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Plato’s Allegory of the Cave
“’Well, they’re hard put to it for words to describe what they do � with laughable results, sometimes. All this squaring, extending and adding. They’re full of utterances of that kind. Everything they say is in terms of doing things, and practical applications, whereas the truth, I take it, is that this is a subject which is pursued entirely for knowledge’s sake.’” (Plato, 57b)
Socrates’ belief that geometry is a genre that is only studied for the sake of knowledge is one that most certainly does not apply to the world today, and not to the world of Ancient Greece either. Socrates, as described in Plato’s Allegory of the Cave finds that mathematics is a very philosophical pursuit because it’s aim is truth and knowledge, not practical applications. It is a flawed view. Mathematics, and especially geometry, are key elements of many aspects of the world. Geometry is studied largely for its practical applications for the simple reason that the human race is inherently pragmatic. Most people are unconcerned with knowledge for knowledge’s sake. They are looking to get something more out of it. Whether it be studying history to know and avoid the mistakes of the past, studying a foreign language to better be able to communicate cross-culturally, or studying geometry to design buildings that won’t topple, every genre of study must have a practical application in order for it to be justified by the majority of the population. Geometry finds an obvious practical application in the fields of engineering, surveying, navigation, architecture, aviation, even in car racing. Engineering uses geometry to design things efficiently, even a tool so basic as the wheel is based in geometry. Surveying uses it to accurately measure distances and areas that cannot be measured conventionally. Navigation is one of the studies that was also important in the world of Ancient Greece. Sailors in that time period would have been absolutely unable to accurately reach their destinations without some geometrical knowledge. Knowing how to aim their ship with precision over long sea voyages required geometrical knowledge and astronomical knowledge to plot their course based on the stars. And more geometry was needed to get their ship to sail in that direction no matter the direction of the wind. Architecture uses geometry to design buildings that are structurally sound, and to maximize interior space while keeping the building interesting to look at. Aviation uses geometry in designing aircraft, navigating them, and maneuvering them safely. Even auto racing uses it to plot the fastest course around the track. In short, geometry plays such a basic role in our everyday life that the amount and variance of ways it can be used are nearly endless.
Geometry, to be sure, can be studied solely for knowledge. Philosophically the subject may be an excellent one to examine without consideration of its practical applications. It is a subject of interest to Socrates because, “it is indeed something that draws the soul towards truth.” (Plato, 57b) Geometry and indeed mathematics in general are a perfect field for the study of truth because they are not at all subjective. The three angles in a triangle are, always have, and always will add up to 180 degrees. While Socrates contends that this is geometry’s main purpose, the majority of the world contends that its use is far more applicable to more practical pursuits.
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Simply because philosophers may be interested in the field for a tool to better understand “the truth” doesn’t necessarily mean that geometry can’t be used in other ways nor that those ways aren’t its primary application. Geometry, in contrary to Socrates’ ideals, is primarily a pragmatic study. While in the world of philosophy geometry may be only “pursued for knowledge’s sake” that is a very untrue view based upon the interests of the rest of the world.
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