Sheep and Goats

Category: Scientists

  • Einstein, Euclid, and Parallel Lines

    Parallel lines eventually meet. All you have to do to prove it is to look down the railroad tracks toward the horizon. You can see clearly that the rails touch.

    A contributor informed me, without much tact, that my scientific method was lacking in rigor. "Sheepandgoats, you moron! It’s perspective! Walk down to where they seem to meet and you will see they are as far apart as ever."

    So I walked down to where they seemed to meet and, sure enough, they were just as far apart as ever. Okay, so apparently they remain separated by an unchanging distance. Parallel lines never meet.

    Or do they?

    With mathematical lines you can accomplish exactly what perspective suggests.

    Imagine a straight horizontal line. Mathematical lines, you will remember, are endless. They extend forever. Now picture a line perpendicular, a vertical line. Of course, the two lines will intersect. Call that point of intersection point I. Now travel two feet up that perpendicular line, two feet above I, and choose another point. Call it point P. We call it P for pivot. Pretend that you can pivot the entire line around that point, as if that vertical line was a compass needle pivoting around the center.

    As you pivot the vertical line, what happens to point I? It moves farther and farther down the horizontal line, doesn’t it? As you continue to pivot your vertical line, so that it is more and more starting to resemble a horizontal line, 2 feet above your original line, point I really zooms out there. And it seems like, when you finally get your “vertical” line parallel (from the pivot point P of view) point I must “jump the track.” It must leave that horizontal line. It must disappear. Otherwise, your two lines can never really become parallel.

    But where is that point of jumping the tracks? Can you identify it? Pick a point at random. Call it point J. That is the last point the two lines have in common. After that the two lines are separate. They never touch, as we’re told parallel lines never do.

    But, geometry also teaches us that between any two points, it is always possible to draw a straight line connecting them. So take a point one foot further than J on the original line. Call it point F. And you can draw a straight line from point P to point F! So point J is not the last common point after all! You can quickly see that there never will be a last common point.

    So parallel lines do indeed intersect, at infinity!

    Obviously, then, mathematics does not really describe reality. Or does it?

    Well….if you build on your new parallel lines derivation, you come up with a different, oddball, non-Euclidian geometry. And it turns out, that geometry does have application in reality, because reality is decidedly oddball, as we know from trying to wrap our heads around relativity. And, what’s even worse: quantum mechanics.

    When science is experimenting in the lab, it is easy to explore and deduct. You just mix chemicals, take cover, and see what happens. You taste or feel or weigh the results. But you can’t do that on the cosmic scale….it’s too far away. And you can’t do it on the subatomic scale….it’s too tiny to insert your fat fingers. Therefore scientists use mathematics to go where their instruments cannot, utilizing the fact that math correlates highly with the way things are.

    A total eclipse of 1919 furnished proof of Albert Einstein’s theory of special relativity, first published in 1905. If Einstein was right, an object of huge mass (the sun) would bend light (from the stars behind it) and the angle of the bend could be recorded by scientists. If Einstein was not right, there would be no bending of light, and that too, could be verified by scientists. Einstein was right.

    But the frizzy haired physicist wasn’t on pins and needles the night before the big test. He wasn’t sweating it. He knew his theory would hold.

    The math worked.
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    If you try the parallel lines trick on your pals, (amaze your friends!!) some, depending on who your friends are, will grasp it right away. Others will argue with you forever. And some will get mad. I suspect the third group feels threatened. Indeed, we may need to live forever to figure this out.

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    “God wrote the universe and the language that he used was mathematics.”      Galileo

  • A GPS System to Tell Me Where to Go

    They really have a lot of cool gadgets these days. Like the GPS navigational system for your car. The really fancy ones feature a feminine voice to guide you along your way, tell you where to get off and so forth. I bought one for my car. So did my correspondent Romulus. But Romulus was unnerved by the female voice and shut it off. If he wanted such an accompaniment, he declared, he would get married.

    Though it took years of counseling, I overcame matrimophobia. I married a woman who is a fine creature, a credit to her species in every way. From what I have observed, most women fall into this category.

    Once in a while, though, you get a clunker. It is a shame that the GPS industry didn’t do its homework before hiring the woman to serve as its navigation voice. I happen to know that the woman’s name is Clara Claptwaddle, and she can be a little…..ahem…..overbearing.

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    In about a half mile, turn left.

    Now drive one mile and turn right.

    Turn right in one half mile

    In about a quarter of a mile, turn right.

    Right turn ahead. Slow down.

    Slower.

    No, that’s not slow enough. Please continue to…..where is your turn signal!?

    Okay, turn here.

    Whoa! You almost wiped out that little old lady. You didn’t see her? I told you to go slower. Are you listening to me, Mr. Sheepandgoats?

    Now, please continue. Our destination is six miles away. I would like to get there in one piece, if you don’t mind.

    In about three miles, turn….please put both hands on the wheel!

    After two miles….pardon me? Don’t you speak to me in that tone of voice! No, I will not be quiet! Listen, I realize this may be painful for you to hear, Mr. Sheepandgoats, but somebody has to tell you how inattentive you are behind the wheel! Somebody has to…..get your hand away from that “off” button!

    There! You see, it made no difference. You need to hear this, and I will not be silenced. Oh, why can’t you be more like my first owner? He knew how to drive. And he knew how to speak to a lady! Now….get on the right side of the road! Where do you think you are, England? Honesty, I don’t know how you got your license and if all you’re going to do is justify yourself, then I have but one thing to say to you! Are you listening to a word I say, Mr. Sheepandgoats? Now I would appreciate it if you would kindly…….

    Ain’t technology great?

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    Better to live in a desert than with a quarrelsome and ill-tempered wife.    Prov 21:19

     

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    Tom Irregardless and Me                No Fake News but Plenty of Hogwash

  • Disabled Kids and Three Aborted Planets

    For whatever is hidden is meant to be disclosed, and whatever is concealed is meant to be brought out into the open.   Mark 4:22  NIV

    A long-dark secret of school textbook publishers has, at last, come into the glaring light. When you see a kid in a wheelchair in your school textbook, interacting with other kids, he is actually able-bodied and doesn’t need a wheelchair at all!

    Why photograph  a kid in a wheelchair when he can walk around like everyone else? Because disabled people are one of the social groups contributing towards our rich diversity. So if you show a bunch of kids at school or anywhere else, one of them had better be in a wheelchair. Trouble is, they can’t find enough disabled kids to model, so Houghton Mifflin sticks able-bodied kids in the “house” wheelchair, kept on hand for just such emergencies. (WSJ 8/18/06) Only a quarter of the disabled kids in photos really are disabled. Publishers therefore have to be careful that a kid in a wheelchair is not seen, a few chapters later, playing football.

    Sometimes the light from one news story can illuminate another. Such is the case here. We are now in position to understand the sudden rush to classify new planets,with our present nine planets expanding to twelve, if the International Astronomical Union’s executive committee has its way. It plainly is an effort to project our wonderful diversity into the very heavens.

    We already have, commendably, a planet for women, Venus, to offset Mars, the one for belligerent guys. There is also a planet for dog lovers, Pluto; a planet for automobile aficionados, Saturn; and a planet for practical jokers: Uranus. (is there life on Uranus?) But, except for women, these groups reflect the diversity of another age. We must now demonstrate sensitivity towards more up-to-date minorities. Thus the three new planets will, no doubt, consist of a gay planet, an Hispanic planet, and a disabled planet.

    The government, of course, will spend an obscene sum of money in naming the new planets. The Whitepebble Religious Institute is angling to land a soon-to-be-awarded naming contract, and it’s track record is good in this regard, since it has mastered the fine art of the low bid. In it’s proposal, the Carriertom organization tentatively suggested Provincetown, Poncho, and FranklinDRoosevelt as new planetary names, just to show that they are on the ball. The real contract money will be made from exhaustive testing to ensure that, God forbid, whatever new names are decided upon do not offend anybody.

    Better still, the contract may be open-ended. There’s lots of rocks and stuff out there that may qualify as planets under the new definition. Tom Whitepebble  eagerly awaits the day when every minority, no matter how tiny, has its very own planet, at $200,000 a pop for the Research Institute.

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    Update: The IAU has voted. They did the completely unexpected! In a contemptuous show of insensitivity, the organization not only declined to recognize the new planets, but they delisted Pluto. Now there are eight planets, not nine, much less twelve.

    This is a politically correct age. Do not think dog lovers will take this lying down. We can expect protests, which will probably begin when they refuse, in retaliation, to clean up after their pooches from now on. One can only hope that when members of the IAU saunter through the park and step in you-know-what, they will reflect upon the great injustice they inflicted on the noble dog lover.

    As for the Whitepebble Religious Institute, looks like it's back to parking cars on its front lawn for nearby stadium events.

    ******  The bookstore

  • Telomeres and Old Folks

    Every decade or so, Awake! magazine looks at the research of aging scientists, that is, scientists who investigate aging, gerontologists. The picture changes dramatically. Twenty years ago, they hadn’t a clue about aging. But with success in mapping the genome, some began to think aging itself could be halted, or at least slowed. They got downright cocky, some of them, and there is still much optimism.

    We all accept death as a finality. But there are things about it that don’t quite square. For instance, who hasn’t heard that we use one tenth of one percent of our brain? The exact percentage doesn’t matter. The question that matters is…..how did that come to be? There’s no way evolution can account for it. Mutations survive to be passed on to succeeding generations only if they give one an edge to survival. But we’ve just stated that we never use the 99.9% extra capacity. So where’s the necessary edge to ensure such excess brainpower is passed on? It’s as if you own a house as big a New York State, yet you only use a few hundred square feet for living.

    Our immune system is also curious. Cut your flesh and your body repairs itself. Organs of the body continually replace cells with new ones so that, every few years, you are physically, an entirely different person. Imagine if your Buick did that. Would you ever need to replace it? With life, however, the repair process itself gradually slows down and stops. But why should that be?

    Frankly, the picture corresponds with the Bible account that man was created to live forever, death coming about only through disobedience. Of course, this would require us to accept…..gasp…Adam and Eve, and painfully few, if any self-respecting scientists would ever make such a pathetic mistake. Still, many have come to view aging as a not inevitable human condition.

    Our chromosomes have segments of repeating DNA at both ends that act much like tips on our shoelaces. Without them, the chromosomes would unravel and become unstable. Named telomeres, some scientists view them as key to aging.

    Every time a chromosome divides to form a new cell, the telomere ends shorten. When they whittle down to nubs, after 50 or so divisions, the cell divides no more and soon dies. But a certain enzyme, called telomerase, prevents that shortening. With that enzyme present, cells in the lab divide indefinitely….they do not die. Unfortunately, they also tend to become cancerous. But it offers intriguing possibilities and consumes much energy from the gerontologists.

    Will scientists figure it out, or will it remain always e beyond their grasp?

    *************************  The bookstore