A Circle is an O is a 0

Recently, I was speaking with my brother while he played a video game. At some point, he wanted me to do something, and eventually I asked him for the button combination to perform a task. In the middle of this sequence, he called the circle button “zero,” to which I invariably pointed out that the button was not zero but circle. Clearly, I meant nothing of this and was simply poking fun at him, but, much to my surprise, he claimed the two were one in the same. Moreover, he claimed a circle is a zero is an o.

To this I quickly responded with “Can you add a circle and an o? Do they represent quantities?” At this point, I am quite sure my brother realized his fault and simply sought some banter. So, he replied saying you could, because if you write that down, you see it is just 0+0=0. We continued for a while in this manner. I defined the three entities: a circle being the curve formed by connecting the locus of all points equidistant from a center, a 0 being the magnitude of the empty set, and an o being the 15th letter in the English alphabet which has certain properties. Moreover, I said that based on these definitions it is clear that the three are distinct, despite the fact that their symbolic representations are similar if not the same. Then my brother surprised me again by asking somewhat incredulously “Aren’t those [the representation and the object] the same thing?”

I am not the first person to be amazed by how important representations can be, nor am I the first person to realize many mistakenly conflate an entity with its representation. In René Magritte’s famous La trahison des images (The Treachery of Images), one sees a depiction of what could hardly be argued to be anything but a pipe, but below that are the words “Ceci n’est pas une pipe.” (For the anglophones out there, this reads “This is not a pipe.”)

Ceci n'est pas une pipe

Magritte’s own explanation is perhaps the most satisfying and succinct. He is quoted as having said the following:

The famous pipe. How people reproached me for it! And yet, could you stuff my pipe? No, it’s just a representation, is it not? So if I had written on my picture ‘This is a pipe’, I’d have been lying!

The distinction between a symbol and the thing it symbolizes is a relatively nuanced one. It requires abstract thinking, and it is often difficult to make when one is not actively considering this duality. Of course the discussion about this is much older than Magritte’s work. One can get quite technical with this in several ways; you can write long philosophical monographs, or you can rephrase this in terms of mathematics, and so forth, but I will not do that here.

In 1931, Alfred Korzybski used the phrase “the map is not the territory,” which was inspired by Eric Temple Bell’s epigram on the subject. And, this is the best way I know to summarize the matter, which is often referred to as the “map-territory relation.” While the map may be similar or dissimilar in many ways with the territory it seeks to represent, it will never, can never, and should never become synonymous with that territory. I can properly experience Marseille, France only by visiting, only then can I touch the monuments, interact with the people, and do all sorts of other things. No representation, no matter how elegant or seemingly perfect, could ever do that.

We should care about this because representations shape our worldview in more ways than we usually recognize. As an example, you may have heard something about different map projections and how cartographers need to make certain choices in making maps, choices which inevitably distort. It is impossible to make a map which preserves all features one would likely care about: relative size, distance, angles, shape, et cetera.

Here is another example: popularity is not an accurate representation of significance. This and related matters are something I have pondered a bit in the last few days after having re-read John Green’s wonderful The Fault in Our Stars. Many wish to die in heroic fashion, with hundreds of mourners, because this would give meaning to their life. They feel people must be extravagant to be important, but this is not the case, and John Green makes the argument in his novel far better than I ever could here, or anywhere else for that matter. Interestingly, this is not the only example of this in John Green’s work either, or even The Fault in Our Stars. A theme in that book that too few notice but that is incredibly important is that fiction is important. Green argues this point using meta-fiction, his author’s note, and other means.

These philosophical matters seem pointless to many, but I hope that the above has demonstrated that they are not.