The Old and the New Normal
This an essay I published earlier on Medium (I have closed my account since).
It was first published on June the 21st 2020. It appears to be a good time because of the opening of the trial of D. Chauvin.
The COVID19 crisis is not a turning point but an upside-down point. The long period of lockdown, which is extreme immobility has awaken us from the big nap. The new normal appears very strange, nightmarishly strange. The thesis I develop in this article is that the new normal is the dual of the old normal. It is shocking because it is easy to confuse duality with symmetry. The most natural property of symmetry is that it is involutive. If you take the symmetrical of the symmetrical you obtain the original. It is not necessarily the case with duality. I am advocating, for instance, that Antifa as a doctrine is the dual of fascism, and the anti-Antifa may also be a version of fascism too.
Caveat: I am using mathematical language loosely in this article. I am using a precise concept because it captures the essence of a phenomenon for which there is not an adequate word in the usual language. There are many ways to relate ideas, the most common way is to use negation or inversion. It is misleading because it wrongly suggests an involutive state of mind: namely that two inversions cancel one another like a double negation. Not not A intuitively is A (or the complement of a complement set). It is not necessarily true for dualities.
I am starting by a small detour to explain why I have chosen this mathematical concept of duality and what I mean by it in our social context.
Duality is not Symmetry
The concept of duality originates from a very abstract approach of mathematics. In its most general way you have a duality when you have a family of F of objects for which there is a correspondence between each object of F to another (maybe itself) object of F. The first object is called the primal and the second object is the dual. An intuitive and practical example are graphs. A graph is given by a set of vertices and edges between those vertices. Think at the map of the subway for instance (this is the map of subways in my city Lyon), the stations (white dots) are linked by lines (of different colors but it is not relevant here):
You can define the dual of a plane graph G as the graph that has a vertex for each face of G. The dual graph has an edge whenever two faces of G are separated from each other by an edge. For instance in the figure below the red and blue graphs are dual from one another.
The point I want to make for this article is to remark is that duality is a kind of correspondence that can be tricky. Clearly the red and blue graphs are different (they don’t have the same number of vertices for once). But for some graphs, like the square with diagonals, they are equal to their dual. In the case of graphs the dual of the dual is the primal. It is not necessarily the case for other mathematical constructions.
We are used to correspondence that are involutive: for instance symmetry is a duality (you have an object and its symmetric version) that is involutive, the same goes with negation (at least in classical logic) where a double negation is equivalent to an affirmation. The operation of complementation on sets (the dual of set S is the set D containing all objects not in S) is also involutive.
We are so used to deal with involutive dualism that it can tricks with your thinking process when you are dealing with dualities that are not involutive. This is a major difficulty in computability theory. The notions around semi-decidability are very hard to grasp for this reason.
It is in this sense that I am using the term “duality” in the rest of this article: it is a correspondence that is not necessarily its self-inverse. That is why I prefer to use duality instead of "inverse" or “Anti" because such words are intuitively linked to involutive operations.
Another lexicographical note: in math the image of a property in the dual is called the “co”-property (co like in converse).
Let us run through recent examples that show how the new normal is a dual of the old normal at many different levels.
Wokeism as coChristianity
It doesn’t require a PhD on sociology to find striking similarities between the woke movement and religion. I would like to focus on two specific features that have manifested themselves in the aftermath of George Floyd’s death. Those two manifestation show how Wokeism is a covariant of Christianity.
The kneeling has become the most widely recognizable symbol of the unrest. Like in Christianity it is a symbol linked to an act of torture. But contrary to the christian version, where the crucifix is in relation to the victim of the torture, the kneeling is in relation to the act of the perpetrator.
In some demonstrations, there were graphic scenes of demonstrators and officials washing the feet of the organizers. It is also directly linked to Christianity but in a dual way: in the gospels it is Jesus that wash the feet of the apostles.
I am not analyzing here why is it so and what could explain these inversions, this time will come. I am only describing in this article the manifest inversions that can be witnessed.
“Words are violence” and “Riots are a way to express oneself”
Another striking example that demonstrates how what appears as “inversions” are not necessarily the inverse of one another. There is this quite recent trend along critical theories that “words are violence”. It is used as a tool to trick first amendment and other free speech legal protections. The limits of free speech are clear: you cannot appeal to violence and shout “Fire!” in a crowded theater. Since those limits are very hard to openly oppose (short of a revolution in the full acception of the word) the easier way to circumvent those limitations is to inflate the meaning of “inflammatory discourse”. The development of “safe space” etc. is a direct consequence of this strategy.
On the other hand, the same people, can perfectly say that riots and unrest are a perfectly acceptable way to express the resentment and rage against the system. In short we have “violence are words”.
The fact that those two ideas can live together in the mind of an activist is not a logical contradiction even if it appears as such at a first glance. Indeed violence has not the same intent in those two ideas. In “violence are words”, it is talked about violence towards activists. In “Violence is a way to express oneself feelings” it is talked about violence from activists towards the other ones (the “system”). They are not the same thing in their minds even if the same word is used.
The most recent slogan “silence is consent” is the cherry on the top of this cake of alternate perceptions of reality. I would be tempted to use “nonsense” if it were not misleading as am I discussing here...
Antifa as cofascism
The fact that Antifa act as thugs that are barely discernible from the original fascists is not a striking news nor is difficult to actually observe. The troubling question is: how is it possible that having the converse hierarchy of values can produce such similar results? I am limiting my analysis in this article by pointing that it shows that objects can be their self-dual in a non trivial way. This is folk knowledge and is known as the “horseshoe” theory: basically that extremism from the right and from left are equivalent.
Maybe an idea coming from category theory is of help here. Category theory is a very abstract mathematical theory in which duality plays a central role. Intuitively, a category is defined by objects and the relation between objects (called morphisms). Morphisms can be seen as arrows between two objects. There is the source of the morphism, the starting point of the arrow, and the target of the morphism, what is pointed by the arrow. Graphically a morphism f between X and Y can be depicted as:
The cocategory of a category is the category having the same objects but having arrows drawn the other way around. Therefore if in category A you have a morphism f having source X and target Y, in the cocategory of A you have a morphism having a source in Y and target in X.
What I want to stress on, in the context of this article, is that not everything is reversed: only morphisms are inversed. The object are the same ones. It gives an intuition on why duality is not like symmetry. There are things that remain the same but there are other things that are inverted. Not everything is upside down. Another imperfect analogy is this one: when you look at yourself in a mirror your left and right hands are inverted but you don’t see your feet in the place of your head (and if you lay down on the floor neither). Something of a similar nature happens between antifa and fascists. In order to stress that I propose to use the term “coFascist” in place of “Antifa”.
Cojustice: the rule of the mob inside courts
The riots following the death of George Floyd were made in the name of “Justice”. Let me be crystal clear here: the actions of Derek Chauvin are appalling and there is nothing more important than this whole case to be prosecuted and precisely analyzed. The problem is that due to the magnitude of the riots following this case, it is almost impossible now to have a trial that follows due process. It is clear that no jury on earth can think about doing something else than pronounce the maximal sentence in this case. If it is not the case, the Rodney King riots will look like a walk in the park. Even a re-qualification of the case as third degree murder or something else that would alleviate the charges against Chauvin will have disastrous consequences: regrettably more property destruction and maybe loss of lives are to be feared.
Therefore there is no longer a choice: Chauvin will be declared guilty or else. I am not trying to diminish the case, neither am I trying to turn Chauvin into a martyr. But he will be sacrificed to appease the mob, there is no way around that. I am not going as far as qualifying him as a scapegoat but it is a part of the story.
Therefore the riots done in the name of “Justice” directly lead to the rule of the mob ruling inside the court house. What is even more tragic is that it is reminiscent of the horrific lynching against what these demonstrations are in the first place. It is because lynching cannot be tolerated in our society, and because of those awful of events of the past, that many people are demonstrating today. But it shows that being against something is no guarantee that you are not doing a similar thing.
White is the new coN word
Another intriguing inversion that is quite recent is the one around negative racial qualifications. The interplay between the use of the N-word in the past and various use of the epithet “white” in a pejorative way, as in “white supremacy”, “white fragility” or “white old male” etc., is striking. There is an inversion along the idea of purity/impurity in those two ways to characterize various phenomenons.
Semi-decidability
The cognitive difficulties that are encountered are not without reminding similar difficulties that student encounter when dealing with some subtle ideas of computability theory. The main issue comes from the slippery notion of semi-decidability. A yes/no problem is decidable if there is a program that once asked a question always halts with the right answer. It has been shown that some problems are undecidable. There are no programs that work 100% of the time correctly to solve those problems. The typical example is the halting problem. There is no way to algorithmically know whether a program is going to halt or not.
The fact that a problem P is decidable or undecidable does not change when you consider the opposite problem coP (meaning that an instance I of coP is “yes” if the answer on I on P is “no” and vice-versa). Indeed if you can answer the question because the problem is decidable (respectively if you cannot because it is undecidable) you just have to switch answers for the coproblem (respectively when you don’t know you just don’t know for the coproblem neither).
The halting problem is not only undecidable but also semi-decidable. A semi-decidable problem is a problem for which, if the answer is yes the program stops one day and answers “yes”. But if the answer is “no”, the program may run forever (and you will wait for an answer at infinity). The halting problem is semi-decidable: you just have to wait. If the program halts you answer yes. Now the tricky part is that you could think that the coproblem of a semi-decidable problem is semi-decidable too, just like it is the case for decidable and undecidable problems. But it is not the case! The complementary problem of the halting problem, is your program going to run forever, is undecidable but not semi-decidable.
It generates tricky situations in which your intuition on what should hold is hijacked in a non trivial way.
We should always be aware of the limitations of the language. Opposition is not reducible to classical logical negation and what, on the surface, appear as raw incoherence may in facts be the witness of subtle dualities.