There is something quite annoying in art discussion communities: finding “deep” meanings that were obviously not intended to be there. Sure, one can open a discussion about what is meaning, how it arises, and whether the whole power of attributing meanings is left to the author’s intentions or viewers can also participate in the process. This discussion can be opened, but it won’t be. Instead, I would like to demonstrate that some things are just not “deep”, and I will prove it mathematically.

For my artsy-mathematical proof I would need to first define the term *isomorphism*. Here is the quasi-formal definition of the mathematical term given by Britannica: “Isomorphism, in modern algebra, a one-to-one correspondence (mapping) between two sets that preserves binary relationships between elements of the sets.” That is pretty confusing. Instead, here is my purposefully reworded definition, partially borrowed from Douglas Hofstadter’s ‘Gödel, Escher, Bach’ (a book of which an angry but praising review will most probably appear as a separate article): an isomorphism is similarity between parts and function of those parts of two distinct things. For example, a functional but weak isomorphism can be drawn between a skateboard and a car; both have four wheels that provide motion, both are used to transport a person, and here the isomorphism ends, we can map no other part of a skateboard onto a car. Two important properties of isomorphisms in number theory are that (1) isomorphisms may fail as soon as rules of a formal system change, meaning that a new, more suitable isomorphism should be found, and (2) isomorphisms cannot dictate the rules of a formal system, meaning that if there is some property in a similar system, it does not mean that the same applies to the system at hand (we cannot reason that because there is a steering wheel in a car, and a skateboard is “something like a car”, then a skateboard should have a steering wheel as well).

By now some might have disapprovingly concluded that I’ve used the word “isomorphism” as a synonym to the word “metaphor” with the only difference that the former makes me seem smarter. (Partially yes, but) No, the distinction was made in order to apply the aforementioned properties to the proof of my main argument.

To demonstrate one (perhaps extreme) example of “deep” metaphor I’d like to share the following meme/tumblr post:

Looking at it, one understands the annoying aspect I have written about earlier. But what is the problem? Why is it a plain satire and not a deep reflection on problems of the educational system? Why can one be so sure of the unimportance of this scene but has troubles doing the same with other instances? For example, English Literature professors rambling about how “an author chose to write that a door in a particular scene of some story is blue, because it reflects the protagonist’s melancholy towards the events unraveling around him” and something of this sort. Maybe, just maybe, the door is blue just because. Once again dodging the discussion about the relation of meanings, author’s intention, and the viewers’ discoveries, I am going to jump straight to semi-mathematical proof.

The problem with building isomorphisms between particular scenes and more broad topics is that those scenes are “particular”; those are cherry-picked scenes/lines which are almost forced to fit the metaphor we want to apply. However, according to rule (1), when the scene changes, the metaphor has to keep holding true (the blue door has to actively represent melancholy all the times it is mentioned), otherwise it should be reformulated. But let us suppose that we really want our deep metaphor to hold true (because it is so beautifully edgy it just has to be true) throughout the whole story/movie/whatever. It means that, in order to keep it true, we have to spread it over to all the other methods, apply a completely new interpretation-system to the whole work. Gee, that is a lot of work that one is not permitted to do. Why? Well, after building a completely different interpretation, one inevitably clashes with the meanings intended by the author. Those meanings are embedded into the work, sort of axiomatic (always true without the need to be proven). Therefore, one would be trying to change the “formal system” (movie/novel), which is prohibited by rule (2).

Thus, I hope I have succeeded to almost-mathematically prove that not all “deep” meanings we want to see are actually true and that some of them should be abandoned.