... but she cannot be healed. -- Jeremiah 51:9
One of the nasty things about crossing an event horizon is nothing happens locally to indicate that a fateful threshold has been crossed and destruction can no longer be averted. If you're busy gazing into your navel, you will remain clueless, though the signs can be seen clearly if you look to the distance. For a two-meter tall human being, the difference in gravitational acceleration between his head and his feet as he crossed the Schwarzscshild radius of the supermassive black hole at the center of NGC 4889 (the largest known black hole) would only be about 5 x 10-11 m/s2 -- smaller than the same difference for a man standing on Earth by a factor of about 100,000.
Wednesday, June 26, 2013
Thursday, June 13, 2013
Not Advancing Because They Are Not Challenged
There was a story on NPR yesterday about how high school students today are reading books intended for much younger children rather than growing into meatier, more sophisticated books. According to Eric Stickney of Renaissance Learning, "The complexity of texts students are being assigned to read has declined by about three grade levels over the past 100 years. A century ago, students were being assigned books with the complexity of around the ninth- or 10th-grade level. But in 2012, the average was around the sixth-grade level." Students have always had difficulties with hard books, but rather than challenging them and -- heaven forbid! -- educating them, the response has all too often been to lower the expectations and find "fun" or "relevant" books at a lower level.
I couldn't help but see the parallel with what has happened to the Mass over the same period. Latin was "too hard", so now we have the vernacular -- and specifically "translations" that were dumbed down in a way that frequently changed the meaning and lacked any kind of beauty. When the translations were recently improved, there were many complaints by lazy priests that the laity could never understand big words like "ineffable" or "consubstantial", as though teaching the Faith were not the responsibility of priests. And heaven preserve us from "relevant" liturgies. If the argument has been that "relevant" liturgies in "simple language" would encourage participation and enhance understanding of the Faith, the results have been exactly the opposite.
I couldn't help but see the parallel with what has happened to the Mass over the same period. Latin was "too hard", so now we have the vernacular -- and specifically "translations" that were dumbed down in a way that frequently changed the meaning and lacked any kind of beauty. When the translations were recently improved, there were many complaints by lazy priests that the laity could never understand big words like "ineffable" or "consubstantial", as though teaching the Faith were not the responsibility of priests. And heaven preserve us from "relevant" liturgies. If the argument has been that "relevant" liturgies in "simple language" would encourage participation and enhance understanding of the Faith, the results have been exactly the opposite.
Wednesday, June 12, 2013
Human Evolution and Japanimation
I can't be the only one who thinks there are some disturbing similarities between this speculation about human evolution and the following video.
Friday, June 7, 2013
A Physicist's Idea of Beauty
One of the criteria that is important in the search for new theories in physics is beauty. Unfortunately, the aesthetic used to make this judgment is not exactly obvious and is rarely explained, even in physics courses; yet general agreement tends to be reached on the basis of shared experience with physics problems. Mostly, though, "beauty" consists of symmetry.
The essence of symmetry is that you can do something that, in general, should make a change, but it doesn't. Consider the small letter b. If you hold it up to a vertical mirror, you get a different letter, d. If you reflect b through a horizontal mirror, you get yet another letter, P. Thus b does not have any reflection symmetries. On the other hand, T is unchanged by a vertical mirror, so it is more symmetric. X is even more symmetric, since it is unchanged by either a vertical or a horizontal mirror.
A good example of symmetry in physics can be found in Newton's Laws. Students learn early on that these laws work just as well in any inertial frame of reference -- a frame of reference that is not rotating and is related to any other inertial frame by only a constant velocity. If you're a passenger in the front seat of a car driving at constant speed along a smooth, straight road, you can toss an apple to a friend in the back seat just exactly the way you would if the car were parked. Both this moving car and the parked car are in inertial frames of reference -- at least when we ignore the rotation of the earth, which is too slow to make a noticeable difference on the apple's trajectory.
In many cases, symmetry is present as a pattern. A good example are the three known "generations" of quarks and leptons. One generation consists of the Up and Down quarks (which combine to make protons and neutrons), the Electron, and the Electron Neutrino. Everyday matter consists mostly of these two quarks and the electron. Then another generation was discovered, piece by piece: the Charm and Strange quarks, the Muon, and the Muon Neutrino. Aside from the neutrinos, whose mass is not well known, these act just like more massive versions of the first generation. So when a Bottom quark, a Tauon, and a Tauon neutrino were discovered, physicists were convinced that there must be another quark to complete the set -- a Top quark. They were right.
This kind of thing has happened so often that physicists would definitely fall for this cartoon gag. The pattern must be completed!
But the history of physics is not an unbroken chain of successes. Over the years the similarity between Newton's Law of Gravity and Coulomb's Law of electrical attraction and repulsion has inspired many physicists to try to combine them into a single law that would be in some sense more symmetric. Einstein himself tried to do this, but it has always ended in failure. Unifying gravity with electromagnetism -- and with the other fundamental forces -- is one of The Big Questions in physics today.
Then there is the magnetic monopole. This is a hypothetical particle that would make magnetism more like electricity by being all "north pole" or all "south pole"; to keep the discussion simple, let's restrict our discussion to the "north pole" magnetic monopole. From whichever direction you approached this particle, you would see that you were approaching the north magnetic pole. This is not the case with familiar, real-world magnets; when you approach from one direction, you're getting closer to the north magnetic pole, but when you approach from the opposite direction, you're approaching the south magnetic pole.
There are two basic reasons why many physicists think that magnetic monopoles probably do exist, even if they have resisted all efforts to find one so far. (They may exist as possible particles, but be hard to produce in particle colliders and decay almost immediately when they are produced.)
1. Magnetic monopoles would make the equations of electrodynamics much more symmetric. Monopoles would act as sources for the magnetic field, similar to the way electric charges act as sources for electric fields and masses act as sources for gravitational fields. Also, just like a current of electric charges generates a magnetic field, and current of magnetic monopoles would generate an electric field.
2. The existence of magnetic monopoles would explain why charges are quantized, coming only in units of the charge on an electron.
Interestingly enough, "magnetic monopoles" of a sort have been observed in synthetic materials. This is less significant than it sounds. The "magnetic monopoles" occur only as quasiparticles in materials, and they apparently are not monopoles of what is called the B-field (the magnetic field of interest, as opposed to the H-field, which includes the effects of the material's magnetization). Also, materials can do strange things, bending the laws of physics beyond anything possible in a vacuum. "Electron" quasiparticles can have effective masses different from the mass of an electron; these effective masses can even be negative. Quasiparticles can have fractional electric charges, unlike real particles that can be observed in a vacuum.
Just a couple more points about the laws of classical electromagnetism. Maxwell's Equations were originally written as 12 separate equations involving the components of vectors. At the time vectors were a comparatively new mathematical idea, and Maxwell was not used to them. Oliver Heaviside rewrote them in vector form. This was not only more compact, it was more "beautiful", in that the vector formulation freed the equations from dependence on a specific coordinate system. Sometimes the geometry of the physical system is spherical (like a cloud of charge that depends only on distance from a point), sometimes it is cylindrical (like a long charged wire or a wire carrying current), and sometimes it is rectangular (like a rectangular waveguide). It is very helpful to be able to use coordinate systems with the same symmetry as the thing you're trying to describe, so it seems "beautiful" to be able to write Maxwell's Equations in a way that works for any coordinate system. In practice, though, after you choose the appropriate coordinate system you still have to expand the vector equations into sets of scalar equations for the components of the vectors in order to solve the problem. So you have a smaller set of equations to use, but they involve more complicated mathematical entities, and in order to actually use them you have to expand them back out again. If this seems complicated, then you are beginning to understand how the scientific idea of "beauty" is a subtle, acquired taste that is hard to explain.
That's not the end. In vector form, Maxwell's Equations require four equations, but they can be written in two equations if we use covariant (and contravariant) 4-vectors and rank-2 tensors. This formulation is more compact, but the complications are not really done away with, only hidden in more complicated mathematical entities. The advantage to this formulation is that it can be seen at a glance that these equations will satisfy Einstein's Special Theory of Relativity; the equations are now explicitly independent of any specific inertial frame of reference. Unfortunately -- you guessed it -- to use the equations you first have to choose an inertial frame of reference and unpack these into four equations, then choose a coordinate system and unpack them into (in principle) twelve equations. Beauty comes at a price.
You won't be surprised that these two equations can be combined into a single equation using even more hideously complicated mathematical entities by using something called Clifford Algebra. We spent so little time on that in grad school that I no longer remember what the point of that formulation might be. It is so far removed from being practical that almost no one seems to use it.
Beauty is an important guide in the development of theories, but beauty, as most adults have come sadly to know, can be deceptive. Philosophers say that in the final analysis, beauty, truth, and goodness are one; this may be true, but it is very bad advice to pretend they are identical in any but an eschatological "final analysis". The world is an astonishingly beautiful place, but we have no right to demand that it conform to our ideas of beauty.
The essence of symmetry is that you can do something that, in general, should make a change, but it doesn't. Consider the small letter b. If you hold it up to a vertical mirror, you get a different letter, d. If you reflect b through a horizontal mirror, you get yet another letter, P. Thus b does not have any reflection symmetries. On the other hand, T is unchanged by a vertical mirror, so it is more symmetric. X is even more symmetric, since it is unchanged by either a vertical or a horizontal mirror.
A good example of symmetry in physics can be found in Newton's Laws. Students learn early on that these laws work just as well in any inertial frame of reference -- a frame of reference that is not rotating and is related to any other inertial frame by only a constant velocity. If you're a passenger in the front seat of a car driving at constant speed along a smooth, straight road, you can toss an apple to a friend in the back seat just exactly the way you would if the car were parked. Both this moving car and the parked car are in inertial frames of reference -- at least when we ignore the rotation of the earth, which is too slow to make a noticeable difference on the apple's trajectory.
In many cases, symmetry is present as a pattern. A good example are the three known "generations" of quarks and leptons. One generation consists of the Up and Down quarks (which combine to make protons and neutrons), the Electron, and the Electron Neutrino. Everyday matter consists mostly of these two quarks and the electron. Then another generation was discovered, piece by piece: the Charm and Strange quarks, the Muon, and the Muon Neutrino. Aside from the neutrinos, whose mass is not well known, these act just like more massive versions of the first generation. So when a Bottom quark, a Tauon, and a Tauon neutrino were discovered, physicists were convinced that there must be another quark to complete the set -- a Top quark. They were right.
This kind of thing has happened so often that physicists would definitely fall for this cartoon gag. The pattern must be completed!
Then there is the magnetic monopole. This is a hypothetical particle that would make magnetism more like electricity by being all "north pole" or all "south pole"; to keep the discussion simple, let's restrict our discussion to the "north pole" magnetic monopole. From whichever direction you approached this particle, you would see that you were approaching the north magnetic pole. This is not the case with familiar, real-world magnets; when you approach from one direction, you're getting closer to the north magnetic pole, but when you approach from the opposite direction, you're approaching the south magnetic pole.
There are two basic reasons why many physicists think that magnetic monopoles probably do exist, even if they have resisted all efforts to find one so far. (They may exist as possible particles, but be hard to produce in particle colliders and decay almost immediately when they are produced.)
1. Magnetic monopoles would make the equations of electrodynamics much more symmetric. Monopoles would act as sources for the magnetic field, similar to the way electric charges act as sources for electric fields and masses act as sources for gravitational fields. Also, just like a current of electric charges generates a magnetic field, and current of magnetic monopoles would generate an electric field.
2. The existence of magnetic monopoles would explain why charges are quantized, coming only in units of the charge on an electron.
Interestingly enough, "magnetic monopoles" of a sort have been observed in synthetic materials. This is less significant than it sounds. The "magnetic monopoles" occur only as quasiparticles in materials, and they apparently are not monopoles of what is called the B-field (the magnetic field of interest, as opposed to the H-field, which includes the effects of the material's magnetization). Also, materials can do strange things, bending the laws of physics beyond anything possible in a vacuum. "Electron" quasiparticles can have effective masses different from the mass of an electron; these effective masses can even be negative. Quasiparticles can have fractional electric charges, unlike real particles that can be observed in a vacuum.
Just a couple more points about the laws of classical electromagnetism. Maxwell's Equations were originally written as 12 separate equations involving the components of vectors. At the time vectors were a comparatively new mathematical idea, and Maxwell was not used to them. Oliver Heaviside rewrote them in vector form. This was not only more compact, it was more "beautiful", in that the vector formulation freed the equations from dependence on a specific coordinate system. Sometimes the geometry of the physical system is spherical (like a cloud of charge that depends only on distance from a point), sometimes it is cylindrical (like a long charged wire or a wire carrying current), and sometimes it is rectangular (like a rectangular waveguide). It is very helpful to be able to use coordinate systems with the same symmetry as the thing you're trying to describe, so it seems "beautiful" to be able to write Maxwell's Equations in a way that works for any coordinate system. In practice, though, after you choose the appropriate coordinate system you still have to expand the vector equations into sets of scalar equations for the components of the vectors in order to solve the problem. So you have a smaller set of equations to use, but they involve more complicated mathematical entities, and in order to actually use them you have to expand them back out again. If this seems complicated, then you are beginning to understand how the scientific idea of "beauty" is a subtle, acquired taste that is hard to explain.
That's not the end. In vector form, Maxwell's Equations require four equations, but they can be written in two equations if we use covariant (and contravariant) 4-vectors and rank-2 tensors. This formulation is more compact, but the complications are not really done away with, only hidden in more complicated mathematical entities. The advantage to this formulation is that it can be seen at a glance that these equations will satisfy Einstein's Special Theory of Relativity; the equations are now explicitly independent of any specific inertial frame of reference. Unfortunately -- you guessed it -- to use the equations you first have to choose an inertial frame of reference and unpack these into four equations, then choose a coordinate system and unpack them into (in principle) twelve equations. Beauty comes at a price.
You won't be surprised that these two equations can be combined into a single equation using even more hideously complicated mathematical entities by using something called Clifford Algebra. We spent so little time on that in grad school that I no longer remember what the point of that formulation might be. It is so far removed from being practical that almost no one seems to use it.
Beauty is an important guide in the development of theories, but beauty, as most adults have come sadly to know, can be deceptive. Philosophers say that in the final analysis, beauty, truth, and goodness are one; this may be true, but it is very bad advice to pretend they are identical in any but an eschatological "final analysis". The world is an astonishingly beautiful place, but we have no right to demand that it conform to our ideas of beauty.
Response to "Religion? You Just Made That Up!"
Fr. Dwight Longenecker had a recent post "Religion? You Just Made That Up!" on his blog Standing on My Head. My response has become a bit long for a comment, so I am providing it here.
An atheist probably "believes in" (in some sense) science, yet science is clearly man-made. That is to say, we humans did not create nature as she is, but we do generate hypotheses, formulate plans of study, and develop theories. Light existed before mankind, but there is no reason to believe that Maxwell's Equations existed before mankind -- especially since they are very, very slightly wrong (certainly at the quantum level). But although they are man-made, they are not exactly arbitrary, either; a different human culture or an intelligent species on another planet would almost certainly derive exactly the same Maxwell's Equations (expressed in their own language) at some point. The process by which mature theories are developed, on the other hand, and intermediate approximations along the way are likely to be much more varied. For example, there have been countless scientific papers trying to explain high-temperature superconductivity -- none of them, to my knowledge, quite succeeding -- yet the diversity of conflicting theories does not mean that high-temperature superconductivity does not exist.
Well, theology is much the same. Not all religions are all man-made, but a case could be made that all theology is man-made. After all, theology is also a science. Anyone with the most basic understanding of Christian theology knows that the full reality of the Holy Trinity is beyond the understanding of any finite being; we can make a few basic statements with confidence, but anything beyond them is at best a good, man-made approximation -- sort of how the approximation π ≈ 3.14 is both reasonably accurate and also convenient for our calculations in the decimal system.
And then, of course, there is pseudoscience. Alongside the descriptions of the interior of the earth given by serious geology one can find (especially on the Internet) the "theory" that the earth is hollow. Some claim that Admiral Byrd flew through a hole near the North Pole and briefly entered the hollow earth; others claim that the hollow earth is populated by technologically advanced reptillians, or by humans living in a sort of hippy Shangri-La.
Why do so many people find pseudoscience credible? Ultimately, I think this usually comes back to the "mystery religion" aspect that I wrote about earlier: the Gnostic thrill of feeling that you are one of the elite few to be smart enough (or brave enough) to know (or face) the truth. Much of the diversity in religious belief comes originally from the same Gnostic thrill.
So, by the way, does most of atheism. Someone who simply doesn't believe in God or who doesn't care is not likely to find the question worth arguing about. Most likely he will just play golf (or watch football, or whatever) on Sundays. He may even give lip service to the ambient religion, perhaps to gain approval from his neighbors or as an assertion of ethnic identity. He may occasionally do this as a cultural exercise -- if you watch travel programs, it's not uncommon for the show's travelers in the Himalayas to burn incense to the Hindu god of the mountain, or for visitors to Maya pyramids to obtain the blessing of a local shaman, etc.
That type of unbeliever is unlikely to think of himself as an atheist and is even less likely to proclaim his atheism to the world, except perhaps as the result of a direct question. No; the kind who draws attention to his disbelief does so because he enjoys feeling that he belongs to a unique and highly exclusive club of the bright and brave. In this he is like the sedevacantist Catholic and the neopagan, though they may have little else in common.
An atheist probably "believes in" (in some sense) science, yet science is clearly man-made. That is to say, we humans did not create nature as she is, but we do generate hypotheses, formulate plans of study, and develop theories. Light existed before mankind, but there is no reason to believe that Maxwell's Equations existed before mankind -- especially since they are very, very slightly wrong (certainly at the quantum level). But although they are man-made, they are not exactly arbitrary, either; a different human culture or an intelligent species on another planet would almost certainly derive exactly the same Maxwell's Equations (expressed in their own language) at some point. The process by which mature theories are developed, on the other hand, and intermediate approximations along the way are likely to be much more varied. For example, there have been countless scientific papers trying to explain high-temperature superconductivity -- none of them, to my knowledge, quite succeeding -- yet the diversity of conflicting theories does not mean that high-temperature superconductivity does not exist.
Well, theology is much the same. Not all religions are all man-made, but a case could be made that all theology is man-made. After all, theology is also a science. Anyone with the most basic understanding of Christian theology knows that the full reality of the Holy Trinity is beyond the understanding of any finite being; we can make a few basic statements with confidence, but anything beyond them is at best a good, man-made approximation -- sort of how the approximation π ≈ 3.14 is both reasonably accurate and also convenient for our calculations in the decimal system.
And then, of course, there is pseudoscience. Alongside the descriptions of the interior of the earth given by serious geology one can find (especially on the Internet) the "theory" that the earth is hollow. Some claim that Admiral Byrd flew through a hole near the North Pole and briefly entered the hollow earth; others claim that the hollow earth is populated by technologically advanced reptillians, or by humans living in a sort of hippy Shangri-La.
Why do so many people find pseudoscience credible? Ultimately, I think this usually comes back to the "mystery religion" aspect that I wrote about earlier: the Gnostic thrill of feeling that you are one of the elite few to be smart enough (or brave enough) to know (or face) the truth. Much of the diversity in religious belief comes originally from the same Gnostic thrill.
So, by the way, does most of atheism. Someone who simply doesn't believe in God or who doesn't care is not likely to find the question worth arguing about. Most likely he will just play golf (or watch football, or whatever) on Sundays. He may even give lip service to the ambient religion, perhaps to gain approval from his neighbors or as an assertion of ethnic identity. He may occasionally do this as a cultural exercise -- if you watch travel programs, it's not uncommon for the show's travelers in the Himalayas to burn incense to the Hindu god of the mountain, or for visitors to Maya pyramids to obtain the blessing of a local shaman, etc.
That type of unbeliever is unlikely to think of himself as an atheist and is even less likely to proclaim his atheism to the world, except perhaps as the result of a direct question. No; the kind who draws attention to his disbelief does so because he enjoys feeling that he belongs to a unique and highly exclusive club of the bright and brave. In this he is like the sedevacantist Catholic and the neopagan, though they may have little else in common.
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