Curious about how programs exchange data securely. Read this article on the RSA Algorithm. I guarantee you'll understand the mathematics of the process after reading this. The RSA Algorithm

Does Perfection Exist?

Perfection as a concept has been reviewed, studied and answers have been proposed for centuries.  It has a paradoxical answer if we attempt to apply its conceptual formalization to material reality. Perfection exists as an abstraction of our minds, but is not attainable in the physical world.  Outside of the objects of our minds like numbers, perfection is never quite realized in the real world. Actually, even with numbers, we have imperfections. The numbers e and π to name two are imperfect numbers as they have no complete formation.  No circle is exactly a collection of equidistant points p from a defined length r, or no line is ever an unerringly straight distance between two points A and B, or we never actually reach absolute zero, or any test we perform which measures anything is never 100% certain or correct. The last one is interesting because the objection could be raised that a test with scored answers and the respondent gets every answer right, must be perfect. That is, this test is a measure of perfection right? Wrong! Any test that is given can never measure the respondent's knowledge of the entire subject the test covers. If a person takes an arithmetic test of 200 questions and gets 200 answers correct, this test isn't a perfect measure of the respondent's knowledge of all arithmetic. The test would have to ask every possible question in the area of arithmetic to show that. Furthermore, if we just confine ourselves to the test itself with the 200 correct answers, that too is not perfect. For you see, we have arbitrarily made this perfect. There is no basis in existence for this to be perfect. It is only when human beings create this category called perfection that this test can have that significance. This is at the heart of the problem with perfection. When human beings create an idea (concept) and set it as a measure, we've gone wrong already. As we shall see below, perfection is contrived. If it were an aspect of reality it could be discovered not prescribed. For instance, The Axiom of Choice in set theory mathematics is a beautiful theorem that was discovered and not contrived. It illustrates that in any collection of things there is a way to specify the relations among the members. That is, we can specify from the members of a set C, the members of a subset say D, that is contained within it. This concept allows us to define greater than, lesser than, and equal to. A fundamental theorem is the root of our arithmetic counting system. It met with some resistance, I should say when it was first proposed, by Ernst Zermelo, but we won't go into that. Let's look at perfection in-depth.  

Some concepts are rooted in existence and are not contrivances of human making. The Law of Conservation of Matter is one example. It is conceptual, but derived from studying reality, then formulating the concept from quantitative analysis. Industrial processes make use of it. Recycling is one that comes to mind. Recycling takes garbage and transforms it into new plastics, artificial wood, energy sources, drugs, new paper materials, metal products, metals alloys, deodorants, textiles, etc. This process can happen again and again, all based on the Law of Conservation of Matter. This empirical law gains validity as all applied concepts in science do, by it having utility in reality. To put it simply: we can use it to make and do things, mainly through the engineering arm of science. It's true because it's pragmatic. Or in even plainer terms: if it works its gotta be true. This concept is not subject to any idea of perfection. It is an empirical law that is well-defined and founded on the inductive study. The Law of Conservation of Matter has no perfect measure. It merely states that matter is neither destroyed nor created. We need not measure LCM's perfection. The following two can be subject to the idea of perfection. The speed of light c, and the universal gravitation constant G are imperfect measures, as they can't be established with absolute certainty.  In fact, throughout the natural world scientists know that empirical knowledge is never perfect in the sense of being absolute. 

I believe that natural perfection does not exist and further that it is a creation of our minds.  It is a concept and not an attribute of reality. And yes, of course, there are those who will argue philosophically that if the concept exists, then perfection is part of reality. Meaning the conception is part of reality. Of course, the concept is. To address this misconception we know, mythological beings have been conceived but don't exist. Are their conceptual existences to be considered some type of tangible reality? If we go further and say since the concept exist, it must have sprung from some material existence. If we accept that, then since there is a concept of nothing nothing must have somehow existed? Which is a contradiction in terms. Because no nothing could ever have existed! Yet, the concept has existed for a long time. Before I digress too far, I must say many of the ideas we have, don't come from our perceptual material existence, while ALL of the ideas we have are rooted in our perceptual existence. That's not as confusing as it might sound. I am merely saying you must have existence, to develop any ideas about reality. That's what I mean by rooted in. Remember, ideas can be imagined things, that don't have to come from actual physical experience. But let's get back to Perfection.  One conceptual notion that developed in mathematics is non-Euclidean geometry. Riemann was one mathematician that helped establish the validity of non-Euclidean geometry.
See this site for details: A. Bogomolny, Non-Euclidean Geometries, Discovery from Interactive Mathematics Miscellany and Puzzles Non-Euclidean Geometries, Accessed 23 June 2013. We can examine this idea to see that it is synthetic and contrived.  It applies to our three-dimensional world, but is not perfect.

A system of non-Euclidean geometries first theorized in differential geometry mathematics was later adopted by theoretical physicists to explain the Theory of Relativity.  These spatial geometries began by denying one of Euclid's spatial axioms from his book The Elements.  For example, we have Elliptic Geometry which denies the axiom that all parallel lines never intersect and replaces it with the axiom that all parallel lines must intersect at exactly two points.  This geometry is great for mapping the Earth's geodesic lines of longitude.  The parallel lines of Euclidean geometry become what are called great curves or geodesics on a restricted spatial plane of the Earth and can be used to measure great distances for ocean-going vessels. They describe the force of gravity on areas of landmass.  Changing what seems a common-sense notion created another conceptual theory that is perfect in the abstract, but never really exists in our spatial world.  Lines don't somehow curve at the terrestrial poles!  They only curve in the rules of the geometric theory.  For those geophysicists that raise the objection that the Earth is one big magnet with N-S polar attraction and thus does setup a curvilinear system of a force gradient, I submit that this system is not always stable and actually switches poles periodically.  Moreover, those lines of magnetic attraction are not even symmetric and always attracted to the polar vertices.  It has been shown they are deviated by solar radiation and the solar wind.   This is evidence of no perfection in reality.  Actually, I don't think any geophysicist would take issue with me on this topic.  I'll be so bold as to state, no scientist would dissent that perfection does not exist in our reality.  The question now becomes if there is no empirical perfection, can there be conceptual perfection?  The easy answer is yes.  But the more prudent answer is: I don't know.

There may be no conceptual perfection either.  I don't believe there is any Perfection, but can't prove this thesis using deductive methods.  If we assume that we can construct an abstract perfection based on logical rules devoid of empirical elements, then we run the risk of this perfection being valid only in its well-defined system and nowhere else.  It becomes vacuous and circular, like religious dogma.  The perfection this reasoning achieves is valid only as long as we accept its assumptions.  It's static and easily overridden by new empirical knowledge that outdates it.  On the other hand, if we marry the deductive theory and empirical one, we get on a treadmill of verifying experience against theory always correcting theory to conform to empirical knowledge.  This is what applied science does, but still applied science destroys the notion that there is any perfection as the feedback process is infinite.  So, again there is no perfection.  By definition perfection is a state that can't be made better.  Thus, I am led to the following odd conclusion:

Perfection is a chimera.  It is one of many human ideas that doesn't exist.  There is not a perfect thing, state or concept.  The concept of perfection itself is flawed.

What I mean by the above statement is we have created this synthetic conception.  Its meaning and substance exist in our cultures and individual minds.  It doesn't exist in reality.  It furthermore doesn't even exist in concept. By conceptualizing it, we are led to a contradiction.  If we define perfection in the abstract of some concept, that concept is always subject to change by new knowledge and thus by definition can't be perfect.  The very idea of perfection leads to a contradiction even in theory.  One problem with perfection is it is always applied to things.  Perfection itself is meaningless without reference to that which it applies.  And the worst contradiction would be if we simply consider perfection the concept unapplied to be perfect.  It would be completely meaningless because a concept without an application has no relevancy at all.  Examples:

The concept of numeration without things, to which it can be applied, invalidates the concept of number.

The conception of space without space, to which it applies, does the same thing.

A second problem with Perfection the concept is it's comparative and mensurative. It is not perceptual. We never experience perfection, we only reflect upon it. Can you objectively tell me when you've ever experienced perfection? I think not. Perfection is used to compare objects, ideas, states of beings, etc. This is done even in the empirical world. Engineers build complex systems based on measures of imperfection in them. For instance measuring the strength of metals, or efficiency of production processes, implementation of designs.... again, etc, etc. While this is useful in our world of technology, it is devoid of any intrinsic meaning.

The Dutch philosopher, Baruch Spinoza brought a strange idea of Perfection to the attention of rationalist philosophers in 17th century Europe. He introduced the idea that God is Perfection, i.e the Being that exists without the need to reference any other existence. That is to say It is not contingent upon any other existence. It is unto itself a complete existing thing with infinity in every possible way. He called infinite space, Extension, meaning in modern parlance spatial geometry. He classified time as Duration, which is in modern terms is time. So, the sum total of that state of being infinitely extended (spatial in all directions) and in all temporal duration was Perfection. Spinoza thought of Perfection as a being that existed in this way. That is, the Being God wasn't just in this world as a thing, it was the stuff of all reality. In Spinoza's world, we were really a part of God not just Its creation! Thus, we and everything combined were God. And since all Reality could have nothing outside it, it was Perfect. Because nothing could exist outside Reality. If taken all together, all things, all space, all time, as a sentient Being, then this Being is Perfect unto itself. Nothing can be referenced to compare It to. There could be no counterexample to God. Spinoza didn't assign any gender reference to God by the way. His contemporary philosophers responded: this is taking all Reality as God and thus reality is Perfection and cried--that's primitive religion! Why that's associating the Eternal Supreme Being with all Nature like animistic religions do! Boy, did they get on this poor guy. It didn't help that he was a converted Jew either. The Catholic Church shut him up real fast! Poor Spinoza. He was already excommunicated from Judaism. Nevertheless, it's the closest thing I can see as Perfection, except for the fact that nothing like this exists. He philosophizes on this in a work called Book of God for those interested. Still, it failed as it must.

My take on the issue is Perfection doesn't exist and is another meaningless creation of our human species. We've got quite a few. What do I mean? Well take the value of human life, a synthetic concept, considering none of us live more than 100 to 200 years and the planets and galaxies are billions of years old, where is there value in human life? How can a being that exists for so short a period of time have value to the universe at large? Or take final ends to our existence on this planet, another synthetic concept constructed to give us some sense of meaningfulness. And, oh yeah.. don't forget the God Myth, and Beauty, and Justice and the Soul. Those four are complete fantasies. Then there is Right and Wrong morally, those are two strange ideas, but at least those ideas are based on our evolutionary heritage and the need to survive, but just as contrived objectively. Why do we come up with these meaningless ideas? What drives us to see meaningful notions where there are none? I have another in this series: Beauty. See the essay below. And after that there is Love. I must write another essay about Love. This one has got to top the list of human synthetic conceptions. Hard to define, and even harder to explain. And since I'm a victim of love as most of us are, it is one exploration I must delay.

Though, I've used the word imperfection and that is an error on my part. If there is no perfection by analogous reasoning, there can't be any imperfection. There is no imperfection as there is no perfection. But, of course, you've figured that out already, right? The next idea we explore will be beauty. Is there really a beauty that is objective? Does beauty exist in more than a woman's face or body or in a mathematical object of symmetry, or a landscape, or a celestial object, or a color, ad infinitum? Isn't it clear this is a synthetic concept of human making?

As the last example of the contrived nature of the concept perfection we can take an example for number theory mathematics. This is the idea of a perfect number. By definition a perfect number is one that is the sum of its positive divisors. That is numbers less than the given one and positive. Example 6 = 1+2+3. Each number divides into 6 evenly, the numbers are positive and when added they equal 6. 28 is another. There are very few of these numbers and there is a formula to calculate a perfect number, which I won't show. You can google it. The point is why would a number with such property be considered perfect? This is even unrelated to the concept of perfect I've explained previously. There is nothing in this property of certain numbers, that makes them perfect in the sense of measuring adherence to a standard. It is just a name some group of theorists has assigned to these numbers.

What is Beauty?

Next, we will look at Love. This may surprise some readers of this series, but I believe some form of love exists for human beings. We can actually divide love into two categories. See this article. .

What is Love?

What is Existentialism? Existentialism is the philosophy that teaches us why such notions as Perfection are without meaning and thus merit. The Existential Concept

Robleh Wais  7/27/10 Updated: 3/17/14

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