About a math opinion.

This is a rather interesting article on math. I invite you to read it, and then read my commentary, which is as follows:

I thought the author had a few important points to make; certain others are ridiculous. For example, the claim that computers can do math is quite misleading. Computers compute. Computation is only one part of math. Math is really all about recognizing patterns in a quantitative way. It's not about formulae. No computer that I know can translate a word problem (practically any math problem worth doing has its origins in a word problem) and spit out the answer. You, the human, if you want to use the computer, must translate the word problem yourself; that is a problem of interpretation which requires its own brand of intelligence. While modern education theory is mostly bunk in my opinion, there is one thing I like: the theory of multiple intelligences. I think this idea in its current form was originated by Howard Gardner and here they are:

Linguistic intelligence (as in a poet);
Logical-mathematical intelligence (as in a scientist);
Musical intelligence (as in a composer);
Spatial intelligence (as in a sculptor or airplane pilot);
Bodily kinesthetic intelligence (as in an athlete or dancer);
Interpersonal intelligence (as in a salesman or teacher);
Intrapersonal intelligence (exhibited by individuals with accurate views of themselves).

The reason I like it is because to me it squares with the idea of different gifts that Paul discusses. Naturally, there is overlap between these.

The author's points here: "Writing is the highest form of reasoning. This is a fact. Algebra is not. The proof of this, Gabriela, is all the people in my high school who were whizzes at math but did not know a thing about history and could not write a readable English sentence." is a rather funny example. It is true that there are many people good at math who can't write at all. However, the fact that people can be good at math and not at writing in no way is support for the statement that writing is the highest form of reasoning. To say so is to be guilty of a non sequitur. The author also reasons in a circle. Second, because this is so, the author has just damaged his own case by a bad form of reasoning, thus showing that writing has its own problems. Logic is logic; we get it from the Bible, and its applications, while not exhaustive, are not limited to any one field. You must use logic in English, math, history, music, art, etc. What is a good mathematician? Well, in the current context, I would classify them into two broad groups: those who do research well, and those who do scholarship well. The distinction is this: researchers work on new stuff, while scholars make clear what is already known for the benefit of others. Thus you can have people quite good at one but not the other. It is rare to find someone good at both, though I know at least two. One good scholarly paper is worth a hundred research papers, in my opinion, but maybe that's just because I'm lazy, and prefer to read clear stuff versus unclear stuff.

I think ultimately, the author is committing the fallacy of the false dilemma: either you're good at math or you're good at writing, but not both. Or at least, the author is trying to say that there's no need to be good at math in today's world. In that case, I would dispute the meaning of the word "need." It depends on who you are, and what are your expectations. I believe bachelor's degrees should not be awarded to anyone who hasn't seen the Fundamental Theorem of the Calculus. Why? Because that theorem is responsible for the modern technological age. A bachelor's degree has been traditionally thought of as being "in the liberal arts." Those are the arts that free. Not to know something as important as FTC seems to me to break with the tradition of the liberal arts. Math is a liberal art.

I think if he rephrased himself a bit, he might get on better. I think it's important for everyone to know how to write. It's not important for everyone to know the Spectral Theorem for Hermitian Operators. While you can get on in life knowing the latter and not the former, your usefulness to society is greatly hampered. You may get the great ideas, but if you can't communicate them effectively, they won't go as far. Classically speaking, I think the following are important: grammar (nuts and bolts of a subject), dialectic (or logic; how the nuts and bolts fit together), and rhetoric (how to express yourself clearly in the context of that subject). As I have said, take anything out of there, and the structure is weakened.

Those are my thoughts.

In Christ.

About Dick Cheney's hunting accident.

So what?

Driving

Right on the heels of the last post...

I do think it important to meditate on God's Law. I was doing that on the way back from evening worship (I love evening worship!), and discovered something: good driving keeps the Sixth Commandment; bad driving breaks it. Here is that treasure-trove on the Ten Commandments, the Larger Catechism:

Q. 135. What are the duties required in the sixth commandment?

A. The duties required in the sixth commandment are, all careful studies, and lawful endeavors, to preserve the life of ourselves and others by resisting all thoughts and purposes, subduing all passions, and avoiding all occasions, temptations, and practices, which tend to the unjust taking away the life of any; by just defense thereof against violence, patient bearing of the hand of God, quietness of mind, cheerfulness of spirit; a sober use of meat, drink, physic, sleep, labor, and recreations; by charitable thoughts, love, compassion, meekness, gentleness, kindness; peaceable, mild and courteous speeches and behavior; forbearance, readiness to be reconciled, patient bearing and forgiving of injuries, and requiting good for evil; comforting and succoring the distressed, and protecting and defending the innocent.

Q. 136 What are the sins forbidden in the sixth commandment?

A. The sins forbidden in the sixth commandment are, all taking away the life of ourselves, or of others, except in case of public justice, lawful war, or necessary defense; the neglecting or withdrawing the lawful and necessary means of preservation of life; sinful anger, hatred, envy, desire of revenge; all excessive passions, distracting cares; immoderate use of meat, drink, labor, and recreations; provoking words, oppression, quarreling, striking, wounding, and whatsoever else tends to the destruction of the life of any.

It's pretty clear, isn't it? Bad driving is dangerous, and tends to the unjust taking away of life.

So how do you know if you're a bad driver? Well, I'll tell you what a good driver is. A good driver follows the Smith System. The Smith System has five keys of good driving:

1. Aim high in steering - avoid collisions by seeing, evaluating and acting upon all the information available.

2. Get the big picture - Fewer mistakes are made when you have the complete traffic picture.

3. Keep your eyes moving - Proper scanning techniques separate safe drivers from people who make costly and daily errors.

4. Leave yourself an out - All that separates drivers from a collision is space. Use it to your advantage.

5. Make sure they see you - Seek eye contact and use your warning devices at the proper time.

Among the most common mistakes I see:

1. TAILGATING!!! This is definitely the worst. Which of the above keys does this violate?

2. Cutting people off when changing into a different lane. Again, which keys get trashed?

3. Speeding. You get the drift of my question, I hope. What if you're following someone who is going the speed limit? I claim you should not be impatient with them; they are trying to obey the law. Would you have them break it, just for you?

4. Not signaling for lane changes. Instead of driving in such a way that others can figure out what you're going to do next, make it obvious.

5. Not scanning. I am a bus driver, and also a bus trainer; I train people on the fixed bus routes for Blacksburg Transit. The most important thing for a bus driver is to scan. Scan, scan, scan. That means looking ahead 15 seconds to see what's coming, looking just ahead to the right and left, checking your speed, and checking your mirrors. It's very important that you know what's going on behind you. For example, what do you do if someone is tailgating you? Speed up? No. You increase your following distance. Generally, the rule I've heard nowadays is this: four seconds following distance normally, plus two seconds for every hazard. A hazard would be: night-time, slippery roads, tailgater, etc. You might object, saying, "If I follow that far behind, someone is sure to cut me off, I'll have to slow down, and I'll take a lot longer to get where I'm going." This is incorrect; you will have to slow down a little. However, the amount of time you lose will be seconds, not minutes. Even supposing it happened ten times in one trip (highly unlikely for a short trip), you might lose a whole minute. It's not worth it. The goal is to get there.

Finally, in conjunction with my last post, I have to say I don't follow these instructions the way I should. I need to focus on my shortcomings. But if you, dear readers, are convicted to follow God's law better, because you have been saved already, and not to save yourself, then God will have done some good through me.

In Christ.

The Problem of this World

The answer to life, the universe, and everything. 42, of course.

Actually, to rephrase somewhat, I ask this question: what is wrong with this world? After much study and contemplation, I have the answer, and I am 100% certain it is the correct answer.

The problem with this world is me.

So often I tend to have this critical attitude towards others, as if they were not performing up to some standard. And there may be truth to that at times. But, as I'm learning more and more, I am not usually the person who can help them. Maybe once in a great while I can, when someone really respects my views on things and will listen to me. More often, I just tend to spout off without having the authority.

No, the problem is me. And what is the solution? Your standard Sunday School answer: Jesus Christ.

Now that doesn't mean all the problems with me go away the moment I believe; rather, it means the fight to solve my problems begins. Christianity is a battle; don't let anyone ever tell you otherwise. We battle against the world, the flesh, and the devil. All three of them formidable. But Christ is stronger still; in the end He will overcome.

In Christ.

Revenge on Susan

Susan posted a few problems to solve here.
Just for revenge, I'm going to post a few of my own.

Each of the following sets of propositions can serve as premisses for a valid sorites. For each, find the conclusion. Note: some of these are from Lewis Carroll, and some from Copi and Cohen.

1. a. No one reads the Times unless he is well educated.
    b. No hedgehogs can read.
    c. Those who cannot read are not well educated.

2. a. When I work a logic example without grumbling, you may be sure it is one that I can understand.
    b. These sorites are not arranged in regular order, like the examples I am used to.
    c. No easy example ever makes my head ache.
    d. I can't understand examples that are not arranged in regular order, like the examples I am used to.
    e. I never grumble at an example, unless it gives me a headache.

3. a. Babies are illogical.
    b. Nobody is despised who can manage a crocodile.
    c. Illogical persons are despised.

4. a. No ducks waltz.
    b. No officers ever decline to waltz.
    c. All my poultry are ducks.

5. a. Every one who is sane can do Logic.
    b. No lunatics are fit to serve on a jury.
    c. None of your sons can do Logic.

Five men who were buddies in the last war are having a reunion. They are White, Brown, Peters, Harper, and Nash, who by occupation are printer, writer, barber, neurologist,and heating contractor. By coincidence, they live in the cities of White Plains, Brownsville, Petersburg, Harper's Ferry, and Nashville, but no man lives in the city having a name similar to his, nor does the name of his occupation have the same initial as his name or the name of the city in which he lives.

The barber doesn't live in Petersburg, and Brown is neither a heating contractor nor a printer - nor does he live in Petersburg or Harper's Ferry. Mr. Harper lives in Nashville and is neither barber nor writer. White is not a resident of Brownsville, nor is Nash, who is not a barber nor a heating contractor. With only the information given, determine the name of the city in which Nash resides.

The following is an LSAT-type game.

Given:
1. Frank is the same height as Hank.
2. George is taller than Frank.
3. Eric is taller than Adam.
4. Adam is taller than David and Carl.
5. Bob is shorter than Carl.

Which one of the following must be false?
a. George is taller than Hank.
b. Carl is taller than David.
c. Adam is taller than Frank.
d. David is the same height as Carl.
e. Bob is the same height as Eric.

Lane's Third Blog

When I wrote the title of this blog entry, I couldn't help but rememeber the Fawlty Towers episode where Fawlty is sitting in his office, and turns on Brahms' Third Symphony. He's got the volume up, and his wife tells him to "turn off that racket." To which he replies, "It's not racket, it's Brahms! Brahms' Third Racket."

Anyway, this is an advertisement for Lane's third blog, entitled "The Accent Translation." You can find it here, and there is now a link to it on the right. This is a fantastic idea of Lane's (please follow the link and read the first entry at the bottom for the idea). To my knowledge, using color coding and accenting in this precise manner has not occurred to anyone before; he's breaking new ground here, and I'm excited about Genesis Chapter 1, which Lane has already posted. See for yourself!

In Christ.

Mao Zedong in Hell.

There's a book by Randy Alcorn called Safely Home. It is about Christianity in China, and is an extremely powerful book. In one section, Alcorn portrays what he thinks Hell is like for Mao Zedong. Yes, that means Alcorn believes there is such a thing as Hell. I believe it, too, and it is no joking matter. If there is a hell, then it is for our eternal good that we contemplate it. Mayhaps God will save us from such a horrible fate.

The way Alcorn portrays Hell here does at least two things for me. The first is that I am inspired more and more to trust God to save me. The second is that I realize just how much I wouldn't wish this fate on anyone.

Some would disparage this hell-mongering. They would claim I am trying to scare people into Christianity. They would claim I am trying to make people feel miserable, unworthy, evil, hopeless. To that I would claim, "Guilty as charged!" Without Christ, we all of us are all those things. But in Christ, the picture is not the opposite. The good is so much more good than the evil is evil. I think the Bible uses the pictures both of Heaven and Hell, because it recognizes that human beings respond better to both positive and negative encouragement.

Incidentally, before I quote this section, which is quite long, I should issue a disclaimer. I'm not sure of the legality of quoting such a long section. If someone shows me I should not have done it, I will delete it from this post and simply provide a reference. Here is the quote.

[begin]

Where is my palace? Where are my servants? Does no one know who I am?

The vast, cold darkness cut into his face. It felt like intense frostbite, burning his skin.

I was the most powerful man in Zhongguo. I created the People's Republic. I was the revered father of my country. They worshipped me. I was god! He waited, listening to the silence. Cannot anyone hear me?

His voice disappeared into the great dark void. It did not echo, for there was nothing for it to echo off. It was immediately absorbed into infinite nothingness. His words went no farther than his blistered lips.

A parade of untold millions marched inside his mind's eye. His sentence was to relive the suffering of each of his victims. He had been here over twenty-five years. Every minute of those years he had relived the sufferings he inflicted on others. Every torture his regime inflicted he now received, one after the next after the next. Eventually, perhaps, they would start over, so the millions he had already endured were but the first installment. The pain was unbearable, yet he had no choice but to bear it. There was no escape into unconsciousness - no drug to take, no sleeping pill, no alcohol. That which he had laid upon others was now laid upon him - endlessly, relentlessly.

He longed to pluck out his eyes, to keep from seeing what he saw, to puncture his eardrums to keep from hearing the wailing misery, to pull out his tongue to keep from tasting the awfulness he had legislated. But he had no ability to destroy himself. He had no control now over his destiny, no power over himself or others. There was no one he could command to fix the situation, no one to prepare him an eight-course meal to assuage the eternal hunger, no one to do his work, no one to punish for their errors. No one to salute him, cower at his voice, or bow heads in his presence.

Where is everyone?

Misery loves company, and he had long sought the consolation of others. But all others were still on earth, secure in heaven, or confined to their own private hells at distances immeasurable.

The aloneness was stifling. He could hear nothing but his victims' cries, feel nothing but their pain, see nothing but their blood, taste nothing but their vomit, sense nothing but their torture. He had only himself. He could not enjoy his own company, for he saw himself as he really was. It was an ugly sight, revolting beyond comprehension.

He felt a burning. A fury welled up inside him. Anger and bitterness, unfocused hostility, frustration leading him to lash out. But there was no one to lash out at. No incompetant aide, no dissident, no Christian pastor, no helpless peasant. No one to beat or shoot or hang or starve. No one to cower in fear at the power of the great chairman, architect of the Republic. No one to shine his shoes or rub lotion upon his burning feet.

Grief and rage warred within him. His hell was a growing cancer, gnawing at him, eating away at him, devouring him. He was like a bush that burned yet was not consumed, so the burning could never stop.

He had come to death entirely unprepared - and now it was too late to prepare. If the torture was not enough, a sickening feeling of foreboding had gripped him from his first moments here. He had hoped it would subside, that he would get used to it. He hadn't. It only got worse.

He could see now through all his rationalizations. His arguments against belief in a Creator had never been intellectual ones, as he had claimed. By rejecting a Creator he thought he could rid himself of a Judge. But it had not worked. His atheism had been the opiate of his soul and the executioner of uncalculated millions. But now his comforting atheism could no longer exist, even for a fleeting moment, for he had been forever stripped of the power to deny reality.

He had lived his short todays as if there were no long tomorrows. He had believed the lie that all were accountable to him and he was accountable to none. He had believed the lie that death would slip him into eternal unconsciousness. He knew now - how well he knew - the curse of always being awake, ever alert, unable to allay his suffering with a moment's sleep or distraction.

The winds of hell blew upon him. On them floated sounds of laughter and joy from a place far distant. These voices were torture. Many he recognized as belonging to Christians he had persecuted, worshippers of the Carpenter he had murdered. He relived what he had done to them, this time on the other end of the cattle prod. By the time he had died, while he and all he stood for were in decline, they and all they embraced were in ascent. They had beaten him. Their King had dethroned him even in the other life - how much more in this one.

As they celebrated in their far-off realm, at first he had imagined they were cursing him, celebrating his demise. He thought of them as his eternal enemies who would forever speak of what a great foe he had been to them. But he had come to realize something far worse. They did not curse him. They did not relive his great campaigns against him. No. They simply did not think of him at all. He was unimportant. Insignificant. In the eternal scheme of things, he did not matter.

Not matter? How dare they ignore me! Don't they know who I am?

He had said, "I want there to be no God; I want nothing to do with him." His atheist's prayer had been answered. The everywhere-present God had chosen to withdraw his presence from this single place, turning it into a cosmic desert. This was a ghetto of massive proportions, yet so small it could slip through a single crack in the tiles of heaven. It was located in some distant and empty place, never to be feared or even stumbled upon by the citizens of Charis. His life, with all his supposed accomplishments, was but a puff of smoke, dissipating into nothingness.

Stop what you're doing and listen to me! Stop or I will... I will...

No power to give meaning to a threat. No reason to be listened to. And no one to hear him.

Thirst without water to quench it. Hunger without food to satisfy it. Loneliness without company to alleviate it. There was no God here. He'd gotten his wish. On earth he'd managed to reject God while still enjoying his blessings and provisions. But it was excruciatingly clear now that God was the author of good. Therefore the absence of God meant the absence of good. He could not have it both ways, not here. No God, no good. Forever.

He had wanted a world where no one else was in charge, where no order was forced upon him. He had finally gotten it. He had secretly wondered if there was something beyond death, but if he went to hell, he'd fully expected to rule there. Yet there was no king, for there were no subjects. Only one prisoner - himself - in eternal solitary confinement.

He missed the sound of laughter. There was no laughter here, nor could there be, for laughter cannot exist without joy or hope. An awful realization gripped him. There was no history here. No story line. No opening scene, no developing plot, no climax, no resolution. No character development. No travel, no movement. Only a setting of constant nothingness, going nowhere. Excruciating, eternal boredom. Nothing to distract him from the torment of the eternal now.

He had charmed his friends and cheated his enemies, but death he could not cheat, hell he could not charm. This nameless, ever-shriveling man writhed in terror. Faced with his own deeds, punished by them, he was receiving in himself the penalty for what he had done. He longed for a visit from a foreign dignitary, delivered by a courier, a request for an audience in his illustrious presence. But no. He knew now none would ever come, or even want to. He could not return to Beijing - and knew Beijing itself would soon be gone, a flower withered in a summer's wind. Perhaps it was gone already.

No one to fear him. No one to revere him. No one to hear him. No one to think about him.

He who had claimed to be savior was forever without a Savior. Ignored and insignificant. Empty and embittered and regretful. Without a following. Without a heart. Without a hope.

Forever, time without end.

[end]

If this unsettled you, good! That is precisely what Alcorn wanted. But there is more than one kind of fear. There is terror such as Zedong has in this passage. But there is also the fear of the Lord, which drives out all other fears. And this fear is not a terror; it is a respect and awe of the One who really does have the power to cast you into the pit of Hell.

There is a way out! You need not fear this Hell. You must believe in the God of the Bible, and repent of your sins, and trust on Jesus Christ to save you from your sins.

But a further word of warning: I would be remiss if I did not tell you what it is you do if you repent and trust in God. You are leaving one kind of slavery and warfare for a different kind of slavery and warfare. Christianity is warfare, and if you are a Christian, you are a soldier. Christianity is not peace with the world, the flesh and the devil. You should not expect a life of ease. You must fight this good fight.

And what is the goal of this fight? Heaven, or Charis as Alcorn calls it. Heaven is rest, perfect peace. Communion with God. Rewards beyond anything you can imagine. Think of the most blissful thing that has ever happened to you, and try to imagine that experience multiplied infinitely over, and deepened and broadened. And then I tell you truly, that has not even scratched the surface of what Heaven will be.

In Christ.

Keeping Track of Blogs.

If you're like me, you keep track of several blogs. It takes a while to go and look at all those blogs, and life is too short to keep track of every blog that might interest you. There is a solution, and free at that. It's the JetBrains Omea program. This little gem, which has a freeware version (no expiration date!), will keep track of new posts to blogs you frequent. Alas, it does not automatically keep track of comments. However, it does have a feature on it which allows you to keep track of comments you have posted quite easily. You can "flag" particular posts on particular blogs you want to monitor; there are several colors you can use to flag them. The program allows you to jump right to that post from within the program. This is much easier and faster than going to the blog and scrolling all the way down to the post of interest. I'd recommend this program! You can find it here. Incidentally, one handy little term you should know: RSS feed. Most blogs have this, and it allows programs like Omea to keep track of new posts. Most times, Omea can find it for you automatically (any blogspot blog will work). Other times, you need to be able to find the RSS feed manually. That usually isn't too difficult. Anyway, here is a way to keep track of blogs (which is quite fun) without feeling guilty about spending all that time doing so. So you can procrastinate in other ways...

In Christ.

The Politically Incorrect Guide to Science

This is a book by Tom Bethell, Oxford graduate. Mr. Bethell is a journalist, not a professional scientist, and so some people may be tempted to write him off as a know-nothing. That would only be a sad indication of the over-specialization we see so much around us. For example, someone in analytic number theory would be completely unable even to begin discussing anything with someone in algebraic number theory.

Mr. Bethell has made some incredibly insightful remarks here. One of his central theses is that science has become over-politicized. Mr. Bethell us undoubtedly a right-winger. How does he avoid the charge he is leveling at the left-wingers? By being honest about his bias. The title says it all. I really think that we modern people have forgotten that real people do science, not infallible gods in pretty white lab coats. There's no such thing as no bias. So the only honest thing to do is come right out and say what your bias is.

Here are the topics Mr. Bethell addresses: global warming, nuclear power, the virtues of radiation, the virtues of modern chemicals, DDT, endangered species, African AIDS, cloning, stem cell research, genomes, cancer, supposed "warfare" between science and religion, intelligent design, and evolution.

"Science at its raucous best," as N. David Mermin would say, is when you realize that 10,000 Frenchmen can still be wrong.

I would like to elaborate on one chapter in particular, chapter 4, on modern chemicals. The idea of this chapter is that "hormesis" is an effective antidote to many highly politicized scare tactics. For example, many people realized that dioxin, an herbicide, is toxic. This is true; however, it matters a very great deal what quantity of dosage you encounter. Many people have assumed a linear relationship between dosage and risk: the more you are exposed, the greater the risk, and the less you are exposed, the less the risk. That second statement should read thus: no matter how small the dosage, there is always a risk. But the evidence simply does not support this. In one experiment with rats, the risk factor actually declined once the dosage had gone below a certain level. So Dioxin was beneficial in lower doses.

Now all of this is not to say there aren't some chemicals that are toxic, even lethal, no matter how small the dose. There might be some of those. But Mr. Bethell claims there are precious few such chemicals. Here is a quote:

Perhaps without even realizing it, we acknowledge that toxic chemicals can be beneficial in small doses when we take multi-vitamin pills. Their ingredients are printed on the bottle. One such product lists the following: iodine, phosphorous, magnesium, selenium, zinc, copper, manganese, chromium, molybdenum, potassium, nickel, boron, and vanadium. All of these are toxic substances - at high doses.

As an example perhaps more of you can identify, let us examine Vitamin A. It is a fat-soluble vitamin, as opposed to a water-soluble vitamin. As most people know, it is a very bad idea to overdose on fat-soluble vitamins (though, granted, the acceptable use may be much large than USRDA would have you believe). This is in contrast with water-soluble vitamins, which one can take at much higher doses before any damage occurs. However, even though fat-soluble vitamins are toxic at high doses, it is beneficial at low doses. Our Vitamin A has good effects at low doses.

Without even being able to vocalize it, this one fact has been the reason I do not subscribe to the organic food idea. In order to pronounce any particular chemical toxic in low doses, the scientist would have to perform experiments in which he administered such low doses. But scientists know that low doses increase the number of variables liable for causing whatever effects they see, on account of the other variables increasing in strength relative to the investigated variable. I can easily imagine a scientist setting up an experiment this way: control group with no chemical plus one group with an enormous dose of the chemical. Without the additional group with a low dose, he could very well miss the hormetic effect.

I simply cannot get all that worked up about all the supposed "bad chemicals" all around us. The health "experts" have changed their mind so frequently that one doesn't know what to believe anymore. You know the kind of thing I mean: butter is good, butter is bad, butter is good (continue this pattern as long as you like, and even longer if you're blond)... I have a strong suspicion that all that much worrying is hazardous to your health. For the same reason, I do not subscribe to the extreme forms of conspiracy theories floating around. I personally think some of those theories leave no room for God's providence. It is true that man is depraved, but let us fear God, not men.

Mr. Bethell's book is copiously documented, a fact, which, while not conclusive, is certainly a requirement for credibility in this sort of writing.