Distaste for "Modern" Architecture

2006-12-12T11:41:00.000-05:00

I am becoming more and more dissatisfied with "modern" architecture. There has been a flurry of new buildings that are being built world-wide that lack structural logic. These buildings a built at dramatic angles and slants in order to make a noticable statement (or so-called art). A term being used recently is "skyline pollution". Several awkwardly shaped buildings clustered together present a very distracting and cluttered skyline.

My main objection to these "modern" buildings are that they are in most cases highly inefficient in both initial cost and long term cost. The engineering expertise needed in order to make these illogical designs work adds dramatically to the cost of the building. The designs are also in most cases difficult to construct and lend themselves to problems with overall service.

People interact with buildings on a daily basis. The buildings should make use of natural lighting and should provide the user with a sense of well-being. I propose a return to structural logic and an efficient use of resources. A building that both makes efficient use of materials, utilizes a logical structural design, provides an efficient solution toward constructability and service, and THEN introduces spatial creativity should be considered art.

Although I favor structurally expressive architecture (where the basic structure reveals itself in the design), I do realize that this is not a solution for every building need. But;

Form should follow function

Probability Problem

2006-10-16T08:52:00.000-05:00

As I sat in Cracker Barrel with my wife awaiting breakfast, I was passing the time playing the triangle / golf tee "thingy" when something incredible happened. I left seven tees! Judging by the instructions on the "thingy", if you leave four tees you are pretty dumb (IG-NO-RA-MOOSE as they say). I got to thinking, "I wonder what is the maximum number of tees that I can leave without having any other options?" It seems to me that there exists less probability of leaving many tees than leaving just one. For example, the more tees left, it seems that there would be a greater probability that I would have an option to jump another tee in close proximity. I tried several times to leave seven tees and I could not do it again...I left at most four or five tees! (Leaving four or five tees is pretty easy) It seems that it is difficult to leave one tee, slightly less difficult to leave two tees, and not very difficult to leave three tees. Likewise, it is very easy to leave four tees, but it becomes increasingly more difficult to leave more than four tees. Imagine a graph of probability versus number of tees that takes on the shape of a parabola. I would like to research the probability of leaving many tees relative to leaving one tee.

Reaching for Infinity

2006-10-11T08:55:00.000-05:00

Introduction
After 22 credit-hours and counting of college level math classes, I have come to be intrigued by the idea of infinity. What exactly is infinity and how can it be explored? Can understanding infinity help us to view God in a clearer way?These are questions I have asked myself and are those that I wish to discuss. It is my hope that a reader of any skill level in mathematics (or even a reader with no skill) can come to appreciate the idea of the infinite.

The Number Line
Imagine a single point in the middle of a piece of paper. Let this point be called the origin and we will call it zero. Where would we be in relation to zero if we moved from our origin to a point two units straight to the right? We would be at positive two. In fact, any number to the right of zero would be positive. If we moved one-hundred units to the right of zero, then where would we be? Besides being off the paper, we would be at positive one-hundred, known simply as one-hundred. These number right of zero are known as the natural numbers, or counting numbers. They are called such because if we counted a particular set of objects, we would count one, two, three...etc. We would NOT count zero, one, two...etc. So, what is the largest number that exists? If we sat at our computer determined to type the largest number, when would we finish? If we had a number that consisted of several trillion digits, this number could always be increased simply by changing the very last digit to the next higher digit. For example, if our several trillion digit number ended with zero, we would already have a bigger number by changing the zero to one...and from one to two, and so on. What if we changed the last digit with many digits, for example several trillion. Now we have a number that is several trillion trillion digits long. As we can see, we can ALWAYS increase any number. So now that we have a digit several trillion trillion units to the right of zero, we are now a great distance from the paper on which we marked our origin.

What about negative numbers? Thinking back to my painful years in high school algebra class, I realize that for many people, the idea of a negative number is difficult to grasp. Afterall, we don't count in everyday life with negative numbers...or do we? If we consider again our number line at the origin (zero), what if we move now to the left of zero by two units? We now find ourselves at the number negative two. As in the positive direction, the negative direction also yields greater and greater numbers without bound as we move further from the origin. Imagine that the entire number system balances on the origin, which is zero. So what are negative numbers good for? As it turns out, many people without math skills beyond simple arithmetic use negative numbers constantly! Think of a checkbook ledger. If you have a balance of two hundred dollars, which is of course a positive two hundred, what happens if you write a check for seventy-five dollars? How does the seventy-five dollars relate to the two hundred dollars? It is seventy-five units back toward zero, our origin. Answer: one hundred, twenty-five dollars. Instead of thinking in terms of subtracting the amount of the check from the balance, think of it as adding a negative number to a positive number. This means that we began two hundred units to the right of zero. We then "used" some of the two hundred so we move to the left by the same magnitude of that which we "used". After traveling on the number line seventy-five units, we arrive at one hundred, twenty-five. I hope that the idea of the number line is very clear at this point.

Reading Between the Lines
What numbers exist between the counting numbers? That is between the numbers one, two three, and so on. We are familiar with numbers such as; 1.0, 2.5, 3.75 (read as one point zero [or just one], two point five [or two and a half], and three point seven five [or three and three quarters]). What if we zoomed in very close to our number line so that we could see all possible numbers between one and one and a half? We could see the numbers; 1.0, 1.1, 1.2, 1.3, 1.4, and 1.5. Could we get closer still? 1.025, 1.050, 1.075, and 1.1. As you can see here, we have only observed 1 to 1.1. Pretty cool, huh? We are still on the number line at the point 1.1. Explicitly, we are 0.1 units to the right of the point 1. How close can we get? Consider the number 1.09999. Is this number equal to 1.1? For practical purposes we may round up to 1.1, but it does not really represent 1.1 for it is really the number 1.09999. It is 0.09999 units to the right of the whole number 1. Consider the number 1.9. This number may be rounded to 2 but it is NOT equal to two. It is only close enough to 2 to be called 2 for many practical applications. What about the number 1.999? It is closer to 2 than 1.9 but yet it is not 2. Again, if we zoom in on the number line on the atomic scale, what would we find? Consider the number 1.99999999999999999999999999999999999999. (Wow) This unpleasant number is even closer to the number 2 than 1.999. How far is it possible to zoom in on the number line? If we add enough 9's to the 1.999...do we eventually reach 2? Nope. What we see forming here is the idea of a limit, as anyone with experience in calculus can attest to. What this means here is that as we continue adding 9's to our 1.999...number, we are approaching the number 2, but we NEVER reach it. This un-quantitative entity is called - infinity.

If we can understand that any number has the potential to grow without bound, we can see that infinity can fit between ANY number, for example, 1.9 and 2. To us, there is only a very small interval between these two numbers, and indeed, there is! While the interval between these two numbers are very small, infinity fits in that interval. As 1.9 takes on more and more digits in an effort to become more and more precise, the number can grow without bound. It appears that the finite world which we know skims along the top of the infinite. The quantitative world in which we live is built upon the unquantitative - infinity.

The ancient Pythagoreans, Greeks, and Romans did not have knowledge of the number zero OR the concept of infinity. Anytime a mathematical idea was introduced that needed zero or infinity, these cultures came to a standstill - there was nowhere to go. There was tremendous fear when it came to contemplating the infinite or the apparent nothingness of zero. The Indians however, embraced the idea of the infinite and nothingness. These ideas did not have such a negative connotation in their cultures as with the others. Even the early Christians chose not to believe the idea of infinity because they could not understand how God could fit in to the "void". (See the book, A Natural History of Zero. I cannot recall the author.) It was not until the Muslims conquered India that the idea of zero and infinity came to be accepted by mathematicians. This led to many new discoveries in the field of mathematics as mathematicians now had access to two very powerful tools - zero and infinity.

The God of the Infinite
The King James Version (KJV) of the Bible states that, "God is a Spirit". What does it mean to be a spirit? Many people think of ghosts and other mystical ideas when they hear the word spirit. Every human being has a spirit. It is the spirit of mankind that drives man to learn, discover, achieve, and dream. It has been the inquisitive nature of the spirit of man that has led to understanding in the fields of mathematics and science. Man is born with a thirst for knowledge. The KJV also states that mankind was,"...created in the image of God". When studied in the original Hebrew text, this states that emotional, intellectual, and inquisitive nature of God was the model used for man, of course on a much smaller scale. By understanding this, it becomes apparent that man is too a spirit, but we also possess a body consisting of matter. It is the spirit of man that enables him to dream and reach beyond his current ability. An understanding of the makeup of man can help us to see God in a more clear way. Likewise, seeing God in a more clear way can help us to understand ourselves better.

A question often asked or at least pondered by many is,"If God is infinite, how can He be involved with man at a personal level?" It is from the idea of infinity that I wish to explain this as I understand it. If there exists an infinite quantity of numbers, and between each natural number we can find small fractions of these numbers. These fractions can be broken into smaller and smaller fractions forever, or to infinity. Infinity without any bound, can be placed between a finite interval, it becomes easier to see how an infinite God can not only be aware of every "finite" piece of matter, but also care about every human being as an individual. Just as the finite numbers seem to skim over the top of the infinite, the natural, "finite" world seems to skim over the top of an "infinite" God. This would agree with a statement made in the KJV of the Bible that says,"The world was made by Him, and by Him do all things consist".

To be continued...

Reach for Infinity

Distaste for "Modern" Architecture

Probability Problem

Reaching for Infinity