Memorial Day May 25, 2009
Posted by Clint Armani in History.2 comments
In my small, rural hometown of Manila, Arkansas, there is small monument on a corner of what we called “Main St” (actually it’s Baltimore St., but it’s the main road through town) and Highway 18. As a youth growing up there, I recall hearing a simple story about Herman Davis – a quiet war hero that almost went unnoticed by locals until near his death when he opened a tackle box full of medals.
Donna Jackson, mother of a high school classmate of mine, wrote an article last year giving a nice summary of Herman Davis’ life. Here’s a link to this short article (well worth a quick read).
Today, as Americans, we remember that millions of others have given their lives for the ideals of this country. Herman Davis didn’t die in action, but he did die shortly after returning home from WWI from complications of being gassed. Sacrifices, as such, only make sense from the ultimate sacrifice of the incarnate Son of God laying down his life for his sheep (John 10). Further, John and Jesus teach us that we show our love for one another by laying down our lives for the other (John 15, I John 3). Without Jesus’ life and teaching, self-sacrifice is futile.
May we hear, with thankfulness, the stories of the men and women who laid down their lives in service to our country. May that cause us to remember, with thankfulness, the ultimate laying down a life for another – God for us. May this cause us to live selfless lives in loving one another.
May We Know As We Ought to Know March 14, 2009
Posted by Clint Armani in Infinity.add a comment
In John Piper’s recent post, “All Truth Is God’s Truth,” Admits the Devil — Meditations on an Academic Slogan, he rightly demonstrates that truth (and the pursuit of truth) is not virtuous unless “it awakens desire and delight in us for the God of truth.”
Indeed, all truth is God’s truth, but even the devil knows that. God’s truth should be known, shown, and most importantly loved. Without loving the God of truth, our knowing and showing is not as we ought.
Those of us involved in science and engineering study and use God’s natural truths. We strive to understand, discover, and design. Some are motivated by comfortable careers, others by knowing and being bearers of the knowledge. But, as Piper points out, unless we are ultimately motivated by loving the God of truth, we are, at best, instrument that pass on truth but do not love truth in a virtuous way. Believers that lovingly embrace more fully the God of truth when we learn or discover these truths then and only then celebrate truth virtuously.
May all of us, scientist or not, know as we ought to know — by loving God more fully through that knowledge.
Great Resource February 26, 2009
Posted by Clint Armani in Bible and Theology.1 comment so far
This past fall one of the best Biblical resources (in my experience) was released — the ESV Study Bible. I received a copy of the hardcover edition for Christmas. It’s the best study bible that I’ve ever used or seen (and I have a shelf full of various study bibles). I highly recommend it to everyone!
Furthermore, I personally believe that the ESV will be the most prominant version of the Bible used in the English speaking world in my lifetime. Therefore, my wife and I have begun re-learning verses in the ESV. It is what we are teaching to our children.
If you don’t have and ESV, get one. Might I recommend the ESV Study Bible. By the way, it will also strengthen your body along with your soul. It’s the heaviest study bible that I own.
Here’s a bonus: a certain Baby Boomer is giving away the premium editon — calfskin leather. Go here to enter the drawing. Thanks, Mr. Porter!
PhD Specialty Exam February 4, 2009
Posted by Clint Armani in Education.4 comments
Today, I was informed that I passed my PhD specialty examination. Over the past week, I took four exams in areas related to all my coursework and research area. For those unfamiliar with this process, the PhD specialty examination is typically a series of exams following coursework that must be passed before a student can proceed with their academic research.
I would be an idolater if I did not bless the Lord for this milestone. All that we know in terms of the beauty of science, math, literature, art, etc. is a derivative of the beauty and nature of God. When we attempt to understand the world around us, we strain to view an infinitesimal component of God’s handiwork. Our minds can’t even imagine all that is really there, but even our frail efforts are a joyous adventure. Our little discoveries, when true and accurate, only scratch the surface of the whole. Reapplying lyrics from one of my favorite songwriter’s seems fitting:
“There is more. More than we can see. From our tiny vantage point in this vast eternity, there is more… There is more than what the naked eye can see — clothing all our days with mystery, watching over everything, wilder than our wildest dreams could ever dream to be – there is more.” Andrew Peterson
Very little credit should go to me. I’m blessed with incredible opportunities. I simply perceive myself on the journey of life endeavoring to observe what’s going on around me. Our senses often give us false impressions. May the Lord give me, and each of us, accurate senses. May our thoughts reflect the superior. Lord, keep us from error! May our feeble explorations tell of His beauty – the one “who was, and is, and is to come.” Bless the Lord!
Is Christianity Good for the World December 29, 2008
Posted by Clint Armani in Bible and Theology.add a comment
See this debate (Thanks D).
Abortionist Turn Pro-Life November 17, 2008
Posted by Clint Armani in Uncategorized.add a comment
Read this amazing article!
Andrew Peterson November 13, 2008
Posted by Clint Armani in Music.add a comment
My favorite music writer was recently interviewed, … twice. I can’t wait to see him live in December.
Greater than the Holocaust November 10, 2008
Posted by Clint Armani in Uncategorized.add a comment
Just recently, I did a comparison of the total number of people killed during the Holocaust to the number of babies killed by abortion since Roe v. Wade. The result was 5:1 in favor of abortions. This is astonishing!
Just do a quick search around the internet or in any history book on the Holocaust, and you will be sickened by the photos and details. The Holocaust was a great tragedy for mankind.
The conclusion that I came to was that we in this day are numbed to the atrocities of abortion. Many of us just don’t think about it. It doesn’t affect our personal, everyday lives. We don’t see it. Well, let me propose that you look at Holocaust photos. Here’s one example. Now, multiply that by 5 (at least and growing).
It was timely (and not coordinated) that my brother-in-law posted a message on this today. His message confirms my comparison. At this rate, our generation will quickly surpass the Holocaust by an order of magnitude. As Jim concludes, so do I — that abortion is the largest civil rights crisis of our time. I’ll also add that abortion may be the largest massacre ever. And we are numb to it!
Recently, I was engaged with friends and co-workers over the election. We talked about many issues. But, every time that I vote I cannot get these helpless little ones out of my mind. I have voted pro-life every time. Other issues are important, but this one is a moral obligation.
Veterans Day November 10, 2008
Posted by Clint Armani in Uncategorized.add a comment
My good friend and Test Pilot School classmate, Johnnie Caldwell, was recently interviewed by Baptist Press. You can scroll through 5 photos at the top. Two of which are of Johnnie.
Beauty of Mathematics September 1, 2008
Posted by Clint Armani in Education, Infinity.1 comment so far
On this day that I am completing my last final exam in my last formal math class for my PhD, I received a newsletter from Veritas Press that contained the following article. After reading the article, I agreed and was also a bit convicted. Overall, I enjoy math–I do see the power and beauty in it. However, as an engineer, I commonly get into the mindset of how is this subject useful. I somewhat jokingly said in a previous math class, that “I’m a math consumer.” Applied math is consumer math. Nonetheless, I thoroughly enjoy talking about mathematical theory with some of my math-major friends. I think that, as an engineer, I commonly get bogged down in the rigors of the details of math and want to see the big picture. But, as I step back, even from this final exam, I do see the power and beauty of math. Without further ado here’s the article:
Mathematics: Powerful and Beautiful
Math students who think about what they are learning, especially those who love to dig deeply in the mines of learning, invariably discover the power and beauty of mathematics. These two qualities have been recognized by thinking people for centuries. While most students realize early on the power of mathematics, at least to solve problems, many have trouble seeing the beauty of the subject. But mathematics is beautiful. Mathematician J. H. Poincare (1854-1912) wrote, “The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful.” Consider for a moment the power and beauty of applied and pure mathematics.
Applied mathematics is the language of the natural sciences, such as physics, chemistry, and astronomy. We call applied mathematics the “language” of those sciences because we use mathematical formulas to describe scientific theories. We do science this way primarily because it gives us power to predict. If I know the height of a rock above the ground, I can use mathematical formulas to predict the time it will take the rock to fall. In the early 1800s, astronomers were aware of aberrations in the orbit of the planet Uranus. Through a careful use of mathematics, these astronomers were able to predict the location of Neptune within degrees of its actual position. Clearly, applied mathematics, being so applicable to the physical world, is a powerful tool.
While few may explore math at very high levels, the power of pure mathematics is found in powerful mathematical theorems, theorems that have both generality and depth. A mathematical theorem is general if it is widely applicable, not necessarily applicable to the physical world like applied math, but applicable in the sense that it can be applied to other areas of math; it can be used in solving other theorems. If a particular theorem is needed to solve other theorems, then it is general, and in that sense powerful. A theorem is also considered to be general if it connects many mathematical ideas together.
The power of pure mathematics is also seen in its depth. Depth is hard to define. It is similar to difficulty-deeper ideas are harder to grasp. Deep theorems require a lot of study and creativity to develop, and often require powerful methods of proof. But once they are proven, especially if they can be used elsewhere in mathematics, they are considered to be powerful.
Mathematics is not only powerful, it is also beautiful. The beauty of math is not often appreciated by non-mathematicians. In his book A Mathematician’s Apology, G. H. Hardy (1877-1947) wrote, “It may be very hard to define mathematical beauty, but that is just as true of beauty of any kind – we may not know what we mean by a beautiful poem, but that does not prevent us from recognizing one when we read it.” Let’s consider beauty first in applied math.
To be recognized as true, a scientific formula or theory must not only be applicable to the physical world (meaning that it works, it has the power to predict), it must also be beautiful, or elegant. In his book The Discarded Image, C. S. Lewis compares medieval and modern cosmology, and writes,
A scientific theory must ‘save’ or ‘preserve’ the appearances, the phenomena, it deals with, in the sense of getting them all in . . . But if we demanded no more than that from a theory, science would be impossible, for a lively inventive faculty could devise a good many different supposals which would equally save the phenomena. . . . we must accept (provisionally) not any theory which saves the phenomena but that theory which does so with the fewest possible assumptions.
So, for example, both Ptolemy’s geocentric theory, the idea that the earth is the center of the universe, and Copernicus’s heliocentric theory, the idea that the sun is the center of the solar system, “save the appearances” of the motions of the sun, moon, and planets in the sky. Ptolemy’s system used 77 circles and epicycles to describe the motion of the planets and the sun around the earth, and was accurate in describing the observed motions to several decimal places. Copernicus, however, was convinced that “nature is pleased with simplicity.” Contrary to all appearances and accepted dogma, he placed the sun at the center of the system of planets. This allowed him to significantly reduce the number of circles and epicycles. His system was more elegant, it made fewer assumptions, and thus Copernicus was convinced it was a superior system – that is, that it was true. Later, Kepler simplified the system even further using elliptical orbits around the sun.
My point here is that these men believed the heliocentric theory to be true for aesthetic reasons: it is a more elegant solution to the problem of describing and predicting planetary motion. Copernicus was convinced of his theory not primarily because it worked any better than Ptolemy’s, but because it was more beautiful. He wrote, “We find, therefore, under this orderly arrangement, a wonderful symmetry in the universe, and a definite relation of harmony in the motion and magnitude of the orbs, of a kind that is not possible to obtain in any other way.” My examples have focused on theories from astronomy, but the point is equally true for other branches of science. The theoretical physicist Paul Dirac (1902-1984) admitted that it was primarily his sense of aesthetics which encouraged him to find a more elegant equation to describe the electron, which led to the successful prediction of antimatter. He went so far as to say that “it is more important to have beauty in one’s equations than to have them fit experiment.” And all scientists, when presented with two solutions which solve a problem equally well, will prefer the more elegant solution. Why? Because we are convinced that the universe must act in an elegant way.
Pure and applied math are closer in their view of beauty than in their view of power. The beauty of pure mathematics is seen in its elegance, truth, and order. A beautiful proof is an elegant proof: it does the most with the least. The truth of a theorem is another element of its beauty. When we recognize that a theorem is true, that the conclusion is inescapable, it strikes an aesthetic chord in us; it surprises us. Like a reaction to a beautiful poem or beautiful painting, we respond, “Wow, that is wonderful!”
A third element of mathematical beauty is order and symmetry. G. H. Hardy wrote,
The mathematician’s patterns, like the painter’s or the poet’s, must be beautiful; the ideas, like the colors or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics.
When we see patterns in mathematics, especially patterns which reveal solutions to problems, we are struck with a sense of delight.
Teachers of mathematics should bring to the attention of their students the power and beauty of mathematics. Let the students not only know what math can do, but let them admire it for its elegance and order, and give glory to God for what He has revealed to man through it.
James B. Nance
Jim teaches math at Logos School, Moscow, Idaho, and has authored two logic textbooks. He is an elder at Christ Church and lives in Moscow with his wife Giselle and their four children.
