I am pleased to announce the first beautiful series! A series is a set of blog posts on a particular topic. This series is on the beauty of math. In particular, I will be highlighting a few of the most beautiful, elegant, and simple topics in mathematics that I have encountered. Unfortunately, a lot of fascinating areas of mathematics are not introduced to students in K-12 education, which I think is partially why mathematics is not appealing to so many students. Some of these topics are introduced in college level mathematics courses, but I think many are simple enough to explain to an interested, young K-12 student, or an adult who hasn't touched math in years.
Furthermore, I think some of the most elegant parts of mathematics are introduced in a way that makes students dislike or even despise them. For example, the topic of proofs. Proofs are the foundation of mathematics (after the axioms used to prove all else). They are the commonality among all of the fields of mathematics, and what really makes the subject the beautiful subject it is. However, when most young students take their high school geometry class, I don't think they get a good impression of what proofs are, why they are important, and why they are beautiful. Perhaps, geometric proofs are taught because they are rather straightforward, easy to teach, and simply require routine applications of axioms and theorems. In a sense all proofs are applying axioms, theorems, and logical rules of deduction to reach a conclusion, but in practice many require creativity, and many can be very elegant. Therefore, I would like to give a taste of this beautiful subject to you, and I hope you will follow along in this journey, especially if you think you don't like math.
I hope you enjoy the background photo of this blog. It is a beautiful combination of art and mathematics. But do not worry. I won't be doing math with many complicated symbols, formulae, and the like. I will try to keep things simple. Some posts may require more mathematical background and will require thought, but others will simply require an elementary/middle school mathematical background. I will also try to go over most of the necessary background, to help you fully enjoy the beauty of math!
Wednesday, December 14, 2011
Tuesday, December 13, 2011
Beauty
O Children of Adam! wear your beautiful apparel at every time and place of prayer: eat and drink: But waste not by excess, for Allah loveth not the wasters. Say: Who hath forbidden the beautiful (gifts) of Allah, which He hath produced for His servants, and the things, clean and pure, (which He hath provided) for sustenance? Say: They are, in the life of this world, for those who believe, (and) purely for them on the Day of Judgment. Thus do We explain the signs in detail for those who understand. (The Holy Qur'an 7:31-32, trans. Yusuf Ali)
'beauty is truth, truth beauty,' --- that is all
Ye know on earth and all Ye need to know 1
On the same hand (the right one), beauty is something many of us probably don't spend time thinking about, but when we see it, we adore it. We each have our own ideas of what beauty is, and beauty can definitely be subjective, whereas truth cannot. (Does this suggest Keats was wrong?) However, I believe there are certain forms of beauty that no human being can deny are beautiful, even if each of us finds them beautiful to varying degrees. In this sense, beauty does have some objectivity to it. It is also important to note that we often think of beauty as physical beauty, or beauty that can be experienced via the five sense. But much of beauty does not fit in this category. How do you experience the beauty of an integral through the five senses? (Well, I must admit I think the shape of an integral "∫ " is one of the most beautiful commonly used symbols.) How do you understand the beauty of a mathematical proof or of a free verse poem? It's true, you need to use your five senses to see the integral or to hear the poem recited, but the senses are merely a means of transmitting these beauties to the brain. I believe many forms of beauty are intellectually and/or emotionally experienced beauty. Even further, some forms of beauty do not even use the five senses, such as spiritual experiences or meditation. Again, many groups of people have given their explanations of beauty (theologians, mathematicians, and philosophers among them), but to my knowledge, there is no unified Theory of Beauty.
Now, you may be wondering what is the point of this blog, and why am I saying some (likely uninformative) statements about truth and beauty? I'm not going to try to give a definition of beauty, or truth for that matter. That would take the fun out of it :). I'm going to try to explore beauty, and bring the beauty out of things that we may often neglect. I'm going to try to look at a variety of things as beautiful, simply beautiful. And in doing so, maybe we'll try to understand how this beauty can lead to a unified truth.
I must warn you, my perspective is (a) biased and (b) amateur. (a) I am a follower of the Ahlul Bayt2 (ع) whom I believe are the human sources of truth, but that doesn't mean I'm here to push my religious views on you. By reading this blog, you will read some of my beliefs and how they relate to beauty, but you will also be reading about a lot of other beautiful subjects, that do not directly relate to my religious views. You can also pick and choose what you read, so if certain topics do not interest you, you can choose not to read them. I will also allow comments and discussions to take place, so we can discuss other opinions and beliefs on the topics I present. (b) I am an amateur in almost every (if not every) topic I am going to discuss. I am in no way an expert in mathematics, science, or poetry for example (but is anyone?), and moreover my training in cooking is limited to having been taught how to cook eggs in a few ways, and watching and sometimes helping my mom (who is in my humble opinion an expert cook), yet I am not afraid to venture in these hidden domains of life, which I believe can reveal beautiful things that would be a pity not to experience. (I apologize if you do not like long sentences.) I want to venture these domains along with you, and I want you to be willing to venture with me. I want us to learn together, to experience together, and to get a grasp on something that humanity has sought, is seeking, and will continue to seek: beauty.
It appears that the more we learn and the older we get, the more specialized we get in very focused areas. Unfortunately, we may even forget the beauty of our areas of expertise, as our studies or work becomes routine. Hopefully, this blog will motivate us to revitalize the beauty that made us interested in the thing we do that we may have lost interest in. But more importantly, I hope to remind us how many beautiful areas of knowledge are floating around us, which we simply swim past in this fast-paced meet of life. There is so much knowledge out there that we do not have the time to invest our lives in. But that doesn't mean we can't greaten our appreciation of these beautiful incarnations of truth. This blog aims to simply remind us to appreciate the beauty around us, and in doing so better appreciate life.
Second to last, but not second to least, as I mentioned I'm an amateur. Unfortunately, it seems to me that blogs are very prone to narcissism. If I'm going to sit here and preach to you what I know that I think you should know, and get happy ever time someone reads my blogpost, then I am doing a great diservice to myself. I am but one person, and while I think I know a lot of things a lot of people don't know that I think a lot of people should know, I also think a lot of people know a lot of things I don't know that I think a lot of people should think I should know. Therefore, if you have any contributions on the beauties of life that you would like to share with us, please contact me, and I would be happy to post your contribution as a blog post, as long as I think it fits within the framework of this blog.
Finally, do not think of this blog as a journal, but rather as a journey: a blog that should not only be read, but experienced. Join me in discovering the simply beautiful.
1 http://en.wikipedia.org/wiki/Ode_on_a_Grecian_Urn↩
2 See http://en.wikipedia.org/wiki/Ahl_al-Bayt and http://en.wikipedia.org/wiki/Twelvers↩
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