It can drive you nuts, and it can help you hear

kw: book reviews, nonfiction, acoustics, signal processing

NOISE by Bart Kosko is the most intensely mathematical book I've yet seen at the local library, outside the Reference section. The author is a professor of Electrical Engineering, a popular author, and judging from the diversity of his formal education, a polymath. Judging from the text, he is also an autodidact in a number of areas.

I'll begin with a quibble: Dr. Kosko has the teacher's habit of repetition—we all know our students don't get it the first time—, but takes it to an extent I found tiresome. There is a little English bird named the great tit (Parus major) that is an easy subject, so it is studied extensively. A number of studies have shown that it sings on a higher pitch in the presence of industrial noise. According to the index to the book, this bird appears three times. The indexer missed the other four times the story is repeated. Dr K? You had me by the second time. Your meme has now successfully reproduced!

Noise has a Jekyll-and-Hyde quality. It helps and it hurts. I have tintinnitus (I think tinnitus is the more modern term) in both ears, probably due to mowing too many lawns without hearing protection. I've never used firearms or listened to loud music; my brother, once a rock drummer, got his hearing problems the musical way. I found out something about tinnitus, when I had physical therapy for a sore neck. Certain head positions caused the ringing to get much louder. I went to an audiologist. He said the cause was that, moving the head that way triggered the "too loud" muscle that closes or narrows the ear canal in response to loud sounds (drummer's earache, my brother called it, when it went on too long and got sore). Tightening that muscle increases the resonance inside the ear, making the tinnitus louder. Tinnitus due to hair cell damage is an actual sound produced in the cochlea; a sensitive microphone can record it.

When I nap, as distinct from sleeping at night, I usually find that turning on the radio so I can barely hear it helps me nod off. It isn't quite white noise, but it masks a lot of other sounds, and its familiarity seems to help. Some noise is helpful. Indeed, noise of my choosing may be sufficient to let me rest when a neighbor is using a lawn mower or stereo up too loud. The author goes into legal implications of noise and noise ordinances, showing his familiarity with law (as it turns out, that's one of his degrees).

Low levels of noise also help detecting certain signals. This works only in nonlinear systems, but I have yet to find a truly linear system in nature. I've also occasionally heard a third tone when a friend and I whistle two loud, different tones. The third tone is always lower, the subtraction of the two higher frequencies. Theoretically, a fourth tone, the sum frequency, is also present but I haven't heard it. This phenomenon arises from nonlinearity, which is slightly present in the air transmitting the sounds, but is much greater at the air-eardrum interface, and perhaps equally so in the drum-stirrup-anvil-cochlea chain.

Anyway, this nonlinearity means a faint sound could be more discernible in the presence of an even fainter hissing noise ("white" noise). I suspect the tinnitus I already have would overcome both signals, so someone else will have to do the experiment.

In the realm of signal processing, myriads of experiments have been performed, as Dr. Kosko writes. He goes quite deeply (for me...and I am a mathematician by trade!) into the math of noise statistics and signal-noise convolutions. One aspect from which I learned much was the diversity of "bell curves". Like most classically-trained statisticians, the only bell curve I knew was the Gaussian normal. Of course, I know quite a variety of bell-like distributions (Weibull, Lognormal, Logistic, and a number of others). However, only the Normal curve has a related central limit theorem. Thanks to this book, I learned that there are a number of central limit theorems, leading to a family of symmetric bell curves, of which the Gaussian is on end-member. There were hints of other families thereof, not as relevant to signal processing.

All of these bell curves apply to the analysis of white noise, which is noise with a flat spectrum. Of course, an entity with a truly flat spectrum from f=0 to infinity is impossible, because the energy required is infinite for any nonzero signal level. In real systems, a signal can have a flat spectrum over a range of interest, but fall off at higher frequencies. Any "near-white" signal will be very jittery, but the shape of the jitteriness can vary. Thus, "well-behaved white noise" with a uniform range of excursions in sound pressure will sound like a steady hiss, "gaussian" noise with a larger number of small excursions and fewer large ones will sound crackly, and more leptocurtic distributions of sound pressure such as "cauchy" noise sound like popcorn over a fainter hiss.

Much more common are pink noise, more rumbly because the sound power at higher frequencies falls off steadily as 1/f. I suspect real "pink" noise is more like lognormal noise, with the lowest frequencies sharply attenuated, but a 1/f response above a low-frequency mode. I learned of brown noise, whose frequency spectrum is essentially the square of pink noise, and black noise, which is cubic or higher. I suspect black noise sounds a lot like an earthquake rumble, or is perhaps felt but barely heard. (NOTE to self: transduce pink, brown, and black signals into WAV files to see how they sound).

Stephen Hawking was once told that each equation in a book cuts the potential audience in half. If this were true, NOISE would have an audience of one or fewer. But the text is actually quite readable, and I can attest that, if one simply skims over the equations and scans the accompanying explanations, sufficient understanding results.

A large part of the book illustrates and explains stochastic resonance, the enhancement of detection that faint noise can confer on small signals. I can add an example. Astronomers have been taking advantage of this for decades. When recording a negative, an astronomer will balance the exposure time so that sky brightness (which is never zero) produces a density of 0.5. This means there is a background speckly gray caused by several percent of the silver grains.

It is known that for the best astro emulsions, it takes ten or more photons to make a grain "convert". If there is a faint nebula in view, so faint that only one or two photons will strike the average grain during the exposure, then statistically a larger proportion of grains will "convert" because of the added contribution of the sky brightness, which is noise to the uninitiated. The nebula would be undetectable in a much darker sky without a much longer exposure (which would then of course be possible).

The author shows how stochastic resonance works for "linear" signals and for images, and how it seems to help our neurons do their job better. He speculates that, though noise probably isn't the cause of life, it probably makes life possible.

The ultimate fly on Washington's tent flap, or Custer's, or on the Oval Office wall

kw: book reviews, nonfiction, history, north american history, historical narrative

In the early 1980s, while living in the Black Hills area of South Dakota, I heard a very entertaining lecture about the events leading to Custer's "last stand". The lecture had been arranged during the Yellow Thunder Camp occupation of part of the Black Hills by followers of Russell Means. It may have meen Means who called the Black Hills the "Sioux Vatican."

In brief, about the time white settlers began to arrive in western South Dakota in large numbers (1850s), the Lakota Sioux had been there less than a century after spreading west out of Minnesota. They first crossed the Missouri and discovered the Black Hills about 1776, calling it Paha Sapa, driving out other tribes that had suffered recent decimation by a smallpox epidemic (The Sioux were on the rebound after their own epidemics in the 1600s and early 1700s). They quickly made Paha Sapa the center of their cultural universe. By 1875, nearly the centennial of their first occupation of the area, they found themselves in a battle for survival against the white military led by Custer. Led by favorite son Sitting Bull, they eliminated Custer's small army in 1876.

The trouble is, they'd unknowningly kicked a giant, and larger, more persistent (and better led) armies followed. One might think the historian's viewpoint might be too Anglo-centric, but checking the facts of the story with friends in the Sioux and Crow tribes, I found they shared the same perspective. Comparing Paha Sapa to the Vatican is actually a better analogy than one might imagine. Vatican City was created in 1929, a remnant of the thousand-year-old Papal States territory. The location is recent, but the tradition is ancient.

The historian brought the events of the mid-to-late 1800s to life. I think this a critical function of historians. If a people who cannot recall their history are condemned to repeat it, then we need history to become a living force for us, and the onus for that is upon out historians. It is a pity so few of them are good writers or speakers.

Byron Hollinshead has gathered twenty essays from twenty historians who really know how to write. The twenty essays, ranging from analytical to speculative in tone, make up I Wish I'd Been There:Twenty Historians bring to life dramatic events that Changed America. Each historian was given the assignment to portray or explain a favorite historical puzzle. It is so incredibly refreshing to read history written by people who love their work!

This historical feast begins in Cahokia (a pre-columbian metropolis, when millions of people lived in the plains, and smallpox had yet to arrive on the continent) by Biloine W. Young, includes peeks into the life of Merriwether Lewis by Carolyn Gilman, and Jenny Lind by Philip B. Kunhards III, and concludes with Lyndon Johnson's bushwhacking of George Wallace to permit the Selma march to proceed. "The Corrupt Bargain" by Robert V. Remini portrays the congressional dickering that cost Andrew Jackson the White House in 1824—and shows that our more recent crop of scoundrels has nothing on their forebears! Have you seen Inherit the Wind? Don't think it is anywhere close to reality. The "epic battle" between Clarence Darrow and William Jennings Bryan resembled a snowball fight, and the greatest speech was not by one of those old scrappers by by Dudley Malone (who?)...you can look it up, and Jonathan Rabb lays it out for us.

A book like this makes history worth reading, and historians worth supporting.

An olive branch, or a slap in the face?

kw: book reviews, nonfiction, evolution, religion, controversy, natural selection

The opening paragraph of Chapter 1, titled "The Future Can Differ from the Past", is very hopeful:

"This is a book of tall claims about evolution: that it can become uncontroversial; that the basic principles are easy to learn; that everyone should want to learn them, once their implications are understood; that evolution and religion, those old enemies who currently occupy opposite corners of human thought, can be brought harmoniously together."

Doesn't that sound like the author is conciliatory, perhaps willing to admit that spiritually-minded people may know something that is not amenable to scientific study but is nonetheless valid? Sadly, after ten chapters of nice talk, we have this, in Chapter 11, titled "Welcome Home, Prodigal Son":

"First, we must abandon the notion that some special quality was breathed into us by a higher power. This does not require abandoning religious faith—many people manage to combine a vibrant religious faith with a fully rationalistic conception of the world—but it does require abandoning certain kinds of religious faith."

The author is David Sloan Wilson, whose book Evolution for Everyone: How Darwin's Theory Can Change the Way We Think About Our Lives is the latest attempt by a well-meaning scientist to bridge the cultural gap between (some) scientists and Christians who believe that the Bible is more than a story book. The arrogance of his position is extreme. I'd answer this way:

David, just who is the prodigal here? This parable is by Jesus, not by Ed Wilson! Jesus wants you to turn to faith in His Father. Religion and Darwinism enjoyed a century of amicable relations, until the sudden resurgence of "biblical inerrancy" views seventy years ago. The earlier, more reasonable Evangelical viewpoint was that the Bible tells us what God wants us to know about relationships, both horizontal and vertical, and that poetic language is not intended to convey exact knowledge of the natural world. This is still the position of the majority of Bible believing Christians. However, to "abandon" the inspiriation of a human spirit by God is simply apostasy. David, to eliminate the "certian kinds of religious faith" that you wish people to abandon would remove every genuine Christian from the planet. You are proposing spiritual genocide. How naïve! Paul wrote in 1 Corinthians 15:19, "If we have hoped in Christ in this life only, we are of all men most to be pitied." Christian faith and practice make no sense without a real God and without hope in His eternal Kingdom.

I distinguish faith from religion. To me the term "religious faith" is meaningless. Religion is practice, regardless of its motive. Faith is a motivation based on a spiritual experience. Christian faith is based on a revelation of God. According to both the Bible and the experience of millions of believers, the human spirit is an organ, distinct from the soul and body, that mediates contact with God and fellowship among His people. The Bible describes this in detail. If it is to be believed—and tens of millions do so believe—faith is the result of a direct revelation from God, an experience that forever changes how a person thinks about God. A Christian is someone who has met God, personally. One cannot "abandon" an experience.

The Bible contains a distinct definition of faith, in Hebrews 11:1, "Now faith is the assurance of things hoped for, the conviction of things not seen." Once faith is received (it isn't natural, not the Biblical kind), a person has an inner conviction of the reality of God and an expectation that the Biblical promises will be kept. Biblical writers even use special words for "know" and "knowledge" when referring to knowing the things of God.

I follow the progress of a number of scientific disciplines. I find today's cosmology quite interesting, if rather quizzical. Certain observations of star motions in galaxies have convinced astronomers that most of the gravitational force keeping the stars in their orbits is generated not by matter as we know it but some kind of "dark matter", and speculation abounds about what it might be. The only thing known is that this stuff has gravitational mass but is not affected in any way (that we yet know of!) by light or other electromagnetic radiation. Thus, something like 85% of the matter Universe is unseen, and perhaps unseeable. Interestingly, some scientists suggest that gravitons (or whatever it is that mediates gravitational force) travel at a speed different from that of light, which increases gravity's effect over galactic distances, thus no "dark matter" is needed. These folks are greatly disparaged, and they can't get funding to do the experiments necessary to determine if their idea has merit. This sounds like a religious controversy to me! The "establishment" scientists have great faith, do they not? They have little else to go on!

Guess what, it just might be religious after all. Some Christians, long before this controversy arose in recent decades, noticed Colossians 1:17, "He is before all things, and in him all things hold together." Could the power of God account for 85% of the Universe? To bring about "The End", perhaps all He need do is simply let go. Personally, I like the gravity idea better. Furthermore, the "dark energy" that seems to be speeding up the expansion of space requires the greatest, most astonishing leap of faith I've ever heard of. I've looked long and hard at the data. It is not yet conclusive. The error bars on every chart I've seen are larger than the effect. This idea is based more on the theory that space "just has to be flat" than on anything truly scientific. Speculation gone wild...or maybe "dark energy", which amounts to three times as much gravitational potential as "dark matter" plus ordinary matter combined, is a further manifestation of divine power. Again, I don't think so. I think it just shows that science is still too limited to deal with cosmology with anything like the precision and completeness that is so arrogantly claimed. Let's give it a century or so of further study and see what else shows up.

So, back to my exhortation: David, you require people who have met God to "abandon" their belief in Him, before you will allow us the right to an opinion. You have not met Him. I have experience and you have ignorance. You claim that "factual reality" is complete, that it is all there is. I claim that it is not. I have shown that many scientists cannot even agree on how much "factual reality" is presently in existence, or even detectable. You must at least admit that I might have actually met God. You must take an agnostic, not an anti-theistic stance, at the very, very least. Otherwise, you have no right to an opinion about faith. You are in a territory such that you are unable to have a valid thought about the subject.

Religion? Go ahead, have all the opinions you want. Religions need no gods. Indeed, a good friend who is a Hindu told me, "My Guru is primary, my family is next, and then come the gods." Another friend, a Buddhist, has explained their entirely godless religion, in which Karma and Reincarnation work blindly in an eternal cycle; their cosmogony could run as a computer program. In fact, any religion could. Religions are rule-based, and I often joke that "You can hang the rules of your religion on the wall, and a robot could do them, but you cannot." Religious practices are quite amenable to scientific study. The desire to (try to) conform to an ethical Rule is nearly universal (sociopaths excepted), so it is certainly an evolved trait (as is sociopathy).

So to evolution. I like 90% of the book. Great examples, a clear teaching method, and I suspect the EvoS project is well worth the undertaking. I may do so myself.

David's thesis is simple. It is worthwhile to bring evolutionary thinking to bear on any observed phenomenon. (As a Geologist and amateur in a number of disciplines including Astronomy, I write and speak of galactic, stellar, planetary, continental, mineralogic, and chemical evolution. Particularly with regard to the concentration and emplacement of ore minerals, a kind of natural selection takes place, but of course there is no genetic/hereditary mechanism to produce new variations [elements and minerals]. Nearly all of geology is a reworking of existing Earth materials...but not quite. The planet does intercept a few tons of new matter daily.)

For example, he shows that, on every level one may imagine, collective behaviors tend to increased prosperity, or fitness, of the group. Units that prefer to exploit the group decrease its overall prosperity and fitness, so groups develop mechanisms to limit such damage, or they vanish. Thus, societies with appropriate laws and sufficiently strong enforcement mechanisms succeed better than anarchic ones (so we can expect nations that support terrorists to decrease in relative prosperity). A metazoan animal, such as a coral polyp, a bandicoot, or a human, is a collective of many cells that usually behave according to strong rules, genetically encoded, that even tell certain cells when to suicide. Cancer results when cells become rulebreakers and self-seekingly abandon behavior for the collective good.

Each cell of a polyp, a bandicoot, or a human, or of a tree, grass blade, or amoeba, is also a collective. Probably 1.5 billion years ago, after 2+ billion years of experimentation with various kinds of collective agglomeration, groups of specific kinds of bacteria became something new, the eukaryotic cell. All the "organelles" in such a cell must originate from bacterial precursors, and groups thereof managed to enclose themselves in a larger lipid membrane derived from that of an extra-large species of bacteria. (Perhaps it was related to the "giant bacillus" found in all human mouths, a brownish critter as large as some eukaryotes: about 15-20 microns long and 2-3 microns in diameter. It has 40-100 times the cell volume of smaller bacilli like E. Coli.)

What usually prevents human cells from turning into tumors or cancers? A lot of our DNA is not for making proteins but for regulating gene expression, particularly genes that affect cell growth. You could call a cell a totalitarian state. There are "police forces" and "executioners" within each cell that detect and edit DNA that mutates in deleterious ways, most of the time. There are similar cellular police in our immune system, and most cells that try to take off on their own are marked "not me any more" and destroyed.

A lot of Evolution for Everyone is devoted to applying evolutionary thinking to human groups, from households to nations. In the process, as the organisms themselves become more able to develop culture, evolution of the culture proceeds more rapidly than that of the biological organisms, yet by similar means. This reaches an extreme level in nations and nationalism. David states that "modern nations represent the current frontier of multilevel cultural evolution." Here is how most nations behave:

Imagine starting a conversation with someone who turns out to be nakedly selfish. Not only does she care only about herself, but she talks to you as if she cares only about herself. You hear all about her schemes for gettint ahead while riding roughshod over other people. Then she reveals how you figure in her plans without the slightest concern for your welfare. You would be doubly amazed at such a person. Only a social idiot would first have such shrunken values and then make no attempt to disguise them.

Yet I have just described the average political speech on international relations.

To me this is evidence that natural selection hasn't been operating very long in the political arena.

Of more immediate interest to me is the idea that the rules, or laws, make a family, church, club, neighborhood, or society livable. I once read that the police cannot enforce any law that is not voluntarily obeyed by at least 85% of the populace. This is the big reason most cars on I-95 go 70 mph or faster: because they can get away with it. The police have determined than the 15% cutoff is about 75 mph, so by going after only the fastest 15%, they establish what the "practical" speed limit is. In any group, if compliance to a crucial rule or law vanishes, pretty soon the group breaks up or falls into anarchy: disfunctional family; churches that split and split again; clubs that disband or fail due to lack of interest; neighborhoods that become hellholes; nations that fail.

But I concern myself with the effect police work has on police. In a recent case, several police fired 30+ bullets into a handicapped man who had failed to "obey instructions" (turned out they were talking too fast, and he was slow of mind), and celebrated their "kill" with high fives and a kind of dance. What happened to them? "You can't wrestle with a skunk and come out smelling like a rose." Police spend all their time with criminals, and guess who influences whom the most?

I am in favor of citizen-deputies, and very few "professional" police officers. In fact, I'd favor universal police service, on a rotating basis. Only in this way would this beleaguered group, our "peace officers", be spending more time with lawkeepers than with lawbreakers.

Much is made by this author and others of the "two island" thought experiment. In one case, populate one island with "good" folks, and the other with "bad" ones. The good will get better and the bad will get worse. Then take one "bad" person to the "good" island: he or she will soon live in luxury, at the expense of the rest. Mix the two groups in equal numbers on one island and "good" behavior will vanish away.

This model supposes that the "good" are uniformly good and never bad, and the converse. Actual people are complex. Every one of us is both good and bad. I lead a church. In a recent church meeting, at a round table discussion, we were talking of the meaning of love, and testing some boundaries. The Va Tech massacre was fresh on our minds, as was a recent suicide bombing in the MidEast. At one point, I remarked, "If you put me in a room with an unarmed terrorist, I could talk to him. But if I saw the same person in an overstuffed trench coat heading for a schoolyard, I'd shoot him in the head." In the ensuing discussion, most agreed this would show the greatest love possible to the potential victims, at the expense of sending one person to his god a bit early. It is Audie Murphy's reasoning: initially somewhat reluctant to shoot at an enemy, he reasoned that killing an enemy soldier saved a larger number.

I hope David becomes willing to allow believers to believe. I've long deplored the lunatic fringe of "inerrancy" folks, but I don't begin a discussion with any of them by demanding that they abandon their most cherished beliefs. I am a Christian evolutionist. God isn't afraid of evolution, and those who think they are defending Him are really only defending their own insecurities. The Bible leaves plenty of room for the eons of planetary and biological evolution to mold Earth and its life into the enviroments we experience today.

God works with human hearts. He seldom messes with nature. I have elsewhere written of the nature of miracles: they are events for which science will not and cannot provide an explanation, because they are produced by One who does not take note of science or technical tests. Such events are few. Don't look for a natural explanation for the sun stopping in the sky when Joshua asked God for that. Either it didn't happen at all, or it happened by a non-natural agency. About such things, science and scientists can only say, "I don't know." Only a person who meets God and receives His faith is able to know. Let us be humble, even though we know God, because that knowledge alone doesn't go very far.

I find it encouraging that this author at least tries to be conciliatory. That is a step too few scientists have been willing to take.

When the earth moves, his name is on everyone's lips

kw: book reviews, nonfiction, seismology, earthquakes, biographies

As a Geology student in about 1970, one big, big thing they drummed into us about earthquakes was the difference between Intensity, which is different at every point, and Magnitude, which is a characteristic of the total event. When an earthquake happens, a section of a fault—a large crack in the rocks of the earth's crust—experiences displacement. By displacement, I refer to the relative motion of rocks on the opposite sides of a flattish area. This area can be small, perhaps the size of a strip of roadway a block long; the relative motion may also be small, perhaps a few inches; in such a case, unless you happen to be lying down right above that section of the fault, you won't feel it. A small quake like this occurs, at the fault, in a second or less.

On the other hand, a section of fault a thousand kilometers long and twenty miles wide may erupt with relative motion of ten meters or more. Such an event is among the largest earthquakes possible, and can destroy most structures in any nearby (100 km, perhaps) cities and shift landscape features over a huge area. Such large slippage also takes longer, from a few seconds to a minute.

February 9, 1971 (3 months after my birthday...I won't say which) I awoke at 6AM sharp when my water bed sloshed and almost dumped me on the floor. I turned on the radio, grabbed a field notebook, and began to take notes. I lived in Alhambra, California at the time, 38 km from Sylmar, where the earthquake occured. Central Alhambra is built on well-consolidated sediments, so the shaking didn't damage my house much—just a few new cracks. Nearby areas built on looser soils, which shook more as the waves passed through, had much more damage.

It wasn't my first earthquake, just the most memorable. The other well-remembered event occurred nearly three years earlier, April 8, 1968, about 6:30 pm. I was at my parents' home for dinner. I'd just left the table to get something from the pantry, and found myself swaying while haning onto the pantry door. I looked toward the table, and the hanging lamp was swaying. My parents and brothers were quite still, with wide eyes. Then a "SPLOP" against the back door announced that a lot of water from the swimming pool had decided to form a mini-tsunami across the back yard. We were in Arcadia, 205 km from Borrego Mountain, so the motions were smoother and gentler, and no damage resulted (to us).

These two earthquakes were of nearly the same "size", with magnitudes of 6.6 (1971) and 6.5 (1968). Yet because of their different distances, the intensity of motion I experienced was quite different. I could not have remained standing had I been awake during the 1971 quake, but I was able to let go of the pantry door and stand in 1968.

OK, what does "magnitude mean"? The answer has everything to do with Charles Richter, as explained very well in the new biography "Richter's Scale: Measure of an Earthquake; Measure of a Man" by Susan Elizabeth Hough, a USGS seismologist and a fine writer. Her explanation of "the Richter scale" focuses on the work Dr. Richter did to produce it, not on the technical details of its use. So, I'll take a bit of a digression here.

As I mentioned early on, earthquakes range from stupendous catastrophes over huge areas to tiny events hardly distinguishable from footfalls. A small thump you can barely hear with your ear to the ground causes ground "motion" that is measured in microns, while the Sylmar earthquake caused the dirt at the tops of hills to jump several feet into the air, and moved some houses right off their foundations into the yard nearby.

In the 1930s, the standard instrument for recording earthquake motions was the Anderson-Wood Seismograph. These days, seismographs record their data digitally, on tape or CDs...or DVDs I suppose. But the principle is the same. A small motion of a sensor is amplified so you can see it. Instruments intended to record stronger events use much less amplification, or even "de-amplify" the motion. The A-W instrument recorded with a light beam on a piece of film, so you had to develop the film, then you could make measurements. Seismology was smelly work.

Basically, after many measurements of many recordings, and taking the suggestion of his colleague Beno Gutenberg of using logarithms, Richter devised a method of reducing the measurements to a standard form. Thus, an earthquake could eventually be given a single number, a Magnitude, that recorded its strength.

A word about logarithms: they are the way our bodily senses work, so it is good to know how they work. If you have one light on in a room and turn on another of equal brightness, the light is twice as bright, and you can easily tell the difference. If you turn on a third, similar light, it is harder to tell the difference. If you have nine lights on, and turn on a tenth, you may find it hard to see the difference without carefully turning it off and on and off and on again as you look at some object all ten are illuminating. But if you have ten bulbs on and turn on ten more, the difference seems the same as when you had one on and turned on another. In other words, doubling the amount of light causes a similar response in you, regardless of the starting light level.

This allows you to see well in a room lighted by one or two 40-watt fluorescent tubes, yet go right outdoors, blink once or twice, and see quite well in full sunlight, though it is a thousand times as bright. There are ten steps of two that cover a range of 1000:1 (actually 2x2x2x2x2x2x2x2x2x2 = 1,024), and if you ask people how bright the sunlight is, compared to a well-lit room, many will say, "Ten times." In terms of the number two, ten is the logarithm of 1,024. This is nature's way to compensate for sensations that cover a very large range. But note: heat doesn't work like this, so don't try to make something "ten times hotter" and touch it! (The range of temperature we can endure without damage ranges from about 0 to 60 degrees Celsius, or 32 - 140 deg F. But in terms of absolute temperature in a physics sense, the range is ~270 to ~330 Kelvins, or about 1.2:1).

So, you take a seismogram and measure the biggest wiggle, or half the distance from the biggest plus to the biggest minus (the full-scale range). You take its logarithm. Shall we use powers of two? It turns out we are less sensitive to motion than to light. We feel one "shake" is significantly bigger than another when the motion is ten times greater. We can detect smaller differences, but it takes most folks some thought to decide if a shaking that is three times another is really that much different, as long as both are relatively small. So Richter decided that a magnitude of 4 would be ten times the motion of a magnitude of 3.

Specifically, as measured on an A-W seismograph set for recording quakes at moderate distance, he chose a 1mm wiggle of the light trace as a basis. Then, when the instrument was 100 km from the epicenter (the location directly above the piece of a fault that moved), a 1mm wiggle would be given a magnitude of 3. At that distance, then, a barely-recordable quake, with a wiggle just 0.01mm, would have a magnitude of 1.

How to correct for distance? Nobody knows when and where a quake will occur, so you take the recording from the instrument wherever it may be. My two most memorable quakes occurred 38 and 305 km from where I was when they occurred. Since they were both about 6.5 in magnitude, they'd have caused a wiggle of more than 3 meters on an A-W seismograph. The film is only 0.4 meters wide, so that wouldn't work anyway. But if the amplification setting is 100 times smaller (the machine then set for recording larger ground motions), the wiggle would be 32mm.

Do you know the inverse-square law? Simply put, if you are twice as far from a source of energy, its intensity is one-fourth, and so on. So a standard A-W seismograph at 305 km from the Borrego Mountain earthquake, in my parent's dining room, would have shown a wiggle of 3200/(3.05*3.05) or 340mm. Large, but it does fit on the film. At the lower setting of the instrument, a 3.4mm wiggle would be seen.

There's another factor to look at. Distance can be measured pretty accurately from a seismogram. Earthquakes make two large waves, a P wave and an S wave. P is for Pressure, and causes squeezing and its reverse in the rocks it passes through. It arrives first. S is for Shear or Shaking, and is a side-to-side motion. It arrives later. The factor for figuring distance (in the western U.S.) is 9.7: if the S-P arrival is 10 seconds, the earthquake epicenter is 97 km away.

A little algebra, with the setting of M=3, A=1mm, D=100km, and the inverse-square law, yields the following equation, where "log" is a "common logarithm", to base 10:

M = log(A) + 2log(D) - 1

Now let's apply it. This example of a seismogram from a modern instrument has the following characteristics:

• Biggest wiggle: 245mm
  
• S-P time difference: 39sec (p arrives at t=0)
  
• The distance to the epicenter is thus 39*9.7 = 380km (rounded from 378)
  

M = log(245) + 2log(380) - 1 = 2.4 + 5.1 - 1 = 6.5

The nomograph in this illustration can do these calculations for you. Try it out. Draw a line from 245 on the right to 380 on the left, and read M in the middle scale.

As it was initially defined, Richter's magnitude scale worked in the range from 1 to 6, for earthquakes in southern California. He continued to revise it, particularly as better instruments were developed, and seismologists have not stood still since his death in 1985. Modern, wide-range instruments of great sensitivity allow a magnitude and location (by triangulation from several instruments) to be assigned quickly. However, a measure of total energy, produced by Moment-Magnitude calculations, is now used to assign a final number to an earthquake. While a difference of magnitude means a difference of 10 in distant ground motions, it means a difference of 30 in total energy released. Thus, while a "sixer" causes 100,000 times as much ground motion as a "one" at 100km distance, it has 24.3 million times the energy.

This is because of two effects. Firstly, an earthquake of magnitude 6 causes shaking over an area of a square mile or so that is as great as the earth's surface can support: accelerations of 1-2 g. This is why hilltops can be thrown into the air in quakes like that in 1971. Larger earthquakes have this level of intensity spread out over greater and greater areas, so a "big one" with a magnitude of 8, with 900 times the energy of a "sixer", will devastate an area of a couple thousand square miles, and knock down some stuff over an area even larger. The biggest earthquake recorded, with a magnitude of 9.5 in Chile in 1960 (May 22), devastated towns and cities throughout the country, and in nearby Argentina, Bolivia, and Peru. But the ground motions of a 9.5 are not a great deal larger in linear size than those of a 6.5. Ground waves a few meters high seem to be the maximum.

Secondly, when you are too close to a large source of energy, the inverse-square law is not accurate. The fault that ruptured in 1960 offshore of Chile must have been half the length of the country of more, perhaps 2,500 km. If you were on the East coast of Argentina, perhaps 1,000km away, the ends of the fault rupture would be 1,600km distant. It's like trying to measure the brightness of a light bulb when you are two millimeters from the filament. You had to be in China or Europe to get an accurate record! At that distance, the greater size of the fault of a really big quake causes the instrument to record a larger excursion than if the quake were a 6 or so, even though someone near the epicenter of both quakes would find it hard to tell the difference (as she dodges falling masonry!).

Thus, an "instant" measure that indicates 8 really means something closer to 9 when all such factors are taken into account. Well, one can tell I savor the technical details. But the summary of these things occupies just one chapter of Dr. Hough's book. The other eighteen chapters detail the life of Caltech's pre-eminent Mystery Man.

Who was Charles F. Richter? He was a most private man. We are incredibly fortunate that he left all his papers to the Caltech archives. Without those, we'd be limited to the stories told by colleagues and a few neighbors, and those are rather thin on the ground. Without those, we'd never know he was a poet and novelist (unpublished); we'd know little of his frequent treks into the mountains; one might stumble on someone who knew him and his wife Lillian as practicing nudists; never would his relationships within the writing circle, particularly writing women, come to light. Without those, including poems in which he laid bare his soul, it would be hard indeed to determine that he suffered from Asperger's Syndrome.

His closest colleagues all regarded him as an odd sort, an eccentric, a mercurial fellow. Few knew of his breakdown at Stanford the one time he tried to move far from his Los Angeles home. Though he traveled the world—a little, on occasion—he was a persistent homebody. His wife took vacations alone, and he usually hiked alone. Even in Caltech circles he stayed in a narrow circle. He seldom went to the campus proper, staying near his office in the Seismological Lab off campus.

Can you tell that I must be at least halfway into Asperger's myself? I can go on for pages and pages in the vein of the first twenty paragraphs, but I find it hard to discuss the man. Psychologically, there are two big differences I can point to (besides the obvious one that he was a true genius, and I am at best a polymath). I have lived in many places, primarily because my family moved eight times before I moved out. Also, while I, as one AS writer states it, felt "like a Martian among Earthlings", I decided as a teenager to produce the personality I clearly lacked. I deliberately gave over a number of IQ points to "social processing", so I could, with only the smallest time lag, respond as expected in social situations I often didn't understand. It took decades, into my late 40s, before I found, hidden under the artificial personality, that a real one had slowly grown. So, the social integration that takes most folks 15-18 years took me 45-50.

It seems Charlie Richter never had this insight, or never thought it worth the hard work. He was frank to the point of bluntness or rudeness when he wasn't making an effort to be accommodating...and he didn't suffer fools gladly. However, he was perceptive enough to give a fellow a couple tries to prove he was a fool before he whisked him out of his life.

The author seems to believe, and with her I agree, that AS was an asset, giving Richter the focus and relentless energy to do the huge numbers of hand calculations that led to the simple formula I show above (or one much like it)...in 1935, when even mechanical-gear calculators were not to be found! His greatest work was done in a time that "computer" was a job description for a woman paid a little more than a secretary's wage to do pen-and-paper calculations for a scientist. Richter did his own computing.

The formidable memory characteristic of AS was an asset throughout his life. Knowledge is always a salable commodity. In the Caltech community, where knowledge is more valued than among the "great unwashed," Richter would have had to be a lot odder than he was to be unwelcome. Health and mental problems he may have had, but he lived to age 85, and was beloved by those who knew him, an odd duck, but one worth knowing.

Jumbo's underground telephone

kw: book reviews, nonfiction, natural history, african elephants

We joke about keeping one ear to the ground. Old Western films show an Indian guide putting an ear down and telling how many and how far away a war party is. As a Geology student, I heard occasional reports of people camping who heard a rattling or banging sound just before feeling the shaking of an earthquake—I guess they were using a rather thin pillow!

Also, as a Geology student, I took the requisite Geophysics course. For a couple of weeks, a bunch of grungy kids tramped about a meadow near campus, laying out geophones and banging a metal plate with a sledge hammer while running a multichannel chart recorder (no digital equipment in 1970). Eventually, most of us figured out that there was a water pipe buried about nine feet down. One or two claimed they could hear the thumps if they got a couple hundred feet away and put their ear to the ground. I reckon they could. None claimed to hear the smaller echo from the pipe.

About ten years ago, Caitlin O'Connell and a couple of colleagues published the first monograph (O'Connell, Arnason, & Hart, 1977 in The Journal of the Acoustical Society of America) describing African elephants' use of seismic signals, "sound in the ground", to communicate farther than their rumbling voices can carry through the air.

Continued work showed that the gel pads in elephant feet, and others between shoulders and head, resemble the "melon" in dolphin heads, that is used to focus sound and transduce between bone and water or air for better sonic efficiency. Also, elephants have an ear flap that they close when listening "below". To sense ground signals, an elephant usually lifts one forefoot, rises onto the toes of the other, and closes the ear flaps. Sound is then efficiently transmitted through the leg bones to the bones around the ear. With both legs on the ground (on tiptoe), the evidence is pretty strong that the animal can determine direction.

In The Elephant's Secret Sense: The Hidden Life of the Wild Herds of Africa Dr. O'Connell narrates her studies of elephants and discovery of seismic listening over several field seasons in Namibia beginning in the early 1990s. Good science is a detective story, and this one is first-rate.

The author and her partner (now husband) Tim Rodwell began with a 3-year grant they almost stumbled onto while taking a break in Africa, before beginning PhD work. They were to study elepants in and near the Caprivi Game Park, with the main goal of reducing elephant depredation on the people's crops...and their fatal retaliation. It was during this period that she first noticed the tiptoe listening behavior that led to her discovery.

Between this study, finishing their PhD work, and further studies in Caprivi and at Etosha National Park, they and a number of co-workers gathered great amounts of data on the relationships within elephant family groups, both matriarchal herds and smaller bull "clubs"; learned that elephants recognize voices, by their differing responses to alarm calls, whether they came from "someone they knew" or not; and determined that an alarm call heard only seismically (through the ground) resulted in alertness, but little excitement.

In the midst of it all, it was easy to observe that elephants are as individually different as people. They are playful, moreso as calves, but somewhat at any age. The amount of bull jousting that goes on has a lot to do with how secure the larger bulls feel, having more to do with personality than with brute strength.

Caitlin and Tim have established an educational and fund-raising organization known as Utopia Scientific, and carry on their studies in Africa and at their American campuses.

How would having neighbors change us?

kw: book reviews, science fiction, first contact, SETI

I read only a portion or two of James Gunn's The Listeners in the 1970s, when it appeared piecemeal. It was refreshing to find the whole volume and devour this 35-year-old classic.

If a civilization on another planet were to send a signal we could receive, what would be its content? Some years ago, some folks devised a message in several parts, and put it, part by part, weeks between them, on a web site for all to decipher. It was clever, and many clever people deciphered it at least in part. As it turned out, not some parts of it were amenable to more than one interpretation. Making a completely unambiguous communication of any complexity is hard, and perhaps impossible (remember the old story "To Serve Man", which turned out to be about a cook book).

Jim Gunn has come up with perhaps the best compromise. The message, once the signal is detected, is composed primarily of a hash of early radio transmissions. The content of those transmissions yields a good estimate of the distance to the alien star: 45 light years. But there is more. Each short segment of the hash is followed by a staticky blip. Each blip contains simply several pulses. Once the project workers realize they can be considered an on-off raster pattern, it doesn't take long to produce an image that gives a few clues to the aliens' appearance and number system, plus a few words.

Much of the dramatic tension in the book surrounds first, the apparent futility of the Project before a signal is detected, and the meaning of the message it conveys. Of course, for the novel to go anywhere after this point, the message must be answered with one of our own; and it is, a similar image. Ninety years later, one would expect an answer, and the denouement follows from that answer.

I found myself wondering, would the world really develop such an extended peaceful period after receiving the first alien message? War and chaos are equally likely, particularly once people realize knowledge coming from an alien source will be a valuable resource like any other: something worth fighting for. We are unlikely to unite in the face of The Other until we physically face The Other.

I think the religious response in the novel is too pat. That a religion could be formed around the "Solitarian" perspective seems incredible. More likely, a "Christian" sect would arise who found the idea of aliens to be some kind of attack on the uniqueness of God.

These are minor flaws. As a classic in the field, The Listeners sets the standard others must still meet.

It isn't your car that is out to get you; it is something much bigger...

kw: book reviews, horror, occult, automobiles, highways

I read very little Fear Fiction. For some reason, I was sufficiently intrigued by the cover blurb to give Destinations Unknown by Gary A. Braunbeck a try. He is certainly a compelling writer; I stayed up a bit too late to finish the first story of the three in the book.

In an essay a decade back or so, Orson Scott Card deconstructs Fear Fiction into three genres, based on the time element. Dread is fear of what might happen, a foreboding. Card happens to be master of the unresolved Dread story. Terror is fear incited by awful events witnessed, or suffered by, the story viewpoint. Horror is remembered terror; it is already over, but you can't get over it. This is used to great effect by consecutive terror-horror-(dread-)terror-horror cyclic "slasher" stories. Braunbeck's writing follows the dread-terror-horror sequence, but of these three stories two end with a cycle-breaking resolution.

The first story, "The Ballad of Road Mama and Daddy Bliss", is by far the best and the best-written. It explores the idea, one sure to twig off droves of conspiracy theorists, that auto "accidents" are really "occurrences", somehow proctored by a godlike entity, The Road, assisted by Road People, including the title characters. It's incredibly well done, and introduces a nearly-believable parallel world for us to contemplate.

The other two stories seem to me to be fillers, to get the book up beyond 200 pages ("Ballad" takes 170). The first, "Congestion", puts the reader under the skin of a fat dude with heart troubles trying to drive himself to the emergency room through a traffic jam. The second, "Merge Right", is a grief fantasy, that goes right about where you'd expect a grief story to go if the depths of grief were physically realized.

Defense of the giant grasshoppers

kw: book reviews, science fiction, historical fiction, medieval period, aliens, first contact

Years ago, I read a novella that placed a time-traveling scientist in a medieval village during the 14th century plague. It devolved to a psychological study of the young woman, herself immunized against Yersinia pestis and a host of other ills, becoming the last person alive in the village, finally burying the village priest.

Eifelheim by Michael Flynn reminded me of it. I know that this book is an expansion of an earlier novella by Flynn, but I haven't determined if it was the one I read or not. There is no time traveler here, though the cosmological theory developed by one character hints at a way to travel in time.

The basic story, 80% narrative of 14th-Century life and 20% vignettes of the lives of the historians studying the earlier events, is of a starcraft that barely escapes crashing in the Black Forest, but lands damaged. Its insectile inhabitants are, rather astonishingly, welcomed by first one, then two or three of the first humans to locate their landing site. Gradually they become accepted by many, but not all, of the villagers. At the end, the ship is repaired, at least enough to take off, though a successful return to home is not assured. A few aliens remain behind, preferring certain, but slow, death in the German village to the rather significant chance of an infinitely-prolonged dying if the ship gets "stuck" in a space warp. Should their fellows succeed, they plan to return for them.

The aliens cannot gain full nourishment from Earth foods, because their biochemistry requires 21 amino acids, while nearly all Earth life lives with 20. The missing ingredient is never found, and the ship does not return. Rather, everyone dies of plague, except the aliens who die of malnutrition, and the village gains the name Teufelheim (Devil's home), later elided to Eifelheim.

Back in the present, a historian is trying to determine why this location alone, now with the name Eifelheim, was never resettled after being depopulated by plague in 1349. His lover, a physicist, is trying to develop a better model of cosmology than 11-dimensioned string theory. About the time she succeeds, she happens to see a strangely-configured illuminated capital letter in a manuscript the historian is studying, and recognizes that it is a circuit diagram similar to one she had designed to detect signs of her theory's special particles. The manuscript and others were located by a librarian who is trying to seduce the historian; at the end, it seems she might have done so, but that strand is left hanging.

In fact, a number of strands are left hanging, in the rather obvious way that is becoming common—it almost harks back to the cliffhanger endings of Perils of Pauline episodes. While the historian and librarian, with the help of a narrator-colleague, do confirm that the "demons" of certain documents really were aliens, no other subplot is completed. It's no surprise that Flynn wishes to write more books. Ending a novel with no more than a hope of the solution is an unsatisfying way to prompt for a series of sequelae.

Virtual life with real consequences

kw: book reviews, science fiction, near-future, wearable computers, digital infrastructure

The title Rainbows End at first made me wonder if it simply embodied the recent trend toward eliminating apostropes. Then I figured it is a declarative sentence, to which I reply, "Yes, I suppose they do." Later in the book, the author makes the same pair of points, leaving his own reasoning obscure.

Halfway through the fourth chapter, I began to wonder if I'd read this before. I checked prior reviews and found that Chapter 4, titled "Synthetic Serendipity", had appeared in The Year's Best Science Fiction 2004, which I reviewed April 12, 2006.

Vernor Vinge throws ideas at you a bucket full at a time. The core plot is the struggle between a somewhat stereotypical mad medico who wishes to "save" the world—which requires enslaving it—and a global watchdog group, an extension of the Dept. of Homeland Security. This latter agency, still called DHS, wishes to prevent development of a technology called YGMB, for "you gotta believe me," a means of making your dictates simply irresistible.

The environment and setting provide the novel's allure. As near as I can figure, the central protagonist, Robert Gu, having been in high school in 1965—it is implied that was his senior year—is either my same age (60 later this year) or at most 2-3 years younger. At age 75, he places the time frame as 2022, or 2025 at the latest. There are allusions to seminal events "in the teens" that are recent memory to adults, but not to most youngsters, who'd have been too young to remember or not born yet.

Wearable computers have become clothing full of tiny processors and communications nodes linked to special contact lenses, which project images directly on the retina. The environment has become infrastructure, with every item bigger than a ladybug having its own digital tag. Thus, someone on a nature walk can call up a view of the landscape in which every bush, tree, and weed is tagged with botanical information, and taking a second look at any bug or other critter calls up appropriate zoological references.

People build their own world, so a row of suburban bungalows may appear as medieval huts to one, as "McMansions" to another, and hobbit-holes to someone else. People watching anything remotely can appear virtually, to anyone caring to see the virtual viewers. With a landscape full of cameras, you can see in any direction you want, including through the wall that happens to be in front of you (I'd find it hard to avoid walking into that wall, myself, at that point!), or from a treetop or spider burrow. Someone who is "wearing" can call up just about anything imaginable.

Call up how? Not with keystokes or mouse clicks. Your shirt and its sensors collaborate with you to build up a physical vocabulary of gestures and postures, in addition to subvocalized commands. When you've made yourself telepresent in a particular "space", things you say and do are heard and seen by others in that space. To communicate with a smaller audience one employs "sming" or silent messaging.

Highly acclaimed poet Robert Gu, aged 75, has the right genetics to respond almost miraculously to treatments that cure his Alzheimer's dementia and return most of his body to a 17-year-old's. His prostate seems to get stuck in his 50s, though, so he still has to get up a couple times nightly. He also finds that he has lost the ability to create poetry. Oh, he can spin words into rhyme well enough, rhymes that still affect others. But the sharp edge that made him a legend is gone. So is the sharp tongue with which he made himself sincerely hated by all who actually met him, family included.

The plot is complex, with several threads. A central thread is the efforts of the aforementioned medical scientist to keep his research secret. Another is the poet's desire to regain his poet's edge. His granddaughter hopes to help him leapfrog into the mid-21st Century by teaching him to "wear" (the word is never in quotes in the book. You just have to pick it up). He gets good enough to participate in what he thinks will be anti-establishment hijinks, but the plot is ever so much deeper than you can imagine, as he finds himself an unlikely savior of Civilization as We (might) Know It. A fun read.

Getting "eyes" for what you really need

kw: book reviews, nonfiction, religion, spirituality

This'll be briefer than usual. Mark Buchanan's new book Hidden in Plain Sight: The Secret of More is a wonderful book, but I've been able only to give it a rapid run-through. I'll need to go back and re-read and ponder. This one will stay in my "ready" area.

Mark Buchanan is a Baptist pastor living near Vancouver. Though I am no fan of the pastoral system, I do recognize the value that can result when a man or woman of God must produce regular, inspiring messages for his congregation. The flip side of "90% of everything is junk" is Bradbury's dictum: "Write every day. Finish one story a week. I defy anyone to write 52 bad stories in a row." Meaning at the end of the year you'll have something worth the effort.

I have come to realize that the true "evidence" of the holy Spirit is persistence, or what is called in the New Testament "endurance." Jesus said, "Whoever endures to the end shall be saved," not talking about eternal salvation but rescue from temptation or the world's allure: practical, daily salvation.

Such endurance, such persistence, such perseverance is right in the midst of the author's message. The book is an exposition of the first nine verses of Peter's second Epistle:

Simon Peter, a servant and apostle of Jesus Christ,
To those who through the righteousness of our God and Savior Jesus Christ have received a faith as precious as ours:
Grace and peace be yours in abundance through the knowledge of God and of Jesus our Lord.
His divine power has given us everything we need for life and godliness through our knowledge of him who called us by his own glory and goodness. Through these he has given us his very great and precious promises, so that through them you may participate in the divine nature and escape the corruption in the world caused by evil desires.
For this very reason, make every effort to add to your faith goodness; and to goodness, knowledge; and to knowledge, self-control; and to self-control, perseverance; and to perseverance, godliness; and to godliness, brotherly kindness; and to brotherly kindness, love. For if you possess these qualities in increasing measure, they will keep you from being ineffective and unproductive in your knowledge of our Lord Jesus Christ. But if anyone does not have them, he's nearsighted and blind, and has forgotten that he has been cleansed from his past sins.

The analogy used to explain the seeming dichotomy—"he has given us everything we need" and "make every effort"—is like delivery day at a building site. You have the land and the plan, and now you have all the materials. It is time to start building. If the plan calls for a hotel, and the materials delivered correspond, then build a hotel, not a bungalow. Don't sell yourself short.

Buchanan's genius is the apt analogy, the telling insight. We are a bundle of contradictions. We need to see. To see the building materials lying ready to hand, and to see the plan showing what goes where, will grow us beyond the contradictions. When Jesus said, "Be perfect as your Father in heaven is perfect," he meant it. Peter's few sentences, and Mark Buchanan's practical explanations, help us to see and to build.

To explain my title...when our son was a pre-schooler we frequently went rock collecting with a club. The fossil hunts were the best. The first time we went to a quarry, where lots of little shelly fossils were "floating" out of the deposits, the trip leader opened a box to show us the kinds of fossils we could expect to find. He held up one particular brachiopod (similar to a clam, but of an extinct order) and said, "This one is quite rare." Our 4-year-old looked at it, trotted off, and came back in ten minutes with three of them. This sort of thing happened on every trip. Once he saw what the target was, he "had his eyes on" for that pattern, and could always find some. Hidden in Plain Sight helps be "get my eyes on" for the virtues I am, every so slowly, gaining.

The unrevealing of Revelation

kw: book reviews, nonfiction, eschatology, polemics, religion

Just a week ago I reviewed a book specifically confronting the theology and eschatology of the Left Behind books. Here I consider a work with a broader scope: A History of the End of the World: How the Most Controversial Book in the Bible Changed the Course of Western Civilization by Jonathan Kirsch. While Kirsch takes issue with the Left Behind books, his target is the apocalyptic phenomenon in general.

The author makes it clear he is not a Bible believer, at least not in any way similar to those who would call themselves "Bible believers." In other words, he is no literalist, and in whatever way he may use the Bible spiritually, he feels free to pick and choose what to trust and what to attribute to human error. Today's Fundamentalists do certainly take their literalism too far, but we must consider that God actually has had a hand in the writing, preservation, collecting, and distribution of the 66 (and perhaps 72) books considered to be the "word of God" by millions worldwide.

The thesis is this: Revelation is failed prophecy. It uses metaphorical language to describe current events and the writer's less-than-pious revenge fantasies. Now, since generation after generation has passed away and the world has "failed to end on time," Bible believing Christians, particularly literalists, must cope with this: either admit that its predictions are false, spiritualize all meaning out of them, or devise an eschatological theory that lets time be very, very flexible in God's hands.

There is actually strong support for the idea that certain periods of time "don't count" on God's calendar. The clearest example is the statement in 1 Kings 6:1, that the period from the Exodus to the Kingdom was 480 years. If you add up all the times in the historical books that go before, you find 612 years, and this is the period Josephus also used. However, during the time of the Judges, if you add up the times that the Midianites and others ruled over the Israelites, you get 132 years. 612-132=480. Many conclude that God's clock doesn't run when Israel is subject to others. It seems the most logical explanation. Such considerations are ignored by Kirsch, and maybe he knows nothing of them.

The chapters of the book outline the history of Revelation, from the time of its writing to the present day. He bases much on Augustine's dichotomy: Some read Revelation "carnally", some "spiritually". The writer, probably John the son of Zebedee (though Kirsch strongly disputes this), announced at the outset that Jesus "made it known by signs" (in KJV, "signified it"). Kirsch rightly emphasizes this term. I recall one speaker saying, "Let's not be too busy about counting heads or toes (the latter referring to Nebuchadnezzar's dream), but about how we are to live."

Like many others, the author expresses surprise and disgust at a book about God's vengeance. Nearly every other part of the New Testament emphasizes God's goodness, love, and caring. Yet this same God said in Deuteronomy 32:35 "Vengeance is mine and so is retribution", which Paul quoted when he wrote in Romans 12:19. Without Revelation and a few shorter passages in Daniel and Zechariah, we gain no insight into when and how He will avenge. When God is love, He is really loving, and when He is severe, He is really severe! Let us realize that, just as we are complex, God is more complex and has ranges of emotion we cannot imagine.

The bulk History of the End is a detailed survey of the various foibles of people who have read Revelation "carnally". The modern focus that most exercises the author is the popularity of the "Left Behind" series of books, and the recent elevation to office of four "born again" Presidents in succession, at least three of whom clearly declared their belief that we are living in "the end times."

Revelation seems to have become a peculiarly American phenomenon. While European christendom was being lulled to sleep, spiritually, in the 19th and 20th Centuries, American Christians have increasingly focused popular theology in the horror stories that result from a too-literal reading. Two groups emerged by the late 19th Century. Many people, millennialist and fundamentalist, took an almost passive stance toward society except for their duty to "preach salvation to a doomed world." They saw no value in social "improvement".

Others, considering the millennium to refer to an earthly condition God's people might bring about, agitated against slavery and for humane social works. Up until 1914, they thought they were making good progress, but the "war to end all wars" disabused them of that notion, and the second great War less than a generation later pretty much killed that idea off...for a time. We actually see a revived "social gospel" these days, in spite of the threat from resurgent Islam; these people think they can reason with the insane.

What do I think? I am of the flexible-timeline persuasion. Those parts of Revelation that seem most amenable to literal interpretation, wedded with parts of Daniel, certain things Paul and the Evangelists wrote, and the last part of Zechariah, produce this rough outline:

• The first four seals have likely been opened.
  
• The world gets worse and worse. Finally, God is ready to reply to the martyrs' call for vengeance.
  
• A major European or Euro-African coalition arises.
  
• Its leader makes a treaty with Israel, with a 7-year duration. Perhaps it includes permission to erect a Temple. This leader, whether a person or a coalition, we can call the Beast (nowhere is Antichrist used in Revelation).
  
• It is most likely that the Beast is a person, a man, whose origin is somewhere in the Macedonia-Bulgaria region. He is not a Jew.
  
• Natural disasters are supplemented, then replaced, by disasters that beggar the imagination. The worst ones, though, do not exceed "one third", which could have various meanings.
  
• Eventually, the Beast breaks the treaty and attempts to subjugate Israel and their religion. Three and a half years have passed.
  
• The first "taking away" (AKA rapture) of "those who are ready" occurs. The timing is uncertain, whether this is before the prior item, or even if they are simultaneous.
  
• There may be two literal prophets speaking in Jerusalem from this point on. About this time, an angel preaches "the eternal gospel." It is according to this gospel that the people remaining alive at the end are judged.
  
• Disasters now take on a supernatural element, and spread to worldwide scope. One is a long drought. Euphrates dries up.
  
• Mongolia is the only possible source of 200 million horsemen, if these are indeed a literal cavalry. Their progress toward Palestine takes about 13 months (a day, a week, a month, and a year).
  
• Other armies also gather to attack. It is not clear whether their target is the Jewish people or the Beast.
  
• The two prophets are killed, to arise and ascend 3.5 days later. Their ascension should be just after the second "taking away" of the rest of the believers, the one that occurs "at the last trumpet".
  
• The final battle follows. Christ intervenes. I don't think the horse or the sword-tongue are literal, but God can do anything...
  
• Supposing the 1260 days refers to the period just ended, the 1290 and 1335 days mentioned by Daniel probably indicate that cleaning up the mess from the battle takes thirty days in Jerusalem and 75 days elsewhere. Then the thousand-year kingdom begins.
  
• Just before the cleaning-up period, Christ will judge those who didn't participate in the battle (all the soldiers are condemned), according to the "eternal gospel." This is the "sheep and goats" judgment referred to in Matthew 25. Many, the sheep, will have secretly defied the Beast and helped the persecuted Christians and Jews during the last three-plus years. For the persecuted ones, this period was their chance to finish "getting ready". Most Christians hate this idea...they don't want to chance being there.
  

It may be that every one of these points has a spiritual applicaition only. That is OK, it is God's responsibility only. But in the light of God's evident desire to destroy "the destroyers of the earth" at least some of these events are probably literal.

It is instructive to see how the eschatology I've been taught is viewed by various "outsiders". These are things we must not insist on. Eschatological doctrine is the most divisive kind. Let us remember that in Jesus' longest prayer (John 17), he prayed three times "that they all may be one." Until that is fulfilled, the rest is moot.