Unedited Ramblings, Episode Three

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reduced echelon formI took linear algebra my last semester of college. On the day of the first exam, the professor entered the classroom and rhetorically asked us how we felt about the test, and the guy behind me said, “I can’t express my feelings in reduced echelon form.” He doesn’t know this, but I later quoted him on tumblr.  It was one of my most popular tumblr posts of all time, partly just because it sounds really deep and partly because someone who saw it came up with the brilliant idea of Echelon Poetry. I really wish that had caught on, even though I didn’t think much of the way some people interpreted that idea. Arranging words in a triangle is not the same as putting words in echelon form. I’m not sure how one would go about putting words in echelon form, but it fascinates me to imagine that there is a way.

But even if we are talking about actual matrices rather than poetry, I have an inclination to want to believe that it ought to be possible to describe emotions in reduced echelon form. There ought to be a way to notate feelings and then perform mathematical procedures to make sense of them.

My last attempt to do so lasted only two days, because there were just so many difficulties involved. How many different kinds of emotions are there? Is humor an emotion? What should the numerical scale be? One to ten? One to twelve? One to eight? One to six? Sixteen point twelve to thirty-nine and a half? Should the arithmetic be done in base ten or some other base? Should I use standard numerals or invent my own form of numerical notation specifically for the purpose of this exercise? Is there any logical reason to do so, or am I only considering that because I want my matrix to be nonsensical and enigmatic to everyone except myself? And perhaps most importantly, when I do the math and find an answer, what will that answer actually mean?

As it turns out, it’s a major inconvenience to carry around a notebook and commit to writing numbers in it every four hours. I could have changed my system so that I didn’t have to collect data so frequently, but I felt like that would compromise the accuracy. Between that inconvenience and the fact that I didn’t actually have any useful information to gain by proceeding with this plan, I ended it. But that doesn’t mean I won’t try again at some point.

Maybe I’m just strange, but I find it horribly frustrating to be incapable of quantifying feelings. There are so many things in life that can be accurately and thoroughly described by little numbers written in little boxes. Those numbers are knowledge and power and safety; not only do they convey information, but they allow you to assume that the thing being described by those numbers is subject to all the normal rules of mathematics. But if something can’t be described in numbers, then it’s unclear what the rules are.

Once, I spent several weeks keeping track of my feelings on a one-dimensional scale from one to ten, while simultaneously assigning a numerical value to every noteworthy event in order to determine how much of an impact it should have on my mood. The point was to determine whether or not my mood was a logical and objective response to the events of my life. As you can probably guess, this experiment also ended mainly because it was absurdly time-consuming. But in the meantime, I noticed that, interestingly enough, my actual feelings corresponded very closely to what they should have been if they were in fact an objective response. This trend quite surprised me even though it was what I had hoped to discover.

As far as I can tell, there are three possible explanations. One is that I took such a subjective approach to the whole project that even the numerical values I assigned to events was determined based upon how I felt about it at that particular time. That is admittedly very likely, but given the fact that I made sure to keep those values constant when an event re-occurred, it would seem that the effects of this bias would have decreased over time, which wasn’t what my numbers indicated. The second possibility is that it’s actually true that my feelings are a rational and quantifiable response to external events. I’d like to believe that, but it seems extremely far-fetched. The third possibility is the really fascinating one. Maybe, the act of trying to quantify feelings is therapeutic in the sense that it actually regulates emotions to the extent that they actually do begin to function in a completely logical way. Maybe, by quantifying one’s emotions, one can actually make them follow an algorithm.

Whether the second or third of those possibilities is the correct answer, that’s a good reason to work towards the goal of finding a way to quantify feelings. But the fact remains that it’s mathematically ridiculous to do so, at least not without somehow taking neurological factors into consideration, allowing for differences between different people, and using an extremely well-informed psychology-based rationale for every aspect of the method of quantification. In other words, such an undertaking is well beyond my capabilities. I am forced to live with the annoying and frustrating reality that I cannot quantify my feelings.


Math and Stuff

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The I Hate Mathematics! Book, by Marilyn Burns, copyright 1975. Yeah, it's pretty old.

The I Hate Mathematics! Book, by Marilyn Burns, copyright 1975. Yeah, it’s pretty old.

There was a book that I needed to buy last week, and I found that it would cost me less money to buy four books than just the one. Evidently, Amazon determined its shipping costs on Logic’s day off. I don’t know whether to thank Amazon or Logic for that, but someone deserves my gratitude, because I have frequently managed to save money by buying extra books, and over the years, that has really added up to a lot of saved money and a lot of acquired books. In this particular case, one of the extra books I bought was something random that I remember from when I was a little kid. If I recall correctly, one of us picked it up at a library booksale where everything was so cheap that my parents let us buy everything that particularly struck our fancies. It was called The I Hate Mathematics! Book and it’s awesome because it’s so completely relatable.

I’m not saying that just because of the title, although that is part of it. When I was little, I remember my mother telling me that she thought I actually liked math, I just disliked math class. The I Hate Mathematics! Book is clearly geared towards that kind of kid. After an introduction that bashes math, it goes on for more than a hundred pages to describe mathematical concepts in a way that has nothing to do with arithmetic or equations or anything frustrating like that. For example, a few pages in, it says, “Ever find yourself thinking about shoelaces? You might be minding your own business, doing nothing in particular, and all of a sudden you start thinking about shoelaces. Then you start noticing shoelaces. Strings tied to people’s feet! And the longer you look, the funnier it seems. That’s when to do a shoelace survey. How many shoes have laces? Half? More than half? Less than half?” The book goes on to recommend sitting near a busy sidewalk and counting shoes and shoelaces for a while, just for the fun of playing with statistics.

This is youThat’s exactly the way my mind worked as a kid and it’s exactly the way my mind still works. My little-kid self thought it was awfully cool to read that kind of thing in a book about something as frustrating and hateful as math. The tone of the book is humorous and light-hearted, the information is presented in a way that makes everything seem like a game or even a practical joke, and it feels like a very light and easy read because the text is fairly sparse. (The book consists largely of sketched drawings, some of which show people with speech bubbles repeating things that were said in the main text, which is for some reason very funny.) Besides that, it was helpful and motivational to read something that showed that there’s more to math than sheets of scrap paper covered in disorganized equations and crossed out numbers and dark, harsh scribbles that symbolized the agony of living in a world that is an evil, evil place, full of hardships and heartbreak and math.

Maybe it would be an overstatement to credit this book alone with the fact that I have more or less made my peace with the academic field of mathematics and even ended up minoring in it in college. (I say “more or less” because, dude, math is hard, and there was a great deal of suffering involved in certain homework assignments and exams that I endured for the sake of that minor.) I suppose it may be true after all that I always had some degree of appreciation for mathematical thought, and just didn’t realize it when I was younger. But this book certainly played a role in convincing me that numbers are actually pretty fascinating things.

Binary CodeWhen I got this book in the mail the other day, I stayed up late to read the whole thing in one sitting, and I noticed some things about it that hadn’t occurred to me when I was a kid. In particular, I noticed that it has an awful lot of question marks. It’s full of “What if”s and “How about”s. For every experiment that this book suggests, it encourages the reader to keep thinking about different aspects of the concept being discussed. For every magic trick or practical joke or bet that it describes, it expects the reader to figure out how to make it work. It doesn’t just point out patterns, it asks the reader to notice further patterns or to speculate about why that pattern exists. Even the section about strategic games, which promises that you can always win if you figure out how the strategy works, doesn’t actually explain the trick. You have to figure it out yourself. I didn’t have all of these answers figured out when I read the book as a kid. And that was okay; it didn’t detract from my enjoyment of the book and it didn’t make me apathetic about the subject material. It was apparent that these were deliberately difficult questions and that a reader wasn’t supposed to know everything off the top of his or her head. That’s one reason that this book was interesting and entertaining, unlike a textbook, which inflicts anguish and despair. A puzzling question is a game if you get to decide for yourself how much effort to put into it, but it’s an unwelcome task if you are required to find the answer and responsible for being sure it’s right.

Another thing I noticed is that this book has a lot of big words for something that’s geared towards kids. (I’m not sure exactly what age range it’s intended for, but if I had to take a guess, I’d say maybe nine through twelve. The mathematical content seems to be at a pre-algebra level, but it assumes competency with basic arithmetic.) For instance, I’m pretty sure that the first time I came across the word “topography” was in this book, and that’s not a word I come across very often even now. It mentions or alludes to exponents and exponential growth, probability theory, and numerous other concepts that you wouldn’t expect a little kid to understand until they’re old enough to officially learn it in math class. But when I read it the first couple times, I don’t recall minding that there were parts of it that I only was just barely capable of grasping. The point is that I did grasp those parts, and that it was pretty awesome. This book assumes that its readers are smart and thereby subtly compliments them the whole time they’re reading. Occasionally, the book is even explicit and direct in its high regard for its own readers; the introduction identifies the individual reader as a mathematical genius in disguise. That in and of itself does a lot to make this book enjoyable and effective. Everyone likes to be told that they’re a genius, especially if they’re accustomed to being horribly frustrated by schoolwork despite the fact that they do have some degree of aptitude for the subject matter after all.



I have frequently said that the problem with math is that the kinds of people who write math textbooks are the kinds of people who inherently understand mathematical ideas and don’t know how to communicate them to someone who just doesn’t think in the same way. What makes this book so great is that it’s written in plain English for kids who understand plain English better than confusing equations. But it does that without dumbing down anything. I’m not trying to claim that such a book can be used to effectively teach math. It doesn’t offer formulas or mathematical procedures for solving certain types of problems; those are things that have to be learned by effort and memorization, not through pleasure reading. But I would recommend this book in particular and this way of looking at math in general for any mathematical geniuses in disguise who hate mathematics.

Why Base Twelve Would Be Awesomer Than Base Ten


If you think about it, it’s silly that people count in base ten. Yes, it’s convenient because we happen to have ten fingers, but it’s inconvenient in numerous other ways. For example, although 1/2 and1/4 and 1/5 and 1/10 can be easily expressed by decimals, other common fractions like 1/3 and 1/6 and 1/8 are just weird if you try to write them in any other form. To give a less abstract example, the amount of time that I spend at work is measured according to a decimal system. That means that each 0.01 hour of work is 36 seconds, which is a kind of random unit of time. On some level, the human race is clearly aware that units of twelve are logical. The year has twelve months, a foot has twelve inches, and many products are sold in groups of twelve. Yet we still insist upon counting in base ten.

handsI think it says something about the selfish nature of humanity that we just assume that numbers are meant to be used in base ten simply because we have ten fingers. The human hand, according to our subconscious thought process, is clearly the standard by which we are supposed to measure everything in existence. No source of authority and no rational point of view outranks the supremacy of the human hand. Or something like that. But, mathematically speaking, there are better ways to count.

The short and simple way to say this is just to insist that base twelve is better than base ten because twelve has more factors than ten. But I’m going to back up a couple steps and ramble about some other things first. In all fairness, I must acknowledge that there’s a book I’m currently reading (How Acceptance of a Duodecimal (12) Base Would Simplify Mathematics by F. Emerson Andrews, copyright 1935 and 1944) that basically says everything that I’m saying in this blog post, and I’m sort of drawing from that book in writing this. But I also would like to point out, just for the sake of being a know-it-all, that none of the information or ideas I’m repeating here were new to me. These were all things I had heard, read, and thought about a long time before I happened to notice that book on the library bookshelf and was drawn in by its awesomeness.

The first thing about which I want to ramble is that even the tally mark system is pretty cool. We couldn’t count very high if it wasn’t for the clever construct of splitting numbers into handy units. If you count on your fingers, you only have two sets of five at your disposal, and you’re going to lose count pretty quickly once you get past ten. And if you try to count by writing down one mark for every unit, that’s not going to improve matters much. But by sorting those individual units into groups of five and then counting fives, you can count an awful lot higher. There’s no particular reason that five has to be the base used or that the notation method has to be tally marks as we know them; it’s the system of individual units and larger group units that is so clever and useful. Even though we take that system completely for granted, it’s pretty awesome when you think about it.

Roman PIN numberEarly forms of number notation were basically always tally-mark-type systems. Even Roman numerals are really just a glorified form of tally marks. You’ve got the individual unit written as I, the group of five units written as V, the group of ten units written as X, and so forth and so on. As an added bonus, numbers could be written in a more concise way by putting a smaller numeral in front of the greater numeral to indicate that the smaller unit is to be subtracted from the bigger unit rather than added onto it. For example, nine isn’t IIIIIIIII or VIIII because that’s kind of hard to read. It would be easy to accidentally confuse VIIII with VIII. So nine is IX, which means I less than X. So the Roman numeral system definitely had its benefits, but it still is of the same caliber as tally mark systems, and it still is really bad for doing arithmetic. (Quick, what’s MCDXXIV plus XXVII?)

But then the world was revolutionized by the numeral zero, which is the awesomest thing ever invented by humanity with the possible exception of that time when some random person thought of the idea of grinding up coffee beans and filtering hot water through them. Of course, the concept of “none” had always existed and there were ways of expressing the quantity of “none” in words. But there was no numeral zero as we use it now, and so place value didn’t work. It’s difficult to attribute the origin of zero to a specific time or place, because various cultures had various different ways of mathematically denoting zero-ness. But the significant advancement was the use of place value that was made possible by the use of the numeral zero, and that came from India and then gradually became commonly used in Europe during the medieval period. It wasn’t until the 16th century that the current system for writing numbers finished becoming the norm.

I think we can all agree that the Hindu-Arabic number system is much easier to use than Roman numerals. It’s easier to look at 1040 and 203 and know right away that they add up to 1243 than to look at MXL and CCIII and know that they add up to MCCXLIII. And it isn’t hard to add 48 and 21 in your head and get 69, but adding XLVIII and XXI to get LXIX is a little messy. A numerical system that relies on place value is inherently simpler to use than a system that doesn’t.

But there’s still that whole thing about base ten. To say that we count in base ten means that ten is the number that we write as 10. 10 means one group of ten plus zero ones. 12 means one group of ten plus two ones.  176 means one group of ten times ten, seven groups of ten, and six ones. But if, for instance, we counted in base eight, then 10 would mean one group of eight and no ones, which is 8 in base ten. 12 would mean one group of eight and two ones, which is 10 in base ten. 176 would mean one group of eight times eight, seven groups of eight, and six ones, which is 126 in base ten. If that sounds complicated, it’s only because we’re so used to base ten. We instinctively read the number 10 as ten without even thinking about the fact that the 1 in front of the 0 could refer to a different number if we were counting in a different base.

I’m not really advocating for getting rid of base ten, because it would be impossible to change our whole system of counting overnight. It took centuries for Hindu-Arabic numerals to replace Roman numerals in Europe, and switching to a different base would be an even bigger overhaul. Base ten is a very familiar system and it would just be confusing for everyone to suddenly change it, not to mention the fact that everything with numbers on it would become outdated and mathematically incorrect. So I’m perfectly content to stick with base ten for the most part, but I still think it’s worth pointing out that base twelve would technically be better. And this brings me to my actual point, which is why exactly base twelve is the best of all possible bases.

It goes without saying that the only feasible bases are positive integers. But I’m saying it anyway just because I am entertained by the notion of trying to use a non-integer as a base. It is also readily apparent that large numbers don’t make good bases. Counting and one-digit arithmetic are basically learned by memorization, and the larger the base is, the more there is to memorize. But small numbers don’t make good bases, either, because it requires a lot of digits to write numbers. Take base three, for instance. Instead of calling this year 2013, we’d be calling it 2202120. (Disclaimer: it’s entirely possible that I made an error. That’s what happens when I use weird bases.) And it wouldn’t be a good idea to use a prime number as a base. Even though I happen to be fond of the number seven and have said before that the people on my imaginary planet count in base seven, I realize that’s weird. (That is, counting in base seven is weird. It’s completely normal that I have an imaginary planet that uses a different mathematical system.) In base ten, we have a convenient pattern; every number that ends in 5 or 0 is divisible by 5, and any number that doesn’t end in 5 or 0 is not divisible by 5. That pattern works because 5 is a factor of 10. Using a prime number as a base would complicate multiplication and division because we wouldn’t have useful patterns like that.

So the numbers that would work relatively well as bases are eight, nine, ten, and twelve, and maybe six, fourteen, fifteen, and sixteen, if we want to be a little more lenient about the ideal size range. Eight and sixteen win bonus points for being 23 and 24, which is nice and neat and pretty, and nine and sixteen win bonus points for being squares. (Squares are cool, y’all) But twelve is the real winner here, because its factors include all of the integers from one to four. That means that it’s easily divisible by three and four as well as by two, and a multiplication table in base twelve would have lots of handy little patterns. Every number ending in 3,6,9, or 0 would be divisible by 3; every number ending in 4, 8, or 0 would be divisible by 4; every number ending in 6 or 0 would be divisible by 6. All multiples of 8 would end in 4, 8, or 0, and all multiples of 9 would end in 3, 6, 9 or 0. As in base ten, all even numbers would end with an even digit and all odd numbers would end with an odd digit. And obviously, every number divisible by twelve would end in 0.Basically, base twelve has the most convenient patterns of any base in the feasible size range.

Base Twelve Multiplication TableTo prove its convenience, I made this multiplication table myself rather than copying the one in the aforementioned book. (For the record, X refers to ten, because the notation 10 now means twelve, not ten, and ε refers to eleven, because the notation 11 now refers to thirteen, not eleven. I got those additional digits from the book. Part of me wanted to make up new ones, but there was some logic to the way it was done in the book, so I decided to just go with that.) I did double check it against the book just to be sure, and I suppose I ought to confess that I made a couple errors in the 5 and 7 columns. 5 and 7 are a little problematic in base twelve in the same way that 3 and 4 and 6 and 7 and 8 are a little problematic in base ten. But this didn’t take me very long at all to do, and the columns for 2, 3, 4, 6, 8, 9, X, and ε were extremely easy. Since basic arithmetic isn’t exactly a great strength of mine, the fact that I found it easy to construct this multiplication table proves the mathematical ease of arithmetic using base twelve.

So, yeah, base twelve is cool and stuff.

Why I’m a Math Minor


knotsAfter the end of classes on Friday, I attended a riveting talk by a guest mathematician who was in town for some sort of conference. He was a knot theorist, and in his talk, he introduced us to the beautiful and extremely interesting mathematical principles of knot theory and topological graphing as related to knot theory. I admit that a good deal of it went over my head, mainly because of unfamiliar terminology, but I still found it fascinating. It was a great way to spend the first hour of my weekend. That may sound like sarcasm, but it isn’t. I truly did enjoy the talk, and I truly did leave it feeling much happier and much more motivated about life in general than I ever have after having heard an inspirational speech. (Inspirational speeches, in my opinion, are quite corny and fairly irrelevant despite the fact that they are specifically trying to be universally relevant.)Despite the fact that I didn’t understand everything the speaker said, I now am interested in finding books and online articles in order to learn more about knot theory. And I almost find myself wishing that I had another semester or two left after this so that I could take more math classes and become a math major instead of a minor.

The cool elevator in the math building at my college

The cool elevator in the math building at my college

People are always surprised when I tell them that I’m minoring in math. In part, this is because I already am a double major and I’m in the honor’s program, and this situation has led to the need to take ridiculous course overloads several semesters. Adding another minor on top of all of that does seem a bit excessive. Besides that, my two majors are dance and English, and both of those fields seem to be very distinct from mathematics. At my college, it seems like most of the English majors hate math with a passion, and most people who have non-humanities majors dislike English almost as strongly. The dance program is actually somewhat of an overlap area; I’m aware of several people who have graduated with a dance/English double major in the past few years, and I’m aware of several current or recent dance students who have also taken a lot of math classes, either as a math major (or minor) or as a business major. In fact, considering how few dance students there are, it’s interesting just how frequently I have had a classmate in an upper-level academic class who is also a classmate in dance. But I don’t know anyone else who has taken upper-level classes in all three programs.

My decision to be a math minor is even stranger in light of the fact that I myself am one of those kinds of English majors who hates math with a passion. I always have. When I was little, math was the bane of my existence, and it only got worse when I got into algebra. I couldn’t wait to get to college, where I could take classes only in things that interested me and never do any math ever again. If someone had told my little-kid self or my high-school-aged self that I would voluntarily take five mathematics classes in college, (not to mention a logic class and a couple of science classes that required mathematical knowledge) and that those classes would be among my favorite college courses because of their structure and objective logic, I probably wouldn’t have believed it. Yet I somehow did become the kind of person who appreciates mathematics for its precision and its order and its sheer usefulness.

The cool stairs in the math building at my college

The cool stairs in the math building at my college

My hatred of math stemmed from the fact that I just wasn’t any good at it. This wasn’t entirely a case of stupidity; I was homeschooled and my parents used a very difficult math curriculum. They still insist that those math books are wonderful and that my siblings and I benefitted greatly from them. I still insist that those math books were evil and that they caused much emotional trauma in my childhood. I blame them for all of the problems in my life, from my social ineptness to my concerns about paying for college to the way my Achilles tendon sometimes makes a disturbing snapping noise in the middle of dance class because of an ongoing case of tendonitis. I’m not quite sure what this has to do with childhood mathematical trauma, but it surely does.

When I started college, I knew I was going to have to take a math class at some point, and I wasn’t happy about it. I took calculus I during the spring of my freshman year, and I went into that class expecting that it would be miserable and that I would do terribly. I resolved to put a lot of time and effort into that class, but I wasn’t optimistic that it would pay off. But it did. In fact, once I somehow managed to get through the first few weeks, it stopped being particularly difficult, and by the end of the term, I was consistently getting perfect scores on homework and exams. That semester was a very frustrating time for me in regards to dance, and it was very reassuring to be doing well in academics. That class ended up being stress-relieving rather than stressful. When I took statistics in fall of my junior year, it was just because I had to take one more math or social science, but it turned out to offer the same comforting stability in my life that calculus had. I didn’t do quite as well in statistics, but I still ended up getting an A with plenty of room to spare. In the meantime, I felt as if my dance and English classes were being graded on a subjective scale according to a secret rubric. It was at some point during that semester that I decided to get the math minor by taking three more math classes over the next three semesters. I took calculus two that spring and am now taking calculus three and linear algebra.

A cool wall in the math building at my college

A cool wall in the math building at my college

It’s too soon in the semester to be making judgments about how well these classes are working out for me, but I feel like things are promising. After struggling in calculus two, I’m not counting on getting spectacular grades in these upper level classes, but then again, my schedule is so much lighter now than it was then, and I’m a year older and smarter, and I’m sure I gained some mathematical proficiency by fighting my way through that course. In fact, my calculus two professor encouraged me towards the math minor because he thought that I was sufficiently competent to do it. So now I have found myself living in a world where advanced mathematics are a major part of my everyday life and I am learning to solve problems that would have terrified me out of my wits not long ago.

When I started studying from my linear algebra textbook for the first time, it struck me what it is that I’m doing. The book occasionally uses phrases like “later in your career”, as if anyone who’s taking that class will go on to be a mathematician or something. Of course, math majors don’t take that class in their second semester of senior year; they’re more likely to take it as juniors, and then they still have several higher –level math classes to take. Those are classes that I’ll never reach, and so my linear algebra book isn’t really talking to me when it defines its audience as future professional mathematicians. Still, these math people are my fellow classmates. I’m taking classes that would be well beyond the scope of my abilities or interest if it wasn’t for the fact that I just couldn’t resist the urge to take on one more thing.

The cool ceiling window (aka Solar Lumination Portal) in the math building at my college

The cool ceiling window (aka Solar Lumination Portal) in the math building at my college

That doesn’t really answer the question of why I would be a math minor. After all, my career plans don’t involve math, and if all I wanted was the sense of logical comfort that I don’t find in an English class, I would have been better off not taking the extra math classes and finding logical comfort in some aspect of life that doesn’t involve the stress of tests and grades. Maybe I was also motivated by the desire to get as many majors and minors as possible in order to feel smart and successful, but I don’t think that played a very large role in my desire to minor in math, because I am well aware of the fact that things don’t work that way. People who graduate with double majors are no more intelligent or accomplished than people with one major, and throwing a minor into the mix doesn’t really make me a better person, either. I think I had another motivation for going for the math minor. It’s that math is hard and it’s made me very unhappy at times, and I can’t let it win.

I would like to point out that this is an incredibly awesome book. It explains simple principles of interesting mathematical topics, such as probability and topology, that aren't generally taught at a grade school level, and it does it all with a tone that is sympathetic to the math-hating child who nonetheless finds it fun to play with numbers.

I would like to point out that this is an incredibly awesome book. It explains simple principles of interesting mathematical topics, such as probability and topology, that aren’t generally taught at a grade school level, and it does it all with a tone that is sympathetic to the math-hating child who nonetheless finds it fun to play with numbers.

I generally enjoy helping my younger sisters with their math. There are several reasons for that, including the obvious facts that they appreciate it and that it makes me feel like I’m clever. The main reason, though, is that I have survived those very same math books, and so I am glad for the opportunity to go back and gloat in their evil faces. My poor innocent sisters now must suffer the same hardships that I did, but here’s the cool part. When I’m helping them with their math, I have the privilege of saying that the math book is stupid, pushing it aside, and doing the problem my way. When I was little, I was never allowed to say that the math book was stupid, and my parents got mad when I insisted that the math book was to blame for my failure to understand certain concepts. But now I’m allowed to look at the book and say, “This doesn’t make any sense. No wonder you don’t get it. No wonder I didn’t get it when I was in this book.”  And then comes the part where I call the book stupid and explain the problem my own way. There have been a number of times that I have succeeded where the book has failed in explaining a concept to my sisters. In other words, by figuring out how to do math, I am defeating my old enemy, the odious math book. I think that’s good motivation for getting a minor in mathematics.

I Don’t Like Aristotle

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AristotleI have this weird thing about Aristotle. I don’t like him. I know that his was one of the greatest minds of all time, I know that he made valuable contributions to just about every field of study in existence, and I know that his influence has played a large part in the course of human history, but something about Aristotle just annoys me. In theory, I ought to like Aristotle, because one of his defining characteristics was a tendency to classify everything, and that is a tendency which I share. (For example, I am in the process of posting my list of top 250 favorite songs on youtube after spending about a month carefully sorting and organizing them, and I am also currently trying to classify emotions into a small set of primary emotions, so that I can better categorize and document the entire range of emotions and collect data on a multi-daily basis in order to determine how various factors of everyday life affect emotion, as well as cognitive ability, which I have already developed a method for quantifying. This is just the kind of thing I do for fun in my spare time.) Some of Aristotle’s contributions to the world include taxonomy, various fields of theoretical science,  the foundations of all mathematics and physics for subsequent centuries, organization of rhetorical techniques, deductive logic, and various other systematic modes of thought that are either dear to my heart or at least appealing to the natural tendencies of my brain. Basically what I’m saying here is that Aristotle was brilliant and apparently obsessed with organized thought, which is reason for me to admire him. But instead, he annoys me like crazy.

Part of this is because there are a few specific things he said that I dislike. The most obvious and significant examples are theological, because Aristotle wasn’t exactly a Christian. (Despite what Plotinus said centuries later)To be honest, I’m not quite clear on what Aristotle did believe, although I’ve always gotten the impression that his beliefs more or less corresponded to what is now called Deism; that is to say, he believed in a God who created the world and invented moral rules, but hasn’t been particularly involved in the world since then. Although Aristotle definitely believed in “The First Cause” and “The First Mover”, he clearly didn’t believe in the triune God and he didn’t discuss sin and salvation in the Christian sense. Yet his philosophical ideas somehow still got tied up into Christianity in medieval times. For this reason, Martin Luther hated him and had some very choice words to say about him, which is enough to verify to me that Aristotle is not to be liked. Granted, Aristotle lived before Christ, but still, the point is that he didn’t believe in THE God; he believed in a god that he made up out of his own logical thought process, which, as brilliant as it was, was still human and thus not entirely reliable.

As long as we’re on the topic of unreliability, it is worth noting that Aristotelian physics turned out to be totally messed up and wrong. They held sway until Newton and Galileo came along, but then it was thoroughly demonstrated that Aristotle was mistaken, which isn’t really all that surprising since he was just making stuff up based upon his casual observations. Yes, I know that theoretical physics means that hypotheses are formed without the immediate verification of precise experimental data, but theoretical physics isn’t good for much unless its conclusions are justified by subsequent developments and experiments. (I feel a need to point out that the physics of the last century plus a few years, based upon Einstein’s postulates and theories, have disproved some of Newton and Galileo’s theories, so Aristotle’s physics is now at two degrees of proven-wrong-ness.)

Categorical SyllogismsIn my logic notes from last semester, there’s a line that reads, “Yet another reason to be annoyed by Aristotle”. I didn’t even bother to write down what that reason was, because I knew I would remember. I was right; I remember both the note and the reason for the note even though I haven’t looked at those notes since the semester ended. This source of annoyance was the discrepancy between Boolean logic and Aristotelian logic in a case where Boolean logic is clearly better. Aristotle says that certain forms of categorical syllogisms are valid if the terms are existing things and invalid if the terms are non-existing things. That makes sense, except that the whole point of distinguishing between valid and invalid syllogism forms is that valid forms are valid regardless of what the terms are. According to the Boolean standpoint, if the truth of the syllogism relies upon whether or not the terms exist, then the form of the syllogism is valid. In other words, it is valid to say, “All unicorns are mammals and all mammals are animals; therefore, all unicorns are mammals” because, if both premises are true, then the conclusion is true. The fact that unicorns don’t exist (or so I’ve been told) is irrelevant because, if they did exist, they would clearly be animals if we can assume that they are mammals and that mammals are animals. But, according to Aristotle, the validity of the entire syllogism depends upon the existence of unicorns. For the sake of my logic class, we had to answer questions from both the Aristotelian standpoint and the Boolean standpoint, but I would like the record to show that I am totally on Boole’s side on this one.

Just look at his arrogant, self-satisfied smirk!

Just look at his arrogant, self-satisfied smirk!

But, despite his flaws in theology, physics, and (in my opinion) the rules of categorical syllogisms, the fact remains that Aristotle was a remarkably intelligent person and that he made remarkable contributions to every aspect of academia and human thought. I can fully justify my disdain of Aristotle only by acknowledging one other reason for it: I’m jealous of him. He is widely regarded as one of the greatest geniuses ever to live, and his thoughts have been among the most prominent thoughts ever thought for more than 2300 years now. My brain aspires to great genius and doesn’t like the fact that there have been minds so great that my mind will never achieve the success and accolade that they did. This may very well be the same reason that I find Einstein annoying and have tried so hard to deny the fact that nothing can travel faster than light. I now reluctantly agree that this is the case, because it has been mathematically demonstrated to me in various fascinating and undeniably clever ways. But I am so totally not happy about it.