Intelligent Design in the Science Classroom
There are several court cases and school board elections in the United States revolving around the issue of the teaching, or even the mere mention, of Intelligent Design in science classrooms. ID is, basically, the idea that the complexity of the world around us shows the influence of an architect; in essence, a divine creator. An example that usually arises is the claim that the human eye could not have evolved because there are too many steps between non-eye and eye. Evolution, supposedly, is sequential, and the fact that a partial eye confers no reproductive advantage, the theory of evolution fails to explain the development of the eye. Only an intelligent designer able to conceive of and construct the entire eye could have brought about the presence of eyes in humans (and other animals.) He did this instantly…no half-measures.
Proponents claim that ID is every much a science as is evolution. At least, ID is no more a religion than is evolution. Therefore, ID should be taught in science class. At a minimum, a statement should be read to science students that the theory of evolution is found wanting in some areas, and Intelligent Design provides the answers.
As a retired science teacher, I find myself in an ironic position. I agree whole-heartedly that ID, or even the statement requested by ID fans, has no place in a science classroom. Yet I discussed ID in my classroom, of my own volition. The difference was, I discussed why ID was out of the realm of science, without actually declaring its truth or falsity.
A recurring theme in my senior physics course was the distinction between religion/belief/philosophy and science. With examples drawn from ancient Greece, from the European eras Galileo, Newton, Darwin, and Einstein, and from twentieth century America, I tried to show how the disciplines differed.
Science deals with observable, repeatable phenomena and provides testable, falsifiable explanations. By definition, an explanation for a specific phenomenon or observation that includes God would not be a valid scientific explanation.
The reason is simple: since God can do anything he wants (or she wants, but we’ll stick with “he” for simplicity) he could make the phenomenon happen or not happen on a whim. Repeatability goes out the window. Similarly, you can’t test for God. To be contrary, suppose that a test does exist for the presence of God. For argument’s sake, we can suppose the test to be the mixing of two liquids, with favourable results being a yellow product. That is, suppose that if we mix the two liquids and get a yellow product, that means God exists. We demonstrate, repeatedly, the positive result: yellow after yellow after yellow. Each time we mix the liquids, the product turns yellow. We say, “See, God exists.” Suddenly, one day, the result is red. What do we say then when we see a result that is contrary to known behaviour of the two liquids? It would be like seeing a falling ball suddenly hovering motionless in the air. We’d call that a miracle (if we had no other physical explanation, such as hidden strings or magnets). But consider: a miracle is evidence of God’s existence. So if the liquids turned yellow or didn’t turn yellow, both results supposedly implied that God exists. Thus the experiment was irrelevant. There can be no test for God.
I tell my students, “I’m not saying that God doesn’t exist, only that there is no scientific test that can confirm it.” The statement “God exists” is philosophical, religious, a statement of belief.
In science, no acceptable explanations for an event can mention God. How did the Grand Canyon form? Explanation: God made it. How was Earth created? God made it. How does haemoglobin carry oxygen? God puts it there. These explanations may be true (who knows?) but are simply not scientific.
A God explanation is an intellectual dead-end for a scientist. And for you, too. Have you watched magic shows? The magician makes a rabbit appear from an empty black hat. Don’t you think to yourself, “How did he do it?” The very act of searching for an explanation shows that you believe that the magician was subject to the same laws of physics as you are, and used no true magic. How disappointing magic shows would be if the true explanation for each trick was “magic”! You might as well not try to figure anything out, if the explanation is “magic”.
Science, the search for physical explanations, deals only with non-God hypotheses. That’s why Intelligent Design is an unacceptable scientific explanation for a phenomenon.
Intelligent Design grew out of (evolved!) from Creation Science. Most creationists were fundamentalists, believers in the literal interpretation of the Bible. They taught that God made the world as described in Genesis, fundamentally as we see it today. He made the mountains, the valleys, the plants, the animals, and the humans. There was no evolution; the Earth was young. Creation Science’s close adherence to the Bible made the religious connection obvious. The US Supreme Court ruled that Creation “Science” could not be taught as a science.
The Intelligent Design proponents try to escape the “religion” label. They say that they are not discussing religion in the classroom (which would be contrary to the US Constitution.) Rather, they are proposing a valid “scientific” explanation for a phenomenon that happens to involve an architect. The distinction between the architect and God is rather tenuous. (And arguing that there is such a distinction is somewhat disingenuous.)
ID looked good at first blush, but fails on a number of planes. As already mentioned, ID requires a deity. But let’s ignore that fatal wound for a minute. ID fails for other reasons. The sequential evolution of the eye can be shown to provide benefits during the intermediate steps. As explained in Dawson’s book The Blind Clockmaker, there are animals on Earth right now possessing “eyes” (or light detecting regions/organs) in a multitude of different shapes and complexities that can be strung together to demonstrate the development of the human eye (or follow alternate paths for the evolution of other eyes, such as that of the octopus or house fly.) The presence of each “partial-eye” is advantageous over the previous step. Second, our eyes, although very good, could have been designed better. The light-sensing cells of the retina are backward, with nerve connections to the brain extending toward the front (i.e. inside the eye) rather than the back. The result is less than optimum light reception, and a blind spot where the bundled nerves pass through the retina on the way to the brain. The “Intelligent” designer was not fully intelligent in the case of the human eye. (Evolution, however, just goes where it goes. The drift is toward improvement, but optimal results are not guaranteed.)
There are many examples where an intelligent designer could have done a better job. Here’s another. Unlike women’s ovaries, men’s testicles hang outside the body, exposing them to potential harm. The reason is that sperm must be formed and stored at below body temperature. Why not just make sperm that “liked” body temperature? Remember, the designer had God-like powers, and God can do anything. He certainly could have made sperm that thrived at 37°C.
At this point, many IDers will say that God must have had some other reason for making eyes or testicles in what appears to be a less efficient manor. This is the old “God moves in mysterious ways” argument. The problem with this damage control spin is a little abstract. “God moves in mysterious ways” makes the original claim of God’s intervention non-falsifiable. Here’s why: when we see an example of something that works as we expect a God would have make it, we say “Look. There’s good evidence for our (God) argument.” When we see something that runs counter to the God-did-it argument, we say “Well, it probably supports the argument too, but we just can’t see the connection.” Thus the God-did-it argument holds regardless of whether we perceive it or not. Evidence is irrelevant.
At a little deeper level, the “mysterious ways” argument is intellectually dishonest. When we announce a connection between the world and what we feel God would have done, we are claiming that humans have the ability to grasp the divine purpose. But when we retreat to “God moves in mysterious ways” we are saying that humans don’t have the ability to grasp the divine purpose. You can’t have it both ways.
I taught all the above, little by little when applicable, to my senior science students. When someone asked “Do you believe in God?” I refused to answer yes or no. My response was that I did not want to influence young person toward either answer. When a student asked “Do you believe in evolution?” my response was, “By using the word “believe” you are asking for my religious position." If the student rephrased the question as "Do you think evolution is a good scientific explanation for the living world as we see it?” my response was, "Yes. Evidence for evolution is wide-spread and overwhelming."
If you ask, “Should science teachers be forced to mention Intelligent Design in their classrooms” my response is “No.” And, if you ask, “Did I mention ID in my classes?” my answer is “Yes”.
Tuesday, December 20, 2005
Sunday, December 04, 2005
God and Why Things Happen
I had an interesting discussion on a car trip last night with my wife Sue and niece, Jenn. We had started with the question of life off the Earth, and touched on parallel universes and extra dimensions, God and science. At one point I mentioned the tube worms and other creatures living around the deep sea vents.Sue: What is the purpose of them being there?
Rob: Do you mean what role do they play in their little ecosystem?
Sue: No, what is the reason they are there?
Rob: Evolution doesn’t happen for a reason, that is, in order to fulfill something. Like giraffes didn’t evolve long necks in order to eat the leaves of tall trees. Its just that longer necked creatures were able to get more food, so stayed healthy, and had more babies. So over the long run, a long-necked creature evolved.
Jenn: So you don’t believe there was a purpose to their evolution.
Rob: “Believe?” Good word, Jenn. You are asking a philosophical question: what is my philosophy or religious position on the matter. Not a question of science.
Jenn: No, no. Science. If giraffes didn’t evolve long necks there would be more leaves left on the trees. They would shade the ground, changing the temperature. They would fall and rot and change the pH. There’s be a different ecosystem.
Rob: Right. Good point. That’s why we have to be careful because when we engineer a change in the ecosystem, a million other things are affected.
Jenn: Right, like adding rabbits to Australia, or using pesticides. So can’t the purpose of the giraffes be that they are needed for that ecosystem?
Rob: But let’s for a moment assume that there are no giraffes. You would say to me “The reason there are no long-necked creatures is that they would eat the high leaves, there would be more sunshine, so the ground would be warmer at the base of the tree. There would be fewer leaves to rot, and the pH would change.
Jenn: (laughs) Same argument.
Rob: Right. Your original argument was, basically, if there are no giraffes, things would be different. When that argument can be used both for and against the point being examined, that argument is valueless as a scientific statement.
Jenn: I see that.
Rob: You could make it into a valid philosophical argument, though. A religious person could say, for example, that if there were no giraffes, conditions would be different and the difference would be bad. Since God would not have wanted the conditions to be bad, God wouldn’t have allowed that (i.e. no giraffes) to happen, and would have created/evolved giraffes in the first place.
The problem with this argument, though, is that, for consistency, it must be applied everywhere. You could say that the malaria mosquito or the TB virus must have been created/evolved for a purpose. So why are we (even “good” religious people) contributing money to eradicate these creatures? Might not we be acting against God’s will?
There are a couple of ways out of this conundrum. One is to say that we are part of God’s creation/evolution, so our purpose was to alter the ecosystem (for the good) by wiping out the bad bugs. Unfortunately, this argument also has too wide a range, because it could be used by the people eradicating the rainforests and polluting the environment, too.
Another escape is the “free will” argument: God gave us free will to do our best to determine what’s good and what’s bad. We see that wiping out giraffes is bad, but wiping out TB is good. (That leaves the question about why God allowed the TB in the first place, if not to test us when we develop the capability of eradicating it. (This heads towards “Why do bad things happen to good people?”, perhaps the deepest, most important religious question.)
Sue: Rob! Pay attention. You’re heading to Niagara falls!
Rob: [cutting across two lanes highway traffic, and driving on the shoulder until we can get into the correct lane] Sorry.
Friday, November 11, 2005
Extra dimensions
Current cutting edge physics talks about the universe being made of eleven or so dimensions, not the three physical and one temperal (x,y,z,t) of Einstein. This concept is very hard to visualize, of course.
One of the best books I have read that helped me get an intuitive grasp of the many dimension idea is Galileo's Finger, by Peter Atkins. I highly recommend the book for thinkers, for people who want to be taken past what they already know.
In my high school classroom, I marry an idea from his book with my own examples to show why extra dimensions arise in physics. In a nutshell:
1. In senior physics, students learn how to solve 2-D collisions. Ball A of a certain mass and velocity hits ball B, with its mass, and velocity, at some angle. The laws of conservation and momentum allow the two final velocities (including direction) to be calculated. Basically, two equations are used to calculate the two unknowns (the two final velocities) from the initial data.
2. What if there were three bodies hitting at EXACTLY the same time? Now there are three unknowns, but still only two equations. So, exact solution can't be calculated. This is the 3-body problem, still unsolved. (We can get approximate solutions by numerical methods, but the exact solution is not known.)
3. How about if one object comes in from the west and hits two identical objects balls lined up in contact north-south? (i.e. ball at 12 o'clock, ball at 6 o'clock touching in the centre of the clock. Other ball comes in from 9 o'clock) This 3-body problem is solvable because of the symmetry. The two stopped balls will pick up the same velociy, different directions but equal angles from 3 o'clock direction.
4. Thus if there is symmetry, we can calculate answers to problems which would otherwise be unsolveable.
5. Atkins points out that a line segment horizontal line segment is equivalent to a vertical line segment. We just rotate it (or turn our head!) Similarly a square and a diamond are equivalent, because one is a rotation of the other. (Turn the square 45 degrees.) Are a square and a hexagon equivalent? No. You can't rotate a square and make it a hexagon. Except that...
6. Draw a square and a cube. The cube is the 3-D object whose shadow is a square. But if you rotate a cube, its shadow can be a hexagon. (To see this, draw a box whose corner is rotated toward you, viewed from slightly above.) Therefore a hexagon and a square can be considered equivalent, or symmetrical, if you think in 3-D instead of 2-D.
7. We have already seen that if you find symmetries you can solve previously unsolveable problems. And we just saw that by viewing a concept from a higher dimension, you can find symmetries that were not apparent (or not there!) in lower dimensions.
8. Physicists are attempting to find formulas to describe the fundamental subatomic particles, and the behaviour of radiation and matter at the very small and large, and quantum theory, and relativity, and gravity (as discussed in general relativity). They haven't succeeded in finding exact solutions to the various equations that combine to describe things. BUT...
9. By working in more directions, symmetries were found that enable solutions.
10. Apparently, solutions exist if you use eleven dimensions.
So, there you are. Like all concepts in science, we find explanations that satisfy us and are useful. Eleven dimensions proves to be useful. Hence, proposing eleven dimensions becomes useful.
Current cutting edge physics talks about the universe being made of eleven or so dimensions, not the three physical and one temperal (x,y,z,t) of Einstein. This concept is very hard to visualize, of course.
One of the best books I have read that helped me get an intuitive grasp of the many dimension idea is Galileo's Finger, by Peter Atkins. I highly recommend the book for thinkers, for people who want to be taken past what they already know.
In my high school classroom, I marry an idea from his book with my own examples to show why extra dimensions arise in physics. In a nutshell:
1. In senior physics, students learn how to solve 2-D collisions. Ball A of a certain mass and velocity hits ball B, with its mass, and velocity, at some angle. The laws of conservation and momentum allow the two final velocities (including direction) to be calculated. Basically, two equations are used to calculate the two unknowns (the two final velocities) from the initial data.
2. What if there were three bodies hitting at EXACTLY the same time? Now there are three unknowns, but still only two equations. So, exact solution can't be calculated. This is the 3-body problem, still unsolved. (We can get approximate solutions by numerical methods, but the exact solution is not known.)
3. How about if one object comes in from the west and hits two identical objects balls lined up in contact north-south? (i.e. ball at 12 o'clock, ball at 6 o'clock touching in the centre of the clock. Other ball comes in from 9 o'clock) This 3-body problem is solvable because of the symmetry. The two stopped balls will pick up the same velociy, different directions but equal angles from 3 o'clock direction.
4. Thus if there is symmetry, we can calculate answers to problems which would otherwise be unsolveable.
5. Atkins points out that a line segment horizontal line segment is equivalent to a vertical line segment. We just rotate it (or turn our head!) Similarly a square and a diamond are equivalent, because one is a rotation of the other. (Turn the square 45 degrees.) Are a square and a hexagon equivalent? No. You can't rotate a square and make it a hexagon. Except that...
6. Draw a square and a cube. The cube is the 3-D object whose shadow is a square. But if you rotate a cube, its shadow can be a hexagon. (To see this, draw a box whose corner is rotated toward you, viewed from slightly above.) Therefore a hexagon and a square can be considered equivalent, or symmetrical, if you think in 3-D instead of 2-D.
7. We have already seen that if you find symmetries you can solve previously unsolveable problems. And we just saw that by viewing a concept from a higher dimension, you can find symmetries that were not apparent (or not there!) in lower dimensions.
8. Physicists are attempting to find formulas to describe the fundamental subatomic particles, and the behaviour of radiation and matter at the very small and large, and quantum theory, and relativity, and gravity (as discussed in general relativity). They haven't succeeded in finding exact solutions to the various equations that combine to describe things. BUT...
9. By working in more directions, symmetries were found that enable solutions.
10. Apparently, solutions exist if you use eleven dimensions.
So, there you are. Like all concepts in science, we find explanations that satisfy us and are useful. Eleven dimensions proves to be useful. Hence, proposing eleven dimensions becomes useful.
Sunday, October 02, 2005
On Astrology
I notice in my Blog profile, my sign of the zodiac is listed. I regret this, but it comes with the territory.
I would rather not have my sign showing, for the simple reason that it reinforces the fraud/delusion/hoax that is astrology. You may say, “Come on, it’s just for fun. Nobody expects that the little reference to astrological sign will have any significant effect.” Try saying something similar to Big Tobacco, which pays hundreds of thousands of dollars to have a star smoke a cigarette once in a picture, just an incidental smoke. Tiny references add up.
Astrology, horoscopes, signs…the whole thing is of course demonstrably false. Experiments show that the location of Mars, say, in the sky when you were born has zero effect on whether you will lose your wallet today or marry a tall, dark stranger tomorrow. Same with the Sun. And to top it off, the dates are wrong. I’m supposed to be a Virgo, meaning that the Sun was in Virgo when I was wrong. Well, it wasn’t. ALL the dates are wrong. Yours, too. That means you have been reading the wrong horoscope in the newspaper all your life. You’ve been waiting for, or avoiding (they cover themselves by giving two options) the wrong person all this time!
Seriously, the fact that so many people accept astrology (and ghosts, ESP, werewolves, psychic fairs, etc.) as valid is disconcerting to me…especially as I am a physics teacher. Carl Sagan said “Extraordinary claims require extraordinary evidence before they should be accepted.” I find it unfortunate that so many people accept stuff for which there is no evidence or even evidence to the contrary.
Pertinent quotes on this subject:
Sagan – “Don’t be so open-minded that your brains fall out.”
Person sitting before a “psychic”, after being asked his name, “Why do you need to ask?”
Me: Did ANYBODY forecast 9-11? (Answer: no.)
I notice in my Blog profile, my sign of the zodiac is listed. I regret this, but it comes with the territory.
I would rather not have my sign showing, for the simple reason that it reinforces the fraud/delusion/hoax that is astrology. You may say, “Come on, it’s just for fun. Nobody expects that the little reference to astrological sign will have any significant effect.” Try saying something similar to Big Tobacco, which pays hundreds of thousands of dollars to have a star smoke a cigarette once in a picture, just an incidental smoke. Tiny references add up.
Astrology, horoscopes, signs…the whole thing is of course demonstrably false. Experiments show that the location of Mars, say, in the sky when you were born has zero effect on whether you will lose your wallet today or marry a tall, dark stranger tomorrow. Same with the Sun. And to top it off, the dates are wrong. I’m supposed to be a Virgo, meaning that the Sun was in Virgo when I was wrong. Well, it wasn’t. ALL the dates are wrong. Yours, too. That means you have been reading the wrong horoscope in the newspaper all your life. You’ve been waiting for, or avoiding (they cover themselves by giving two options) the wrong person all this time!
Seriously, the fact that so many people accept astrology (and ghosts, ESP, werewolves, psychic fairs, etc.) as valid is disconcerting to me…especially as I am a physics teacher. Carl Sagan said “Extraordinary claims require extraordinary evidence before they should be accepted.” I find it unfortunate that so many people accept stuff for which there is no evidence or even evidence to the contrary.
Pertinent quotes on this subject:
Sagan – “Don’t be so open-minded that your brains fall out.”
Person sitting before a “psychic”, after being asked his name, “Why do you need to ask?”
Me: Did ANYBODY forecast 9-11? (Answer: no.)
A Challenge for the Reader
I have been working on a science fiction novel recently. To help me, I bought most of the How-To-Write-A-Novel books at the local bookstore. Now when I read novels, instead of being able to enjoy them, I find myself looking to see if the author followed the instructions in the books.
I also do this with movies, which are novels writ small. One technique that I notice is how the movies tell us the backstory, the background of the major characters and how they got to the position they occupy when the movie begins. Usually one character will say to another, in the first few minutes, “I know you have been a cop for the last five years…” or “Remember when we were together in college and you fell for that girl?” The characters are really telling us, the viewers. It’s so obvious when you know what to look for.
Something really clever, though, is the way well-written movies set up later events or conversations by an earlier image. I don’t mean the obvious way where, in a murder mystery, the camera lingers on an upside down book. You just KNOW that when the hero wraps up the case, he or she will link the book to the murderer.
No, I’m talking about something deeper. Let me illustrate what I mean. Many superb examples occur in one of the best-written movies, The Right Stuff. For instance, near the beginning Chuck Yeager gets knocked off his horse by a cactus plant. Did you know that it was the SECOND time we saw his arm get struck by a cactus plant? Find the earlier interaction, which must surely have been in the script to set us up, if only subliminally, for the bigger one. Others are needed to make sure the viewer is informed. When you see Glamorous Glennis painted on the plane, how do we know who Glennis is? The author made sure we heard Yeager call his wife by name earlier. How do we know the CEO of Life Magazine is important? We saw Cooper reading an issue of Life earlier (twice). How about Glenn’s humming during his descent…when did you hear that before? And look at Cooper sleeping in his capsule before its launch…when did you see that before? Another purpose of this technique is to hint what is to come. What did Cooper foreshadow when he dropped a tiny toy capsule into Gus’s glass of water? I can find over a dozen examples where the screenwriter or director set up a later event by an earlier reference. I challenge you to find them (and enjoy once again an excellent movie.)
I have been working on a science fiction novel recently. To help me, I bought most of the How-To-Write-A-Novel books at the local bookstore. Now when I read novels, instead of being able to enjoy them, I find myself looking to see if the author followed the instructions in the books.
I also do this with movies, which are novels writ small. One technique that I notice is how the movies tell us the backstory, the background of the major characters and how they got to the position they occupy when the movie begins. Usually one character will say to another, in the first few minutes, “I know you have been a cop for the last five years…” or “Remember when we were together in college and you fell for that girl?” The characters are really telling us, the viewers. It’s so obvious when you know what to look for.
Something really clever, though, is the way well-written movies set up later events or conversations by an earlier image. I don’t mean the obvious way where, in a murder mystery, the camera lingers on an upside down book. You just KNOW that when the hero wraps up the case, he or she will link the book to the murderer.
No, I’m talking about something deeper. Let me illustrate what I mean. Many superb examples occur in one of the best-written movies, The Right Stuff. For instance, near the beginning Chuck Yeager gets knocked off his horse by a cactus plant. Did you know that it was the SECOND time we saw his arm get struck by a cactus plant? Find the earlier interaction, which must surely have been in the script to set us up, if only subliminally, for the bigger one. Others are needed to make sure the viewer is informed. When you see Glamorous Glennis painted on the plane, how do we know who Glennis is? The author made sure we heard Yeager call his wife by name earlier. How do we know the CEO of Life Magazine is important? We saw Cooper reading an issue of Life earlier (twice). How about Glenn’s humming during his descent…when did you hear that before? And look at Cooper sleeping in his capsule before its launch…when did you see that before? Another purpose of this technique is to hint what is to come. What did Cooper foreshadow when he dropped a tiny toy capsule into Gus’s glass of water? I can find over a dozen examples where the screenwriter or director set up a later event by an earlier reference. I challenge you to find them (and enjoy once again an excellent movie.)
Saturday, July 16, 2005
Russell and Godel - What's so important?
A former student emailed me about Russell's discovery of the inconsistency inherent in considering the set of all sets that don't contain themselves. "What's all the fuss?", he asked.
I mentioned how this led Godel to the discovery and proof that in any formal system (like geometry) there are statements that have been proved to be true, statements that have not yet been proved to be true but are provable, and, unfortunately (and this is the big shocker!) true statements that will never be able to be proved to be true (and we won't know which of the unproved statements belong in this category.)
He still wondered why this was so important. Here's my response.
Imagine you have some organized system, like geometry. You start with some axioms (assumptions), and derive theorems. Each of the theorems is proved. You KNOW therefore that your system is consistent. Sometimes you make lucky guesses by seeing patterns, so you propose new theorems, but you call them postulates because you haven't proved them yet (like the Four Colour Map Postulate or the Congruence Postulates). Eventually, either a counter-example is discovered so the postulate is dumped, or you prove the theorem. The FCM postulate is now the FCM Theorem because it has been proved. The conguence postulates remain unproved. We use them, though, but in the back of our minds we have that tiny reservation that everything proven using congruent triangles as an intermediate step is suspect. Our dream, of course, is completion: we prove all true theorems in our system.
What if the system has an infinite number of possible theorems. OK, so we can't get completion in a finite time, but completion (at the end of time!) is possible in principle.
BUT, suppose (heaven forbid!) that there are true theorems in the system that are forever unprovable and YOU DON'T KNOW WHICH ONES THEY ARE!
You would be calling them postulates because you haven't proved them yet, but you have a gut feeling that they are true, so you are devoting time to proving them. This time will be ultimately wasted, even if you devote an INFINITE amount of time, because the statement you are trying to prove happens to be one of the unprovable statements.
Russell/Godel's work showed that this horrendous situation exists in ALL formal systems. (Formal=axiom/theorem/ proof system.) There will ALWAYS be true but unprovable statements, so you will never know the system is complete. Persistance is futile!
This was a great shock to mathematicians and logicians. It's like discovering that the earth is not the centre of the universe, or that humans evolved from non-humans. Ever since Euclid, mathematicians delighted in thinking of their discipline has solid and objective. Opposite angles are equal not because we want them to be so, or some king demands them to be so, but because we can PROVE them to be so. What fantastic advances came from the development of formal systems: number theory, set theory, calculus, etc. I think it's more than just the worry that a mathematician might be wasting time trying to prove a true-bue-unprovable-theorum. It's deeper. What makes THAT theorem (i.e. the unprovable one) different from the other proveable theorems? No one will ever know! --sigh--
A former student emailed me about Russell's discovery of the inconsistency inherent in considering the set of all sets that don't contain themselves. "What's all the fuss?", he asked.
I mentioned how this led Godel to the discovery and proof that in any formal system (like geometry) there are statements that have been proved to be true, statements that have not yet been proved to be true but are provable, and, unfortunately (and this is the big shocker!) true statements that will never be able to be proved to be true (and we won't know which of the unproved statements belong in this category.)
He still wondered why this was so important. Here's my response.
Imagine you have some organized system, like geometry. You start with some axioms (assumptions), and derive theorems. Each of the theorems is proved. You KNOW therefore that your system is consistent. Sometimes you make lucky guesses by seeing patterns, so you propose new theorems, but you call them postulates because you haven't proved them yet (like the Four Colour Map Postulate or the Congruence Postulates). Eventually, either a counter-example is discovered so the postulate is dumped, or you prove the theorem. The FCM postulate is now the FCM Theorem because it has been proved. The conguence postulates remain unproved. We use them, though, but in the back of our minds we have that tiny reservation that everything proven using congruent triangles as an intermediate step is suspect. Our dream, of course, is completion: we prove all true theorems in our system.
What if the system has an infinite number of possible theorems. OK, so we can't get completion in a finite time, but completion (at the end of time!) is possible in principle.
BUT, suppose (heaven forbid!) that there are true theorems in the system that are forever unprovable and YOU DON'T KNOW WHICH ONES THEY ARE!
You would be calling them postulates because you haven't proved them yet, but you have a gut feeling that they are true, so you are devoting time to proving them. This time will be ultimately wasted, even if you devote an INFINITE amount of time, because the statement you are trying to prove happens to be one of the unprovable statements.
Russell/Godel's work showed that this horrendous situation exists in ALL formal systems. (Formal=axiom/theorem/ proof system.) There will ALWAYS be true but unprovable statements, so you will never know the system is complete. Persistance is futile!
This was a great shock to mathematicians and logicians. It's like discovering that the earth is not the centre of the universe, or that humans evolved from non-humans. Ever since Euclid, mathematicians delighted in thinking of their discipline has solid and objective. Opposite angles are equal not because we want them to be so, or some king demands them to be so, but because we can PROVE them to be so. What fantastic advances came from the development of formal systems: number theory, set theory, calculus, etc. I think it's more than just the worry that a mathematician might be wasting time trying to prove a true-bue-unprovable-theorum. It's deeper. What makes THAT theorem (i.e. the unprovable one) different from the other proveable theorems? No one will ever know! --sigh--
Saturday, March 26, 2005
General Relativity Lite
When I taught secondary school physics, I always tried to take the students a little farther than required by curriculum guidelines. The goal was to give them just enough so that future learning might be easier. In complex topics such as relativity, cosmology, string theory, fractals, or chaos, the aim was turn on in their head a little light bulb so they might say “OK, I sort of get it.” I’ll try that here with general relativity. It's a little tricky without a diagram, but do you want to try it?
General Relativity: Curved space and a Theory for Gravity
Background (and you don’t really need this)
You may remember that an object’s weight is mg, where m is the mass and g is the Earth’s gravitational field strength. Remember also that Newton’s second law is F = ma. A subtle point about these formulas is that the two m’s needn’t be the same thing. The m in mg is the gravitational mass, that quality of a body that causes it to be attracted to another object. The m in F=ma is the inertial mass, that quality of a body that causes it to resist being accelerated. Writing g in N/kg and giving it a value for Earth’s surface of 9.8 N/kg gives both the m’s the same unit (kg) and the same value (because a N/kg equals a m/s2, and the gravitational acceleration is 9.8 m/s2 down at Earth’s surface.)
Does it actually matter that these m’s might be different? Not for general relativity, because Einstein started general relativity with the assumption that they ARE the same thing. That led to …
Curvature of Space
Being in an accelerated frame of reference, like a box accelerating "upward" in empty space at 9.8 m/s2 is equivalent to being in a gravitational field where g=9.8 N/kg. That is, you can’t tell the difference. All experiments must come out the same. If you release a ball in that accelerating box, it seems to fall to the floor. (It travels up with the speed it had in your hand, but the floor’s speed is increasing, so the floor comes up and hits the ball. To you inside, it looks as if the ball is falling.)
But what if you release two balls, one from each outstretched hand? In the box, the balls fall on parallel paths to the floor. They hit the ground the same distance apart as they were when you released them. But on Earth’s surface the balls fall toward Earth’s centre, so should converge. But Einstein supposed that both experiments should come out the same. To rescue the assumption, he makes a great intellectual leap (but one that is simple and logical.) He says that in the gravitational field case, the balls DO fall on parallel lines, EVEN THOUGH they appear to be converging, because space is curved! How does this work? Imagine you and your friend walking north on Earth’s surface. You are walking parallel to your friend but converging. So parallel lines converge on (positively) curved surfaces. If VOLUME is curved, that could happen in space. So Einstein proposes that space is curved in the vicinity of masses.
So what’s gravity? Remember dropping the ball in the box that was accelerating upward in empty space? Inside, you observe (and feel) a force down even though there was really no force down on objects in the box. (Same thing in a rotating frame of reference…you feel a force to the outside (which you call centrifugal force) even though there is no such force. Objects in rotating frames of reference are tending to travel STRAIGHT, the paths they travel in the absence of force.) In accelerated frames of reference fictitious forces are felt.
Are you ready for General Gelativity Lite - An Explanation for Gravity?
Gravity
If space is curved, then when you think you are travelling a straight line, you are actually travelling a curved path (through space-time, actually). So when you think you are in a non-accelerated frame of reference, you are really in an accelerated frame of reference. Therefore you feel a fictitious force. That “force” is gravity.
When I taught secondary school physics, I always tried to take the students a little farther than required by curriculum guidelines. The goal was to give them just enough so that future learning might be easier. In complex topics such as relativity, cosmology, string theory, fractals, or chaos, the aim was turn on in their head a little light bulb so they might say “OK, I sort of get it.” I’ll try that here with general relativity. It's a little tricky without a diagram, but do you want to try it?
General Relativity: Curved space and a Theory for Gravity
Background (and you don’t really need this)
You may remember that an object’s weight is mg, where m is the mass and g is the Earth’s gravitational field strength. Remember also that Newton’s second law is F = ma. A subtle point about these formulas is that the two m’s needn’t be the same thing. The m in mg is the gravitational mass, that quality of a body that causes it to be attracted to another object. The m in F=ma is the inertial mass, that quality of a body that causes it to resist being accelerated. Writing g in N/kg and giving it a value for Earth’s surface of 9.8 N/kg gives both the m’s the same unit (kg) and the same value (because a N/kg equals a m/s2, and the gravitational acceleration is 9.8 m/s2 down at Earth’s surface.)
Does it actually matter that these m’s might be different? Not for general relativity, because Einstein started general relativity with the assumption that they ARE the same thing. That led to …
Curvature of Space
Being in an accelerated frame of reference, like a box accelerating "upward" in empty space at 9.8 m/s2 is equivalent to being in a gravitational field where g=9.8 N/kg. That is, you can’t tell the difference. All experiments must come out the same. If you release a ball in that accelerating box, it seems to fall to the floor. (It travels up with the speed it had in your hand, but the floor’s speed is increasing, so the floor comes up and hits the ball. To you inside, it looks as if the ball is falling.)
But what if you release two balls, one from each outstretched hand? In the box, the balls fall on parallel paths to the floor. They hit the ground the same distance apart as they were when you released them. But on Earth’s surface the balls fall toward Earth’s centre, so should converge. But Einstein supposed that both experiments should come out the same. To rescue the assumption, he makes a great intellectual leap (but one that is simple and logical.) He says that in the gravitational field case, the balls DO fall on parallel lines, EVEN THOUGH they appear to be converging, because space is curved! How does this work? Imagine you and your friend walking north on Earth’s surface. You are walking parallel to your friend but converging. So parallel lines converge on (positively) curved surfaces. If VOLUME is curved, that could happen in space. So Einstein proposes that space is curved in the vicinity of masses.
So what’s gravity? Remember dropping the ball in the box that was accelerating upward in empty space? Inside, you observe (and feel) a force down even though there was really no force down on objects in the box. (Same thing in a rotating frame of reference…you feel a force to the outside (which you call centrifugal force) even though there is no such force. Objects in rotating frames of reference are tending to travel STRAIGHT, the paths they travel in the absence of force.) In accelerated frames of reference fictitious forces are felt.
Are you ready for General Gelativity Lite - An Explanation for Gravity?
Gravity
If space is curved, then when you think you are travelling a straight line, you are actually travelling a curved path (through space-time, actually). So when you think you are in a non-accelerated frame of reference, you are really in an accelerated frame of reference. Therefore you feel a fictitious force. That “force” is gravity.
In Twenty Five Words or Less
If this phrase means something to you, welcome to the over-50 club! These days (i.e. for the last 35 years!) most contests that people enter by writing their names on a coupon or an entry blank are sweepstakes. When I was young, contests on the back of cereal boxes required some additional element, such as drawing a picture, writing a joke, or composing a poem. I must have been about ten when I entered a contest printed on the back of a box of Nestle's Quik, a chocolate milk powder. I had to write, in twenty five words or less, why I like Nestle's Quik. I don't remember what I wrote, but I won a watch!
It was disappointing that, a few years later, the contests changed to becoming straight draws. (Of course, my earlier win could have been drawn from the hat, too...I'll never know.) Evidently, the Canadian government very strongly disagreed with the change, because they brought in the infamous skill-testing question rule. Apparently, voters (or some prominent legislators) objected strongly to people winning money without actually demonstrating that they deserved the prize. From then on, to claim the prize you had to earn your prize by computing 9 times 8 divided by 4 minus 3.
I still see the skill-testing question on some sweepstakes entry blanks, so I guess the law is still on the books. I wonder if it has ever been enforced.
If this phrase means something to you, welcome to the over-50 club! These days (i.e. for the last 35 years!) most contests that people enter by writing their names on a coupon or an entry blank are sweepstakes. When I was young, contests on the back of cereal boxes required some additional element, such as drawing a picture, writing a joke, or composing a poem. I must have been about ten when I entered a contest printed on the back of a box of Nestle's Quik, a chocolate milk powder. I had to write, in twenty five words or less, why I like Nestle's Quik. I don't remember what I wrote, but I won a watch!
It was disappointing that, a few years later, the contests changed to becoming straight draws. (Of course, my earlier win could have been drawn from the hat, too...I'll never know.) Evidently, the Canadian government very strongly disagreed with the change, because they brought in the infamous skill-testing question rule. Apparently, voters (or some prominent legislators) objected strongly to people winning money without actually demonstrating that they deserved the prize. From then on, to claim the prize you had to earn your prize by computing 9 times 8 divided by 4 minus 3.
I still see the skill-testing question on some sweepstakes entry blanks, so I guess the law is still on the books. I wonder if it has ever been enforced.
Sunday, January 30, 2005
To Discover Magazine: It's about time.
I finished high school in 1968. The physics textbook we used was the P.S.S.C. text, an American textbook. There were no inches, miles, feet, or pounds in that book.
It is now 2005, 37 years later. Yet Discover Magazine, my favourite science magazine, still uses those units, instead of metres, kilometres, and kilograms. Two entire generations of American children have grown up with the metric system in science. When will Discover Magazine slide into the twenty-first century and realize that American adults and youth are ready to read scientific articles that contain the units as the rest of the world uses; indeed, the same system of measurements that the scientists in their own country use daily?
I finished high school in 1968. The physics textbook we used was the P.S.S.C. text, an American textbook. There were no inches, miles, feet, or pounds in that book.
It is now 2005, 37 years later. Yet Discover Magazine, my favourite science magazine, still uses those units, instead of metres, kilometres, and kilograms. Two entire generations of American children have grown up with the metric system in science. When will Discover Magazine slide into the twenty-first century and realize that American adults and youth are ready to read scientific articles that contain the units as the rest of the world uses; indeed, the same system of measurements that the scientists in their own country use daily?
Lucky to have been a teacher
This is my last year teaching. I am so lucky to have been in this profession. Imagine being able to tell people about things you find interesting every day. When you return from a good movie, don't you want to tell everyone about it, persuade them to go see it, too? That's the way it has been for me in physics, computers, science, astronomy, math.
And I have been so fortunate to be able to live out fantasies: waving my hands in front of the junior band is the equivalent of conducting a symphony orchestra; my girl's baseball team is my Blue Jays; when directing a musical, I'm standing on Broadway.
I have had a decent salary and great holidays. Of course, the general public doesn't know I marked papers and developed handouts, on average, about 16 hours a week at home. That's just the way it is, teachers work longer hours than anyone realizes. But I'm not complaining, just stating.
If you like interacting with youth, creating intellectual resources, teaching something different every day, you could do worse than enter the teaching profession. You must be able to handle change, be willing to bring your work home with you, and have something prepared for every period of every day. (Nothing is worse, or more pressure-inducing, than facing 30 young people with nothing for them to do!)
I have been so lucky to have been able to help a couple of generations of young people get a start in life. The amazing thing is that someone has actually paid me to spend 32 years doing what I love. I hope you are as fortunate.
-RS
This is my last year teaching. I am so lucky to have been in this profession. Imagine being able to tell people about things you find interesting every day. When you return from a good movie, don't you want to tell everyone about it, persuade them to go see it, too? That's the way it has been for me in physics, computers, science, astronomy, math.
And I have been so fortunate to be able to live out fantasies: waving my hands in front of the junior band is the equivalent of conducting a symphony orchestra; my girl's baseball team is my Blue Jays; when directing a musical, I'm standing on Broadway.
I have had a decent salary and great holidays. Of course, the general public doesn't know I marked papers and developed handouts, on average, about 16 hours a week at home. That's just the way it is, teachers work longer hours than anyone realizes. But I'm not complaining, just stating.
If you like interacting with youth, creating intellectual resources, teaching something different every day, you could do worse than enter the teaching profession. You must be able to handle change, be willing to bring your work home with you, and have something prepared for every period of every day. (Nothing is worse, or more pressure-inducing, than facing 30 young people with nothing for them to do!)
I have been so lucky to have been able to help a couple of generations of young people get a start in life. The amazing thing is that someone has actually paid me to spend 32 years doing what I love. I hope you are as fortunate.
-RS
Tuesday, December 14, 2004
Here in Canada the Supreme Court has just ruled that the refusal to allow gays to marry is discriminatory and unconstitutional. It has affirmed that a specific church may refuse to provide a service if that marriage contravenes that religion's edicts. But the government cannot deny civil marriage.
I am proud of the court, and the way the Prime Minister is handling the issue. He has announced a free vote on a law OK'ing the removal of "opposite sex" from the marriage definition BUT has said that the cabinet is ordered to support the bill. (I might take issue with the general principle that members of parliament should ever be forced to support a government position regardless of what they think is right or what they feel their constituents want. But that's another issue.)
Both Supreme Court and the PM have walked a sensible line. The court ruled wisely by reaffirming freedom of religion while making sure that discrimination against homosexuals cannot be made by government. (I disgree with discriminatory church policies. But that, too, is another issue.) And the PM announced that MP's can vote their conscience but gave a clear message that the cabinet is expected to support gay marriage. This is a courageous (and just) position.
I am proud of the court, and the way the Prime Minister is handling the issue. He has announced a free vote on a law OK'ing the removal of "opposite sex" from the marriage definition BUT has said that the cabinet is ordered to support the bill. (I might take issue with the general principle that members of parliament should ever be forced to support a government position regardless of what they think is right or what they feel their constituents want. But that's another issue.)
Both Supreme Court and the PM have walked a sensible line. The court ruled wisely by reaffirming freedom of religion while making sure that discrimination against homosexuals cannot be made by government. (I disgree with discriminatory church policies. But that, too, is another issue.) And the PM announced that MP's can vote their conscience but gave a clear message that the cabinet is expected to support gay marriage. This is a courageous (and just) position.
Wednesday, November 10, 2004
No coat hooks, part 2
Twenty years ago, when VCR's were new, my school had once player. It was kept in a geography classroom on the second floor, just overtop of my physics classroom. There was a tree outside the window. One night, someone climbed the tree, broke a window, and stole the VCR. There had been intruder sensors in the halls, but this enterprising thief beat the system by entering and leaving the upstairs window via the tree.
How did the principal respond? He had the tree cut down! Because our school was ringed with windows (it was built before the period of fortress-like schools with tiny windows), cutting down the tree reduced the number of accessible windows from about 250 to 249. I couldn't believe this ridiculous over-reaction.
Don't you think this story, although less tragic, is similar to that of the removal of the coat hooks mentioned in the previous posting?
One difference is that the tree decision was made by one person. Nowadays, I think it's the lawyers who call the shots. Lawyers told our board of education that teachers were not to be taking students to Europe during the March Break (during holidays!) because if there was a terrorist attack somewhere and the trip got cancelled, the students might lose their deposits and the school board would get sued. So, no more educational trips.
I had taken students to Greece, Italy, and Spain. I protested. I got a letter from the tour company saying that money would be refunded if a government travel alert was sounded for the trip destination. The board official responded that the students would be too disappointed if a trip was cancelled so they were not going to allow the possible disapointment to occur! I guess they felt that no one would be disappointed if there were no trip offered at all. Thank you Board of Education lawyers.
Probably it was the lawyers who recommended removing the hooks. Imagine, they would have said, what would happen if there were a repeat of that tragic situation: what if a student in this board of education were killed by being hung on a coat hook? The parents' lawyers would say in court "You KNEW that a student had been killed on a coat hook previously, yet you DID NOTHING to prevent it happening in your schools?"
The darn thing is, the lawyers would be right. That argument would win, wouldn't it? So what's wrong. The lawyer's advise was probably good. By following the advise the board was acting in its own best interest, and, perhaps, in a now-not-to-be-killed child's best interest, too. Yet I can't help thinking that the removal of the coat hooks was a dumb overreaction to an extremely rare event. If that's so, where is the flaw in the logic? How do we fix this paradox?
Twenty years ago, when VCR's were new, my school had once player. It was kept in a geography classroom on the second floor, just overtop of my physics classroom. There was a tree outside the window. One night, someone climbed the tree, broke a window, and stole the VCR. There had been intruder sensors in the halls, but this enterprising thief beat the system by entering and leaving the upstairs window via the tree.
How did the principal respond? He had the tree cut down! Because our school was ringed with windows (it was built before the period of fortress-like schools with tiny windows), cutting down the tree reduced the number of accessible windows from about 250 to 249. I couldn't believe this ridiculous over-reaction.
Don't you think this story, although less tragic, is similar to that of the removal of the coat hooks mentioned in the previous posting?
One difference is that the tree decision was made by one person. Nowadays, I think it's the lawyers who call the shots. Lawyers told our board of education that teachers were not to be taking students to Europe during the March Break (during holidays!) because if there was a terrorist attack somewhere and the trip got cancelled, the students might lose their deposits and the school board would get sued. So, no more educational trips.
I had taken students to Greece, Italy, and Spain. I protested. I got a letter from the tour company saying that money would be refunded if a government travel alert was sounded for the trip destination. The board official responded that the students would be too disappointed if a trip was cancelled so they were not going to allow the possible disapointment to occur! I guess they felt that no one would be disappointed if there were no trip offered at all. Thank you Board of Education lawyers.
Probably it was the lawyers who recommended removing the hooks. Imagine, they would have said, what would happen if there were a repeat of that tragic situation: what if a student in this board of education were killed by being hung on a coat hook? The parents' lawyers would say in court "You KNEW that a student had been killed on a coat hook previously, yet you DID NOTHING to prevent it happening in your schools?"
The darn thing is, the lawyers would be right. That argument would win, wouldn't it? So what's wrong. The lawyer's advise was probably good. By following the advise the board was acting in its own best interest, and, perhaps, in a now-not-to-be-killed child's best interest, too. Yet I can't help thinking that the removal of the coat hooks was a dumb overreaction to an extremely rare event. If that's so, where is the flaw in the logic? How do we fix this paradox?
There are no coat hooks in my school
About 10 years ago a little boy in an Ontario elementary school was lifted up and suspended on a coat hook. He suffocated. Police were unable to find who killed him. Now all the coat hooks in all the washrooms in all the schools, elementary and secondary, in my board of education have been removed.
This brings up an interesting, though unsettling, question: was the removal of all the coat hooks a vast over-reaction? In over 200 years of public education in Canada, one student in one school was killed on a coat hook. Now, intellectually, it is hard to argue against a position that if the removal of the hooks saves even one child, the policy is worthwhile. How can you measure the cost of a life of a child against the inconvenience of hot being able to hang a coat or jacket on a hook?
On the other hand, as callous as it seems, we might say that there are many ways and times, in 200 years, that someone can be killed, and you can't stop them all. There are more children killed falling down stairs than being hung on coat hooks, and we still build multistory schools.
Sometimes a reality check is needed.
About 10 years ago a little boy in an Ontario elementary school was lifted up and suspended on a coat hook. He suffocated. Police were unable to find who killed him. Now all the coat hooks in all the washrooms in all the schools, elementary and secondary, in my board of education have been removed.
This brings up an interesting, though unsettling, question: was the removal of all the coat hooks a vast over-reaction? In over 200 years of public education in Canada, one student in one school was killed on a coat hook. Now, intellectually, it is hard to argue against a position that if the removal of the hooks saves even one child, the policy is worthwhile. How can you measure the cost of a life of a child against the inconvenience of hot being able to hang a coat or jacket on a hook?
On the other hand, as callous as it seems, we might say that there are many ways and times, in 200 years, that someone can be killed, and you can't stop them all. There are more children killed falling down stairs than being hung on coat hooks, and we still build multistory schools.
Sometimes a reality check is needed.
Sunday, October 24, 2004
Are the religious right right?
CBC Radio ran an interesting program today in which a committed, evangelical, fundamentalist Christain minister took the CBC reporter into his home for a week. The program, told entirely in alternating first-person accounts, related how they came to respect each other even though their viewpoints about God, homosexuals, abortion, G.W.Bush, and almost everything else, were so different. Each told how wary they initially were about each other, how they became friends, and respected the other (even though his view was wrong!)
Here's what bothers me a little about the certainty of strongly religious people. Throughout history, religious people have always been strongly convinced of the correctness of their own beliefs. A while ago, African Americans were unworthy of treatment as humans; before that Native Americans, witches, heretics, "infidels" in the holy lands. Jews have been persecuted by Christians for a couple of millennia. Church doctrines have changed over time.
At each instant in history, I will bet that committed religious people have always said that they were certain their beliefs were true. They would have said that those who lived before them were misguided; that, in fact, EVERYONE who thinks differently is wrong.
My question to an evangelical, fundamentalist person of any religion is this. Isn't it worth considering that all of the people in those earlier eras felt as strongly that they are absolutely right as you do? You have been born and raised (or otherwise come) to accept certain tenets as absolute truths. If you are truly open-minded and rational, shouldn't you acknowledge that there is a rather low probability that you happen to have been born at just the perfect time in history that your generation was taught the absolute truth, while all those who came before (or believe different things now) are the ones who are wrong? How can honest, clear-thinking, fair evangelicals be so certain of the correctness of their positions?
CBC Radio ran an interesting program today in which a committed, evangelical, fundamentalist Christain minister took the CBC reporter into his home for a week. The program, told entirely in alternating first-person accounts, related how they came to respect each other even though their viewpoints about God, homosexuals, abortion, G.W.Bush, and almost everything else, were so different. Each told how wary they initially were about each other, how they became friends, and respected the other (even though his view was wrong!)
Here's what bothers me a little about the certainty of strongly religious people. Throughout history, religious people have always been strongly convinced of the correctness of their own beliefs. A while ago, African Americans were unworthy of treatment as humans; before that Native Americans, witches, heretics, "infidels" in the holy lands. Jews have been persecuted by Christians for a couple of millennia. Church doctrines have changed over time.
At each instant in history, I will bet that committed religious people have always said that they were certain their beliefs were true. They would have said that those who lived before them were misguided; that, in fact, EVERYONE who thinks differently is wrong.
My question to an evangelical, fundamentalist person of any religion is this. Isn't it worth considering that all of the people in those earlier eras felt as strongly that they are absolutely right as you do? You have been born and raised (or otherwise come) to accept certain tenets as absolute truths. If you are truly open-minded and rational, shouldn't you acknowledge that there is a rather low probability that you happen to have been born at just the perfect time in history that your generation was taught the absolute truth, while all those who came before (or believe different things now) are the ones who are wrong? How can honest, clear-thinking, fair evangelicals be so certain of the correctness of their positions?
Save "me", please
English may be a living language, but the proper use of "me" is dying. Often bad language comes up from the bottom: kids, TV shows, wrestling matches. Over the last ten years, an error that bugs me came down from the top, from adults, from professionals. It is the use of the word "myself" when the speaker or writer means "me."
e.g. Turn your documents into Kevin or myself by 3:00.
e.g. (worse) Dave and myself will be away tomorrow. (should be "I")
I turn in documents to you, not to yourself. I see her, she sees herself. You play with me, I play …
On second thought, I guess the word "me" is not imperiled as I first thought. Almost every student says "Me and her are going to the mall." Hearing that always gives myself a headache.
English may be a living language, but the proper use of "me" is dying. Often bad language comes up from the bottom: kids, TV shows, wrestling matches. Over the last ten years, an error that bugs me came down from the top, from adults, from professionals. It is the use of the word "myself" when the speaker or writer means "me."
e.g. Turn your documents into Kevin or myself by 3:00.
e.g. (worse) Dave and myself will be away tomorrow. (should be "I")
I turn in documents to you, not to yourself. I see her, she sees herself. You play with me, I play …
On second thought, I guess the word "me" is not imperiled as I first thought. Almost every student says "Me and her are going to the mall." Hearing that always gives myself a headache.
Thursday, October 21, 2004
If we only knew
I'm old enough to remember "Whites Only" drinking fountains and regulations in the American South that blacks had to sit in the back of the bus and give up their seats to white people. This concept looks so repulsive now. (It was repulsive then, too, but not for many southerners...bear with me.) If whites in Mississippi, Alabama, and Georgia in 1960 could have looked ahead 45 years, they would have seen the disgust that people today have for their attitudes. If they knew, then, how their attitudes would appear to people 40 years in the future, would they have continued to hold their values?
My parents grew up on the Toronto Islands. Up until the 60's there were no Jews allowed in the bowling and baseball leagues, nor at the events in the Clubhouse. And my parents and their friends were otherwise very good people. Why didn't they see how wrong this was? If someone told them what people in 1980 would think of this policy, would they have changed it sooner?
Or take Sadam Hussein. He wanted to be known as a great leader, like Saladin. If he had known that he would be despised by future generations, would he have acted differently?
Let's assume that people would change their behaviour if, magically, they found out what future generations thought of them. The question becomes, then, what are WE doing today that people in 2040 will say "How could they have thought THAT? How disgusting! How could they have behaved that way?"
A couple of suggestions might be
"How could they (i.e. we) have ignored/contributed to global warming so much?"
"How could they have treated homosexuals that way?"
"How could they have destroyed so many species?"
Are there any things about us that you think might disgust future generations as much as those behaviours from the near past, like routinely-accepted racial descrimination, that disgust us now?
I'm old enough to remember "Whites Only" drinking fountains and regulations in the American South that blacks had to sit in the back of the bus and give up their seats to white people. This concept looks so repulsive now. (It was repulsive then, too, but not for many southerners...bear with me.) If whites in Mississippi, Alabama, and Georgia in 1960 could have looked ahead 45 years, they would have seen the disgust that people today have for their attitudes. If they knew, then, how their attitudes would appear to people 40 years in the future, would they have continued to hold their values?
My parents grew up on the Toronto Islands. Up until the 60's there were no Jews allowed in the bowling and baseball leagues, nor at the events in the Clubhouse. And my parents and their friends were otherwise very good people. Why didn't they see how wrong this was? If someone told them what people in 1980 would think of this policy, would they have changed it sooner?
Or take Sadam Hussein. He wanted to be known as a great leader, like Saladin. If he had known that he would be despised by future generations, would he have acted differently?
Let's assume that people would change their behaviour if, magically, they found out what future generations thought of them. The question becomes, then, what are WE doing today that people in 2040 will say "How could they have thought THAT? How disgusting! How could they have behaved that way?"
A couple of suggestions might be
"How could they (i.e. we) have ignored/contributed to global warming so much?"
"How could they have treated homosexuals that way?"
"How could they have destroyed so many species?"
Are there any things about us that you think might disgust future generations as much as those behaviours from the near past, like routinely-accepted racial descrimination, that disgust us now?
I realize that English is a living language, but would you help me save the word "me" from extinction? Often bad language comes up from the bottom: kids, TV shows, wrestling matches. Over the last ten years, an error that bugs me came down from the top, from adults, from professionals. It is the use of the word "myself" when the speaker or writer means "me."
e.g. Turn your documents into Kevin or myself by 3:00.
e.g. (worse) Dave and myself will be away tomorrow. (should be "I")
I turn in documents to you, not to yourself. I see her, she sees herself. You play with me, I play …
On second thought, I guess the word "me" is not imperiled as I first thought. Almost every student says "Me and her are going to the mall." …Hearing that always gives myself a headache.
e.g. Turn your documents into Kevin or myself by 3:00.
e.g. (worse) Dave and myself will be away tomorrow. (should be "I")
I turn in documents to you, not to yourself. I see her, she sees herself. You play with me, I play …
On second thought, I guess the word "me" is not imperiled as I first thought. Almost every student says "Me and her are going to the mall." …Hearing that always gives myself a headache.
Wednesday, August 25, 2004
String Theory
You may have read about physicists proposing that everything is made of vibrating strings. It’s hard to get an intuitive grasp of this concept, but perhaps the following will help get you started.
Light can be thought of as a particle or a wave, depending on what experiment you do to detect it. If you look to see how it exposes a photographic plate or hits a screen, you discover that light particles, photons, have one-to-one collisions with molecules and land in a specific place on the screen (rather than wash across a screen like a wave washes up on a beach.) If you check to see how light passes through tiny holes you see interference patterns, places where light waves cancelled and reinforced.
It turns out that all particles (not just light) have a wave nature. For example, electrons travel through slits and produce interference patterns. You’ve heard of the electron microscope, which uses electrons rather than light to view tiny objects. The electron’s wavelength is smaller than that of visible light, so we can us electron waves to detect smaller objects.
Three formulas, two formulas from Einstein, and one from de Broglie, are helpful here. The first is Einstein’s famous E=mc2, which tells how much energy is needed to create a particle of mass m, or how much energy will appear if a particle of mass m vanishes. (c is the speed of light.) The second, also from Einstein, is E = hc/λ, where λ is the wavelength of the wave associated with that particle. This gives the energy of a particle with a given wavelength.
The third formula is λ = h/mv, where λ is a particle’s wavelength, h is a constant, m is the particle’s mass and v is its velocity.
String theory? Here goes.
First, get the idea of strings made of atoms out of your mind. Forget what they are made of and just consider them to be imaginary. Here’s how they work, in a nutshell.
Consider a tiny particle, like an electron, proton, muon, whatever. The particle has a mass. When moving, it has a wavelength (equation 3) and an energy (equation 2). Now picture two girls turning a skipping rope. They are making a standing wave. Their shoulders are nodes, hardly moving. Most of the energy of the wave is near the centre of the rope where the amplitude is greatest. Picture a particle to be equivalent to a standing wave: the “probable location” of the particle is where the energy is greatest. But the particle does not actually exist in a spot, its energy (and mass, equation 1) are spread out all the way between the nodes.
If the girls wiggle their arms differently, they could set up a standing wave with two loops and a stationary point, a node, in the middle. (You never actually see this when kids are skipping, but you can do it with your stretched-out phone cord if you try. Turn it at twice the rate of the “skipping rope” turning.) In this case there are two high-energy locations, the loops or antinodes. This wave is the first overtone of the original, which is called the fundamental. Buglers (and all brass instrumentalists) make use of the overtones to get different notes without changing their fingers. (Buglers can’t change their fingers: they have no valves!)
Now the intuitive step. What if the overtone represents a different particle from the original? That is, since every particle has a wave nature, we could think of particles as different resonances of a vibrating string, different frequencies where standing waves can be set up. The more massive the particle, the more energy (equation 1). The more energy, the smaller the wavelength (equation 2). The more massive particle could be a standing wave of higher frequency or an overtone of the wave associated with the less massive particle.
String theory is much more complicated than this, of course. But the idea here is to turn on a little light bulb in our brain, a little spark of intuition. Because of the wave-particle duality of light and matter, perhaps we can think of particles as resonances of strings. It is space itself which is resonating, not actual pieces of thin rope.
To test out the theory we can use some symmetry considerations to predict a resonance that no one has seen before. This leads to a frequency and wavelength prediction. That gives an equivalent mass and velocity (equation 3). When we let high speed particles race down linear accelerators and smash into atomic targets, tiny particles are produced. They don’t last long, and when they vanish, they give off a burst of light. The photon will have an energy equivalent to that particle’s mass (equation 1). This energy has an associated wavelength (equation 2) which translates to a colour. So, when we fire up our linear accelerators, synchrotrons, and cyclotrons (“atom smashers”) we can look for a burst of light of that colour. If we see it, we can say that we have discovered a new particle and announce its mass.
Alternatively, if we have a tiny understanding of string theory, we can say we have witnessed a new resonance of one of the strings of which the universe is made.
You may have read about physicists proposing that everything is made of vibrating strings. It’s hard to get an intuitive grasp of this concept, but perhaps the following will help get you started.
Light can be thought of as a particle or a wave, depending on what experiment you do to detect it. If you look to see how it exposes a photographic plate or hits a screen, you discover that light particles, photons, have one-to-one collisions with molecules and land in a specific place on the screen (rather than wash across a screen like a wave washes up on a beach.) If you check to see how light passes through tiny holes you see interference patterns, places where light waves cancelled and reinforced.
It turns out that all particles (not just light) have a wave nature. For example, electrons travel through slits and produce interference patterns. You’ve heard of the electron microscope, which uses electrons rather than light to view tiny objects. The electron’s wavelength is smaller than that of visible light, so we can us electron waves to detect smaller objects.
Three formulas, two formulas from Einstein, and one from de Broglie, are helpful here. The first is Einstein’s famous E=mc2, which tells how much energy is needed to create a particle of mass m, or how much energy will appear if a particle of mass m vanishes. (c is the speed of light.) The second, also from Einstein, is E = hc/λ, where λ is the wavelength of the wave associated with that particle. This gives the energy of a particle with a given wavelength.
The third formula is λ = h/mv, where λ is a particle’s wavelength, h is a constant, m is the particle’s mass and v is its velocity.
String theory? Here goes.
First, get the idea of strings made of atoms out of your mind. Forget what they are made of and just consider them to be imaginary. Here’s how they work, in a nutshell.
Consider a tiny particle, like an electron, proton, muon, whatever. The particle has a mass. When moving, it has a wavelength (equation 3) and an energy (equation 2). Now picture two girls turning a skipping rope. They are making a standing wave. Their shoulders are nodes, hardly moving. Most of the energy of the wave is near the centre of the rope where the amplitude is greatest. Picture a particle to be equivalent to a standing wave: the “probable location” of the particle is where the energy is greatest. But the particle does not actually exist in a spot, its energy (and mass, equation 1) are spread out all the way between the nodes.
If the girls wiggle their arms differently, they could set up a standing wave with two loops and a stationary point, a node, in the middle. (You never actually see this when kids are skipping, but you can do it with your stretched-out phone cord if you try. Turn it at twice the rate of the “skipping rope” turning.) In this case there are two high-energy locations, the loops or antinodes. This wave is the first overtone of the original, which is called the fundamental. Buglers (and all brass instrumentalists) make use of the overtones to get different notes without changing their fingers. (Buglers can’t change their fingers: they have no valves!)
Now the intuitive step. What if the overtone represents a different particle from the original? That is, since every particle has a wave nature, we could think of particles as different resonances of a vibrating string, different frequencies where standing waves can be set up. The more massive the particle, the more energy (equation 1). The more energy, the smaller the wavelength (equation 2). The more massive particle could be a standing wave of higher frequency or an overtone of the wave associated with the less massive particle.
String theory is much more complicated than this, of course. But the idea here is to turn on a little light bulb in our brain, a little spark of intuition. Because of the wave-particle duality of light and matter, perhaps we can think of particles as resonances of strings. It is space itself which is resonating, not actual pieces of thin rope.
To test out the theory we can use some symmetry considerations to predict a resonance that no one has seen before. This leads to a frequency and wavelength prediction. That gives an equivalent mass and velocity (equation 3). When we let high speed particles race down linear accelerators and smash into atomic targets, tiny particles are produced. They don’t last long, and when they vanish, they give off a burst of light. The photon will have an energy equivalent to that particle’s mass (equation 1). This energy has an associated wavelength (equation 2) which translates to a colour. So, when we fire up our linear accelerators, synchrotrons, and cyclotrons (“atom smashers”) we can look for a burst of light of that colour. If we see it, we can say that we have discovered a new particle and announce its mass.
Alternatively, if we have a tiny understanding of string theory, we can say we have witnessed a new resonance of one of the strings of which the universe is made.
Women with guns.
How many TV shows have you seen where the woman gets the bad guy's gun and points it at him, trembling? He steps slowly toward her. "You won't shoot. Give me the gun." And she ends up giving it to him, giving away her only advantage. Sound familiar?
Everytime I see that I think "Don't give it to him. At least shoot him in the leg so he can't chase you." But she never does.
I watched one movie, a pretty good one, actually, for this genre. The woman got the gun away from the guy whose accomplice was holding her daughter. The idea was that the girl would be killed if the bad guy didn't telephone in every hour. What could she do but give him back his gun? And of course she did!
I decided to write an alternative version. What follows is an off-the-cuff account of what I figure the woman should have done. I backed it up a bit to show how she might have got the gun away from him. See if you think it's reasonable.
Don't Give Up The Gun
[Man with gun is in woman's appartment. His accomplice has her daughter in an unknown location. She dare not leave or cause trouble, or her daughter might be killed. Story resumes.]
With apparent carelessness, Barb came out of the kitchen carrying two mugs of coffee. Hearing her approach, the man turned his eyes from the television screen and watched her cautiously. She tried not to let her rising nervousness cause her hands to shake; she had to keep him from guessing her intentions. The fingers of his right hand drummed the nearby table, beside the gun. She tried not to look at it, staring instead down at the coffee. While preparing the coffee in the kitchen she had decided that she had only one chance. She fought the nausea bubbling up from inside, trying to stay focussed, to appear as if spilling the hot liquid on the rug was her biggest worry.
She jiggled a little coffee on the table, grimacing “Ow, that’s hot!” she exclaimed, hoping that just the right amount of anguish was in her voice. She was right in front of him now. Slowly she offered the mug to him, coffee filled to the brim. She was holding the mug's handle, so he’d have to put his hand around the mug. “Careful, it’s full”, she warned him. Please let him take it in both hands, she pleaded silently, as she extended it toward his his left hand.
The ruse worked. His fingers closed around the mug, and she released it. As she hoped, the scalding hot mug was too painful for his fingers. The man brought his right hand up quickly to take the mug by the handle. Just as he pulled the mug out of his his fingers she acted. She flung her steaming hot coffee in his face.
The man screamed and jerked back in the chair, involuntarily bring his left hand up, too late, to protect his eyes. Years of habit worked to prevent him from dropping the mug for a split second. An instant was all Barb needed. She grabbed the gun and jumped back out of reach.
Cursing, the man flung away the cup of coffee and grabbed for her, but missed. “Freeze, asshole” she yelled, and levelled the gun at his face.
“God damn it! You bitch.” he cried, wiping coffee from his eyes. “You’ve had it. Your little girl’s dead now.” He took a step toward her.
She pointed the gun at the ceiling and pulled the trigger. The boom was deafening, causing her to gasp and step back. Quickly she lowered the gun and pointed it at him. “Don’t come any closer!” she screamed.
The blast worked. The man’s survival instincts kicked in, and he froze. “OK. OK” he said. “Take it easy.”
Time stopped as they eyed each other, wondering what was going to happen next. Then she spoke sharply. “Sit down” she commanded. The man didn’t move and she made a motion toward him with the gun.
“OK,” he said, and he eased back into the chair. He took a big breath, and let his face relax. Inside, he was seething, furious at himself for getting taken by this woman. Doing his best to look confident, he smiled “Good move,” he said. “I’m impressed.”
Barb snorted with disgust, her eyes shooting daggers at him.
“No, really,” he continued. “That was a smooth move. You’ve got guts, I’ve got to say.” He paused, and the smile faded. “But playtime’s over. Put down the gun.”
“You’ve got to be kidding,” Barb replied grimly.
“You’re forgetting. My partner Barney’s got your daugher. If I don’t phone Barney to say that your husband’s wired the money, he kills her.”
“I’ll kill you.”
“No you won’t,” he said. “You can’t chance it. You’re not going to trade your daughter for me, are you?” He smiled confidently, as he saw the tears well up in her eyes. “Who’s more important to you? Me or her?”
“Sh..sh..shut up,” she stammered, but kept the gun aimed at his nose.
“He might phone to see if everything’s OK any minute. If I don’t tell him everything’s fine, he’ll kill her and split town. Think carefully.” He watched her carefully as she burst into tears, watching the gun waver in her hand, looking for the right moment to leap.“You’ll never see her alive again”, he taunted.
“I said shut up,” Barb wailed. “Let me think”, she shouted. For a moment they stared at each other, then she waved the gun.
“Reach the phone and tell him to bring her here” she ordered.
“Can’t do that, Missy. He’ll smell a trap.”
“Do it anyhow.”
“No.”
“I – I’ll kill you.”
“No you won’t. Like I said, you can’t take that chance. You might as well give me the gun.”
“Here’s how I see it,” Barb replied, her voice steadier now. “I figure you are going to kill us anyhow.”
“No, we just want the money.”
“I’ve seen your face. My daughter’s seen you friend’s face. You’re going to kill us.”
“Of course not. You won’t tell because we have accomplises that will kill you, your husband, and your little girl if you do.” He shrugged. “But not me. I’m not a killer, just a business man.”
She stared at him. He had a handsome face, could have been a tennis player, she thought. Or the guy next door. His little smile mocked her. Amazing that he was so cool, considering she had a gun pointed at him. She looked deep into his eyes and shivered. The eyes told the real story. He hated her guts. He’s a charmer, that’s for sure, she thought. But those eyes.
A surreal calm seemed to come over her as she came to a decision.. “Here’s what I’m going to do,” she announced calmly. She took a step toward him, and took a deep breath. Suddenly, she pointed the gun down at his right thigh and pulled the trigger.
She was ready for the blast this time, but the man jumped in surprise and pain. He howled. “Oh! Shit! Shit!” He grabbed his leg. “You shot me! Oh, shit that hurts” Blood poured through his fingers. He moaned, and continued to curse.
“Hurts more than they pretend on TV?” she asked.
“God, yes! Why did you do that?” he demanded angrily. “That’ll cost you. You daughter’s dead. Do you understand me?”
“If she dies, so will you,” Barb replied, matter-of-factly. “Perhaps you should put your belt around your thigh before you bleed to death.”
“Put your hand on this while I take my belt off?”
She laughed. “Not a chance.”
He glared at her, then reached for a nearby pillow. He placed it over the wound and held it there with his elbow while he struggled to pull his belt off. She watched as he fed it under him and pulled it tight around his thigh.He wiped his bloody hands on the pillow, a little triumph.
She shrugged. “Now you’re going to phone your friend and tell him to bring back my daughter.”
“Won’t work. He won’t do it.”
She shrugged again. “Better hope he does, or you’ll bleed to death.”
“You bitch!” he spat. “I never hurt you!”
“Sorry.”
She walked over to the corner table and took the remote phone from its cradle. She tossed it into his lap. “Phone him,” she directed.
The man eyed the phone then stared at her insolently. He made no move to pick it up.
Without any warning, she stepped forward and fired, hitting him in the other leg below the knee.
“God! Damn you! Oh, God!” he shrieked. “My leg!” She waggled the gun. “OK. OK” he moaned.
“Phone him now.”
“OK
She squatted by the phone jack as he dialed. She could hear the phone ring on the other end. “Hi, Bud?” He looked at her carefully, then started to shout. “Bud, this bitch …”
Quickly she pulled the phone cord out of the wall. “That was a mistake,” she said, calmly. “Which arm do you want me to shoot?”
The man’s incredible confidence seeped away quickly. “N-n-no. No. Sorry,” he shrieked. “Don’t do that.”
Suddenly, her calm state cracked. “Then get me my daughter back, you asshole,” she shouted. “The next shot goes through your crotch. You’ll sing soprano if I let you live. Are you ready to try again?”
He nodded.
“Is there a donut shop or all-night convenience store anywhere near there?” she asked.
“Ya, a Mac’s Milk.”
“Then tell him there’s been a change in plans, that I’m going to pay a huge ransom. and that he’s to drop her at the Mac’s Milk and drive away. Tell him that when the owner of the store calls to say that she’s safe, you will leave here with the money.
“Do you think you can do that?” she asked, pointing the gun at his gut.
“Yes.”
“You’d better, or you die.”
“You’re still playing with your daughter’s life. If my pal smells a rat, she’s in trouble.”
“Then see that he doesn’t. I think your life is worth more to you than my daughter’s is to you, isn’t it? Didn’t I hear you say something like that before?”
He grunted, then, after she plugged in the phone cord, he dialed. “Hi Bud. Sorry about that. She started to run, and I had to chase her. Stupid bitch…Ya…How’s the girl? OK…Good…Look, something’s come up.”
Barb got ready to pull the plug.
“The bitch has some jewels, and a lot of money right here in a safe. If you bring back the girl she’ll open it. No, I can’t make her…No, don’t threaten her with the girl…No, she’s looney. She’s convinced we’re going to kill the girl anyhow and she figures this is her only chance…Here’s what you have to do.”
He told the man the new plans.
“She’ll open the safe when she hears from the store guy.”
“And my daughter.” Barb called.
“Ya, after she speaks with her daughter she’ll open the safe…Sure she will, or she dies…Ya, I’ll kill her. She knows that. All she cares about is the kid….Don’t argue, just do it….OK.”
As the man clicked off the phone, Barb nodded approvingly. “Good job. Throw me the phone.”
She caught the phone and dialled 9-1-1. “Get me the police….Yes. My daughter’s been kidnapped. The kidnapper’s accomplice is here, and he will tell you where she is being held. She’ll either be there, or the kidnapper will be taking her to a nearby Mac’s Milk…Yes. This is no joke. I’ve got a gun on him. I’m going to put him on and he’ll tell you where she is…What if he lies?” She laughed grimly. “I think he knows what will happen.”
How many TV shows have you seen where the woman gets the bad guy's gun and points it at him, trembling? He steps slowly toward her. "You won't shoot. Give me the gun." And she ends up giving it to him, giving away her only advantage. Sound familiar?
Everytime I see that I think "Don't give it to him. At least shoot him in the leg so he can't chase you." But she never does.
I watched one movie, a pretty good one, actually, for this genre. The woman got the gun away from the guy whose accomplice was holding her daughter. The idea was that the girl would be killed if the bad guy didn't telephone in every hour. What could she do but give him back his gun? And of course she did!
I decided to write an alternative version. What follows is an off-the-cuff account of what I figure the woman should have done. I backed it up a bit to show how she might have got the gun away from him. See if you think it's reasonable.
Don't Give Up The Gun
[Man with gun is in woman's appartment. His accomplice has her daughter in an unknown location. She dare not leave or cause trouble, or her daughter might be killed. Story resumes.]
With apparent carelessness, Barb came out of the kitchen carrying two mugs of coffee. Hearing her approach, the man turned his eyes from the television screen and watched her cautiously. She tried not to let her rising nervousness cause her hands to shake; she had to keep him from guessing her intentions. The fingers of his right hand drummed the nearby table, beside the gun. She tried not to look at it, staring instead down at the coffee. While preparing the coffee in the kitchen she had decided that she had only one chance. She fought the nausea bubbling up from inside, trying to stay focussed, to appear as if spilling the hot liquid on the rug was her biggest worry.
She jiggled a little coffee on the table, grimacing “Ow, that’s hot!” she exclaimed, hoping that just the right amount of anguish was in her voice. She was right in front of him now. Slowly she offered the mug to him, coffee filled to the brim. She was holding the mug's handle, so he’d have to put his hand around the mug. “Careful, it’s full”, she warned him. Please let him take it in both hands, she pleaded silently, as she extended it toward his his left hand.
The ruse worked. His fingers closed around the mug, and she released it. As she hoped, the scalding hot mug was too painful for his fingers. The man brought his right hand up quickly to take the mug by the handle. Just as he pulled the mug out of his his fingers she acted. She flung her steaming hot coffee in his face.
The man screamed and jerked back in the chair, involuntarily bring his left hand up, too late, to protect his eyes. Years of habit worked to prevent him from dropping the mug for a split second. An instant was all Barb needed. She grabbed the gun and jumped back out of reach.
Cursing, the man flung away the cup of coffee and grabbed for her, but missed. “Freeze, asshole” she yelled, and levelled the gun at his face.
“God damn it! You bitch.” he cried, wiping coffee from his eyes. “You’ve had it. Your little girl’s dead now.” He took a step toward her.
She pointed the gun at the ceiling and pulled the trigger. The boom was deafening, causing her to gasp and step back. Quickly she lowered the gun and pointed it at him. “Don’t come any closer!” she screamed.
The blast worked. The man’s survival instincts kicked in, and he froze. “OK. OK” he said. “Take it easy.”
Time stopped as they eyed each other, wondering what was going to happen next. Then she spoke sharply. “Sit down” she commanded. The man didn’t move and she made a motion toward him with the gun.
“OK,” he said, and he eased back into the chair. He took a big breath, and let his face relax. Inside, he was seething, furious at himself for getting taken by this woman. Doing his best to look confident, he smiled “Good move,” he said. “I’m impressed.”
Barb snorted with disgust, her eyes shooting daggers at him.
“No, really,” he continued. “That was a smooth move. You’ve got guts, I’ve got to say.” He paused, and the smile faded. “But playtime’s over. Put down the gun.”
“You’ve got to be kidding,” Barb replied grimly.
“You’re forgetting. My partner Barney’s got your daugher. If I don’t phone Barney to say that your husband’s wired the money, he kills her.”
“I’ll kill you.”
“No you won’t,” he said. “You can’t chance it. You’re not going to trade your daughter for me, are you?” He smiled confidently, as he saw the tears well up in her eyes. “Who’s more important to you? Me or her?”
“Sh..sh..shut up,” she stammered, but kept the gun aimed at his nose.
“He might phone to see if everything’s OK any minute. If I don’t tell him everything’s fine, he’ll kill her and split town. Think carefully.” He watched her carefully as she burst into tears, watching the gun waver in her hand, looking for the right moment to leap.“You’ll never see her alive again”, he taunted.
“I said shut up,” Barb wailed. “Let me think”, she shouted. For a moment they stared at each other, then she waved the gun.
“Reach the phone and tell him to bring her here” she ordered.
“Can’t do that, Missy. He’ll smell a trap.”
“Do it anyhow.”
“No.”
“I – I’ll kill you.”
“No you won’t. Like I said, you can’t take that chance. You might as well give me the gun.”
“Here’s how I see it,” Barb replied, her voice steadier now. “I figure you are going to kill us anyhow.”
“No, we just want the money.”
“I’ve seen your face. My daughter’s seen you friend’s face. You’re going to kill us.”
“Of course not. You won’t tell because we have accomplises that will kill you, your husband, and your little girl if you do.” He shrugged. “But not me. I’m not a killer, just a business man.”
She stared at him. He had a handsome face, could have been a tennis player, she thought. Or the guy next door. His little smile mocked her. Amazing that he was so cool, considering she had a gun pointed at him. She looked deep into his eyes and shivered. The eyes told the real story. He hated her guts. He’s a charmer, that’s for sure, she thought. But those eyes.
A surreal calm seemed to come over her as she came to a decision.. “Here’s what I’m going to do,” she announced calmly. She took a step toward him, and took a deep breath. Suddenly, she pointed the gun down at his right thigh and pulled the trigger.
She was ready for the blast this time, but the man jumped in surprise and pain. He howled. “Oh! Shit! Shit!” He grabbed his leg. “You shot me! Oh, shit that hurts” Blood poured through his fingers. He moaned, and continued to curse.
“Hurts more than they pretend on TV?” she asked.
“God, yes! Why did you do that?” he demanded angrily. “That’ll cost you. You daughter’s dead. Do you understand me?”
“If she dies, so will you,” Barb replied, matter-of-factly. “Perhaps you should put your belt around your thigh before you bleed to death.”
“Put your hand on this while I take my belt off?”
She laughed. “Not a chance.”
He glared at her, then reached for a nearby pillow. He placed it over the wound and held it there with his elbow while he struggled to pull his belt off. She watched as he fed it under him and pulled it tight around his thigh.He wiped his bloody hands on the pillow, a little triumph.
She shrugged. “Now you’re going to phone your friend and tell him to bring back my daughter.”
“Won’t work. He won’t do it.”
She shrugged again. “Better hope he does, or you’ll bleed to death.”
“You bitch!” he spat. “I never hurt you!”
“Sorry.”
She walked over to the corner table and took the remote phone from its cradle. She tossed it into his lap. “Phone him,” she directed.
The man eyed the phone then stared at her insolently. He made no move to pick it up.
Without any warning, she stepped forward and fired, hitting him in the other leg below the knee.
“God! Damn you! Oh, God!” he shrieked. “My leg!” She waggled the gun. “OK. OK” he moaned.
“Phone him now.”
“OK
She squatted by the phone jack as he dialed. She could hear the phone ring on the other end. “Hi, Bud?” He looked at her carefully, then started to shout. “Bud, this bitch …”
Quickly she pulled the phone cord out of the wall. “That was a mistake,” she said, calmly. “Which arm do you want me to shoot?”
The man’s incredible confidence seeped away quickly. “N-n-no. No. Sorry,” he shrieked. “Don’t do that.”
Suddenly, her calm state cracked. “Then get me my daughter back, you asshole,” she shouted. “The next shot goes through your crotch. You’ll sing soprano if I let you live. Are you ready to try again?”
He nodded.
“Is there a donut shop or all-night convenience store anywhere near there?” she asked.
“Ya, a Mac’s Milk.”
“Then tell him there’s been a change in plans, that I’m going to pay a huge ransom. and that he’s to drop her at the Mac’s Milk and drive away. Tell him that when the owner of the store calls to say that she’s safe, you will leave here with the money.
“Do you think you can do that?” she asked, pointing the gun at his gut.
“Yes.”
“You’d better, or you die.”
“You’re still playing with your daughter’s life. If my pal smells a rat, she’s in trouble.”
“Then see that he doesn’t. I think your life is worth more to you than my daughter’s is to you, isn’t it? Didn’t I hear you say something like that before?”
He grunted, then, after she plugged in the phone cord, he dialed. “Hi Bud. Sorry about that. She started to run, and I had to chase her. Stupid bitch…Ya…How’s the girl? OK…Good…Look, something’s come up.”
Barb got ready to pull the plug.
“The bitch has some jewels, and a lot of money right here in a safe. If you bring back the girl she’ll open it. No, I can’t make her…No, don’t threaten her with the girl…No, she’s looney. She’s convinced we’re going to kill the girl anyhow and she figures this is her only chance…Here’s what you have to do.”
He told the man the new plans.
“She’ll open the safe when she hears from the store guy.”
“And my daughter.” Barb called.
“Ya, after she speaks with her daughter she’ll open the safe…Sure she will, or she dies…Ya, I’ll kill her. She knows that. All she cares about is the kid….Don’t argue, just do it….OK.”
As the man clicked off the phone, Barb nodded approvingly. “Good job. Throw me the phone.”
She caught the phone and dialled 9-1-1. “Get me the police….Yes. My daughter’s been kidnapped. The kidnapper’s accomplice is here, and he will tell you where she is being held. She’ll either be there, or the kidnapper will be taking her to a nearby Mac’s Milk…Yes. This is no joke. I’ve got a gun on him. I’m going to put him on and he’ll tell you where she is…What if he lies?” She laughed grimly. “I think he knows what will happen.”
Thoughs on whether God exists
I often think how lucky I am to be born a Canadian. I could have been born one of India’s teeming impoverished children. I could have had to grow up in the middle of sectarian warfare in Ireland, Serbia, or Iraq, or under a tyrannical dictatorship in the U.S.S.R. or North Korea. How fortunate I was that my parents happened to be Canadians!
The fact that the majority of citizens happen to have the citizenship of their parents is obvious and of little significance. Yet, when applied to religion, the observation leads to some serious questions in my mind. The vast majority of people end up following the religion of their parents. Of course some people convert to other denominations, Anglican to United. Some cross larger chasms, converting from Judaism to Christianity, or Christianity to Buddhism. It is surely safe to say, though, that most people who grow up in a family of a given faith become members of that faith themselves. That is, they accept the beliefs of the faith of their parents, or at least their surroundings during their formative years.
At first glance, this observation seems of as little significance as the citizenship “coincidence”. After all, how can you accept the beliefs of, say, Muslims, if you haven’t been exposed to that faith? The difference comes, though, with the importance believers of a faith usually place on the truth of their beliefs. Canadians do not go about announcing that Canada is the only true country. But many religious believers proclaim that their faith is the only true faith. That is, they feel that their God is the only God, or the practices or beliefs of their faith provide the only way to reach God or heaven, The Roman Catholic Church has, with no embarrassment, openly proclaimed itself as the one True Church. Devout Christians seize upon the word “only” in the scriptures and state that the only way to salvation is to accept Christ as the Son of God. Jehovah’s Witnesses tell the world that those who survive the coming apocalypse will be from their ranks only.
It is at this point that the coincidences become a little too much to accept. The good luck of being born Canadian pales compared to the good luck of being born into the only true faith.
When I think deeply about religious matters, such as the existence of a Creator, whether there is an afterlife, or whether there is a God who can hear your silent prayers, I wonder about the certainty that many believers possess. When I see good, intelligent, devout people disagreeing on what constitutes the absolute truth in these matters, I wonder what right have I to assume that my beliefs are the true beliefs? The conclusion that I have the monopoly on truth seems of low probability, and quite egotistical or chauvanistic.
I would like to pose some questions to religious people about this point. Because of my lack of knowledge of the other world religions, I will address the questions to fundamentalist Christians who consider their beliefs to be absolutely true. But I believe my questions have general applicability to other faiths, if tailored to their specific beliefs.[1]
Question 1: Does it concern you that you happen to believe what your parents believe? Do you ever worry that such a “coincidence” could be the result of indoctrination rather than free choice, uninfluenced by your superiors or upbringing?
Certainly, no one can be uninfluenced by his or her upbringing. No one is, or should be, brought up empty of knowledge and void of concepts of right and wrong. After all, that’s why we have universal education. Suppose, though, a button could be pressed which causes all preconceived notions about religion could be wiped from a 25 year old’s brain. (Perhaps the Men in Black have one!) Gone would be the suggestion that there is a God. Gone would be the assumption that the Bible is the literal truth (the question was addressed to fundamentalist Christians, remember.) I anticipate that the majority of such mind-blanked people would attain a belief in God. There seems to be a universal human nature or need to feel that someone is looking out for them, or there is life after death, or that their presence on Earth has a grand purpose. But would most pick up the Bible and say “You know, I this script seems to be the actual Word of God.” My guess is that many would see the Bible as representing something else: what ancient people thought was the word of God, or what early religious leaders wanted their flock to think was the word of God, or what early devout leaders though God would say if He were currently speaking to them. The point of my question and this subsequent impossible (some would say ludicrous) hypothetical scenario is to try to find out if fundamentalist Christians accept (their interpretations of) the teachings of the Bible because they have been told the Bible is absolute truth or because they have concluded, independent of their upbringing, that it is absolute truth.
I would be more satisfied intellectually to accept claims of religious fundamentalists if I felt that their ideas and passions did not come from parents or upbringing. Please remember that I am not claiming that the beliefs of religious fundamentalists, or any religious people for that matter, are untrue. I am saying that if I were to hold these (or any) beliefs myself, the “my parents thought that, too” coincidence would give me pause.
Question 2: Have you ever wondered what changes in your beliefs would results if the Bible were not absolutely true? Or, more to the point, have you ever wondered if the Bible might not be the literal Word of God?
Again, I would be more impressed with a fundamentalist’s convictions if he or she concluded that the Bible was literate, historical truth after honestly and fairly considering the question. I fear that it may be impossible to fairly question a fundamental tenet of faith that has been part of a person’s upbringing from day 1. True, some people convert to other religions, which suggests that open-mindedness is possible. On the other hand, conversion might indicate that they never actually accepted the article of faith in the first place. Unfortunately, this leads to a situation with no solution:
Convert: Yes I accepted it…now I reject it.
Skeptic: You never accepted it, you just think you did.
Convert: No, I actually accepted it.
Skeptic: No, you just think you actually accepted it…
It worries me that belief in God, based on the Bible’s claim of God’s existence, is subject to circular reasoning:
Person A: God exists.
Person B: How do you know?
Parson A: It says so in the Bible?
Person B: How do you know that the Bible is true?
Person A: Because God wrote it.
Person B: But how do you know that God exists in the first place?
Person A: It says so in the Bible.
Is it possible to come to accept that the Bible is the literal Word of God without first being told that it is? Perhaps. A fundamentalist might say “I get evidence for this every day, throughout my life.” My worry here is that such acceptance occurs in other situations which are too similar to be ignored: the concept of the self-fulfilling prophesy, the Rorschach ink-blot test, vision of God in the clouds or the devil in the smoke from the World Trade Centre, the “my horoscope sounds like it applies to me” claim. My grandmother says “I’ve played Bingo all my life and I think I’m a little ahead.” No bingo player thinks otherwise.
[1] (For the purpose of this essay I am defining fundamentalist Christians as those who believe that the Bible is the absolute word-for-(Hebrew)-word literal truth. This would take in standard Baptists and Nazarenes. Fundamentalist, but not Christian, would apply to Jehovah’s Witnesses’ interpretation of the Old Testament. For example, they would say that there actually was a Daniel in a lion’s den who plucked a thorn from the lion’s paw. Anglicans and Catholic standard doctrine would see the same passage as a fable showing the value of belief in God and charity to your enemy. For a non-fundamentalist, the Bible’s truth would be of a more general nature: a moral or educational truth, rather than a literal one. Similarly, for a fundamentalist Adam and Eve were real people. For a non-fundamentalist, Adam and Eve were characters in a creation myth that tells us many truths about how God wants us to behave. Of course there are many Anglicans and Catholics, and people of other faiths, who would consider themselves fundamentalists, so the questions that follow are not directed solely toward Baptists.
I often think how lucky I am to be born a Canadian. I could have been born one of India’s teeming impoverished children. I could have had to grow up in the middle of sectarian warfare in Ireland, Serbia, or Iraq, or under a tyrannical dictatorship in the U.S.S.R. or North Korea. How fortunate I was that my parents happened to be Canadians!
The fact that the majority of citizens happen to have the citizenship of their parents is obvious and of little significance. Yet, when applied to religion, the observation leads to some serious questions in my mind. The vast majority of people end up following the religion of their parents. Of course some people convert to other denominations, Anglican to United. Some cross larger chasms, converting from Judaism to Christianity, or Christianity to Buddhism. It is surely safe to say, though, that most people who grow up in a family of a given faith become members of that faith themselves. That is, they accept the beliefs of the faith of their parents, or at least their surroundings during their formative years.
At first glance, this observation seems of as little significance as the citizenship “coincidence”. After all, how can you accept the beliefs of, say, Muslims, if you haven’t been exposed to that faith? The difference comes, though, with the importance believers of a faith usually place on the truth of their beliefs. Canadians do not go about announcing that Canada is the only true country. But many religious believers proclaim that their faith is the only true faith. That is, they feel that their God is the only God, or the practices or beliefs of their faith provide the only way to reach God or heaven, The Roman Catholic Church has, with no embarrassment, openly proclaimed itself as the one True Church. Devout Christians seize upon the word “only” in the scriptures and state that the only way to salvation is to accept Christ as the Son of God. Jehovah’s Witnesses tell the world that those who survive the coming apocalypse will be from their ranks only.
It is at this point that the coincidences become a little too much to accept. The good luck of being born Canadian pales compared to the good luck of being born into the only true faith.
When I think deeply about religious matters, such as the existence of a Creator, whether there is an afterlife, or whether there is a God who can hear your silent prayers, I wonder about the certainty that many believers possess. When I see good, intelligent, devout people disagreeing on what constitutes the absolute truth in these matters, I wonder what right have I to assume that my beliefs are the true beliefs? The conclusion that I have the monopoly on truth seems of low probability, and quite egotistical or chauvanistic.
I would like to pose some questions to religious people about this point. Because of my lack of knowledge of the other world religions, I will address the questions to fundamentalist Christians who consider their beliefs to be absolutely true. But I believe my questions have general applicability to other faiths, if tailored to their specific beliefs.[1]
Question 1: Does it concern you that you happen to believe what your parents believe? Do you ever worry that such a “coincidence” could be the result of indoctrination rather than free choice, uninfluenced by your superiors or upbringing?
Certainly, no one can be uninfluenced by his or her upbringing. No one is, or should be, brought up empty of knowledge and void of concepts of right and wrong. After all, that’s why we have universal education. Suppose, though, a button could be pressed which causes all preconceived notions about religion could be wiped from a 25 year old’s brain. (Perhaps the Men in Black have one!) Gone would be the suggestion that there is a God. Gone would be the assumption that the Bible is the literal truth (the question was addressed to fundamentalist Christians, remember.) I anticipate that the majority of such mind-blanked people would attain a belief in God. There seems to be a universal human nature or need to feel that someone is looking out for them, or there is life after death, or that their presence on Earth has a grand purpose. But would most pick up the Bible and say “You know, I this script seems to be the actual Word of God.” My guess is that many would see the Bible as representing something else: what ancient people thought was the word of God, or what early religious leaders wanted their flock to think was the word of God, or what early devout leaders though God would say if He were currently speaking to them. The point of my question and this subsequent impossible (some would say ludicrous) hypothetical scenario is to try to find out if fundamentalist Christians accept (their interpretations of) the teachings of the Bible because they have been told the Bible is absolute truth or because they have concluded, independent of their upbringing, that it is absolute truth.
I would be more satisfied intellectually to accept claims of religious fundamentalists if I felt that their ideas and passions did not come from parents or upbringing. Please remember that I am not claiming that the beliefs of religious fundamentalists, or any religious people for that matter, are untrue. I am saying that if I were to hold these (or any) beliefs myself, the “my parents thought that, too” coincidence would give me pause.
Question 2: Have you ever wondered what changes in your beliefs would results if the Bible were not absolutely true? Or, more to the point, have you ever wondered if the Bible might not be the literal Word of God?
Again, I would be more impressed with a fundamentalist’s convictions if he or she concluded that the Bible was literate, historical truth after honestly and fairly considering the question. I fear that it may be impossible to fairly question a fundamental tenet of faith that has been part of a person’s upbringing from day 1. True, some people convert to other religions, which suggests that open-mindedness is possible. On the other hand, conversion might indicate that they never actually accepted the article of faith in the first place. Unfortunately, this leads to a situation with no solution:
Convert: Yes I accepted it…now I reject it.
Skeptic: You never accepted it, you just think you did.
Convert: No, I actually accepted it.
Skeptic: No, you just think you actually accepted it…
It worries me that belief in God, based on the Bible’s claim of God’s existence, is subject to circular reasoning:
Person A: God exists.
Person B: How do you know?
Parson A: It says so in the Bible?
Person B: How do you know that the Bible is true?
Person A: Because God wrote it.
Person B: But how do you know that God exists in the first place?
Person A: It says so in the Bible.
Is it possible to come to accept that the Bible is the literal Word of God without first being told that it is? Perhaps. A fundamentalist might say “I get evidence for this every day, throughout my life.” My worry here is that such acceptance occurs in other situations which are too similar to be ignored: the concept of the self-fulfilling prophesy, the Rorschach ink-blot test, vision of God in the clouds or the devil in the smoke from the World Trade Centre, the “my horoscope sounds like it applies to me” claim. My grandmother says “I’ve played Bingo all my life and I think I’m a little ahead.” No bingo player thinks otherwise.
[1] (For the purpose of this essay I am defining fundamentalist Christians as those who believe that the Bible is the absolute word-for-(Hebrew)-word literal truth. This would take in standard Baptists and Nazarenes. Fundamentalist, but not Christian, would apply to Jehovah’s Witnesses’ interpretation of the Old Testament. For example, they would say that there actually was a Daniel in a lion’s den who plucked a thorn from the lion’s paw. Anglicans and Catholic standard doctrine would see the same passage as a fable showing the value of belief in God and charity to your enemy. For a non-fundamentalist, the Bible’s truth would be of a more general nature: a moral or educational truth, rather than a literal one. Similarly, for a fundamentalist Adam and Eve were real people. For a non-fundamentalist, Adam and Eve were characters in a creation myth that tells us many truths about how God wants us to behave. Of course there are many Anglicans and Catholics, and people of other faiths, who would consider themselves fundamentalists, so the questions that follow are not directed solely toward Baptists.
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