CommonLisp; Also, The Silver Chair... and Abstract thought

So, OOP has been too ingrained in my skull for me to properly use Scheme for an AI project I have to do, so I've decided to use CommonLisp- It's still Lisp, right? I now know full well why people say "CommonLisp is more powerful than Scheme." There are some really useful things you can do easily with CommonLisp. However, I also know full well why people say "CommonLisp is ugly and convoluted compared to Scheme." Line-noise like this: (format t "~{~a:~10t~a~%~}~%" cd) is why I don't want to learn perl... And I now have to deal with it when programming in lisp. Granted, it does a lot, but is it really worth memorizing all the syntax? Probably, but also definitely not.

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On a (probably) more interesting note, I really, really love the scene in the Silver Chair during which the Queen tries to convince the children, the prince, and Puddleglum that Narnia is a dream. Her arguments, which fall absolutely flat when you're outside the scope of the novel are used so often. Of course we can't explain God's presence, it isn't something we have a concrete understanding of.
Questions:
How does someone with Synesthesia describe the shift and change of colors as they hear music? How does one describe the sun to a blind man? Music to the deaf? Snow to someone from the tropics? A computer to a tribesman?
Answer: In metaphor and simile.
But of course metaphors and similes will present the object in question as a twisted version of the concrete object it is being compared to, rather than a distinct object with a similar sensation.

tangentially,
I can (sort of) understand how a synesthesiac thinks, because I have a similarly abstract and incommunicable thought-process. The best way, I think, to describe it is as imagism. I perceive, with all 5 senses and abstract thought an "emotional and intellectual complex" whenever reading, writing, drawing, seeing, doing math, coding, ...
My thought process is a string of Pound-ian images, which shift, move, fall, rise, appear and disappear in conjunction with everything that enters my brain through any medium. There are uncountably many stories, scenes, colors, sounds, tastes, ideas and so much more that pass through my mind every second, and over any period of time, and also distinct from time.

So, how does this relate to synesthesia? If I equate these images to colors (or whichever other sensation the synesthesiac perceives), I see the same thing.

Moving back to my string of questions, is there any way to truly describe my thought process? I've given a quick description; everything I said is true, but there is so much more to the mental "image" than the scenes and Pound-ian images I've described.

The Weight of Glory

I've been thinking quite a bit lately about The Weight of Glory by CS Lewis. It is a truly excellent analysis of the Christian experience. But from the second or third day after we read it in Small group, something has bugged me about it. I think I finally have a coherent enough "argument" at this point to actually put it online.

Let me preface this by saying that I really do admire and respect CS Lewis. Not only was he a great apologist, but he was clearly a man abounding in faith-- a man who seemed to sit and enjoy God's presence constantly.
That being said, we Christians have an obsession with the afterlife. Not that the afterlife is bad, or anything we shouldn't look forward to, but God's presence and spirit here, now, is so beautiful and so amazing, and so ignored. Throughout the essay, Lewis talks about the "proper reward" of various things. The "proper reward" of love is marriage; the "proper reward" of fighting is victory; he likewise discusses food in metaphor, and (he may actually say this) were he to name the "proper reward" of food, I can hardly imagine it would be anything but health.

Does something seem missing in all of these cases? I submit that there is. You do not fall in love in order to marry; there is no justice in deciding to fight solely because you will achieve victory; food is not merely a way to avoid illness, weakness and death.
Marriage is the proper reward of correct and sustained love, but love comes with more immediate, more beautiful and tangible rewards. Victory is the end reward of proper combat, but fighting for victor as an end is perverse. Health is the end reward of eating, but if you eat solely for sustenance, you will never enjoy food, and you are quite truly eating wrong.

There are, to every action, an immediate reward-- which I will call the excitement-- and an eventual reward-- which I will call the fulfillment. Any action done with no consideration of the fulfillment is sinful-- aesthetic as Kierkegaard puts it, hedonistic would be the more common word. Likewise, any action done with no consideration for the excitement is self-denial-- the actions of the knight of infinite sorrow, according to Kierkegaard, ascetic is a more understood term.
This latter action, self-denial, is the "unselfishness" that Lewis speaks out against in the fist paragraph of his essay. You are denying your immediate excitement because you know that the fulfillment of your action is "good".

But! There is so much more to what God has for us than heaven. There is so much on earth, so many beautiful things that God has given, and so many incredible ways He spends time with us, and enlightens us. We are missing God completely if we hope only for the fulfillment-- even the "selfish" fulfillment of heaven. God is here, right now! And He wants you to be excited in Him. Do not simply drudge along waiting for heaven, because you will get bored and distracted and all will be lost. How long can you eat food only for sustenance before you despise the sight of food? But if you eat food not only for sustenance, but also for enjoyment, how much more will you want food! Then, you will acquire a taste for so much finer, more complex and exciting foods that you would have missed completely if you had neglected your taste-buds.

So it is with God. Seek God's beauty out, and leave heaven at the back of your mind, except when God brings it to the forefront. And you will develop a taste for beautiful things God has done and will continue to do that you would have misunderstood, or disliked, or missed completely.

God is beautiful! God is exciting! And that excitement is tangible and real and all around us!

On Abstraction and Education

I had started writing a rather in-depth post a while ago, and sort of lost the drive... Here's how far I got. It is a complete thought (mostly), but it isn't everything I wanted to talk about... Ce'st la vie.

Abstraction...
Abstraction is at the heart of knowledge, at the heart of learning, and thus, education. It works as follows:
Start with something we have a concrete understanding of. Now, decide there are certain properties of this object that we are interested in, and everything else is unimportant. Now create (in your mind) a conceptual version of that object with only those properties you are interested in. This is the abstraction step. The beautiful thing is that you now can analyze those properties that are interesting. The other beautiful (and perhaps more useful) thing is that you can now find another concrete object which shares the interesting properties, and you will now know things about it. It doesn't matter whether any other property is different, there will be properties of this new object which you have already analyzed.

This is how education works. Abstraction. Take something the student knows and abstract the object so that you only pay attention to the properties which will tie it to the next thing they need to learn. Through this abstraction, the student has a lens through which to view the new, unknown object. A good educator will not only make an abstraction clear (not necessarily explicit), but will show the abstract relation between the new object and multiple known objects.

There are, of course, other very important things in education. I realized a few of these tonight as I was helping Danielle learn to program. Perhaps more important than clear abstraction is do not let the student take a passive role. This is reiterated everywhere, and I'm sure my readers (all 2 of you) will have heard it somewhere. But it tends to be meaningless babble if it isn't explained. So I will explain, using my experience this evening as an example.

First, you must force the student to think. This is, perhaps, the hardest part. It is especially difficult when the student is frustrated with the subject material (as is often the case when tutoring someone). A frustrated or disinterested student will not want to put in the mental effort required to draw connections to previous understanding (read: to abstract). If you can force the student to think about the material, she will move from the known ideas to the abstract without you, and you can focus on shaping the lens, and pointing out key differences between the previous and new material. So, how do you get someone to think?

An answer (among others) is the Socratic Method. Pose questions which lead the the student toward the knowledge you are trying to pass on. If she is stuck, either explain a little more information that is related to the answer, and re-ask the original question, or ask a new, more specific question. In this way, you provide them a context and framework with which to understand the new knowledge. Looking at our example: At the beginning of the night, Danielle was not only lost, but not even trying. As the night continued on, I first began explaining what I was doing to change what she had done (basically copied), and then began to ask her questions, leading her to write her own code, in her own style.

By the end of the night, she was finishing her code by herself with almost no prompting by me, and I was able to focus on correcting small details and providing notes that would make her code cleaner or more efficient. By forcing her to actively think, my position as instructor changed from "I'll show her what I'm doing" to "I'll provide additional knowledge to help her do this better." In essence, I changed from a position of carrying her along, to a position of pointing out paths for her. Granted, she still has a lot to learn, but I was helping her for less than 2 hours, and she went from knowing nearly nothing, to anticipating what I was going to tell her. The amazing thing is that by putting in that extra care and effort, it actually made it easier for me and in the end, easier for her. It was harder for both of us at the beginning but once she started to pick it up, it went very smoothly and efficiently. She accomplished more in the last 10 minutes than in the first 45.

If We Taught English the Way We Teach Mathematics...

This was originally posted by "Coryoth" (interesting, same name) on K5. It's an interesting approach to the subject, but I think it's pretty good. There's probably more to say on the subject, but he gets the point across: [Edit! It seems it was first posted by Leland McInnes at The Narrow Road, which I highly, highly recommend you read, as it is even better than the following]

Imagine that your only contact with "English" as a subject was through classes in school. Suppose that those classes, from elementary school right through to high school, amounted to nothing more than reading dictionaries, getting drilled in spelling and formal grammatical construction, and memorizing vast vocabulary lists -- you never read a novel, nor a poem; never had contact with anything beyond the pedantic complexity of English spelling and formal grammar, and precise definitions for an endless array of words. You would probably hate the subject.

You might come to wonder what the point of learning English was. In response perhaps the teachers and education system might decide that, to help make English relevant to students, they need to introduce more "Applied English". This means teaching English students with examples from "real life" (for varying degrees of "real") where English skills are important, like how to read a contract and locate the superfluous comma. Maybe (in an effort by the teachers to be "trendy") you'll get lessons on formal diary composition so you can better update your MySpace page. All of that, of course, will be taught using a formulaic cookbook approach based on templates, with no effort to consider underlying principles or the larger picture. Locating the superfluous comma will be a matter of systematically identifying subjects, objects, and verbs and grouping them into clauses until the extra comma has been caught. Your diary will be constructed from a formal template that leaves a few blanks for you to fill in. Perhaps you might also get a few tasks that are just the same old drills, just with a few mentions of "real world" things to make them "Applied": "Here is an advertisement for carpets. How many adjectives does it contain?".

In such a world it wouldn't be hard to imagine lots of people developing "English anxiety", and most people having a general underlying dislike for the subject. Many people would simply avoid reading books because of the bad associations with English class in school. With so few people taking a real interest in the subject, teachers who were truly passionate about English would become few and far between. The result, naturally, would be teachers who had little real interest in the subject simply following the drilling procedures outlined in the textbooks they were provided; the cycle would repeat again, with students even worse off this time.

And yet this is very much how mathematics tends to be taught in our schools today. There is a great focus on the minutiae of the subject, and almost no effort to help students grasp the bigger picture of why the subject might be interesting, and what it can say about us, and about the world. Mathematics has become hopelessly detail oriented. There is more to mathematics than mindlessly learning formulas and recipes for solving problems. And just like our imaginary example, the response to students lack of interest in mathematics has only served to make the problem worse. The "applications" and examples of using the mathematics in the "real world" are hopelessly contrived at best, and completely artificial at worst, and still keep a laser like focus on formulas and memorizing methods without ever understanding why they work.

Of course the opposite situation, with no focus on details, can be just as bad. Indeed, that is where English instruction finds itself today, with students never learning the spelling, formal grammar, and vocabulary needed to decently express the grand big picture ideas they are encouraged to explore. What is needed is a middle ground. Certainly being fluent in the basic skills of mathematics is necessary, just as having a solid grounding in spelling and grammar is necessary. What is lacking in mathematics instruction is any discussion of what mathematics is, and why mathematics works as well as it does.

The discovery and development of mathematics is one of the great achievements of mankind -- it provides the foundation upon which almost of all modern science and technology rests. This is because mathematics, as the art of abstraction, provides us the with ability to make simple statements that have incredibly broad application. For example, the reason that numbers and arithmetic are so unreasonably effective is that they describe a single simple property that every possible collection possesses, and a set of rules that are unchanged regardless of the specific nature of the collections involved. No matter what collection you consider, abstract or concrete, it has a number that describes its size; no matter what type of objects your collections are made up of, the results of arithmetic operations will always describe the resulting collection accurately. Thus the simple statement that 2 + 3 = 5 is a statement that describes the behaviour of every possible collection of 2 objects, and every possible collection of 3 objects. Algebra can be viewed the same way, except that instead of abstracting over collections we are abstracting over numbers: elementary algebra is the combination of objects that represent any possible number (as numbers represent any possible collection with the given quantity), and the set of arithmetic rules for which all numbers behave identically. Numbers let us speak about all possible collections, and algebra lets us speak about all possible numbers. Each layer of abstraction allows us to use an ever broader brush with which to paint our vision of the world.

If you climb up those layers of abstraction you can use that broad brush to paint beautiful pictures -- the vast scope of the language that mathematics gives you allows simple statements to draw together and connect the unruly diversity of the world. A good mathematical theorem can be like a succinct poem; but only if the reader has the context to see the rich connections that the theorem lays bare. Without the opportunity to step back and see the forest for the trees, to see the broad landscape that the abstract nature of mathematics allows us to address, it is rare for people to see the elegance of mathematical statements. By failing to address how mathematics works, how it speaks broadly about the world, and what it means, we hobble children's ability to appreciate mathematics -- how can they appreciate something when they never learn what it is? The formulas and manipulations children learn, while a necessary part of mathematics, are ultimately just the mechanics of the subject; equally important is why those mechanics are valuable, not just in terms of what they can do, but in terms of why they can do so much.

So why is it that this broader view is so rarely taught? There are, of course, many reasons, and it is not worth trying to discuss them all here. Instead I will point to one reason, for which clear remedies to exist, and immediate action could be taken. That reason is, simply, that far too many people who teach mathematics are unaware of the this broader view themselves. It is unfortunately the case that it is only at the upper levels of education, such as university, that any broader conception about mathematics becomes apparent. Since it is rare for people going into elementary school teaching to take any university level mathematics, the vast majority of elementary teachers -- the math teachers for all our children in their early years -- have little real appreciation of mathematics. They teach the specific trees outlined in textbooks, with no real idea of forest. A simple but effective measure that could be taken is to provide stronger incentives and encouragement for prospective elementary school teachers to take extra math; whether it takes the form of courses, or math clubs, doesn't matter, the aim is to get teachers more involved and better exposed to mathematics in general so that they can become familiar with the richer world beyond the specific formulas and algorithms. This exact approach was tried in Finland as part of their LUMA project starting in 1992. As a result the number of teachers graduating with higher level had increased dramatically by 1999. And the results are also clear: Finland finished first, showing continued improvement in mathematics and science, in the 2003 PISA survey of the reading, math, and science skills of 15-year-olds in OECD countries (Finland finished second, just behind Hong Kong, in the mathematics section). Finland has continued to do extremely well in other more recent (though less major) studies.

Whether you view mathematics as an important subject or not, it is hard to deny that, currently, it is being taught poorly in many countries around the world. With such scope for improvement, and clear examples such as Finland showing the way, isn't it time that we took at least some of the obvious steps toward improving the quality of mathematics education?

Tell them it's movement, movement, movement!

So, God sparked a flame over the weekend, among the people who went to winterfest. It's going to be exciting to see where this goes.

Through Sully and Katie today, God softened my heart. I'm still stubborn and prideful. I'm still rather hard-hearted, wicked, and foolish, but God is working, and it is exciting. The spiritual pit I've been in for a while seems to be gone, and it's exciting!

Anyway,
God bless.

Cum hoc ergo propter hoc

There's a common error that's bugged me for a while. It's related to "post hoc ergo proter hoc" (after this, therefore because of this), and apparently is called a spurious relationship statistics.

Anyway, the argument that bugs me goes something like this:

A happens,
Later B happens;
they seem to be related, thus A leads to B.

Now, I see this all over the place.

I recently read an article that suggests that if people (particularly women) take AP calculus in high school, they're more likely to be engineers. This is true, but she was using this fact to encourage women to take AP Calc, in order to increase their chances of become engineers.

The problem with this argument, is that she ignores the (10 or) 11 years of schooling prior to taking AP calc. The reason women who take AP calc go onto be engineers more often is that women who take calc in high school are better at math than at other subjects-- this was the conclusion of her study. People who are better at math than other subjects go on to engineering related careers more often than those who don't.

Event A: Woman takes calc in high school.
Event B: Woman becomes an engineer.
Cause C: Woman is better at math than english.

Somehow, this cause which she argues is forgotten. If she encourages more women who are "well-rounded" students to take calculus, the relationship between C and A weakens; hence, the relationship between A and B weakens.

The general idea has always baffled me, especially since spurious relationships almost always come up as a way to rectify problems with the cause. How can you argue a causal relationship and then forget about the implications of the cause? That's what a causal relationship is!

A Short Bit on Faith

I started writing this a few months ago, and forgot to actually finish it until today. I understand that it is all over the place, but I'm not terribly worried about that...

For all of history, people who pushed for something greater have been mocked and ridiculed; even today, when much of America claims to be Christian, nearly anyone who dare profess the absurdly idealistic love that Christ represents would be ignored, or, at best, called a hopeless romantic who needs to awaken to the real world. When I hear this, I think of Puddleglum's speech:

"One word, Ma'am. One word. All you've been saying is quite right, I shouldn't wonder. I'm a chap who always liked to know the worst and then put the best face I can on it. So I won't deny any of what you said. But there's one thing more to be said, even so. Suppose we have only dreamed, or made up, all those things-- trees and grass and sun and moon and stars and Aslan himself. Suppose we have. Then all I can say is that, in that case, the made-up things seem a good deal more important than the real ones. Suppose this black pit of a kingdom of yours is the only world. Well, it strikes me as a pretty poor one. And that's a funny thing, when you come to think of it. We're just babies making up a game, if you're right. But four babies playing a game can make a play-world which licks your real world hollow. That's why I'm going to stand by the play-world. I'm on Aslan's side even if there isn't any Aslan to lead it. I'm going to live as like a Narnian as I can even if there isn't any Narnia. So, thanking you kindly for our supper, [...] we're leaving your court at once and setting out in the dark to spend our lives looking for Overland. Not that our lives will be very long, I should think; but that's a small loss if the world's as dull a place as you say."

The key word in this whole speech is "important". He does not say that the made-up things are more "fun" or "interesting" he says they are more important. This choice of words changes the whole speech from a confession of willful delusion to a statement of purpose. Puddleglum is not deluding himself into believing that the Overworld exists, he is saying that, since that world is more fulfilling, more alive, it is more real, whether it is tangible or not. We shouldn't stop fighting for true love, for brotherhood, for God, just because people call them romantic concepts designed only to give us hope; Oh, no! They are of greater consequence, of more value than any end on this earth, so even if they do not exist, they are still worth more than this hollow, dark, empty pit of a cave through which we wander hopelessly.

What is it, exactly, that makes them more important? Just before Puddleglum makes this speech, the queen, Jadis, is telling them that all these things are silly exaggerations of real things: Aslan, the large lion, is just a house cat; the sun is merely a large lamp, the sky just a large roof, and so on. The things she mentions are the things we need in order to live: Shelter, light, someone/something to comfort us and keep us company. The things Puddleglum mentions fulfill all the same functions, except they are more fulfilling. The sun is warmer and brighter than any houselamp, the light more comforting; Aslan is like a house cat, only larger, warmer and gentler; Narnia is just like the large underworld, only more just. Likewise, God's love, the kingdom of God and pure romance are more fulfilling than the "real-life" equivalent. Note, however, that this is not a Utopian, happily-ever-after sort of fulfillment; it is satisfaction, which is the reward of action. Effort is required for satisfaction: Anyone who tells you Christianity does not require tremendous force of will has never felt God; anyone who says that a relationship is not difficult has never committed to another person; anyone who says there is no stress in loving your fellow man has never helped out a friend in need. But this love, this faith, has more power, more value than any end on this earth. Is there any loss in living for these things? You will miss whatever the "normal" purpose of life is, but to quote Puddleglum again, "It's a small loss if the world's as dull a place as you say."

What's even more important than anything Puddleglum says is that the Overworld does exist. Puddleglum is in fact not a dreamer who has committed himself to a non-existent cause, but rather a lone seer, who has stepped out of Plato's cave into the warm sunlight. How, then, can we be assured that we are right, that the world is blind and stubborn, while we walk in Truth? How can we convince others that we walk in the Truth? Unfortunately, there is no certain way; there is no proof that God exists, no proof that there is a higher purpose, and the cave is as empty and meaningless as the Underworld. However, stronger and more convincing than any clever display of logic is the experience of these things. Those of us who proclaim the power of God have seen His light; those who hold love as a greater end than anything on this earth have loved and been loved in such a way that they cannot deny its power.

Once again: how can we convince others of this? Only by showing the same that we've seen. We have to spread love, God, and brotherhood, not by word of mouth, but by deed. We cannot just talk, convincing people of the Truth because Truth is not a reasoned conclusion. It is not a statement of the form "p therefore q." God is not something you know, it's something you feel, something you understand. In Stranger in a Strange Land, Heinlein invented the "Martian" word grok to describe this concept. Literally, grok means "drink", and it should be no surprise that Jesus used the same term to describe living in faith; when you drink something, it becomes a part of you, a part of everything you do, and every decision you make. We must drink in God's love until it flows out of us like a fountain. Only by spreading this, by sharing the same beautiful experience of God's presence can we hope to expand God's kingdom.

There is no knowledge, no action, no speech which can by itself convince anyone of God's existence and love. Even if someone understands philosophically that God exists, that does nothing for them. "You believe that there is one God. Good! Even the demons believe that- and shudder." (James 2:19) Faith is not an intellectual adherence to doctrine; it is a statement of purpose a commitment to live "as like a Narnian as possible, even if there isn't any Narnia." Once you experience God's love-- once you have that first sip of grace-- you cannot be content with anything less than the whole cup. "If only you knew what it would have meant to drink the thimbleful of fire. But, alas! you swear you already know its taste! and yet your belly remains intact."

If there is no way to convince people of the Truth, we must then live our lives to the fullest-- live in God's joy and freedom all hours of the day-- and pray and wait for them to reach up and grab the thimble from Jesus' hand. When that happens, and only then, will they understand the fire that consumes the believer. We cannot wait for our lives to end, for Heaven, "the afterlife" to experience God's Grace. There is so much more on earth than we see around us, so much more than we accept and feel content with. Why then are we sitting here waiting to die? We must reach out, and search for Narnia! We must go out and find Aslan! If God is there, reaching for our hands, why would we sit here and wait for him to? Shouldn't we strive with all our heart, soul, mind and strength to reach up and grab at his gentle strength?

And you, will you look and think and pray? Or sit, and simply wait?