math

Okay, I have to admit that I haven’t done much math since high school. With the exception of balancing my checkbook and the grocery store, I haven’t practiced the mathematical skills in about three years. I apologize for the math vocabulary I’ll probably abuse in my explanations; I’ve forgotten a lot of the terms, but I think I remember how to apply them.

First of all, the odd and even numbers. I think the easiest way to prove that the product of two odd numbers is odd and the sum of two odd numbers is even is by factoring out numbers. Here’s the process I used:

2n = even
2n + 1 = odd

odd + odd = even
2n + 1 + 2n + 1 = even
4n + 2 = 2n
2(2n + 1) = 2n [factor out a 2 and you get 2 times an integer]

odd * odd = odd
(2n + 1)(2n + 1) = odd
4n² + 4n + 1 = 2n + 1
2(2n² + 2n) + 1 = odd [factor out a 2 and you get 2 times an integer, which is an even number, plus one, which makes an odd number]


Now, I’ll try to tackle geometric angles. The two angles on the straight line will always come to 180 degrees. So angle A plus angle B equals 180. Equally, Angle B plus angle C equals 180. Since this is true we can say angle B plus angle C equals angles B plus A. When you subtract angle B from both sides you get angle A equals angle C. Therefore, vertical angles are congruent:
line E = 180º
line F = 180º
angle A + angle B = 180º
angle B + angle C = 180º

angle A + angle B = angleB + angleC
- angle B - angle B
angle A = angle C


Statistics. I don’t think we place too much value on statistics, but I do think we can trust them too much – if that is a distinction I can make. Statistics allow researchers, the public, etc. to quickly estimate current preferences, feelings, opinions, and trends of a population. I don't think they should be taken as definitive findings, but statistics provide a strong first step in beginning to understand a topic or focus research. Of course, there are a lot of problems that make statistics fallible. There will always be outliers in the data - unaccounted extremes on either end of the spectrum. Margins of error and varying confidence levels reveal that statistics can be wrong or misleading. Researchers must avoid attributing causation to correlation. Statistics can't account for the human nature of a topic - the social and psychological side of things. The nature of percentages usually means there is a chance - however small it may be - that things can go the "other way." Statistics are far from perfect, but I think they have value when used carefully.

Robert Browning

The first week of class is in the books, and cross-curriculum connections are already being created. As Mary noted in class the other day, in Nature and History of Language we recently read Plato's thoughts on names, words, and the reality that surrounds these symbols. Our discussion in class the other day helped me better understand Plato's thoughts. The ideal reality, whatever that may be, is in our minds or subcounscious and the manifestations of that ideal are what we experience. Apparently, some manifestations are more like the ideal than others. That's all starting to make sense.

We talked the other day about how the ideal-manifestation idea can be found in Scripture. My mind went to a passage like I Corinthians 13 - the love chapter. My brothers and I used to have to write this chapter out when we got in trouble in our childhood years, so it is near and dear to me. I've come to realize though that the love, or charity, described in these verses is a perfect love that I don't think we, as fallen beings, can fully and perfectly achieve. It's an ideal form of love - like the love God exhibits towards us - that we work toward. As we mature, our manifestations of this love may become closer and closer to the ideal, but I don't think we will ever nail it down.

That strive for personal betterment in love can be applied to all sorts of Biblical themes and aspects of our lives. The 19th century British poet Robert Browning had an interesting view of this strive for perfection. His dramatic monologue "Andrea del Sarto" is about a Renaissance artist who has mastered technique; he is a perfect painter, as far as mechanics go. However, he lacks the spiritual touch to his artwork; he has no soul - so to speak. Browning implies that if we could create an ideal world, then we would have nothing to strive for - we would become stagnant. This concept is the philosophy of the imperfect, and it makes a lot of since. If we could create the ideal reality then we wouldn't need God or his salvation. It's the gap between the ideal and the manifestation that reminds us there is a perfection to strive for; it's why we need the Savior to bridge that gap. It's why the Word became flesh.

That's cool. See you in class...

"Ah, but a man's reach should exceed his grasp,
Or what's a heaven for?"
- Robert Browning

new beginning

the exchange of ideas, postulations, and information can now commence. why mile markers? i run a lot and that is when i do some of my best and deepest thinking.