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”.

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.

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.

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.)

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.)

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--

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.

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.

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?

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