Brief Math Review

Thoughts on mathematics

I wanna start by saying that I feel like I am not a whiz kid with mathematics. It takes me a while to learn and become fluent with the many forms of modern math. I will say however that when I do learn of the significance of a mathematical idea I feel empowered, and for that reason I love mathematics. Growing up I avoided math in school, you know, passed the courses but never really let the coursework enhance my ability to analyze inevitable day to day occurrences. I never saw the beauty in numbers and equations at first. At the age of 26, I began to study physics at UVU. I feel like I chose physics because it allowed me to connect and analyze the structure of the talents and hobbies I had developed over the years. For example my love for track and field behooved my mastering elementary mechanics. When I entered into my degree program I barely knew any algebra however, let alone the necessary tools to excel in a freshman calculus based physics course. I've got to tell you, I felt like a little league footballer lowering his head down and scrunching up his face as he charges into the unknown field of tacklers. I look back and think of how simple some of that stuff was, yet I feel it necessary not to forget those past feelings of doubt and confusion for they will always be an inspiration to me. I also feel as though while discussing any remedial idea with friends or young men at church I have a hunch of how rich, and maybe counter intuitive the idea could be at first. Patience is now a growing virtue of mine because of my struggles. I also look back and feel like I did begin studying physics at a young age, the experimental form, completely absent of any mathematical models and structures. I hope this may be to my advantage as I enter the purely theoretical realm.

Choices and Empowerment

Mathematics cannot help me make all the correct choices in life. This to me testifies of our finite understanding of the world. In application of math the trick is first to trust the classical foundations and then know when to use them. I say trust because before I estimate the purchase price of a list of items at the store I don't question the axioms of elementary algebraic addition or multiplication, I just use the count and add ideas given to me in school. This of course is an easy situation for placing trust in math, consider a more involved situation like the purchase of a house or maybe the opening of a bank account. These situations may cause me to think twice about whether or not my actual mathematical operations are the right ones to use, let alone if the ones I choose to use have been proven. Or, maybe I don't even know what I am supposed to do for my own benefit! For this reason there is a default bag of math tools I was given from my K-12 years, anything beyond that is assumed to be taken care of by someone with the appropriate bag. So not only is my bare essential use of mathematics limited, but so is my ability to do so, and this by no means empowers me. It is the places in my mind that math takes me, whether or not I ever believe I could apply it, in which upon my return to existence mundane I feel empowered.

Definitions with 2+2

What is 2+2? Until I have assumed a few things, I don't know. It's most likely 22, 4, 1 or maybe even # because this symbol has four lines in it. I do know that I need the qualitative nature of a common language to even begin to convey more thoroughly my abstract absence of understanding this statement more than an actual number could. Does this mean that I need only numbers to interchange quantitative ideas? Oh to think there is a gray area where the qualitative and quantitative intertwine. It is knowing where you're at along this gray-scale that allows you to more efficiently apply and contribute to mathematics. But it is purely definitions that would allocate, so therefore, the result of interpreting the simple equation above is either "4" or it is "a mathematical expression representing the combination of similarly defined objects". It also has the possibility of being a mix called a quantiquality or a qualiquantity depending where you're at in the spectrum. With the traditional definitions it seems we can not get any more information out of this statement like color, direction, flavor or political party of the resultant. We would need more uniqueness to do this, hence the expansion into physical application where we have units and space.

Numbers that mean something

Let us consider something called "position" which is a numerical representation of the location of an object in dimensions of length. This is an incomplete idea until we have established a unit unto which we base our dimension upon, let's use meters. We now have a quantity which means something real and tangible. With out the units however, it becomes just a number which we cannot see! We would need the units, whether it be apples or meters, to begin to see the meaning of the number.

Tim Wendler

Manuel Berrondo   Jean-Francois Van Huele   J. Ward Moody   Scott Bergesen  Gus Hart