Imperfections: Within us and the world beyond.
It has become a trivial statement that nobody is perfect, implied when we try to justify our shortcomings, or better still find solace in, well, our imperfections. But have you taken time to ponder why we are imperfect? As a mathematician, our job is to generalize concepts so I will give a generalized view of imperfections!
Let us get the ground set up. Whether you like it or not, all humans are imperfect. Why? We all know that no individual can have a perfect level of all the desired qualities of a human, eg beauty, strength, and intelligence to name but a few. Deeply analyzing what an ideal human comprises leads us to conclude that there is no universally accepted standard of an ideal human being. The concept of an ideal human is culturally bound such that there could be no universally agreed qualities of the ‘perfect’ individual. Hence absolute perfection is relative, let’s dive into subjective perfection.
When defining perfection usually we are constrained within ‘our’ world-view — one’s cultural, moral, and social perceptions. Thus anyone who believes or is perceived to be nearing perfection is only classified thusly by a distinct group of individuals. We don’t universally conform to a distinct group’s claims since there might be some quality — out of a multitude of qualities that could be chosen — that this individual lacks as compared to some other humans. You might be muscular but not smart, thus not perfect according to a group that perceives smartness as a major factor in nearing human perfection!
If we rule out unidimensional thinking that allows the concept of perfection to flourish, for example, the emphasis on a certain thickness of the body is viewed in some social circles as a symbol of perfection, and encourage multidimensional thinking, it becomes apparent that no human can be perfect for the reasons alluded in the previous paragraph.
For the following reasons, no single human is perfect: no one individual can manifest all qualities that are defined to represent perfection, and as a population, we will barely absolutely agree upon what qualities constitute perfection out of the plethora of qualities existing in a multidimensional sense in individuals. Thus when one group decides on one quality that is the standard of perfection eg skin color, problems like racism might appear. One can argue that the group might thrive in a certain area eg concentration of highly intelligent individuals but history says we go back to the same problem. The problem is, given that our brains are all different, no two people are equally (100%) intelligent so even in a society of smart people you will find there is someone who is mocked for being the dumbest among themselves!
An interlude…
We spend time in front of mirrors/doing makeup or editing photos trying to achieve perfection, undergoing surgeries to have hourglass figures to achieve our dream body, or even reading extensively to become smarter. Some of us have been there and the worst case is it usually leads to anxiety, the best case being you might snatch your desired partner or grades. But decades later you laugh at what you thought was perfection (this usually doesn’t apply to acquiring knowledge eg learning math). We believe perfectionism increases the chances of success. But if you’ve been following up to now, you should know we cannot achieve perfection, thus do not confuse perfectionism with striving to do your best. Some might argue that spending lots of time in front of the mirror is striving to get their best look, so the interlude is over haha!
Back to imperfections.
We should not worry about becoming perfect because we are not. We should not see disabled people as imperfect. We should not see a specific type of body structure as being perfect.
Assuming that we have accepted that all humans are imperfect, let’s get on to some technicalities.
Do you think the speed on the speedometer of your car is the actual speed? The reason is in how many digits of pi you use in estimating the speed using the rotation of the wheels. Using pi = 3.14 can get you acceptable speedometer readings (within 5mph) according to the US Department of Transportation. Well, you know that area of a circle is π times the square of the radius. The basic definition of pi (π) is that it’s the ratio of the circumference and the diameter of a circle. Pi, being a transcendental number is still known up to 62.8 trillion digits as of 2021, as calculated by some supercomputers. The point I am trying to make is even things we interact with daily are not perfect. As circular a wheel appears, it’s not a perfect circle, engineers know this well.
Even in your physics classes, you estimated acceleration due to gravity to be g = 9,81 meters per second squared, sometimes even a value of 10 would suffice for some problems! We are not much bothered about, maybe 400 digits of g since a few digits work for our daily calculations or experiments. Well, the previous points could be summarized by a well-known principle (my favorite) in quantum mechanics. The Heisenberg uncertainty principle states that we cannot know both the position and speed of a particle, such as a photon or an electron, with perfect accuracy. However, engineers do not lose sleep over striving for perfection, since the uncertainty principle is indiscernible on the macroscopic scales that humans experience. Thus even our best laws of physics or the natural sciences are imperfect in the sense that they approximate nature both at macroscopic and microscopic levels. At least in the sciences, we have a notion of what perfect is, for example, in calculations, you can work with the irrational square root of two, or our lovely pi (π), or even g (acceleration due to gravity) without substituting its approximate digits to get a precise formula, for example, your weight due to g is given by a precise simple formula F = mg. Well, this quickly sends us to the realm of mathematics.
As mathematicians, we like to brag that we deal with the most perfect objects, unlike other fields. Talk about perfect spheres, we can approximate the epsilon-delta arguments in the mundane limit of function definitions to any accuracy you need. Of course, mathematics is a human creation and is not tangible for lack of a better word. As an example, the number 1 is just an abstract notion you can’t see, feel or touch but can assign things with it. As much as math is purely a human’s creation, it tends to approximate nature so wonderfully.
Here’s a funny thought. Imagine one day aliens visit us and we show them the best of our mathematical theories and how it has enabled us to peek through the galaxies, deep inside subatomic particles, etc, and they laugh at us saying, ‘Ahh, math, we have been there before, it only works up to blah blah blah!’. It might mean they have some other method that is better than math at deciphering the laws of nature! In math, we base everything on logic, and it is perfect at showing internal consistency given a set of axioms upon which to express itself. However, Gödel’s incompleteness theorems showed that logic by itself is insufficient (i.e. that any non-trivial system cannot be proven due to the problem of the axioms being unable to be proven within the system.). This is beyond the scope of this article but interested readers might look it up. So even math does not have the issue of perfection solved, perhaps because it is created by us, who are imperfect? Do not misquote me here, the Pythagoras theorem among all other mathematical theorems are perfect as described by their axioms!
This doesn’t mean that mathematics is wrong. Indeed, the assumption that mathematics is consistent has proven to be incredibly useful. My point is only that our justifications for this assumption cannot come from mathematics itself.
Maybe now it’s a matter of language/semantics. Is anything perfect? Religious people come up with a solution, God is perfect because they believe He got all qualities that we can think of plus others that we cannot even think of! But God being perfect does not mean His creation is, if it is that means God is creating Himself since He is the only perfect being!
My advice for the so-called perfectionists is, to be careful of the negative effects which tend to devour the positive effects when averaged out. We should not worry about becoming perfect because we are not. We should not see disabled people as imperfect. We should not see a specific type of body structure as being perfect. Do not become anxious about trying to portray a perfect image, but instead embrace the imperfections. Embracing your flaws or insecurities will allow you to have the right perspective, both on the world and yourself.
Let me end with an interesting logical paradox to pick your mind, the so-called Barber paradox. The barber is the “one who shaves all those, and those only, who do not shave themselves”. The question is, does the barber shave himself?
Answering this question results in a contradiction. The barber cannot shave himself as he only shaves those who do not shave themselves. Thus, if he shaves himself he ceases to be the barber. Conversely, if the barber does not shave himself, then he fits into the group of people who would be shaved by the barber, and thus, as the barber, he must shave himself.
