In this blog by computer scientist Boaz Barak makes a distinction between the speakable and the unspeakable. He writes:
In fact, Computer Science has about as much to do with computers as English has to do with printing technology. The point of computer science is not about mechanizing some calculation but about finding a novel way to express a concept we couldn’t grasp before. Finding such a way enriches us whether or not it ends up being programmed into a computer, since it lets us access what was heretofore unspeakable.
Now, what here is referred to as the unspeakable is so because its perfect calculation would take so much time and resource that it is rendered practically unspeakable. However, if one gives up on perfection and attempts to gain an estimate that is inexact, it may lead to a conceptual insight about something that was considered un
Boaz Barak further claims that the source of his inspiration is the adage from Voltaire which says that ” The Perfect is the Enemy of the Good” . If we accept this ‘cult of the imperfect’, we will rediscover the utility of a sensible notion of the ‘good’. We are reminded of Aristotle’s adage about the good being related to the notion of the mean. Besides also his insistence that the good is not some abstract notion removed from the actuality of practice but that its worth is reaffirmed through its resonance with the most-commonplace beliefs. The demand for a perfection so ideal as to be unreal , can be debilitating.
Computer science extracts a quantitative insight from a moral precept. While computation allows for greater precision in the solution of many problems, the search for precision does not succumb to the demand of perfection but works through notions of approximation, instead. These notions of approximation reveal the rich structures of the road to perfection. Perfection is a mere bait to develop new concepts.
The foundations of computer science as laid out by Turing were indeed meant to define what it meant for something to be perfectly computable. Deploying the ideal of perfection endowed a fundamental clarity to notions of computability. However, there emerged bamboozling classes of problems that resisted computability. Motivated by this negative thesis, the holy grail is to define problems that are perfectly unsolvable and yet keep approaching these black holes through imperfect approximation. In other words, only because we value the approximate and the imperfect, we remain wise enough to continuously revise what we deem as the perfect.
The perfect must be the necessary crony of the good, not its enemy!