We can draw an analogy between the creative process in art, and complex computational problems, by extending Kant's idea of the genius (creator of art) using the concept of NP-completeness and the NP-problem.
Kant’s Concept of the Genius
Kant sees the genius as someone who is naturally gifted, able to produce art that cannot be fully explained by rules or learned through teaching.
The genius creates something new, original, and universally compelling, where the imagination and understanding interact in ways that produce aesthetic ideas.
NP-Complete Problems in Computation
In computational complexity theory, NP-complete problems are those problems that are verifiable in polynomial time, but solving them from scratch seems computationally infeasible (i.e., it requires an impractically long time).
A problem is in the set of NP if a solution can be verified efficiently, but finding that solution might be as hard as any other problem in NP. Think of Sudoku as an example of this type of problem.
The Analogy Between Genius and NP-Complete Problems
1. The Creative Problem as NP-Complete:
Just as an NP-complete problem does not have an efficient algorithm for being solved, the artistic problem the genius faces can be likened to an NP-complete problem.
The genius does not follow predetermined rules or formulas to arrive at an artistic creation; instead, they seem to find a solution (i.e., an artwork) through intuition, inspiration, or some form of creativity that cannot be systematically reproduced by others.
2. Verification of Genius’s Work:
Kant suggests that the genius's work is recognized as art because it resonates with others in a way that can be immediately perceived and appreciated.
This is similar to the idea that once a solution to an NP-complete problem is found, it can be verified quickly. The artistic genius produces work that, while difficult to generate, can be universally recognized and appreciated.
3. Genius as the Solver:
The genius, in this analogy, is like a solver of NP-complete problems who operates beyond normal cognitive algorithms.
While most people might not be able to "solve" the artistic challenge directly (i.e., produce such original art), they can recognize the genius's solution as valid and beautiful when they see it.
The genius operates as if they have access to a shortcut (which in computational terms would be a non-existent or highly unlikely "P = NP" scenario).
4. Ineffability of the Process:
Just as the process of solving NP-complete problems is inherently difficult and often involves trial and error or heuristic methods, the genius’s creative process is ineffable.
Kant’s genius doesn’t follow a clear, teachable method. In computational terms, this is akin to solving NP-complete problems without an algorithm that guarantees success within a reasonable time.
5. Inspiration as Approximation:
The genius might not always fully solve the artistic "problem" but instead arrives at an approximation that is still profoundly moving and insightful.
In fact, an artist’s output is always an approximation of the idea that was in their mind that they wanted to share, and it takes a lifetime of honing skills to make that approximation better reflect the artist’s mind. I call that act, balancing the throat chakra.
This mirrors how NP-complete problems are often tackled through approximations or probabilistic methods in practice. The genius provides a work that feels complete, though the path to it might have been complex and obscure.
In Essence
By extending Kant’s idea of genius with the notion of NP-completeness, we frame the creative process as one of tackling inherently complex and seemingly unsolvable problems where the genius transcends standard cognitive methods.
The genius, like an adept solver, finds their way through the exponential tree of possibilities and arrives at an aesthetic solution that can be appreciated nearly or totally universally, though the process that led there remains mysterious and beyond formal articulation.
This highlights the brilliance of the artistic process, where the final product (art) is recognizable, but the method of creation remains elusive, often even to the artist themselves.
