Egalitarianism

Here
these ears.
They do not hear.

Eyes
eye iris,
skin splashes skin.

Ears?
Not ears.

Nose
notice nose.
Always, tongue tastes tongue.

Ears.
Oh ears.
Envious little ears.

Ears!
You thing.
Your mirrors where?

What's the Point of Transparent Metaphors?

Ian Pilfre lives a comfortable life, entrenched in the world of the American upper-middle class, due to a prestigious position he holds at a Pennsylvania engineering firm. Imperium, a subdivision of this firm focusing on military research and development, draws its funding mainly from the Federal and State governments. However, staunch political pressure has resulted in a dramatic overhaul of funding levels causing Imperium to significantly curtail its operations. As a result, Ian faced the choice of either demotion or termination. He wisely chose to the former, but now Ian has several important decisions to make in his life.

Ian still earns a considerable salary which allows him to comfortably provide for his family. His family will not have to deal with the horror losing their house, going hungry, or falling into debt. All is not perfect though for the family. Throughout the years, Ian’s lofty salary had made them accustomed to certain amenities which now seem unsustainable. Being an amateur art collector, Ian has several fountain sculptors on his property which he likes to keep running continuously. Ian’s wife Eve has grown accustomed to lavish jewelry and other gifts that allow her to brag to her coworkers. His children have been spoiled with elaborate vacations to theme parks and tropical locations throughout the year.

Ian sits at a crossroad. How should he react? His income no longer warrants these expenses. However, it is difficult to tell his loved ones that they will no longer be able to continue living in this manner. Further, he fears this could place unnecessary strain on his relationship with his wife due to pernicious fights which have been occuring. He sees three possible solutions to his dilemma. He could bite the bullet and go through with the necessary lifestyle changes. This is the least preferable of his options. This will be his last resort.

His more insidious and preferred scheme is to raise revenue through two complementary means. He will first begin to take a small amount of money from the pockets of those in his community. The people in his geographical area live comfortably and will not miss the tiny amount he requires from all of them. He understands that this may not cover all of his expenses and that the method on a large scale will be infeasible. The remainder of his funds will be acquired by taking out loans in his neighbors names. Again, the loans will be small when divvied up among his community so they need not worry about the cost. He feels he is justified. After all, when he has these amenities it allows him to work harder and more efficiently. He kids and wife will be happier. Since his business contributes to all of society by providing defense, everyone will benefit since they’re only paying for something that enriches everyone.

Finally, as a middle ground, Ian could lobby to have Imperium increase the costs of its products to raise the additional revenue. He realizes that this will not be doable to cover all of his lost income since the shareholders of Imperium are hesitant to pass costs on to its customers and wary of the long-term decrease in demand that could occur from such policies.

Ultimately, Ian successfully combines the second and third options to continue his lifestyle. What should we make of this? Specifically, is this moral and is this the method which optimizes utility?

Local community colleges face this choice. A majority of them have chosen the same path as Ian. One’s overall opinion of the need for funding public education does not necessarily factor into this discussion. Waste abounds in these institutions. Professional development budgets are absurdly high and offer little besides bragging rights for professors and opportunities to take college paid vacations. Utilities run constantly for aesthetic purposes. Events are organized with little educational value that target only small groups of people. Professors and administrators apply for new toys on the taxpayers’ dime which contribute nil to the education of students.

Instead of making the tough decision to take away these unnecessary niceties from faculty, schools have opted to raise tuition and lobby for more funds. The former is of questionable morality to me given the circumstances. At the very least, it describes poor business that stands antithetical to the philosophical mission of a community college. Rather than trimming useless and frankly despicable practices, community colleges force marginal consumers to opt to not seek an education. The latter practice is criminal. Regardless of your views of taxation (be it present or future), taking ever greater sums of money, in times of economic turmoil, under the false justification of providing cheap education is unjustifiable. Education is not at risk here. Only the egos and fancies of spoiled professors and administrators face extinction.

You Know You Work in Government when the Least Intelligent People Have the Most Powerful Jobs

Recently, lost in the abyss of state funded academia, I found myself in a group discussion with other professors and administrative personnel. A nameless woman in charge of assuring academic excellence in teaching moderated the discussion. This highly educated woman had accumulated all the knowledge known to man regarding the process of learning and imparting information. Here I stood in this room, being paid to hear her teach about teaching, rather than teaching the students in need of teaching because of my absence from my regular duties. Like most establishment minds, she and I did not see eye to eye.

The friction between us turned to a spark when, as a passing comment, she said, “… when you are lecturing, well you know what I mean, I hope nobody in this day and age is still lecturing…”. Being an instructor who almost exclusively lectures, I asked her why lecturing need go extinct. Her response: It has been shown that lecturing is an inferior form of instruction; studies have shown it over and over again. I snidely responded, “Inferior for whom? Inferior for what?”. Expressions in the room led me to believe that questioning this fact bordered on taboo. The expression on the woman’s face led me to believe she didn’t know anything about instruction. Since simple English questions seemed to overwhelm her, she asked that I rephrase the question.

After rephrasing, she answered my inquiry with equivocation. Stripped of the verbal pomp, she believed that all students and all subjects and all instructors should be taught and teach in the same manner, one that involves minimal lecturing. Moving past this, my follow up question was , “Which studies showed this? How did they measure this?”. What ammunition did she possess for her counterattack? Nothing. A blank stare. Then, I whimper of “I’ve read articles that show it.”

I’ve already talked about the problem of homogeneity in education. I won’t say much more. Asking the questions, “lecture is good for whom?”, “lecture is good when delivered by whom?”, and “lecture is good for teaching what?”, is incredibly important in this situation. If a person gives boring, dry, unimaginative, or confusing lectures maybe he shouldn’t be using that mode of instruction. If a person lectures like some artists write novels, then maybe it’s a very good idea. Don’t force round pegs into square holes and expect results. What works to teach advanced linear algebra to gifted graduate students does not work to teach beginning algebra to continuing education students. Don’t expect these kinds of courses to remotely resemble each other.

Now onto my bigger point, besides the obvious point that the public education system is a rotting corpse of misinformation and waste, up to and including the community colleges. Intelligent people do not read a newspaper article about a study. An intelligent person reads the study. An intelligent person reads the actual study. Intelligent people do not just read the abstract and the conclusions. That is not science. That is not thinking. Reading a journalist’s summary of a study, or the author’s summary of a study, is worthless. One may as well just invent truths from nothingness. An appointed expert in the field should especially not be partaking in this behavior. Researchers do two important things which require that you read their actual work: they lie, and they make mistakes. They’re human. They have agendas, and they have flaws. They want money, fame, and power like most people. The peer review process does not nullify this. Similarly, you must know two things about journalists: they rarely understand what they’re writing about, and they report stories not the truth. Journalists are writers. They’re not scientists. They usually don’t have the skills, or the will, to do rigorous research into the actual results and methodology of a study, and more importantly, they want money, fame, and power. The headline, “Research shows that current teaching methods work for some people and not for others. Results were largely inconclusive.”, doesn’t exactly bring much attention to you and your work. The headline, “New research shows sweeping reform needed in our educational system.”, has a much better shot. Read the studies and questions them.

I must say that the closer to a problem you are, the more depressing it seems.

Why Oh Why Did Why Die?

To begin part 2 of n in my series on pedagogy, I want to share a story. If I possessed a time machine, and inexplicably used it to go back to meet my childhood self, myself would probably describe myself as a strange frustrating child. I liked to ask a lot of questions, especially to things that most adults see as having no answer. In preschool, we were treated to a series of books wherein letters of the alphabet would go about their daily lives interacting with lots of objects that happened to begin with the same letter. I loved these books because they entertained my imagination which had the sneaking suspicion that each letter had its own personality. On this particular day that I’m recalling, Mr. M went to the market. Mr. M was in the produce aisle. Mr. M was buying melons (can’t remember this exact detail, it may have been mangos which are also delicious) because they were his favorite fruit. I raised my hand and had roughly this exchange with the teacher:

Me: Why were melons Mr. M’s favorite fruit?

Teacher: They were his favorite because that is what he enjoyed the most.

Me: But why were they his favorite?

Teacher: Well I’m not sure why they would be his favorite. The book just says that.

Me: Why would the book say that though?

Teacher: The author must have thought that melons would be a good favorite fruit.

Me: But why would they be the favorite?

Teacher: Patrick. If you keep asking me questions the rest of the children won’t be able to hear the end of the story.

Me: Maybe you should do a better job of answer them then you unimaginative bitch.

Okay that last thought may be my present self projecting, but I think we get the point. This experience taught me a valuable life lesson that would be reinforced every year of school until I entered a field predicated on breaking this lesson, “Don’t question authority.”

Of course, there’s nothing particular to the teacher mentioned. This occurs constantly, in one form or another, in educational institutions across the nation. Now as a shepherd of man I have two huge problems with the actions of the teacher in the above example.

1) The supposed purpose of the education system is to educate. The actual system we employ more resembles a process by which inquisitive and creative children forcibly deteriorate into automatons who access information from a database, placed in them by visionless hacks called teachers, like computers. Which is more indicative of an educated and successful person: the accumulation of dates, facts, and trivia or the desire to see the world, question what one sees down to the core, and to be excited about the process of the discovery? The former makes me a jeopardy champion while the later makes for an intelligent person. The former can be learnt by any person and some lower species while the later cannot be taught and is rarely reacquired after it has been snuffed out. We focus on one of these aspects and complete discourage the other. Questioning is actively discouraged in the classroom. There’s a variety of reasons. Teachers are petty and don’t like being questions. Teachers are too stupid to know the answers to the questions. Teachers are too lazy to deviate from the format of a lecture. Teachers are stressed out by the system. Kids need to learn a certain set of material, in a certain frame of time, and pass certain tests to prove that this has been done. Whatever the particular reason in your sample classroom happens to be, it is a given that this process occurs. Questioning should be encouraged and rightly be seen as fundamental to the education process. Questioning by a student is now viewed more as a weakness rather than as strength. We should be actively trying to reverse this perception.

2) This response to a question reinforces the flawed flow of information present in classrooms. The current delivery method mimics the sprinkler you use to water your lawn. The water comes from a single sprinkler which delivers the nourishment to the grass. The water flows in one direction only. The sprinkler alone possesses water and needs no water. The grass needs the water but has none of its own. Information flow should more resemble natural selection. Ideas are generated freely and without guidance from each individual member and brought into the classroom environment. At this point the classroom tests the knowledge. Those items surviving the questioning and thought process survive as true information. Those deemed insufficient are left to die. Obviously the teacher still has a focal role in weeding out the bad ideas, but the responsibility does not rest solely with the teacher.

Now I may be somewhat contradicting myself going through this whole rant. I did just say in my prior post that no method can effectively work for all students. However, certain methods will be more effective in general. Changing the information flow in classrooms and the role of the student will go a long way towards rearing a more intelligent population. It took me several years to recover from the horrors of current education system and regain the ability for independent thought and excitement about acquiring knowledge. My philosophy of education stems from two basic beliefs: Children are educated, and children love to learn. We’ll go a long way if we simply stop destroying what is already basic to children.

The Continuum Hypothesis: You Can't Count for Shit

Warning: TL;DR

In an effort to write more, and to watch SportsCenter reruns less, I’m beginning a series of blogs which will (hopefully) present an understanding of The Continuum Hypothesis and its “solution” to the lay person. The Continuum Hypothesis is suitable for a number of reasons. Most importantly it’s a result primarily in logic, so it requires little formalized mathematics, which can be stated fairly easily. It’s interesting to me because it does not resemble math and has absolutely no application to anything in the corporeal world.

Mathematics’ ability to force one to reexamine, and frequently discard, long held assumptions about the nature of the world interests me immensely. It’s one of the reasons I find the discipline so fascinating. For example consider the following, if you have two groups of things, group A and group B, such that group A contains everything in group B and more, then you would say that group A must be bigger than group B. As young children we deduce this, and it serves us well throughout our lives. If I draw two circles, one surrounding the other, then the surrounding circle must be bigger. If you have every single comic book that I do, plus a collector’s edition that I don’t have, then you have more comic books than me. The logic seems to check out. In general though, this assumption is unfounded.

The give us some minimal technical jargon, mathematicians like to call any group of stuff a set. If something is in a set, we simply say it is an element of the set. If set A has everything that set B has in addition to something that set B doesn’t have, we say that B is a proper subset of A or dually that A is a proper superset of B. To be concrete we could say set A is the group of numbers {1,3,5,8} and set B is the group {1,5,8}. B here is a proper subset of A. You don’t care about what grey bearded aloof professors call things though. I just dropped a bombshell on you. You want to hear more about that.

Where did the logic go wrong? Well as children we did something that makes every mathematics professor cringe and every beginning mathematics student bomb a test he thought he passed, we made a tacit assumption. The assumption probably seems good as children. It probably seems pretty good to most adults. We assumed that we can count everything and give it a number. In the above I can say that set A has 4 elements. It seems like a good bet that we can always do this, but unfortunately we can’t. When we can, our childhood logic holds true. The “proof” goes like this: Set A has everything that set B has. I can count the things in set B. Set B has x elements. Set A has things that set B doesn’t have. I can count those things. Set A has y things that set B doesn’t have. Therefore set A has x+y things. x+y things is more than x things. So set A is bigger than set B. So sets are always bigger than their proper subsets. Sometimes though, this breaks down.

A common breakdown in logic occurs when we attempt to jump from familiar finite cases, which we test through our daily experiences, to the world of the infinite, of which it seems we have a poor understanding. Suppose we had the set of numbers, called the counting numbers (N), {1,2,3, …} and the set of numbers, called the integers (Z), {…, -3, -2, -1, 0 , 1, 2, 3}. Which one is bigger? By our faulty logic, Z contains all of N, plus a bunch of stuff N doesn’t have, so that Z is bigger. But we can’t say this. We don’t really know how big either of them are. How many things are in N? The way we usually count doesn’t work here. We can’t assign a usually number to the size of N. We can’t physically count all of them up. The same applies to Z. The “proof” used earlier to verify our logic breaks down here. How many elements are in N and Z? How many more elements does Z have? These questions can’t be sufficiently answered. There’s no number to assign to the size of each.

Let’s bypass this problem. Instead of worrying about giving a name to the size of each, let us just find a way to say if two things are the same size. Consider the following thought experiment. We have a classroom of students. There’s some number of kids in the classroom. There’s some number of desks in the classroom. I want to know if I have the same number of students as desks. If I could count each up, this would be an easy exercise. However, we want this method to work for things infinitely big so we can’t do that. I propose a different method. I’ll take each kid and assign him to a desk. I’ll assign every single kid to one desk and only one desk. I will assign no two kids to the same desk. If at the end, I see that every desk is filled with no kids left, I can say that there is the same number of kids as desks. Simple right? Take a moment to make sure you agree that this method captures the essence of two things being the same size. Make sure you see the importance of the fact that every kid gets only one desk, every kid gets his own desk, and every desk is filled.

Here’s some more jargon to impress the ladies at the bar. A function is a way of assigning things from a set A to exactly one thing in another set B. In the above, me assigning kids to desks was a function from the set of kids to the set of desks. If no two kids share a desk, that is if a function sends everything to a different place, it is called injective. If every desk is filled by a kid, that is if a function ensures that everything in set B has something from set A sent to it, the function is called surjective. If we have an injective and surjective function from what set to another, we can say that the two sets are the same size. Now back to the narrative.

Now that we have a way to compare sizes, what can we say about those two sets that previously eluded our examination? Can we say that Z is bigger than N? The shocking answer is no. These two things are actually the same size. Cool huh? To see how, we’ll start assigning students to desks. The elements of N will be our students, and the desks here will be the elements of Z. I’m an idiosyncratic teacher so here is how I tell the students to get in their desk. I’m going to tell student 1 to sit in desk 0. Now for every other student who has an odd number, I’m going to have him sit in the desk that is half than one less of his number ( [x -1]/2). In this way student 3 goes to desk 1, student 5 goes to desk 2, and so on. Now for all those students with even numbers, I’ll have them sit in the desk which half of his number and negative (-x/2). In this manner, student 2 goes to desk -1, student 4 goes to desk -2, and so on. With this method of assigning seats, I’ve given every student a place to sit and only one place to sit. I’ve also done it in such a way that every desk will be filled. Therefore, contrary to popular belief, the two sets are the same size even though Z has infinitely many things in it that N does not. Behold the power of arcane mathematics.

Objection! Objection! says the weary observer. I claimed that every “desk” needed to be filled. How can that possibly happen here? It is true that in physical reality we can never have every single desk filled in this manner. However, in reality the sets themselves couldn’t exist. It should be remember that infinity is really just a concept. You could never actually have every number in N. Instead I would say that for any number you can think of, N contains a number that is bigger. In the same way this desk assignment process, think of any number of desks that you wished to have filled. The process detailed above will fill more than that if you give it enough time. It we imagine that this process could carry on forever, in this imaginary land of infinity I would actually fill up all the desks.

Let’s briefly go back to my method of assigning desks. What did I actually do? Since I was assigning the number {1,2,3, …} to each desk labeled by Z, in reality what I was actually doing was counting the desks. Imagine the Z desks were lined up in order. You are standing at the zero desk with the positive desks extending forever to your right and the negative desks extending forever to your left. What I described was a way to count these. My method told you to first point at the desk right in front of you and count it as one. Then you were to go to the first negative desk and call it two. Next we go to the first positive to call it 3. To finish counting them all, you just need to keep alternating between positive and negative as you count. For this reason, sets that are the same size as N are frequently called countable sets. Notice that the way that I counted was very important. If I just attempted to first count all the positive desks, and then count all the negatives, I would never have been able to count everything. When calling something countable, or when showing two sets are the same size, we only need to find one way to do the assigning. If there are billions of ways that we can’t count the set, but just a single way that we can, the set is still countable.

The German mathematician Georg Cantor introduced these concepts in 1874. The mathematical community at the time violently reacted to his work. Unfortunately, scientists conduct themselves no differently than the average man. They are biased, selfish, and blinded by their beliefs. His work gradually gained acceptance after a period of ridicule. Georg Cantor spent the final days of his life driven to the brink of insanity pondering the extensions of this simple idea of counting. He died in a sanatorium consumed by what became to be known as the Continuum Hypothesis.

To fully introduce this idea, next time we will ask whether there are sets that cannot be counted. Intuition begs us to call this question absurd. As we have seen though, intuition has no place in the realm of the infinite.

The Solution to our Education System : There is none.

This post begins a series that I will pen (in theory only) to reveal the superficialities of my theory of pedagogy. I’ll point out what is wrong with the American Education System, as I now find myself to be firmly a part of it. My overall belief is that the system will never be fixed. To do so would require that many rich and powerful people losing their money and prestige, common folk accept extremely discomforting realities and the education system attempts to educate children rather than adhere to its historical purposes.

Education progresses cyclically. Every two decades or so a new revolution in reaching occurs which quickly claims to eradicate our education woes. The zealots of the movement cite some loosely related, over-reaching articles drawn from the social sciences to give credence to the unstoppable force that is this new theory. The fact that this approach to education mimics a previous failed approach never gets mentioned. Millions of dollars are spent in training, curriculum reform, textbook changes, and new school projects to accommodate the “new” untested solution which has won over a select group of bureaucrats and politicians, forced to make some change as inaction spells political suicide. Another massive failure reveals itself as false hope subsides, and another faux solution rises from the ashes of previous ineptitude.

Humans have been able to accomplish an awful lot. We’ve tackled seemingly more difficult problems than the question of how to properly educate our children. To invoke the mantra of every complaining S.O.B. on the face of the Earth, “We can send a man to the moon, but we can teach Johnny to add fractions?” In the face of such monumental failure to solve a problem well within our means to solve, it helps to examine the underlying axioms that theorists use. For centuries, astronomers were unable to explain the precession of the perihelion of Mercury despite the extraordinary success of celestial mechanics. The problem, as Einstein eventually revealed, was that everyone operated with the innocuous and friendly assumption that time is an unyielding constant. Bad assumptions give you junk results every time. The educator’s assumption is just as seemingly benign as the physicist’s. Educational theorists began with the axiom, “There is a solution.”

Unfortunately, there isn’t.

Malcolm Gladwell touches on this same point in a TED talk (here if you’re interested). He talks about sauces, but the overarching principle remains valid. Social scientists have a nasty habit of treating people like physical scientists treat control populations: heterogeneous and indifferent to the act of observation and experimentation. However, an individual’s subjective evaluations vary remarkably from person to person. The population of people to be educated gives a myriad of differing curiosities, strengths, weaknesses, educational levels, social pressures, desires, career paths, learning styles, and reactions to stimuli. We’ve been operating as if we’ve failed because we’re trying to jam a round peg into a square hole. We could succeed if only we could find the right dimensions to carve. In reality, we’ve been trying to jam thousands of fractal images into neat polygons that we carve one at a time.

With this idea in mind, centralized academic control is a cancer to society. This isn’t a Republican talking point. I’m not suggesting that we just need to abolish the Department of Education, offer a voucher system, or let kids pray in the classroom. The issue is much, much deeper. This is an admonishment of private schools as much as it is of public schools. Returning education to State control would allow for some heterogeneous products. However, State’s are still behemoth sized beings. Most families do not have the fluidity necessary to move across State lines just for a set of educational standards. Add to it the fact that these would still be at the whim of feeble minded, reactionary bureaucrats and this is even less of a feasible solution.

To truly provide the diversity of instruction methods to meet the abound diversity of the individual, all forms of regulation on the delivery of knowledge must be eradicated. Education cannot exist alongside academic standards. All forms of (governmental) accreditation and certification must be thrown into the dustbin of history. Along with them must follow the laws which dictate mandatory attendance in institutions of learning.

This is the first step towards a coherent system of education with this one being more of an organization than a pedagogical nature. Nobody has the correct answer for how to educate the nation. The answer doesn’t exist. However, methods can be devised to educate the person, but the mechanics which will do so cannot operate bound to a small group of individuals’ preconceived notions of what is right or proper. This is not a free market argument. The nature of the individual dictates this regardless of what economic system is actually ideal.