Technology has transformed society in innumerable ways, but one thing that never gets mentioned is how it has transformed ignorance. Two centuries ago (and still today in parts of the globe), if you had a poor education, your world was one of superstition. You planted crops for a harvest that your life literally depended upon, and you appealed to a supernatural deity to sustain you and your family for another season. If you were the curious type and had questions about nature, you may have sought answers from a religious leader. Non-religious superstitions prevailed as well: lucky horseshoes, old wives’ tales, ghosts, goblins, and demons, not to mention your occasional witch hunt or burning-at-the-stake.
Naturally, with the advent of public education and mass communication, superstition in the developed world has waned. People in First World countries don’t go through life without learning certain things, for example what those little specks of light in the night sky actually are. However, ignorance seems to be roaring back — in a different, more insidious form.
Conspiracy theories seem to be taking over the role formerly held by superstition. The best way I can illustrate this is through the incredible “chemtrails” theory. (I had never even heard of this until I made a few videos about “9/11 Truth” in 2011.) Some people believe that the government is keeping the masses under mind-control by spraying the skies with soporific chemicals that are released at high altitude by jet aircraft. That’s what those supposed “condensation trails” are, you see, that can stretch all the way across the sky. Have you ever noticed how sometimes the trail dissipates quickly, and other times it lingers for the better part of an hour? And have you also noticed that low-flying aircraft never release these trails of chemicals? It’s a huge conspiracy by the government, you see. The only reason why you think it isn’t a conspiracy is that your mind has been successfully zombi-fied by the government’s chemicals. (Somehow the believers of the theory are immune to the effects.)
Of course, there’s a perfectly rational explanation for condensation trails, and it’s available for anyone to read.
Centuries ago, a widespread superstition or old wives’ tale might have been killed off by the existence of a high-quality information source that anyone could read, at home. (Sadly, there hasn’t been a good old-fashioned witch hunt in my village for years.) Religion remains widespread, but only because it forms a major part of many people’s identities. Life is tough for a fringe superstition these days; there’s just too much reliable information, and it’s too easily accessed, for most people to go on believing in witches and such. What’s a person to do if he wants to wallow in ignorance?
Reject the information. This is the prime strategy of the conspiracy theorist: The information that would debunk the chemtrails theory, for example, is part of the conspiracy. The “official explanation” has been created by the conspirators to keep you from asking questions. This is how an ignorant person attempts to propagate his ignorance throughout society: by telling others that “official” information is a lie, by denegrating the sources of the information (“science is just another religion”), by denegrating those who accept mainstream ideas (“go back to sleep, you sheep”), by appealing to anti-authority sentiments, and by appealing to common sense through oversimplification. I wrote about these techniques in an essay called The Bullshit Syndrome and How to Spot It.*
In the modern world, superstition can even morph into conspiracy theory. A few years ago there was a film called Expelled: No Intelligence Allowed, about how the “intelligent design” movement is being squelched by mainstream science. What was originally a superstition — God created all living things — has ended up being a vast conspiracy: God did create all living things, but “big science” (the term used in the film) has done everything to ensure that you think otherwise. Most recently, Rick Santorum announced that President Obama is a “snob” for advancing higher education. The word “elite” and “elitist” are interchangeably bandied about by politicians, who pander to voters by telling them they are naturally smarter than “Ivy League intellectuals.” Yeah, down with know-it-all snobs!
This trend is dangerous, but I don’t have a solution. In the past, ignorance went away when people were exposed to reliable information, but these days, information can have the opposite effect. It makes some people hunker down in their ignorance, as they confine themselves to echo-chamber talk-radio programs, blogs, and news sources. Perhaps ridicule and satire are the best way to go.
Note: This article was paid for by a generous grant from the elitists at the government, who don’t want you to think for yourself.
* In the “Bullshit” article I profiled an amateur physicist who believes that pi is exactly 4.0 and that green light doesn’t exist. Most of his articles are about how smarty-pants intellectuals don’t want you to understand how math or science really works. It turns out, he also believes that Obama isn’t a U.S. citizen, and that no commercial jets hit the World Trade Center on 9/11/01. And Wikipedia is the hugest conspiracy of all. None of this is surprising — these paranoid delusions are consistent with the profile I have described.
Monday, March 26, 2012
Friday, March 9, 2012
Gravity Is Not A Rubber Sheet
Every physics demonstration of gravity uses the familiar “rubber sheet” model: We are shown a stretched piece of rubber, or perhaps the surface of a trampoline. A heavy ball is placed in the middle, distorting the sheet. Now a smaller ball, pushed in the general direction of the heavy ball, will follow a curved path, as if “attracted” by the mass. If given a particular kind of shove, it will circle around the heavy ball for a while, “orbiting” like a planet around a star. Thus the model demonstrates how an object with mass warps the fabric of space, causing the paths of other objects to curve in the direction of the larger object. Objects follow straight paths through space, but if that space happens to be curved by a massive object nearby, their paths will curve. Since Einstein, we’ve known that this is what causes gravitational attraction.
When I was first getting interested in physics, the rubber-sheet model of gravity bothered me. For one thing, it only works in gravity! It seemed that the rolling ball was just curving downhill. Tilt the sheet without warping it, and its path will curve the same way. In the weightlessness of the International Space Station, I figured, the model wouldn’t do anything. I didn’t like that gravity was required in order to demonstrate how gravity works. It was like a model that shows where wind comes from, but which only works when it’s windy.
Something else disturbed me. When the rubber-sheet model is presented in diagram form (in books, for example), the diagrams are often inconsistent. Empty space is depicted as a flat grid of straight lines, but when a massive object is added, some of the lines suddenly form circles. The graph-paper grid turns into a pushed-in dartboard or spider-web pattern, with circular elements representing potential orbits around the mass. Thinking that maybe I had discovered something, I wondered: At what point do the open-ended straight lines of empty space start joining together to form closed circles? If we took an empty region of space and gradually started adding mass to it, when would the circles appear? I was perplexed — the diagrams never show that transition, just the before and after!
What’s wrong with this picture?
The problem of course lies not in Einstein’s theory, but in the rubber-sheet model. It isn’t a perfect analogy for gravity.
It’s a coincidence that real gravity on Earth causes a rubber sheet to warp in a manner that suggests the warping of space. You could just as easily turn the model upside down, and push the ball up against the rubber sheet, and the sheet would be warped in the same way (just in the opposite direction). The rubber-sheet model of gravity is intended to demonstrate how a massive object causes space to curve, so it’s the warping of the sheet that’s important, not the direction.
When a two-dimensional surface is curved into a third dimension, its geometry changes. No longer do the laws of Euclid, which most of us learned in 9th grade, apply: The angles of a triangle do not add up to 90°, for example. In ordinary geometry, two parallel lines never meet; in the non-Euclidean geometry of a curved surface, parallel lines can meet. Imagine that you and a friend began walking from the equator to the north pole. Initially, your paths would be exactly parallel, but since the Earth’s surface curves, the paths would intersect at your destination. Similarly, if two objects were moving in parallel from empty space toward a star, their paths would eventually converge — even with no sideways forces acting upon them.
As it happens, the rubber-sheet model would work in zero gravity, if you warped the sheet with some other force (say, by pushing the end of a broomstick against it), and if you got the rolling ball to remain on the surface somehow (perhaps with a bit of static electricity). In that case, the ball’s path would appear to curve as it attempted to follow a straight line on this non-flat surface. And two balls, nudged along parallel paths toward the depression, would approach each other as the surface under them began to curve.
As for the grid that’s often laid over the rubber sheet, it’s only there to help you see the shape of the surface. The straight or circular lines are a human invention; there is no such grid in space. The actual paths that objects trace through warped space are, well, the actual paths that they trace. These can be circles, ellipses, parabolas, or hyperbolas, depending on the trajectory of the object.
Planets and comets go their own way — they have no use for grid lines.
The rubber-sheet model does give a general idea of how gravity deflects the path of an object. But it’s a crude demonstration, as the Earth’s gravity fouls the geometric effect that the model is intended to demonstrate.* When you see the rolling ball get “attracted” to the larger ball, much of that deflection is just the ball rolling downhill, as it would on a tilted, flat surface. A true tabletop demonstration of gravity, where objects follow stable orbits along a surface due to geometry alone — would be interesting to watch. Until then, don’t take the conventional version too seriously.
* Consider what would happen if you rolled a ball inside the surface of a vertical tube in a frictionless vacuum. Under Earth’s gravity, the ball would inevitably spiral down to the floor. But in zero G, it would follow a circular path forever. This circular orbit, not the spiral, is the accurate representation of the “straight-line path” that would be followed on the surface due only to its geometry.
When I was first getting interested in physics, the rubber-sheet model of gravity bothered me. For one thing, it only works in gravity! It seemed that the rolling ball was just curving downhill. Tilt the sheet without warping it, and its path will curve the same way. In the weightlessness of the International Space Station, I figured, the model wouldn’t do anything. I didn’t like that gravity was required in order to demonstrate how gravity works. It was like a model that shows where wind comes from, but which only works when it’s windy.
Something else disturbed me. When the rubber-sheet model is presented in diagram form (in books, for example), the diagrams are often inconsistent. Empty space is depicted as a flat grid of straight lines, but when a massive object is added, some of the lines suddenly form circles. The graph-paper grid turns into a pushed-in dartboard or spider-web pattern, with circular elements representing potential orbits around the mass. Thinking that maybe I had discovered something, I wondered: At what point do the open-ended straight lines of empty space start joining together to form closed circles? If we took an empty region of space and gradually started adding mass to it, when would the circles appear? I was perplexed — the diagrams never show that transition, just the before and after!
What’s wrong with this picture?The problem of course lies not in Einstein’s theory, but in the rubber-sheet model. It isn’t a perfect analogy for gravity.
It’s a coincidence that real gravity on Earth causes a rubber sheet to warp in a manner that suggests the warping of space. You could just as easily turn the model upside down, and push the ball up against the rubber sheet, and the sheet would be warped in the same way (just in the opposite direction). The rubber-sheet model of gravity is intended to demonstrate how a massive object causes space to curve, so it’s the warping of the sheet that’s important, not the direction.
When a two-dimensional surface is curved into a third dimension, its geometry changes. No longer do the laws of Euclid, which most of us learned in 9th grade, apply: The angles of a triangle do not add up to 90°, for example. In ordinary geometry, two parallel lines never meet; in the non-Euclidean geometry of a curved surface, parallel lines can meet. Imagine that you and a friend began walking from the equator to the north pole. Initially, your paths would be exactly parallel, but since the Earth’s surface curves, the paths would intersect at your destination. Similarly, if two objects were moving in parallel from empty space toward a star, their paths would eventually converge — even with no sideways forces acting upon them.
As it happens, the rubber-sheet model would work in zero gravity, if you warped the sheet with some other force (say, by pushing the end of a broomstick against it), and if you got the rolling ball to remain on the surface somehow (perhaps with a bit of static electricity). In that case, the ball’s path would appear to curve as it attempted to follow a straight line on this non-flat surface. And two balls, nudged along parallel paths toward the depression, would approach each other as the surface under them began to curve.
As for the grid that’s often laid over the rubber sheet, it’s only there to help you see the shape of the surface. The straight or circular lines are a human invention; there is no such grid in space. The actual paths that objects trace through warped space are, well, the actual paths that they trace. These can be circles, ellipses, parabolas, or hyperbolas, depending on the trajectory of the object.
Planets and comets go their own way — they have no use for grid lines.The rubber-sheet model does give a general idea of how gravity deflects the path of an object. But it’s a crude demonstration, as the Earth’s gravity fouls the geometric effect that the model is intended to demonstrate.* When you see the rolling ball get “attracted” to the larger ball, much of that deflection is just the ball rolling downhill, as it would on a tilted, flat surface. A true tabletop demonstration of gravity, where objects follow stable orbits along a surface due to geometry alone — would be interesting to watch. Until then, don’t take the conventional version too seriously.
* Consider what would happen if you rolled a ball inside the surface of a vertical tube in a frictionless vacuum. Under Earth’s gravity, the ball would inevitably spiral down to the floor. But in zero G, it would follow a circular path forever. This circular orbit, not the spiral, is the accurate representation of the “straight-line path” that would be followed on the surface due only to its geometry.
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