Is Perfection Overrated? Why A Little Imperfection Is Desirable

Is it possible for anyone to draw a perfect circle?

This question may be of interest not only to mathematicians but also to ordinary people.

Though occasionally reports used to appear in a certain journal about someone having succeeded in drawing a perfect circle, some people particularly eminent science writers like Timothy Ferris have been sceptical about the authenticity of such claims.

For one thing all such circles looked alike.

The perfect circle drawn by a priest in Italy appeared identical with the one drawn by a cowboy in Arizona. This naturally led to a suspicion that the people who were publishing such accounts probably kept a readymade circle handy as an expedient, printing its image whenever a new free hand perfect circle arrived by post.

Of course, one might be tempted to conclude that the publishers were simply making up the news items or that they had failed to detect or identify circles drawn with the aid of a compass or by tracing the outline of a coin.

The idea that they were only using a single circle to “stand in” for all circles seemed comparatively more convincing.

But the question arises whether such an archetypical, stand-in circle was itself really perfect considering that the inking was coarse, having been stamped onto a page in the comics.

How could one know, Ferris asks, whether minute imperfections lurked in the thick hoop of ink. Even if drawn with a very sharp pencil, a circle would be irregular since no pencil draws a perfectly regular line.

Hence keeping an eye out for an indubitably perfect circle would have to remain a futile exercise, an unrewarding task.

Indeed, it may be impossible to find a perfect circle in the whole universe.

The planets for example orbit the sun in ellipses, not circles. The sun is flattened at the poles by its rotation as is every other star. The moon is lumpy, the earth is not a sphere but an oblate spheroid. No fish eye in the sea or sand dollar in the beach is quite perfectly circular.

Man-made technology does not come to our aid in seeking geometrical perfection.

Circles projected optically are subject to the vagaries of the lenses employed to project them. The best bearings made on earth are not perfectly spherical nor are their successors manufactured in space likely to achieve perfection, though they will approach it more closely.

As Ferris opines, the imperfection of the world’s forms is not limited to the circle but infects all other ideal shapes as well even the unpretentious line.

As Einstein discovered, the straightest of lines, from the International Metre bar to beams of starlight are not straight at all but bent along the subtle curvatures of the spacetime continuum.

If therefore nature is devoid of perfect circles and perfectly straight lines, then geometrical perfection is obviously absent from the outer world and must exist if anywhere, only in the mind.

The Greek philosopher Plato had held that perfection is to be found only in abstract concepts and that the physical world is composed merely of pallid approximations of those perfect abstract forms.

Thus, each horse can only be regarded as an approximation of the archetypical perfect horse. This appeared reasonable in-so-far as it took into account the notorious imperfections of real horses.

This theory would perhaps earn the appreciation of the director of a movie who in order to create the illusion of a single perfect Arabian horse took pains to employ six horses five of which were dyed black.

Notwithstanding such assertions, doubts remain regarding the alleged perfection of the abstract forms. Some people find that they are unable to form a mental picture of a perfect horse, or a perfectly straight line.

As for circles, Walt Disney once produced an amusing cartoon about Mathematics, that portrayed Donald Duck trying to imagine a perfect circle. It kept sagging, undulating, meandering away.

Indeed, people trying the same feat are likely to find themselves no better at it. One may not be willing to accept the story that the great German mathematician Gauss while at school had been able to draw a perfect circle every time on his slate without much effort.

Our language is full of talk of perfection, but most of it upon examination turns out to be just literary exaggeration.

Mathematicians talk of “perfect numbers” but this is merely jargon for a number such as six that equals all the positive integers that are sub-multiples of it.

Composers and musicians refer frequently to “perfect intervals” within the octave, but the octave is a compromise full of imperfections and the ability to identify its imperfect notes on first hearing, is all that is meant by “perfect pitch”.

If perfection is neither indubitable in the abstract nor exemplified in the outside world, then are we to conclude that the cosmos is a slapdash mistake? Or was our search for perfection perhaps naive?

One must perhaps turn one’s attention from perfection to error. Attention is a form of affection. It is perhaps better to invest “error” with the affection people have had in “perfection” till now. For in error, people can find plausible explanations for many strange phenomena observed in nature.

From the biologists we learn that the very evolution of life depends upon error. The process by which RNA replicates the DNA molecule is not perfect. The RNA molecule sometimes breaks as it peels away from the lanky DNA molecule scrambling the code by which it tells a frog how to make a new frog or a human, a new human. An erroneously coded DNA molecule results and if the experience has left it still able to reproduce, the result is a mutation, the genesis of originality in living creatures, the author of the species.

Were it not for the mistakes of DNA, its inability to reproduce perfectly, life on earth would have stalled at the level of the first creatures, unicellular, unisexual and identical, swimming in a chemical broth untroubled by thoughts of perfection.

It is, thanks to the imperfection of DNA that life abounds with such diversity as is found today on this planet.

From the physicists we learn that down in the realm of the particles a world so small that by comparison the DNA molecules are like galaxies, Heisenberg’s uncertainty principle reigns supreme.

It holds that our knowledge of the subatomic world is and must forever be but an approximation, a crude statistical determination based upon the gross behaviour of billions of particles, like studying Japan without even getting to know a single Japanese.

There can be no perfect knowledge of physical reality in detail according to the “uncertainty principle” of Heisenberg.

Philosophically by requiring that we consider the role of the experimenter in each experiment the uncertainty principle has obliterated the old notion that we regard ourselves as apart from the rest of nature. It has reintroduced us into the material universe as Darwin returned us to the fraternity of earthly life.

Scientifically the inherent imperfection in the relationship between mind and matter provides a scaffolding upon which the theories of Physics may be constructed.

The building blocks of matter need not be elusive fundamental particles but can be thought of as a space-time foam defining the limits of certitude in our perception of physical reality.

As Jacob Bronowski has opined, uncertainty is the essential safeguard, the essential degree of coarseness which makes it possible to work with abstract entities in the real world.

Cosmologically the" uncertainty principle” has been credited with answering the riddle of why something exists rather than nothing.

When cosmologists try to reconstruct how the expansion of universe began in the fiery cauldron described as the “Big Bang’, their calculations indicate that “error” was present at the creation. Had the primeval fireball been perfectly homogenous, the universe today would still be homogenous — a lightless, lifeless fog of hydrogen and helium gas.

For the universe to have evolved the richness and diversity it now manifests, the fireball had to have been less than perfect; it must have been marred by inhomogeneities, little curls and knots that became the seeds of the planets and the inhabitants of the planets.

In short, according to some scientists, we may have overrated perfection. As a concept it certainly is inspiring and worth our admiration but it seems that it is not from perfection but from imperfection that all creation has sprung.

If we seek a better understanding of the universe, we should admire not just the occasional perfect circle which someone claims to have drawn, but the imperfect circles too and the garbled scrambles of gas and dirt on their untidy way towards making stars and the last freakish proto-ape of the old Serengeti Plain in Africa whose descendants evolved into man.

Must we then give up the quest for perfection?

Perhaps yes.

All said our perfection is constructed by our human instrument and its limitation. When science reveals the universe beyond our conditioned sense of perfection and hence beauty we are shaken — perhaps as Einstein was and he had to be told by Niels Bohr that he should stop telling the Lord whether or not he should play dice.

That is the reason why, what Sabine Hossenfelder, the physicist who researches "possible experimental signatures of quantum gravity" says about beauty also applies to perfection — our human conception and experience of perfection In our search for new ideas, beauty plays many roles. It’s a guide, a reward, a motivation. It is also a systematic bias.

In her book ‘Lost in Math’ (2018), she further illustrates this with the example of Paul Dirac’s science career. He instructed his students that they should strive to achieve what he called ‘mathematical beauty’ in their equations describing natural laws.

According to Helge Kragh the historian of science the fact that Dirac largely failed to produce physics of lasting value after 1935 was also because "the principle of mathematical beauty" started governing his thought process after this period.

So, obsession for beauty and perfection can become obstacles to good science which is always unveiling the truth.

A little imperfection is desirable not only in stellar bodies but also in all objects and even living things on our planet.

Poets seem to know this intuitively. The famous English Poet Robert Herrick wrote the following lines about the erotic appeal of the imperfections in his sweetheart’s apparel.

“A sweet disorder in the dress

Kindles in clothes a wantonness;

A lawn about the shoulders thrown

Into a fine distraction;

An erring lace, which here and there

Enthrals the crimson stomacher;

A cuff neglectful, and thereby

Ribands to flow confusedly;

A winning wave, deserving note,

In the tempestuous petticoat;

A careless shoe string in whose tie

I see a wild civility;

Do more betwitch me, than when art

Art Is too precise in every part”.