inch to one mile, the measurement is averaged out by drawing straight lines from one point to another, but that ignores the undulations between the end points of that line, so you draw a new line, half the length; and it too has inlets and outcrops, so the line gets smaller and smaller and smaller and still you cannot get down to measure the definitive length of Norway’s coastline, which instead just keeps growing towards infinity.

Each small part of the coastline is unimportant as regards the full coastline of Norway, and the more accurate the geographer wishes to be in his measurement, the less important each constituent measurement becomes. He arrives at the point where he can, and because he is human and seeks his constructed perfection, happily does dispense with some of his supposedly superfluous measurements and, does not affect the total calculation to any measurable degree. At that point, the minuscule lines described around Norway’s coastline do not exist. And yet, without them, Norway would have no coastline.