All Quiet on the Western Front

          In Barron's Notes, Christine R. Barker and R. W. Last analyze the philosophy of Erich Maria Remarque’s modern classic All Quiet on the Western Front. They believe  the book to theorize that the world has fallen so far into decay that it no longer makes sense. This worldview is justified through the eyes of one who is not Christian, but not for one who is saved.

         Barron's Notes states that “human existence can no longer be regarded as having any ultimate meaning.” They accredit this, not to the inabilities of the characters to reason, but to the near impossibility of seeing order and reason in a world of hate and violence. The authors of Barron's Notes wrote that “Remarque refuses to lull his reader into a false sense of security, into thinking that God is in his heaven and all is right with the world.”

         The idea that the Remarque did not write All Quiet on the Western Front to have any “ultimate meaning” is correct. The main character joined for the glory and camaraderie, but left saying “Let the months and years come, they can take nothing from me, they can take nothing more. I am so alone, and so without hope that I can confront them without fear. The life that has borne me through these years is still in my hands and my eyes. Whether I have subdued it, I know not. But so long as it is there it will seek its own way out, heedless of the will that is within me.”The men instinctively do not want to make sense of war, in all its murder and hellishness.  In that, they do not want to see God as being involved in that war, for they do not truly believe that such a Being could permit such chaos if He were not Himself violently disposed.

           In truth, life is to be lived for the glory of God, and all people are called to worship Him (Romans 15:7-12). Without a grasp on the ultimate will of God, one can not make sense of the way the world works. When such an understanding is reached,life, event

         Barron's Notes demonstrates rather accurately the ideology behind All Quiet on the Western Front. The hopelessness and helplessness exhibited in Remarque’s classic is symbolic of the philosophies of many people worldwide. All Quiet on the Western Front shows the often-made choice to refuse to understand the purpose behind an action in defense of a sin-stricken humanity, and people that shaped history begin to fall into line that points towards the second coming of Jesus Christ. 

  

Are All Horses White?

Here’s a homework assignment I had a few weeks ago in Elementary Number Theory:

Find the flaw in the following ‘proof by induction.’

CLAIM: Alexander the Great has been always riding a white horse

PROOF: It suffices to prove that all horses are white, since then, in particular, the horses ridden by Alexander the Great were always white.  To prove the latter, let us employ mathematical induction.

One can certainly find a white horse.  This establishes the base for induction. 

Suppose that any k horses are white, k≥1.  Let us show that any (k+1) horses are white.  Take k+1 horses.  Choose any k of them.  By assumption, these are all white.  Take one of the chosen k horses and exchange it with the (k+1)-st horse.  The new group of k horses, by assumption consists of white horses only and the new (k+1)-st horst is now white, because it was chosen from among white horses.  Thus all of the k+1 horses are white and the validity of the inductive step has been established.

By the principle of mathematical induction, all horses are white.

Basically, the idea is to prove that every horse that has ever existed is white, so therefore every horse that Alexander the Great has owned has been white.  The proof says that there is a group of k horses, where k is any number.  Since this proof starts where k=1, let’s take one horse.  Because any k horses has to be white, the horse has to be white.  When you add a second horse, you have a group of k+1 horses.  Because k=1, the added second horse is also a group of k.  Because any group of k horses must be white, both horses in the set of k+1 have to be white.

Since we showed that the proof is solid for any group of k=1 horses, let’s look at a larger sample.  For inductive proofs, we have to show that, for any number k that is a natural number (any number greater than 0: 1,2,3,…) the statement must be true for k+1.  

For example, let k=3.  There are three white horses in the group.  If you add one horse to the group, you will have k+1 horses, or 4.  Based on the statement that three (k) horses in the group HAVE to be white, you can take any random grouping of three horses and they must all be white horses.  This being said, if you take a group of 3 (k) horses and it includes the horse that was added last (the 4^th horse), all of the horses in that group must be white.  That cycle would continue until it is proven that every horse in the group of k+1 (4) horses HAS to be white.

That’s OBVIOUSLY not true.  But it seems airtight at first glance, right?

Here’s the problem: We started with a group of k=1.  Of COURSE every horse in a group with only one horse in it is going to have only ONE color of horse.  Duh.  If we started with a bigger group, such as k=2, you would significantly cut down on this error as you can’t make the same assumption that both horses in a group where k>1 are the EXACT same color.

Well, there’s the mathematical version!  Let’s look at it from a few other points of view.

PHYSICS:

Think about the definition of color.  Color is the refraction of specific wavelengths of light from different objects.  Black is the absence of light or when all light is absorbed into an object and no color is reflected (by the way, black is not actually a color as it is a LACK of color/light).  Color is, therefore, dependent on the presence of light.  It can therefore be argued that all things are black when light is absent.  Also, it can be argued that everything is black… plus light and color.  Speaking from a physicist’s point of view, everything is black and color is a side-effect of the presence of light.

BIOLOGY:

Consider an albino horse.  PURE white. 

Albino horses are the result of a genetic mutation where melanin is not being made.  Melanin is the pigmentation of skin, hair, and eyes.  Without melanin, it is impossible for there to be any color present in the fur, skin, or eyes of a horse.  Therefore, speaking from a biologist’s standpoint, EVERY horse could be called white. 

If albinism is the absence of melanin, then every horse is white… plus color!  Every horse contains the potential to be albino as they have the same properties of an albino horse… plus melanin.  Horses are all white, plus color! Think of it like an equation:

Albino=Horse-Melanin
Horse=Albino+Melanin

Conclusion?  There are always multiple ways to look at one problem.  Don't get tunnel vision, you might miss out on some really amazing facts!

Infinity

The idea of infinity is something that nobody can fully comprehend.  The idea of “forever” is something thrown around by Hallmark, TV commercials, and stupid love letters but is rarely used for anything other than gross exaggeration.  How to understand such an amazing concept as infinity?

The English word “infinity” is derived from the Latin term “Infinitas,” which can be translated as “the state of being without finish.”  The Greek term, “apeiros,” means “endless.”  Can we ever really understand that? 

Mathematically, the idea of infinity is still hard to grasp.  For every number “n,” there exists a number “n+1.”  For every number “n” there also exists a number “n-1.”  Forever.  Always.  The set of all Real Numbers (1,2,3,4,…) is infinite and the set of all Integers (…,-3,-2,-1,0,1,2,3,…) goes from negative to positive infinity.  John Green, in The Fault in Our Stars, "There are infinite numbers between 0 and 1.  There's .1 and .12 and .112 and an infinite collection of others.  Of course, there is a bigger infinite set of numbers between 0 and 2, or between 0 and a million."  Can you imagine that?  There’s ALWAYS a bigger value and ALWAYS a smaller number, no matter how high or low of a numeral you choose!  Try to wrap your head around that.

There’s something called “Menger’s Sponge,” introduced by Karl Meger,that was designed to be a sort of 3-dimensional model of infinity.  Take a cube, and divide each side into nine equal squares.  Remove the middle square.  Take the remaining 8 squares on each side of the cube, divide each square into nine equal squares, and remove the middle square.  This would theoretically go on for an infinite number of squares, never ending.

Theoretically, this is a perfect example of infinity, you could always take out more, always remove another square.  In reality however, consider a block of concrete.  You can cut out the middle squares and repeat maybe… 10 times.  After that, though, the block would be in danger of cracking or falling apart.  There is a limit to the practical application of Menger’s Sponge in that, in reality, no structure would be stable after a certain amount of mass had been removed.

Biblically, we know that God has no beginning and no end.  This can be related to a mathematical statement that there are infinitely many numbers, positive and negative: you can accept it as truth, but no one can fully grasp the sheer magnitude of such a set.  Human ability to understand infinity is like a practical understanding of Menger’s Sponge.  We’ll never be able to understand God’s infinite nature, infinite grace, and infinite abilities beyond a certain extent as our mind simply cannot comprehend the concept of infinity. 

Does this mean that we stop trying to learn about God or stop trying to understand His greatness?  No, of course not!  What it does mean, however, is that we can appreciate Him all the more.  If we can appreciate a philanthropist for doing a good thing that we can understand, how much more can we appreciate and be amazed by the works of One who is so great and awesome that we literally are incapable of understanding the magnitude of His grace?

Principal Stress and Henry Wadsworth Longfellow

I’ve been sitting here all day on a SATURDAY writing a lab report.  The young adult in me still wants my Saturdays to be full of cartoons, hiking or running outside, spending time with friends, or basically anything not work-related or requiring a thought process of any kind.  Starting to hate writing, Mechanics of Materials, and labs in general, I began thinking about who even cares about this mess.  Honestly!  Who is ever going to care about the principal stresses and strains that occur at every point on a cantilever beam, and why is it worth my time! 

                For those of you who may not know exactly what that means, let me explain.  Everything in the universe is under stress of some kind, be it gravity, air pressure, the weight of another object, etc.  Based on the fact that we exist in a 3-dimensional universe, scientists and engineers analyze the world along three Cartesian axes, x, y, and z.  Principal stresses are the magnitudes of the stress normal (perpendicular) to the Cartesian axes system.  Essentially, stress is on every object in every direction, inescapable and all-encompassing.

Unable to get the numbers to work out, reworking each of about 20 calculations multiple times to try to find the error, I finally gave up and took a break.  Then I realized the importance of what I was studying. 

Stress.  Everywhere. “Inescapable and all-encompassing.” Sounds a little applicable to life, right? 

The title of this blog is “Aspiration and Entropy.”  This is representative of my view that life is comprised of hope in spite of a fallen world.  Nothing is perfect on this planet, everything is degrading by the laws of physics.  We are all under stress at all moments in time, much like the theory behind principal stresses. 

The real trick to life is learning to handle the stresses that surround and act upon us constantly.  It may sound cheesy, but survival means fighting stress and seeking peace and joy consistently.  The world tries to bring you down with work, commitments, human relations, and personal outlooks.  It is a person’s response to these challenges that shapes who they are.  Henry Wadsworth Longfellow wrote a poem entitled “The Ladder of St. Augustine,” which encapsulates wonderfully how man must always fight through the stresses and strains of life.  Anyways, enjoy the poem!  I'm back to work... hopefully for the last time!

The Ladder of St. Augustine

  Saint Augustine! well hast thou said,

  That of our vices we can frame

A ladder, if we will but tread

  Beneath our feet each deed of shame!

All common things, each day's events,

  That with the hour begin and end,

Our pleasures and our discontents,

  Are rounds by which we may ascend.

The low desire, the base design,

  That makes another's virtues less;

The revel of the ruddy wine,

  And all occasions of excess;

The longing for ignoble things;

  The strife for triumph more than truth;

The hardening of the heart, that brings

  Irreverence for the dreams of youth;

All thoughts of ill; all evil deeds,

  That have their root in thoughts of ill;

Whatever hinders or impedes

 The action of the nobler will;--

All these must first be trampled down

  Beneath our feet, if we would gain

In the bright fields of fair renown

  The right of eminent domain.

We have not wings, we cannot soar;

  But we have feet to scale and climb

By slow degrees, by more and more,

  The cloudy summits of our time.

The mighty pyramids of stone

  That wedge-like cleave the desert airs,

When nearer seen, and better known,

  Are but gigantic flights of stairs.

The distant mountains, that uprear

  Their solid bastions to the skies,

Are crossed by pathways, that appear

  As we to higher levels rise.

The heights by great men reached and kept

  Were not attained by sudden flight,

But they, while their companions slept,

  Were toiling upward in the night.

Standing on what too long we bore

  With shoulders bent and downcast eyes,

We may discern--unseen before--

  A path to higher destinies.

Nor deem the irrevocable Past,

  As wholly wasted, wholly vain,

If, rising on its wrecks, at last

  To something nobler we attain.

“The Raven” vs. “There is a Budding Morrow in the Midnight”

Christina Rossetti makes fun of Edgar Allen Poe’s “The Raven” in her piece “There is a Budding Morrow in the Midnight.”  She attacks the loveless, depressed, and lonely state of “The Raven” with passion and beauty.  She taunts “The Raven” in her reversed interpretation of its characteristics.

The theme of “The Raven” is found in its continual use of the phrase “never more.”  The despair of the phrase fits perfectly with the subject’s growing deficit of love, sanity, and soul.  “The [Raven’s]” main topic is one of eternal and entire loss.

Rossetti attacks Poe’s sense of depression with an amoretto description of love that surpasses the loss of “sweet things.”  While the main point of “The Raven” is to demonstrate that all things are lost and darkness stays, Rossetti describes how beauty passes, but love does not.  Christina Rossetti turns the phrase “never more” into “evermore.”

“The Raven” is assaulted for its eternal doom, as Rossetti composed a mocking poem that is a reciprocal of Edgar Allen Poe’s classic.  Her ridicule of Poe’s famous verses dig through many layers, from the setting to the interpretation.  Christina Rossetti’s poem “There is a Budding Morrow in the Midnight” is a derision of Edgar Allan Poe’s “The Raven.”

"The Raven" by Edgar Allan Poe

"There is a Budding Morrow in the Midnight" by Christina Rosetti