Perfection

Perfection is a concept that describes a state of completeness, flawlessness, or supreme excellence. The term is used across many different fields of study. The English words "perfection," "perfect," and "to perfect" come from the Latin verb "perficere." This Latin word means to finish or to bring something to an end.

Because the idea is so broad, people use it to describe everything from mathematical numbers to moral behavior.

Ancient Greek thinkers provided some of the earliest detailed definitions of this concept. The Greek word for perfection was "teleiotes." The philosopher Aristotle, who lived from 384 to 322 BCE, identified three distinct ways to understand perfection. First, he described perfection as that which is complete and contains all necessary parts. Second, he defined it as something so good that nothing could be better. Third, he viewed perfection as something that has successfully attained its intended purpose.

Some thinkers have proposed paradoxical ideas about what perfection actually looks like. Scholars such as Joseph Juste Scaliger and Lucilio Vanini held a unique view. They suggested that the greatest perfection was actually imperfection. Their reasoning was that if the world were already perfect, it could not be improved further. This perspective aligned with the Baroque aesthetic. Similarly, the polymath Marin Mersenne believed an artwork reaches perfection when a spectator completes the work through contemplation.

Mathematics offers a very specific and technical definition of perfection. The ancient Greeks referred to perfect numbers as "teleioi." In this context, a perfect number is a number that equals the sum of its divisors that are smaller than itself. For example, the number 6 is considered perfect because 1, 2, and 3 add up to 6. Around 300 BCE, the mathematician Euclid created a formula for even perfect numbers. This formula involves prime numbers, denoted as $p$ and $2^p - 1$. Even after two millennia of study, mathematicians still do not know if there are infinitely many perfect numbers. They also do not know if any odd perfect numbers exist.

In the field of physics, perfection is often used to describe fictitious or ideal entities. These are not real objects found in nature, but they serve as useful scientific tools. Scientists use these ideals to set physical extremes that nature can only approach asymptotically. For instance, a perfectly black body is an object that would absorb all radiation falling upon it.

A perfectly rigid body is one that would not be deformed by any applied force. Other examples include a perfectly plastic body, which would deform indefinitely under a load, or a perfect gas where molecules have no volume and do not interact. A perfect fluid is defined as being both incompressible and non-viscous.

Perfection has also been a central theme in ethics and religion throughout history. The philosopher Plato suggested that the concept of "the good" was essentially the same as perfection. In Christianity, the ideal of perfection is embraced, as seen in the instruction to be perfect as a heavenly Father is perfect. Saint Augustine, a Roman North African, argued that perfection belongs to those who strive unreservedly for it. By the 5th century, two views emerged in the Church regarding whether perfection was attainable by human power or required divine grace. During the 18th-century Enlightenment, the focus shifted from religious to secular ideals. Thinkers like Immanuel Kant and Johann Gottfried von Herder discussed the coming perfection of humanity. Many others, including David Hume and John Locke, believed perfection could be reached through secular processes.

Finally, the concept plays a major role in aesthetics, or the study of beauty. The Pythagoreans in the 6th century BCE believed perfection in art came from correct proportions and harmony. Plato believed that beauty and perfection were one and the same. He specifically felt that the ratio of a square's side to its diagonal was a perfect proportion. Aristotle viewed the circle as the most beautiful and perfect form.

During the Renaissance, views became more diverse. Artists like Michelangelo were seen as perfect in their individual styles rather than following a single rule. Today, the goal in many fields has shifted from seeking absolute perfection to pursuing continuous improvement and excellence.