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"Why are rainbows curved? Is it because of refraction in the drops of water?"

Robert Greenler of the physics department of the University of Wisconsin-Milwaukee sent in this response:

"In answering this question, it is helpful to start with a description of the path followed by the rays that form the rainbow. As can be seen in this diagram, a ray of light from the sun enters one side of a water drop, gets refracted as it enters, reflects internally off the other side of the drop, and emerges again from the other side, again with refraction. We can consider rays of light from the distant sun to be parallel.

"If you trace a large number of parallel rays that strike a drop of water at various points on the drop, you will discover that a concentration of rays emerges at one specific angle, 42 degrees from the angle at which the light entered. So we have a picture of parallel rays coming from the sun, striking a lot of raindrops, and then being reflected and refracted back from the drops--but not straight back, rather at an angle of 42 degrees.

"Now comes the crucial question: where in the sky do you look to see the light returning from the raindrops? Let us start by defining a direction in space: a direction exactly opposite the sun, called the antisolar point. If you are standing outside during the daytime, the antisolar point is marked by the shadow of your head. To see the light coming back from the raindrops, look 42 degrees away from that antisolar point. Of course, the region of the sky 42 degrees away from that point is not just one direction but a whole collection of directions, one that forms a circle around the antisolar point.

"So, to summarize, look to the antisolar point, and then shift your gaze to 42 degrees away--you are now looking at the rainbow. Rainbows will always appear at that same angle from the antisolar point. The height of the rainbow, however, will depend on how high the sun is above the horizon.

"And what about the colors of the rainbow? Each color of the spectrum gets refracted by a different amount when it passes from air to water or from water to air, the same as happens when light passes through a prism. Consequently, the rainbow circle is not 42 degrees for all colors. The circle is smaller for blue rays than it is for red rays, so the primary rainbow is blue on the inside and red on the outside, with the intermediate colors of the spectrum spread out in between.

"It is also possible for some of the light rays entering the drop to undergo not one but two internal reflections before they emerge. If you look at a whole collection of such rays, you see a concentration of light coming back at an angle of 51 degrees. These rays produce a secondary rainbow, also centered on the antisolar point, having an angular radius of 51 degrees; the secondary rainbow therefore appears outside of the primary bow. The sequence of colors is reversed in the secondary bow.

"More information about rainbows and other atmospheric optical phenomena can be found in my book 'Rainbows, Halos and Glories' (Cambridge University Press, 1990)."

"If a diet of caloric restriction can extend the life span of laboratory rats, then does the lifestyle of an athlete, who burns calories at a rapid rate, hasten the aging process?"

-Terence Cross, Dublin, Ireland

Barbara C. Hansen, professor of physiology in the School of Medicine at the University of Maryland and director of the university's Obesity and Diabetes Research Center, responded as follows:

"The effects of caloric restriction on life span in mammals have been demonstrated only among rodents. At present, there are no studies that can definitively say whether caloric restriction extends life span in any primate, so it is premature to draw conclusions about the possibility of extending the maximal human life span.

"We are currently researching caloric restriction in nonhuman primates (monkeys). Our monkey study has been going on for 13 years. We began the study on young adult monkeys, equivalent to humans 20 to 25 years old. The animals were placed on a weight-control regimen, designed so they could not put on middle-age weight. We set a monkey's caloric intake for each week based on whether he has gained or lost weight since the previous week.

"There are two key issues under study here: Does the average monkey live longer, and is the maximal life span of the monkeys extended? For rodents, caloric restriction has been shown to extend both average and maximal life span. For monkeys, we already know that the animals in our group are living longer than average, if you judge by the 50 percent death point (the time at which half of the animals in the group have died). We have also observed general improvements in health and decreases in disease, which are likely to translate into longer lives. For example, restricting the caloric intake of a monkey sufficiently to prevent the onset of middle-age obesity completely prevents type II diabetes, even though these animals are prone to diabetes.

"What we do not know is the effect on maximal life span. Will the longest-lived calorie-restricted monkey survive longer than any other monkey has survived? The monkeys in the University of Maryland study are now at an age equivalent to that of 50- to 60-year-old humans, so we won't know the answer to that question for another 10 to 15 years; monkeys are thought to live well into their thirties under laboratory conditions.

"There are two other, related primate studies under way. Richard Weindruch started a similar one at the University of Wisconsin about five year after our own. George Roth and Mark Lane are running a slightly different program at the National Institute on Aging. Roth and Lane are working with several groups of monkeys; they started some of the monkeys on a program of caloric restriction before the animals reached adulthood. This study will produce the best data on the effects of early caloric restriction. It is not yet clear whether early caloric restriction has a net positive or negative influence on health.

"We do know enough to say that caloric restriction to prevent obesity during adulthood is likely to be very beneficial, to humans as well as to monkeys. Nobody knows whether the health benefits are because of the positive effects of not having excess adipose tissue or because of altered metabolic activity. My colleagues and I just finished a paper showing that caloric restriction increases the efficiency with which the body burns calories. The problem is, we do not know how that change occurs--that is what we are studying right now.

"Incidentally, there is no evidence that excessive leanness is healthy. In fact, most evidence shows that there is an increased mortality associated with excessive leanness. It seems that there is an increasing risk of disease and risk at both ends of the weight range, though probably for different reasons.

"Turning back to the original question, we must consider several issues separate from caloric restriction. The lifestyle of an athlete would normally extend life span because it would involve exercise, a healthy diet, absence of obesity, absence of smoking and absence of alcohol and drug abuse (one would hope!). Such behaviors reduce the risk of various diseases, including cardiovascular disease. The athletic lifestyle won't necessarily cause you to live to 100, but it might extend your life span from, say, 70 to 80.

"The rapid rate at which an athlete burns calories is not associated with either an increase or decrease in life span. There is, in fact, a theory that animals have only a fixed number of calories to burn during their life, but it is pure speculation, intended to explain why calorie-restricted rodents live longer. There is no evidence that an enhanced turnover rate of calories hastens the aging process. Based on our current level of knowledge, we would expect athletes to have longer or at least healthier lives than they would if they were not athletic.

"Exercise, diet and genotype all interact in complicated ways. Despite all our attempts to take our destinies into our own hands, genes seem to play a significant role in determining life span, susceptibility to disease and probably the effects of caloric restriction."

"What is "fuzzy logic"? Are there computers that are inherently fuzzy and do not apply the usual binary logic?"

Your confusion is understandable; the term "fuzzy logic" is now as likely to appear in advertising copy as in technical journals. A number of workers wrote in to share their perception of this dynamic area of research.

Charles Elkan, an assistant professor of computer science and engineering at the University of California at San Diego, offers the following definition:

"Fuzzy logic is a generalization of standard logic, in which a concept can possess a degree of truth anywhere between 0.0 and 1.0. Standard logic applies only to concepts that are completely true (having degree of truth 1.0) or completely false (having degree of truth 0.0). Fuzzy logic is supposed to be used for reasoning about inherently vague concepts, such as 'tallness.' For example, we might say that 'President Clinton is tall,' with degree of truth of 0.9.

"It turns out that the useful applications of fuzzy logic are not in high-level artificial intelligence but rather in lower-level machine control, especially in consumer products. Usually, fuzzy controllers are implemented as software running on standard microprocessors. A few special-purpose microprocessors have been built that do fuzzy operations directly in hardware, but even these use digital binary (0 or 1) signals at the lowest hardware level. There are some research prototypes of computer chips that use analog signals at the lowest level, but these chips simulate the operation of neurons rather than fuzzy logic."

Shlomo Zilberstein, an assistant professor in the computer science department at the University of Massachusetts at Amherst, provides additional information and more fuzzy analysis of the U.S. president:

"Fuzzy logic is a technique for representing and manipulating uncertain information. In the more traditional propositional logic, each fact or proposition, such as 'it will rain tomorrow,' must be either true or false. Yet much of the information that people use about the world involves some degree of uncertainty. Like probability theory, fuzzy logic attaches numeric values between 0 and 1 to each proposition in order to represent uncertainty. But whereas probability theory measures how likely the proposition is to be correct, fuzzy logic measures the degree to which the proposition is correct. For example, the proposition 'President Clinton is young' may have a degree of correctness 0.8.

"The important distinction between probabilistic information and fuzzy logic is that there is no uncertainty about the age of the president but rather about the degree to which he matches the category 'young.' Many terms, such as 'tall,' 'rich,' 'famous' or 'dark,' are valid only to a certain degree when applied to a particular individual or situation. Fuzzy logic tries to measure that degree and to allow computers to manipulate such information.

"Fuzzy logic was formulated by Lotfi Zadeh of the University of California at Berkeley in the mid-1960s, based on earlier work in the area of fuzzy set theory. Zadeh also formulated the notion of fuzzy control that allows a small set of 'intuitive rules' to be used in order to control the operation of electronic devices. In the 1980s fuzzy control became a huge industry in Japan and other countries where it was integrated into home appliances such as vacuum cleaners, microwave ovens and video cameras. Such appliances could adapt automatically to different conditions; for instance, a vacuum cleaner would apply more suction to an especially dirty area. One of the benefits of fuzzy control is that it can be easily implemented on a standard computer.

"Despite its commercial success, fuzzy logic remains a controversial idea within the artificial-intelligence community. Many researchers question the consistency and validity of the methods used to 'reason' with fuzzy logic."

Jacoby Carter of the National Biological Service's National Wetlands Research Center in Lafayette, La., clarifies the difference between fuzzy and traditional logic; he also offers a more upbeat assessment of the potential of fuzzy logic for artificial intelligence (AI):

"Traditional logic theory, sometimes called 'crisp logic,' uses three logic operations--AND, OR and NOT--and returns either a 0 or 1. Similarly, traditional set theory, or 'crisp set theory,' assigns to objects either membership or nonmembership in a class or group that has been assigned strict mathematical boundaries so that, for example, 80 degrees Fahrenheit is warm and 81 degrees F is hot. In fuzzy logic, the three operations AND, OR and NOT return a degree of membership that is a number between 0 and 1.

"Fuzzy set theory has been used in commercial applications of expert systems and control devices for trains and elevators; it has also been combined with neural nets to control the manufacture of semiconductors. By incorporating fuzzy logic and fuzzy sets in production systems, significant improvements have been gained in many AI systems. This approach has been particularly successful with ambiguous data sets or when the rules are imperfectly known."

Heidar A. Malki, an assistant professor in the College of Technology at the University of Houston, provided further perspective on the likely applications of fuzzy logic:

"Increasingly, people in industry and academia are exploring the benefits of of fuzzy logic and its related technologies. Fuzzy logic can be used for situations in which conventional logic technologies are not effective, such as systems and devices that cannot be precisely described by mathematical models, those that have significant uncertainties or contradictory conditions, and linguistically controlled devices or systems. As Lotfi Zadeh once stated, fuzzy logic is not going to replace conventional logic (computers) or methodologies, rather it will supplement them in circumstances where conventional approaches fail to solve a problem effectively.

"In recent years, there has been a growing interest in fuzzy logic, both in industry and academia. Current applications include modeling, evaluation, optimization, decision making, control, diagnosis and information. In particular, fuzzy logic is best suited for control-systems fields. For instance, fuzzy logic has been applied in areas such as breakdown prediction of nuclear reactors in Europe, earthquake forecasting in China, and subway control in Japan.

"One prominent application of fuzzy logic is in the anti-lock braking system found in many modern automobiles. The control rules that describe an anti-lock braking system may consist of parameters such as the car's speed, the brake pressure, the brake temperature, the interval between applications of the brakes and the angle of the car's lateral motion to its forward motion. The range of values of these parameters are all continuous, open to interpretation by a design engineer. One such rule in an anti-lock braking system could be:

IF brake temperature is 'warm' AND speed is 'not very fast,' then brake pressure is 'slightly decreased.'

"The temperature might have a range of states such as cold, cool, warm and hot; the range of these linguistic terms can be precisely determined by defining membership functions by an expert.

"There are many consumer products that use fuzzy logic in their operation. There are also many fuzzy logic chips (processors) that are built to do special tasks without using conventional computers. The outlook for fuzzy logic is therefore very promising."

Not everybody can ignore the humorous potential in a concept such as fuzzy logic. Jim Diederich, a professor of mathematics at the University of California at Davis, is working on the applications of fuzzy logic in biological systems. He recently tried out fuzzy logic techniques on one specialized set of biological systems--his students--when he proposed the following rules for one of his courses:

Fuzzy Sets, Numbers and Logic

Course Information

1. A midterm will be given around mid term.
2. The final will be given around final time.
3. Homework will be assigned fairly regularly.
4. The midterm and final each will normally count as a substantial part of the grade.
5. The homework will not be insignificant in counting as part of the grade.
6. An excellent final will result in a somewhat excellent grade.
7. Solid work in two of the three areas, midterm, final and homework, will result in a solid grade.
8. Good homework will offset poor exams somewhat.
10. If you don't understand this by the end of the quarter, your grade will reflect it.

On homework assignments for this class, Diederich reports that he graded in fuzzy terms: good, somewhat good, very good. His students made him promise that he would provide a numerical grade on the midterm.

"I lived a long time in the tropics and often heard of, but never saw, the "green flash" that is said to occur just at sundown. Does it actually exist, and if so, what causes it?"

-Kaa Byington, San Francisco, Calif.

Jerry Nelson of Lick Observatory and the University of California at Santa Cruz passed along the following information about the mysterious "green flash":

"The green flash does indeed exist. It occurs when the sun is rising or setting. It is a consequence of the dispersion of light by air. Light from the sun is bent (refracted) by the Earth's atmosphere; the shorter the wavelength, the greater the amount of bending. Hence, blue light is bent more than green, which is bent more than yellow, which is bent more than red. Further, the amount of bending increases as the sun approaches the horizon.

"By the time the apparent sun (that is, the sun as we see it in the sky) just starts to set, the actual sun (as we would see it if there were no atmospheric refraction) has completely set. The bending due to refraction at sunset is just about 0.5 degree--roughly the same as the angular diameter of the disk of the sun. One can imagine the image of the sun in the various colors of the spectrum, each deflected a slightly different amount by refraction. At the horizon, the blue apparent sun is highest and the red apparent sun is the lowest. This color shift is rather small, even at the horizon, but it is key to understanding the green flash.

"Note also that the atmosphere scatters blue light much more effectively than red light. (That is why the sky appears blue.) When the sun is setting, its light passes through a lot of atmosphere. As a result, the light of the blue sun is strongly scattered and attenuated. The green sun, however, is less diminished by scattering.

"In the evening, the red sun sets first, so there is a period when the red sun has set but the green sun--or at least a tiny sliver of it--is still above the horizon. Thus, at the last moments of a sunset we can get a green image of the upper edge of the sun: the green flash. If it were not for the scattering of the atmosphere, we could get blue flashes. At sites that have very clear air, one sometimes can see turquoise flashes.

"All of this happens much more clearly when the sunset is truly at the horizon, so sunsets over the ocean in a cloudless sky offer the best chance of catching the green flash. Sunsets occur more quickly near the equator than at higher latitudes, so the green flash is a shorter phenomenon in the tropics. It is sometimes easier to see the green flash through binoculars, but DO NOT STARE AT THE SETTING SUN. Wait until just a few seconds before the end of the sunset to look with binoculars.

"The green flash is gorgeous, and well worth the patience it takes to find an appropriately clear day during sunset (or sunrise)."

Jay M. Pasachoff, Field Memorial Professor of Astronomy at Williams College in Williamstown, Mass., adds some details to the above explanation:

"The green flash is visible at sunrise and sunset when you have a perfect view of the horizon; it is usually best seen when you are looking over the ocean. Atmospheric refraction spreads out the sun's image, with red at the bottom and blue at the top. Think of an overlapping set of disks in the colors ROY G BIV (red orange yellow green blue indigo violet).

"The blue-indigo-violet colors do not come through the atmosphere because of intense Rayleigh scattering when the sun is low above the horizon. Further, when the sun is low, the orange and yellow are absorbed by water vapor. So we get a green image above the red image, with the two largely overlapping. When the red image entirely sets, the top of the green image is visible, but only briefly--for a second or so. The brevity of the green flash is one of the reasons it is so rarely seen.

"A photograph of the green flash appears in the book 'A Field Guide to the Stars and Planets' by Jay M. Pasachoff and Donald H. Menzel (Peterson Field Guide Series, Houghton Mifflin, 2nd ed., 1992) on page 54, with an explanation of the phenomenon on page 422."

(We also call interested readers' attention to "The Green Flash," by D. J. K. O'Connell, in Scientific American, January 1960, pp. 112-122.)

"Where does the "meter" come from? My professor said that the meter comes from the length of a pendulum that has a period of one second. This definition is close but not right on. My dictionary says the meter was originally defined as 1/10,000,000 of the distance from the equator to the pole, but I notice that is not exactly right either. When was the original meter defined? Is it just coincidence about the pendulum?"

-Robert L. Power, Salt Lake City, Utah

Barry N. Taylor of the Fundamental Constants Data Center at the National Institute of Standards and Technology writes:

"The origins of the meter go back to the 18th century. At that time, there were two competing proposals for how to define a standard unit of measure, or meter. The astronomer Christian Huygens suggested that the meter be defined by the length of a pendulum having a period of one second; others favored a meter defined as one ten-millionth the length of the earth's meridian along a quadrant (one fourth the circumference of the earth). In 1791, soon after the French Revolution, the French Academy of Sciences endorsed the meridian definition because the force of gravity varies slightly over the surface of the earth, affecting the period of a pendulum.

"Researchers measured the arc from Dunkirk, France to Barcelona, Spain; on June 22, 1799, the French Academy Archives adopted its standard meter, recorded on a platinum bar. (The French government made the meter the compulsory standard of measure in 1840.) The French, however, miscalculated the flattening of the earth due to its rotation. As a result, the meter in the Archives is 0.2 millimeters shorter than one ten-millionth of the quadrant of the earth.

"Despite its flaws, the French definition of the meter stuck. The Treaty of the Meter was signed in 1875, and in 1889 a platinum-iridium bar was established as the International Prototype Meter. (It was selected from several candidate meters because it was the closest to the called the Meter of the Archives, the platinum bar held in the French Academy.) So in fact at that time, a meter was really defined as the length of a metal bar.

"The meter bar lasted a good long time; but it became cumbersome and error-prone to refer to a specific, physical meter bar. Finally, after 71 years, a new standard emerged. In 1960 the General Conference on Weights and Measures redefined the meter in terms of the number of waves of a very precise color (wavelength) of light emitted by krypton 86 atoms. That revision did not last so long. In 1983 the Conference discarded the krypton standard and redefined the meter in terms of the speed of light--what might be called a theoretical definition. The meter is now officially 1/299,792,458 the distance traveled by light in a vacuum in one second.

"These changing definitions offer a good example of what happens in the field of measurement: as the tools and available precision change, the standards change with them. These days, you can buy a laser from Hewlett-Packard and create a reference meter on your own; the level of accuracy is far beyond what any scientist could achieve a century ago."

Fred Decker, a meteorologist at Oregon State University, offers some additional insight:

"I was for some years starting in 1946 an assistant to Willibald Weniger, a truly great physics teacher, from whom I took over the Engineering Physics course here at Oregon State. Weniger spiced his teaching of the principles of physics with stories such as this description of the origin of the meter.

"The standard meter was intended to be one ten-millionth of the distance from pole to equator along the meridian through Paris. This came out of the standardization attempted at the time of the French Revolution. The basic measurements had inevitable error, which led to the markings on the bar at Sevres being slightly different from that definition. The bar was, however, still considered the standard, just as the British standard yard was legally established as the distance between two scratches on a bronze bar. Both systems are arbitrary in this sense, although the standard meter was at least intended to have its length related to the dimension of the earth.

"There is a lot of the history of the growth of economic activity as well as political development involved in all these standards. For example, someone will inevitably want to know why the meridian of Greenwich became the prime meridian, rather than that of the great observatory at Paris! That is an intriguing anecdote itself. Seafarers sailing from the Thames synchronized ship time to the dropping of a ball at Greenwich; the sailors set their chronometers there and then computed their longitude at sea based on ephemerides of heavenly bodies.

"It is interesting also that habit and convenience in daily use seems to keep the British units in use, despite very determined efforts for decades to encourage popular acceptance and of metric system units in the U.S. and U.K."

"How is the plane of the earth's solar system oriented with respect to the plane of the Milky Way galaxy? Are the two aligned?"

This is one of those questions that readers can directly answer for themselves. Set out on a clear, dark evening. First, trace out the constellations of the ecliptic (zodiac); any decent star chart will enable you to do so. Then look for the faint glow of the Milky Way. What is the angle between the two?

Readers who don't want to wait for nightfall, or who live in areas where the Milky Way is not easily visible, can also find an answer here

"Is there a biochemical test that accurately diagnoses bipolar disorder? I heard on the radio today that millions of people in the U.S. have bipolar disorder and that 75 per cent of them are undiagnosed and untreated."

-James R. Spradling, Oro Valley, Arizona

The following response comes from Fred Petty, the director of the Mental Health Clinic at the Dallas Veterans Administration Medical Center and profesor of psychiatry at the University of Texas Southwestern Medical School:

"The current best estimate is that adult lifetime prevalence of bipolar disorder in the U.S. is about 1 percent for severe cases and 2 to 3 percent if milder cases are included--cases that would include cyclothymia and 'bipolar 2.' Given the population of the U.S. (about 250 million), those numbers translate into about two to three million with severe bipolar disorder and some five to seven million total, including those with mild symptoms. So the figures you heard on the radio seem reasonable.

"I have seen estimates that two thirds to three quarters of the people with depression are undiagnosed and untreated. I haven't seen the corresponding statistics for bipolar disorder, but I would say that, looking at mood disorders overall, most patients are still undiagnosed and untreated.

"Right now the diagnosis of bipolar disorder is a clinical diagnosis, which means it is made by a physician based on information about the patient's symptoms, mental status and medical history. It is important that people obtain a medical evaluation, because there are some conditions, such as thyroid disease, which can mimic the symptoms of bipolar disorder.

"There is, at present, no routinely available biochemical diagnostic tests for bipolar disorder. My laboratory has published some work looking at the blood levels of an amino acid called GABA (gamma amino butyric acid), which functions as a neurotransmitter in the brain. Bipolar patients often show low levels of GABA in the bloodstream. The GABA test is currently used only for research purposes; GABA levels appear abnormal only in about one third of the patients who are bipolar. Also, this test is not specific for bipolar, because low GABA levels are also found in people exhibiting non- bipolar depression.

"One of the likely reasons that GABA is not a universal indicator is that bipolar disorder is heterogeneous. In other words, the syndrome we call 'bipolar' actually results from several different causal conditions (etiologies); it is possible that in some cases the low GABA level is the predominant etiology, but not in all. In this sense, bipolar is somewhat like diarrhea--we call it one thing, but you can get it a variety of ways (through colitis, food poisoning, and so on)--or like heart failure, which has a multiple etiology. But low GABA readings look useful because the anomaly persists even after the person improves clinically. If my group can get its grants renewed, we would like to look at GABA levels in children whose parents have bipolar disorder.

"There is also some very interesting work being done with PET scans, which can show deficits of the neurotransmitter serotonin in the brain, associated with depression. Serotonin deficits seem to persist even after the depression lifts---suggesting that it is a real biological marker. PET scans of serotonin in bipolar patients have not yet been done, to my knowledge. Brain imaging using magnetic resonance has been applied to bipolar research; some bipolar patients show brain lesions in these images.

"Another very exciting area of investigation involves the search for a genetic locus for bipolar illness. Bipolar is probably the most genetic of all psychiatric illnesses, and psychiatric illnesses in general have a strong genetic component. If you have one parent with the illness, you face a 25 percent risk; if both parents are bipolar, you face a 50 percent risk. Among identical twins, there is an 80 percent concordance for bipolar disorder. Ideally, we would like to diagnose the illness in young people before they express any severe symptoms. In this way, we could save a lot of human suffering; the earlier a patient gets into treatment, the better the prognosis."

"I read that the sun's surface temperature is about 6,000 degrees Celsius but that the corona--the sun's atmosphere--is much hotter, millions of degrees. How does all that energy get into the corona without heating up the surface?"

-Leigh Peck, Menlo Park, California

This question strikes at one of the most active areas of current astronomical research. Not surprisingly, several scientists wrote in to give their answers.

David Van Blerkom, a professor of astronomy at the University of Massachusetts at Amherst, provides a nice overview, focusing on the second part of the query:

"The fact that the outermost region of the sun's atmosphere is at millions of degrees while the temperature of the underlying photosphere is only 6,000 kelvins (degrees C. above absolute zero) is quite nonintuitive. One would have expected a gradual cooling as one moves away from the central heat source. A related question is why, if the corona is so hot, it does not heat up the photosphere until it has an equally high temperature.

"I will address these questions in reverse order. Let us first ask what it means for a gas to have a high temperature. The answer is that temperature is a measure of the average kinetic energy of the gas atoms, that is, a measure of how fast they are moving. A high temperature gas has atoms with a larger average velocity than a low temperature gas of the same composition. We thus infer that the atoms in the corona are moving much more rapidly than those in the photosphere.

"In order for the corona to make the photospheric temperature rise, the coronal gas must cause the photospheric atoms to move faster. It could do so by colliding and mixing with the cooler gas and thus transfering some of its kinetic energy. Another way is also possible: At a temperature of millions of degrees, the gas in the corona is highly ionized, that is, electrons are stripped off neutral atoms and move freely. Because electrons are thousands of times less massive than atoms, the hot electrons have very high speeds. These electrons could travel into the photospheric gas and collide with the atoms there, again increasing their velocities. These two heating mechanisms are called convection and conduction, respectively.

"A gas at millions of degrees also radiates energy; much of it is emitted in the form of very high-energy x-ray photons. X-ray photons impinging on the photosphere could also transfer energy to the gas atoms there. This heating mechanism is radiation.

"Yet the three traditional methods of heating do not raise the photospheric temperature for a simple reason. Suppose, as a thought experiment, one had a thermometer that could measure temperatures of millions of degrees and placed it in the corona. In order to make a temperature measurement, the coronal atoms or electrons must strike the thermometer, or x-ray photons must impinge upon it. The corona, however, has such a low density that the thermometer will almost never be hit. So while the thermometer is technically sitting in a gas that is at 2,000,000 kelvins, it doesn't know it. The gas has a high temperature but a low heat content. There are just not enough atoms around to heat our hypothetical thermometer or the underlying photosphere.

"The question of why the corona has such a high temperature is harder to explain, and probably the last word on the physical mechanism has not yet been given. Most astronomers assume that the gas is heated by the magnetic field that pervades the corona. The solar magnetic field has long been known to cause the sunspot cycle, and the physical shape and activity in the corona also varies with the sunspot cycle. Magnetic fields are known to be able to transfer large amounts of energy to the solar atmosphere, sometimes explosively as in flares. Huge magnetic loops can be seen to rise far into the corona, and it is quite plausible that the solar magnetic field is the ultimate source of physical heating of the corona."

Vic Pizzo of the Space Environment Center in Boulder, Colo., reiterates how mysterious this process is:

"The precise mechanism by which the corona overlying the solar surface is heated to temperatures of one to two million kelvins remains one of the outstanding problems of solar physics. It has long been suspected that turbulent motions in the lower solar atmosphere are propagated outward as waves in some form, which ultimately shock the thin atmosphere above the surface (the photosphere). The shocks thereby dissipate mechanical energy in the waves as heat. When magnetic field lines reconnect, they release energy; some researchers suspect that fine-scale magnetic reconnections above the sun's surface provide the energy to heat the corona.

"Whatever the cause, some heat does indeed leak back toward the solar surface, but the total amount of energy so transported is really quite small, and cannot raise the photospheric temperature very much. The reason for this is the extremely rapid fall-off of mass density with height above the solar surface. That is, although the material in the corona is very hot, it is also very tenuous. Thus, the energy transported back toward the surface is dissipated into an ever increasing mass of material as it works its way down, whereas the heat transported outward is readily dissipated into the vacuum of space. "

Leo Connolly, the chair of the department of physics at California State University, San Bernardino, adds the following information:

"You are quite right about the corona being much hotter than the photosphere of the sun. The photosphere is the outer layer of the sun that produces the visible light we receive. The corona is a large, tenuous layer of gas whose structure is governed by the Sun's magnetic field. The gas in the corona is actually escaping from the Sun, forming the solar wind.

"What accelerates the atoms of gas to high velocity and temperature in the corona? It is likely that the solar magnetic field provides the necessary energy, but the mechanism is poorly understood. At the photosphere, the temperature is about 6,000 kelvins. The region of interest is above the top of the photosphere, where the temperature actually drops (to about 4,500 kelvins at a level of 500 kilometers above the photosphere). At 1,500 kilometers, the temperature starts to rise and by 10,000 kilometers above the photosphere the temperature reaches one million kelvins. Between 1,500 kilometers from the top of the photosphere and 10,000 kilometers is a region called the 'transition zone,' which is where the atoms are accelerated. The corona starts at 10,000 kilometers and extends out to about 10 million kilometers, where the gas finally escapes the sun's gravity and becomes part of the solar wind.

"We know that atoms, stripped of one or more electrons, are trapped by magnetic fields and move along the field lines. But what causes these atoms to be accelerated, producing the high temperatures of the corona, is not understood. All we know is that it definitely occurs in the transition zone."

Last but not least, Jay M. Pasachoff, Chair of the Department of Astronomy at Williams College in Williamstown, Mass., offers a perspective on some of the current attempts (including his own) to solve the riddle of the solar corona:

"One of the nice things about astronomy is that questions that are simply phrased often turn out to be profound. The manner in which the solar corona is heated to millions of degrees Celsius is one of the important unsolved problems of astrophysics. I have conducted experiments during a series of total solar eclipses to address the question, and there has been much theoretical work in this area recently. The problem was much addressed at a NATO Advanced Research Workshop on Observational and Theoretical Problems Related to Solar Eclipses, held in Bucharest, Romania in the first week of June 1996; the proceedings of that workshop will be available in a year or two.

"Basically, one cannot account for the heating of the corona by a radiative flow, so we think the corona is heated by some sort of magnetohydrodynamic (MHD) wave flowing out of lower levels of the sun. Images of the sun in the far ultraviolet and in X-rays (acquired most recently by the Solar and Heliospheric Observatory spacecraft, the Yohkoh satellite, and the NIXT rockets) show that the heating of the corona is localized in solar active regions, which indicates the important role played by the magnetic field. There are perhaps a dozen specific models that have been proposed to account for the high temperature of the corona. These models involve fast-mode MHD waves, slow-mode MHD waves, Alfren waves, et cetera. The older idea that acoustic waves flowing out of lower levels heats the corona was abandoned in the 1970s, when the Orbiting Solar Observatory 8 spacecraft did not see such waves in the chromosphere, the layer just above the photosphere (the apparent 'surface' of the sun in visible light). It remains possible, however, that some acoustic waves can be formed at higher levels.

"My work on the coronal heating problem is summarized in my chapter 'Measurements of 1-Hz coronal oscillations at total eclipses and their implications for coronal heating,' in Mechanisms of Chromospheric and Coronal Heating (Proceedings of the Heidelberg Conference), edited by P. Ulmschneider, E. R. Priest and R. Rosner (Springer-Verlag, 1991). The book also contains many other theoretical and observational papers."

"What are the processes that determine the strange shape of a mushroom cloud after a nuclear, thermonuclear or major chemical explosion?"

-Aasmund Skjaeveland, Stord, Norway

David Dearborn, a physicist at Lawrence Livermore National Laboratory, responds:

"Contrary to a common misconception, the shape of the mushroom cloud does not depend on the nuclear or thermonuclear component; as you note, a massive detonation of chemical explosives would produce the same effect.

"A mushroom cloud forms when an explosion creates a very hot bubble of gas. In the case of a nuclear detonation, the bomb emits a blast of x-rays, which ionize and heat the surrounding air; that hot bubble of gas is known as a fireball. The hot air is buoyant, so it quickly rises and expands. The rising cloud creates a powerful updraft which picks up dust, forming the stem of the mushroom cloud.

"The central part of fireball is hottest, creating a rolling motion as it interacts with the outer portions. Thermal instabilities, called Kelvin- Helmholtz instabilities, occur at the interface between the fireball and the neighboring cool air. If you watch a movie of a nuclear detonation, you can see entrained material swirling outwards as a result.

"All atomic bombs produce a bulge and a stem, but the really huge, flat clouds--the ones that could be described only as mushrooms-- come from the very high-yield explosions caused by thermonuclear weapons (hydrogen bombs). The fireball from an H-bomb rises so high that it hits the tropopause, the boundary between the troposphere and the stratosphere. There is a strong temperature gradient at the tropopause, which prevents the two layers of the atmosphere from mixing much. The hot bubble of the fireball initially expands and rises. By the time the bubble has risen from sea level to the tropopause, it is no longer hot enough to break through the boundary. (In other words, the bubble encounters material that has more energy than it does, so it is no longer buoyant.) At that point, the fireball flattens out; it can no longer expand upward, so it expands to the side into an exaggerated mushroom cap. The same thing happens to big summer thundercloud when they rise up to the tropopause, producing a characteristic flattened-anvil shape.

"Those interested in learning more about mushroom clouds and other atomic-bomb phenomena might want to look at the book The Effect of Nuclear Weapons, compiled and edited by Samuel Glasstone and Philip J. Dolan (U.S. Department of Defense and U.S. Department of Energy, 1977)."

"How close are scientists to knowing the origin of life on earth? When, if ever, will we be able to explain the origin of life in purely scientific terms?"

-Karuppiah Chockalingam, Box Hill North, Australia

James P. Ferris, a researcher in the chemistry department of Rensselaer Polytechnic Institute in Troy, New York, has conducted extensive work on the ability of clay minerals to catalyze RNA reactions. He submitted the following response:

"Scientists are not close to knowing the exact processes that took place on the earth which led to the origins of life. They may never know the exact answer because the evidence for this very primitive life has probably been destroyed by the more efficient life which evolved from it. But scientists have made important progress in understanding the types of chemical processes that may have led to the origins of life.

A simple example may help to illustrate this difference between knowledge of the exact answer and possible answers to the question. A friend of mine called to tell me that he is in San Diego; he then asked me to deduce the exact route he followed in getting there from Troy, NY. From the time of my last encounter with him I can guess whether he traveled from Troy by airplane, or car. Then I can try to decide which airline he took or which highways he followed, but I will never know unless I can gain access to the computer systems of all the airlines and can find his reservation, or can travel all the routes from Troy to San Diego, stopping at gas stations and asking if they remember seeing this person. Short of having this detailed information, I will have to be satisfied with developing plausible scenarios based on my knowledge of the starting and ending points and the approximate time it took him to make the trip.

"We are in a similar predicament with our understanding of the origin of life. Since we don't have detailed information on the exact steps we will have to be content with developing plausible scenarios based on information concerning conditions on the early earth around the time life originated nearly four billion years ago. One plausible scenario holds that the first life on earth was based on ribonucleic acids (RNA), a simpler chemical cousin of DNA. Many researchers have focused on RNA because it can store genetic information and it can catalyze reactions; these are essential processes in living systems. In this scenario, it is proposed that RNA, a polymer (long-chain molecule), arose from the gradual stringing together of repeating chemical units, known as monomers, that naturally arose on the primitive earth.

"Recently it has been shown that it is possible to form RNA from monomers on the surfaces of clays, which can catalyze, or chemically assist, the polymerization reaction. Experiments done in test tubes (in vitro) have shown that RNA with one type of catalytic activity can evolve to an RNA with different catalytic properties. These two sets of experiments suggest that it may be possible to demonstrate how clay minerals could have permitted the formation of complex RNA molecules that are capable of evolving in form. If this inference is correct, then the research provides support for a plausible scenario for the origins of life. But, as with the question concerning the route my friend took from Troy to San Diego, we will never know for sure. Just as my friend may have reached San Diego by flying east to Europe and Japan, life may have evolved by an equally circuitous route."

"The Beginnings of Life on Earth" by Christian de Duve
"The Origin of Life on the Earth" by Leslie E. Orgel

"Most unbred animals (English sparrows, for example) all look alike to me. People, of course, not so. Do I just not recognize the traits that distinguish one animal from another, or do they really lack the individual distinctiveness of humans?"

-Ed Martin, Buffalo, New York

James R. Northern of the Moore Laboratory of Zoology at Occidental College in Los Angeles, California, noted the following:

"If you were to take a group of people and shrink them down to the size of an English Sparrow, they would loose much of the individual characters that you use for recognition of individuals. The distinctive characters would still be there, but much harder to see, since they would be smaller.

"Birds recognize each other by their voices or calls. They can identify mates, parents or offspring by voice, much as a blind person might do. During courtship and pair formation, birds learn to recognize their mate by 'voice' characteristics, and not by visual appearance."

Pamela J. Pietz of the Northern Prairie Science Center in Jamestown, North Dakota, considered two parts of the question--how do we tell animals apart, and how do they distinguish each other. Her reply follows:

"Humans can tell individual animals apart in many species, but it takes some familiarity with the species of interest. For example, researchers can recognize individual humpback whales because each whale has a unique black-and-white pattern on the underside of its tail flukes. Biologists studying great right whales (such as Roger Payne in Argentine Patagonia) recognize individuals by the unique patterns of whitish growths, called callosities, on the whales' heads.

"Craig Packer and Anne Pusey of the University of Minnesota use whisker patterns to tell individual lions apart in their African research. For short-term identification, some researchers use scarred skin, missing feathers or other physical anomalies to tell animals apart. Researchers record tears and notches that they observe on the edges of elephants' ears to distinguish African elephants from one another, for instance.

"The common aspect of all these recognition systems is that the people who devised them spent lots of time looking closely at lots of individuals of one species. It is likely that we could recognize individuals of many species if we spent enough time observing them carefully. Of course, individuals of some species do look more alike than individuals of some other species. For example, some invertebrates have reproductive systems that lead to many individuals being very closely related to each other genetically (much like identical twins in humans). The less genetic variability there is among individuals of a species, the more closely they will resemble one another.

"We should also remember that visual markers are not the only possible way to tell individuals apart. Humans tend to rely on visual cues more than other types of cues because our vision is more highly developed than our other senses.

"Individual animals of a given species probably can tell one another apart as easily as we can tell humans apart, but they may use sound, smell, and other senses instead of, or in addition to, vision. Birds are strongly visually oriented (that's why they are so colorful), so they may use visual cues to recognize individuals; they also have excellent hearing, however, so they may respond to differences in individual voices as well, much as humans do. Reptiles use chemical signs (akin to 'smell') to gather information about their environment, so they probably likewise rely on chemical signs to tell individuals apart. Some animals see beyond the visible light spectrum (bees and some birds see ultraviolet wave lengths), and some animals hear sounds that are too low (e.g., elephants) or too high (e.g., dogs) for humans to hear. Thus, some animals may use cues to tell each other apart that are not available to us."

"Many science fiction stories, like Babylon 5 on TV, include spacecraft that use centrifugal force to simulate gravity in outer space. What would artificial gravity be like for the inhabitant of a space station? Is this technique actually feasible today?"

-Jim Daly, Sayre, Pennsylvania

Robert Ehrlich, a physicist at George Mason University, sent in the following reply:

"As in the movie '2001,' the space station would presumably be in the shape of a giant spinning torus or doughnut, with gravity pointing outward from the spin axis, so that your head would point towards the central axis.

"The strength of gravity would depend on the rate of spin. If the station had a diameter of 640 meters, it would need to rotate about once per minute to simulate the Earth's gravity. Only if the space station had a fairly small diameter would simulated gravity feel any different from the real thing. For small diameters, the strength of gravity would vary at different points of your body depending on their distance from the axis of rotation, with the result that you would be slightly stretched. For example, if the radius of the space station were only 20 meters (about 10 times your height), gravity would be 10 percent stronger on your feet than your head when you were standing upright. For a 150-pound person, it would feel like a 15-pound force were stretching you.

"The main problem regarding feasibility today would be the difficulty of constructing a large space station that had sufficient structural strength to remain intact under the simulated gravity."

John Taylor of NASA's Marshall Space Flight Center in Huntsville , Alabama, explains why nobody is racing to exploit artificial gravity just yet:

"We go to space to get away from the Earth's gravity; we have no incentive to try to create it artificially.

"The international Space Station is above all a human physiology research facility. Before we can ever hope to explore the solar system, we first need to know what effects long-term exposure to the hostile space environment will have on the human body. We already know that in the absence of gravity we see rapid changes in such things as bone mass and muscle mass. Radiation poses unknown hazards as well.

"Aboard the Space Station scientists will try to sort out the attacks and possible countermeasures. They will also carry out important microgravity research. Both the physiology (life sciences) and microgravity (biotechnology, materials etc.) research depend on the absence of gravity. Any attempt at artificial gravity would turn Space Station into little more than an observation platform.

"Once we have the answers we seek, we may find that it would be beneficial to use artificial gravity for long-term travel in space. Or maybe not. If we do want to try this for some reason, it could be achieved by having two Space Station-sized modules attached end-to-end to a central node or core. These could be rotated around the core. Or, you could simply swing a pair of modules on opposite ends of a long tether, with nothing in the middle. Right now, creating artificial gravity is not very high on anybody's priority list, so not much effort is going into this kind of engineering. But we do know how to do it, at least in principle."