Where did the Messerschmitt Jet Crash?

Bobby Shaftoe was walking into town, when he saw an experimental Luftwaffe jet aircraft coming across the Gulf of Bothnia (pages 564ff of Cryptonomicon). He estimated that it crossed the shoreline "a couple of miles north of Otto's cabin," which he had just left. Perhaps he based that estimate on knowing the particular clump of trees behind which it disappeared. He did not know either the size of the aircraft, or its speed, which would be the usual information employed in assisting such an estimate.


He counted seven seconds between seeing the fireball of the crash, and hearing the explosion. Using the 'five seconds per mile' algorithm, which he had learned in the Boy Scouts (that is where I learned it), the crash must have been about 1.4 miles from where he then stood. Already, there is a problem; the two estimates don't agree very well, because the airplane had kept going beyond that point on the shoreline.


Bobby walked three more kilometers into Norrsbruck, where he told Günter Bischoff what he had seen (page 583). Bobby specified the distance as "... seven kilometers from where I was standing. So, ten clicks from here."


There are several problems with that statement. The numerical problem may be the most obvious. Just from knowing that a distance of three miles is approximately five kilometers, the metric version of the algorithm must be 'three seconds per kilometer'. The accepted value for the speed of sound (about 330 meters/second in dry air at zero degrees Celsius), means that this metric form of the algorithm is a much better approximation to reality, than is 'five seconds per mile'. Thus, either the time delay was 21 seconds, or the distance was 2.3 kilometers, or perhaps neither number was correct.

The visibility problem arises only if the time delay was indeed 21 seconds, so that the distance was properly 7 kilometers, or about 4.2 miles. I have never been to Sweden, but maps (e.g., http://www.sverigeturism.se/smorgasbord/smorgasbord/service/sweden-map.html ) show several rivers flowing into the Gulf of Bothnia, which implies erosion of valleys. I have lived many years in central Illinois (where Neal Stephenson has also lived) and central Kansas. Both are considered rather flat, and effectively treeless. I would not count on seeing the immediate fireball in either place, at a distance of seven kilometers, because the crash could have happened in a valley. The trees in Sweden would make it even less likely for the fireball to be visible. The ultimate column of smoke would certainly become visible, but it is hard to say just how long that would take.

This military slang usage of "click" for kilometer (better "klick"), was either an anachronism, or a separate creation which died with Bobby and Günter. I served in the U.S. Army during the Korean War, and I never heard that usage. It was widespread during the Vietnam War, and some dictionaries (e.g., http://www.urbandictionary.com/ ) suggest that it arose during the 1950s. I would guess that it was invented during joint training exercises, involving U.S. forces and other NATO forces. Based on numbers of countries, if not numbers of individual soldiers, the U.S. military was outvoted on the question of yards and miles, versus meters and kilometers. Everyone needed to agree on maps, road marches, and firing tables for artillery. (Even the British, who invented the yard and the mile, abandoned them in favor of metric units.) Perhaps "klick" started as a face-saving joke.

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Location of Golgotha (Part 2)

Let us now consider how well Lieutenants Goto and Ninomiya might actually have done, in finding the latitude and longitude of the entrance to the Golgotha excavation, where gold was later stored. Stephenson described their method, on pages 789-792 of Cryptonomicon.


I don't know details of a Nipponese sextant of vintage 1940, but it was unlikely to have been better than modern instruments. The best (or at least, most expensive) sextants for amateur navigators, that I have found online, are the Cassens & Plath Horizon Ultra ( http://www.cassens_plath.de/catalog_web/sextantse_n.htm ) and the Tamaya Spica (http://www.stanleylondon.com/TamayaSpica.htm ). Their specifications are similar. The arc is stated to be accurate within 9 or 10 arc-seconds. The vernier on the drum of the tangent screw reads to 0.2 arc-minute. The aperture of the largest available telescope is 40 mm. Much less expensive sextants (made mostly of plastic) have similar specifications, except that the arc is typically accurate only to 30 arc-seconds.


The angular resolution of such a telescope is about 16.8 micro-radian, or 3.5 arc-second. Thus the precision of angular measurements is limited primarily by the vernier and the arc, both of which might contribute. With good technique, and information about the sun's declination and apparent radius from a nautical almanac, the astronomical latitude could be measured to about the nearest 15 arc seconds, or about 460 meters. This is better than one needs for navigation on the ocean surface. You can see much further than that over open water, and can correct your landfall.

I do happen to know about "a pretty good German watch" of vintage 1940, because I used to own one. Mine was actually made in about 1946, but it undoubtedly used a prewar design. It ticked 5 times per second, and the sweep-second hand jumped at every tick. However, I quickly realized that I couldn't do anything useful with the fifths of seconds. If I was looking at some event, and then looked at the watch, it was almost impossible to determine the time of the event, to any better than the nearest second.


It also wasn't good enough that the watch was "... zeroed against the radio transmission from Manila this morning, ..." If my watch went more than a few months from its last visit to the jeweler's shop, it would be gaining or losing several seconds per day. It was at least as important to determine its current 'rate of going', by checking the watch against a standard for several days in a row.


I have never personally tried 'shooting the sun' with a sextant, but I have read about the technique used at local noon. (I have read every story in the Hornblower series by C. S. Forester, even more often than I have read Stephenson's stories.) One turns slowly, following the sun in azimuth, while rotating the tangent screw to keep the bottom edge of the sun's reflected image in apparent contact with the horizon. The sun's angle of elevation increases as it approaches the celestial meridian, stops increasing exactly as it crosses the meridian, and thereafter decreases. I don't know how easy it is to see these stages, and to say "Mark!" to the timekeeper, exactly when the elevation is maximum.


I would guess that the very best that one can do, is to get the meridian crossing time within one second on the chronometer. [This would apply in the tropics (e.g., the Philippines), because the maximum elevation would be large, and the sun's elevation would change rapidly. At high latitudes, the maximum elevation and the rate of change would be smaller. It might not be possible to identify the time of the maximum, to closer than several seconds.] If the zero and the rate of going of the chronometer are both good enough, then the Greenwich time is also known within one second. The longitude can then be calculated to within 15 arc-seconds, using the information about the sun's right ascension from the almanac.


Unfortunately, Stephenson does not allow Goto and Ninomiya to use this good standard navigational technique, although he does not give an adequate description of what they must have done instead. He specifically states: "They reach it [the highest summit] at about two-thirty in the afternoon, ..." At that time (well after noon), the sun's azimuth and elevation are both changing continuously, and both must be measured, as nearly simultaneously as possible. The best choice would probably be to measure the elevation with the sextant, and the azimuth with the transit, using the compass needle in the transit. This might be dangerous for the observer using the transit, because transits may not have provision to protect the user's eyesight from the sunlight, as most sextants do.


Each observer would continuously track an edge of the sun, but there was no third person to be a timekeeper. One of the observers would say "Mark!" when his own observation was in good alignment, to tell the other observer to stop tracking. The one with the watch would then look away from his telescope, in order to read the time. I doubt that this could be done reliably to better than two seconds in time.


The time of the observation and the almanac identify the latitude and longitude of the sub-sun point, i.e., the point on Earth for which the sun is then at the zenith. The zenith angle, i.e., the complement of the elevation angle, defines the angular separation between the observation point and the sub-sun point. The azimuth angle runs from the observation point to the sub-sun point. One then solves the spherical triangle of those two points and the pole, in order to determine the coordinates of the point of observation.


The near-disaster, which Stephenson imposed upon his characters, was the necessity for using a magnetic azimuth. (If they had stayed on the summit over a night, they could have determined astronomical north by observing circum-polar stars.) The compass needle, between the brackets for the telescope of the transit, might be 12 cm long, or 6 cm from pivot to tip. A protractor of that radius could be divided into degrees, with marks about one mm apart. Even with a decimal vernier on the needle, an azimuth could be measured only to the nearest 6 arc-minutes. That uncertainty in solar azimuth would introduce an uncertainty in the position of the observation point of about 3 arc-minutes, mainly in latitude.


A generous reader could suggest that Stephenson had merely made a typographic error. He may have intended to say, "They reach it at about twelve-thirty, just before local apparent noon, and immediately wish they hadn't because the sun is beating almost straight down on top of them." Notice that this also makes the geometry of the sun's rays much better. Two hours later, the zenith angle of the sun would be about 30 degrees, or even more.


Normally, places in the tropics never bother with daylight saving time. However, the Nipponese armed forces typically maintained the standard time of Tokyo (GMT + 9 hours), and enforced it upon conquered areas ( http://www.absoluteastronomy.com/topics/Japan_Standard_Time ). The standard time of Manila is GMT + 8 hours, so that the watch was effectively keeping the equivalent of daylight saving time.


Stephenson carefully avoided mentioning the degrees and minutes for the location of Golgotha, and rarely mentioned dates in Cryptonomicon. However, the pile of gold bars (also on Luzon) was at about 122 degrees east longitude, so that the sun crosses the meridian there about 8 minutes before it crosses the center of time zone +8. Without knowing the date, we cannot guess how fast or slow sun time was, relative to mean time (the equation of time).


At any rate, with an appropriately chosen earlier arrival time, it would have been possible for Lieutenant Ninomiya to shoot the sun in the standard manner. However, the resulting precision of 15 arc-seconds, in both latitude and longitude, is insufficient to allow him to say, "I have the peak exactly -- ..."


There was a corresponding typographic error in another time specification. Stephenson may have intended to say, "At one-o'clock sharp, the enlisted man down in the tree begins to flash his mirror at them, a brilliant spark from a dark rug of jungle that is otherwise featureless." Unfortunately, the very next sentence includes another inadequacy: "Ninomiya centers his transit on the signal and takes down more figures."


What Ninomiya needs to determine at this time, is the displacement (distance and direction) from the summit to the tree near the entrance of Golgotha. A modern transit with a laser rangefinder can do that in a single operation. However, in 1944, there was no such thing as a laser. His transit could only measure a (magnetic) azimuth to the spark. To get a distance, he must do triangulation, using both ends of a baseline of measured length and azimuth. At each end, he must measure the angle between the spark and the marker, which defines the other end of the baseline. The soldier in the tree had to be instructed to keep flashing for a long enough period of time, so that the transit could be carried along the baseline and realigned for the second measurement.


Fortunately, the next sentence offers a possible way out of these difficulties: "In combination with various other data from maps, aerial photos, and the like, this should allow him to make an estimate of the main shaft's latitude and longitude." The mention of "aerial photos" is in the nature of a bad joke. Stephenson has gone to great length to make the point, that in this area of a multiple-canopied tropical forest, it is impossible to see through the foliage from either above or below. Radar imaging from aircraft would be ideal, penetrating the forest to show the ridges and stream valleys of the solid ground. However, that application of radar was a post-war development.


The last opportunity lies in the mention of "maps". We know that a large-scale map of Bundok Site existed, drawn on a linen bed sheet (pages 730-734). Because it was a reasonably accurate representation of the Site, it was probably generated from a well made map at smaller scale.

The history of mapping in the Philippines was intimately associated with the fact that the U.S. controlled the Philippines, from after the Spanish-American War until World War II, and for a few years afterward. (See a brief history by Joseph F. Dracup: http://www.ngs.noaa.gov/PUBS_LIB/geodetic_survey_1807.html .) The surveying and mapping was done with the advice of the U.S. Coast and Geodetic Survey, using the same type of instruments and techniques as had been employed to survey and map the continental U.S. (Not all of the triangulation surveys in the Philippines were done to the same high standard of accuracy as in the U.S.)

The data were presented using Luzon Datum 1911, which incorporated a reference ellipsoid with axes of exactly specified lengths, a single surface point whose latitude and longitude had exactly specified values, and an orientation specified by the azimuth to another point. I have not seen the specifications of Luzon Datum 1911, but it is easy to find the specifications of the analogous North American Datum 1927 ( e.g.: http://www.discoverosborne.com/Document.aspx?id=5572 ). The Nipponese captured all of the data from these surveys in 1942, so that they could produce maps that were the equivalent of what the U.S. could produce.

I have not seen U.S. military maps of World War II, but I saw and used maps of Korea, for that war. Almost everything else used by the U.S. in the Korean War was essentially identical to that used in World War II, so I would guess that the maps were equivalent also. The largest-scale Korean maps were at 1:50,000 ( http://www.koreanwar.org/html/korean_war_topo_maps.html ). Each map quadrangle had its edges labeled by latitude (north and south) or longitude (east and west). A grid of latitude and longitude lines subdivided the interior of the map. The smallest things printed on the map (e.g., contour lines of elevation and the grid lines) were about 0.1 millimeter wide, which represents 5 meters on the ground.


Thus, if one makes the highly optimistic assumption, that every single landscape feature printed on the map is in the correct position within the width of those lines, then its latitude and longitude can be determined to a precision of 0.2 arc-seconds (6 meters), by interpolation between the grid lines. (Personally, I am not nearly that optimistic about the accuracy of any maps of that era.)


This happens to be just good enough, because Stephenson stated that the tenths digits were even, for both coordinates (page 1064). Thus they could have represented fifths of an arc-second, rather than tenths. Ninomiya would have looked for the bends in the Tojo River, as shown on the map, because the entrance was very close to the river. (Note that this means that the observations on the summit of Mount Calvary were totally unnecessary.)

The final consideration concerns styles in GPS receivers. In the present generation (2009), GPS receivers are typically aimed at urban explorers, who might want to find the nearest restaurant or night club, and who need to be told which way to turn at the next intersection. Some previous generations of GPS receivers were aimed at wilderness explorers. They might have wanted to record or relocate mineral deposits, or populations of particular biota, or farm cemeteries with ancestral graves, or sunken submarines, or gold bars.


Some of those receivers came with the capability of changing the datum, to be used to display the positions, at the user's choice. Thus, if Randy's receiver offered Luzon Datum 1911, he could indeed get to the same point, in the map grid, which Lieutenant Ninomiya had selected in 1944.

If everything else had gone well since 1911, Golgotha would be there.

Location of Golgotha (Part 1)

One of the most important continuing items in Cryptonomicon is the location (latitude and longitude) of the entrance to Golgotha, the excavation at Bundok Site, in which a large quantity of gold was stored near the end of World War II. On pages 789-792 is a description of the method, used by Lieutenants Goto Dengo and Ninomiya, to determine that location in 1944. On pages 1039-1040, Randy Waterhouse recalls the values he had decrypted from the Arethusa intercepts: "In the seconds figure, the Golgotha numbers have one digit after the decimal point, which implies a precision of ten feet. GPS receivers can give you that kind of precision. Randy's not so sure about the sextants that the Nipponese surveyors presumably used during the war."


This stated precision of the Global Positioning System (GPS) was consistent with Randy's earlier experience. On page 601, Randy is told the coordinates of a different site, accurate to hundredths of a second. On page 633, Randy mentions this encounter in an email to his colleaues, saying "... , implying a maximum positional error on the order of the size of a dinner plate." On page 655, Randy reports finding a stack of gold bars there, with the help of his GPS receiver.


On page 1064, Randy and Goto Dengo verify that they both know the coordinates of Golgotha, as of 1944. On pages 1089-1090, Randy reaches that point, as shown by his new GPS receiver.


Let us start out with the simplest question: What distance on Earth corresponds to one second of arc? The original definition of the the meter was that the Paris meridian, from pole to equator, should measure ten million meters. (They didn't get it quite right.) That quarter circle contains 90 x 60 x 60 = 324,000 arc-seconds, so that one arc-second corresponds to 30.9 meters or 101.3 feet. There is no point in keeping more decimal places in this discussion, because Earth's surface is approximately an ellipsoid of revolution. The polar radius b is shorter that the equatorial radius a. [This relationship is often expressed by the flattening parameter f, in the form b = a (1 - f).] The distance corresponding to one arc-second depends upon the latitude, and upon the direction of the displacement. Thus Stephenson was reasonable in both of his statements about the precision of GPS.


Prior to the development of GPS, there were two ways in which the position of an arbitrary point could be determined. One method involves astronomical observations, to measure the latitude and longitude directly. It works at any place on Earth, on land or water. The other method is by survey, to measure the distance and direction to that arbitrary point, from some point whose latitude and longitude are already known. It works just as well in an archipelago such as the Philippines, as on a continent such as North America, so long as water gaps can be spanned by lines of sight between triangulation stations on land.


There are two levels at which one can ask whether the 1944 measurement was possible, with that stated precision. At the higher level, what must you have and what must you know, in order to measure latitude and longitude to 0.1 arc-second, without using GPS, but matching GPS? At the lower level, what precision could Goto and Ninomiya reasonably have attained, with their equipment and technique?


The problem of measuring longitude by astronomical observations, has historically involved measuring the time of some event with sufficient accuracy. [Stephenson even mentioned "the longitude problem" in The System of the World (e.g., pages 345-348).] In order to know longitude to 1/10 arc-second, the time must be measured to the nearest 1/150 second. This is completely impossible, if human reaction time is involved.

The best astronomical clocks before World War II were typically based on a vibrating quartz crystal in a controlled environment. The frequency of the crystal was divided electronically, and used to control an electronic alternating-current source at some convenient frequency. The alternating current drove a synchronous electric motor, and reduction gears from the motor shaft drove analog second, minute, and hour hands. Such a clock was much more accurate over long periods than any clock with a mechanical escapement, but it is not obvious how one could pull out the times of external events, to this desired precision.


Purely electronic clocks, which essentially count the oscillations of some atomic or molecular system, are a product of the development of radar during World War II. It is almost trivially easy to pull out the time, to much better precision than this, without disturbing the clock itself. However, such clocks did not exist in 1944.


The astronomical event itself must appear to be no larger than 1/10 arc-second. That typically means that it must involve a star, which acts as a point source to be viewed by a telescope. The standard relationship, for the diffraction pattern produced at a circular aperture, is that the first zero occurs at the angle such that the path difference, through points across the diameter of the aperture, is 1.22 wavelengths. For light of wavelength 550 nanometer (the peak of the response of the human eye), and an angle of 0.487 microradian (1/10 arc-second), the aperture must exceed 1.38 meter (54 inches). This is a major astronomical instrument.


The event would typically be the passage of the star across the local celestial meridian, defined by the local vertical and the celestial pole. The longitude of the telescope would be determined by the time of passage, as the star image moves behind a cross-hair, which is aligned with the meridian. The latitude of the telescope would be determined from the angle of elevation of the star image above the local horizontal, or equivalently, by the angle between the local vertical and the star image.


Of course, the coordinates of the star (right ascension for longitude and declination for latitude) would have to be known to a precision of 1/10 arc-second. This was completely unavailable in 1944. According to my Encyclopedia Britannica, star atlases even in 1989 (the date of publication) were typically good to only 1/4 arc-second.


One remaining problem in making very accurate positional measurements by astronomical observations, and comparing them to GPS measurements, is hidden in the above mentions of "local celestial meridian" and "local horizontal or vertical". (The following discussion is taken from the texts which I used for teaching an introductory course in Earth Science.)

If the mass of Earth were distributed with rotational symmetry, and with density decreasing from the center to the surface, then Earth's surface could indeed match the reference ellipsoid of GPS. At any point on such a homogeneous planet, the local vertical (as revealed by a plumb line) would be perpendicular to the reference ellipsoid. The local horizontal (as revealed by an undisturbed liquid surface) would be tangential to the reference ellipsoid. The local celestial meridian would be defined by the axis of the reference ellipsoid and the point itself.


In the actual Earth, the mass distribution has considerable lack of homogeneity. The scale of the inhomogeneities ranges from continents versus oceans, to mountain ranges versus oceanic trenches, to ore bodies versus petroleum deposits. One effect of inhomogeneity is gravitational anomalies. Directly above a region of greater (lesser) density, the measured acceleration of gravity would be stronger (weaker), than on a homogeneous planet. Another effect is variation of sea level. The ocean water would tend to pile up near a positive anomaly, but would tend to sag near a negative gravitational anomaly.

The remaining effect is deflection of the vertical. The acceleration of gravity g would tend to point toward a region of greater mass density, and away from a region of lesser mass density. This effect is obviously involved in position determination. Any north-south component of g would cause the astronomical latitude to differ from the GPS latitude, and any east-west component would similarly affect the astronomical longitude.


All of these effects can be combined in the concept of the 'geoid'. This is defined as a surface of constant gravitational potential, which matches Earth's mean sea level at every point. It can be specified by its elevation, at every point, relative to the reference ellipsoid. A plumb line is everywhere perpendicular to the geoid. The geoid is the zero for measuring elevations using 'bubble' instruments. Once the geoid is known, then g can be calculated for any point on or outside it.


Early attempts to determine the geoid were based on gravimetric surveys, in which the magnitude of g and the elevation were measured at a grid of points on Earth's surface. A complete determination would have required the grid to extend over the entire surface of Earth. However, that requirement was eased with the launch of artificial satellites in near-Earth orbits. The orbit of a satellite depends upon the exact strength and direction of g at every point of the orbit. When satellites have been tracked in enough different orbits, that information can be combined with gravimetric surveys to give a complete geoid, typically in the form of an expansion in spherical harmonics.


The deflection of the vertical at any point could be found from the slope of the geoid there (relative to the reference ellipsoid), but it can also be found directly from the expansion of the gravitational acceleration g in spherical harmonics. I have not found online any report of determination of the deflection of the vertical for the Philippines. Such a report is available for survey stations in Canada (see http://www.geod.nrcan.gc.ca/hm/pdf/evaluationofegm08_e.pdf ), where both the north-south and east-west deflections are as large as 23 arc-seconds.

A contour map of the gravitational anomaly, which is nearly equivalent to that for the geoid, was recently published [O. Andersen et al, Physics Today 62, 4, 88 (April 2009)]. It shows a texture near the Philippines comparable to that across Canada, so that I would expect the deflections of the vertical there to be comparable. Of course, the deflection must itself be known to the same precisi0n as the astronomical position to be adjusted, here 0.1 arc-second.


The final problem in comparing astronomical positions to GPS positions, is that the two systems do not share the same 'datum', or coordinate system. In particular, a GPS receiver does not read longitude zero, in the fundamental datum of GPS (WGS 84), when it is at the meridian telescope of the Greenwich Observatory. The position of that instrument historically defined zero longitude, for astronomical determinations.

Essentially, each system is compatible within itself, but it should not be expected to be compatible with the other system.


Even if all of the above problems could have been anticipated in 1944, so that the location of Golgotha was correctly known to within three meters, it still might not have been found there fifty years later. The notion of continental drift, or plate tectonics, had been proposed earlier, but the evidence to support it was developed after World War II. I don't know the actual speed of the Philippine platelet, but that distance and time represent a speed of 6 centimeters per year. That is exactly in the range of speeds reported for other plates, e.g., India colliding with Asia, to produce the 2008 earthquake in China.


All in all, I am forced to conclude that it was impossible, that any astronomical method in 1944 could have produced a position for Golgotha, which matched that given by GPS later.


A separate posting will consider how well Lieutenants Goto and Ninomiya might actually have done, in determining the location of Golgotha.

Tides in the Mediterranean

Jack Shaftoe saw a "high tide mark" on the beach at Algiers (page 4 of the Confusion). Months later, "the tide was quite low", when he visited Malta (page 209). When I was reading Julius Caesar's De Bello Gallico in the original Latin in 1944, I learned that there were no significant tides in the Mediterranean Sea. Caesar's unfamiliarity with the phenomenon of tides caused him problems with military operations, on the Atlantic coasts of Gaul and of Britain. [Undoubtedly, that lack of knowledge also contributed to the failure of his attack on Qwghlm (page 256 of Cryptonomicon).] I cannot recall now whether the absence of Mediterranean tides was mentioned by Caesar himself, or only in the classroom discussion. For sure, there is no Latin equivalent to the English word 'tide'. (See an online English-Latin dictionary, such as http://www.freedict.com/onldict/lat.html .)

As a matter of fact, there are noticeable vertical tides at the head of the Adriatic Sea (near Venice), and at the 'corner' of the Gulf of Gabes. Both places were nearly uninhabited at the time of Caesar. Vertical tides have been measured at Malta, but they are inches at most. The scuba diving establishments there advertise: "Throw away your tide tables." (See http://www.aquatours.com/gozo/malta_bugibba-diving.htm .) There are also significant horizontal tidal currents near Malta, and especially in the straits of Messina and of Sicily.

Unfortunately, Neal Stephenson built this 'invisible' tide into the story. It is only implicit at Algiers, in that the galley, on which Jack was a slave, had been beached to have its barnacles scraped. That is very easy to do on a tidal beach, but without tides, the slaves would have to pull it out of the water by hand. When finished, they would either drag it back into the water, or dig a channel to bring the water to the galley. None of this was mentioned by Stephenson. At Malta, he explicitly needed the piers to be higher than the galleys, in order to advance the story.

Surely, if the basin of the Mediterranean were different (in length, width, or depth, or in some combination), there could be significant tides almost anywhere in it. My knowledge of proper oceanography is so scanty, that I can't even start working on this problem.

Introduction

This blog will analyse various topics of science and technology, which Neal Stephenson incorporated into his four books of historical science fiction. That composite genre offers pitfalls to the unwary author, as well as opportunities to the readers. Typical science fiction is set in the future, so that authors can invent almost any new scientific "facts", and their technological applications, that they want. However, Stephenson chose to put part of the action of Cryptonomicon in World War II, and all of the action of his trilogy, The Baroque Cycle, in the period 1655 t0 1715. In both of those eras, actual technologies existed, and were recorded and preserved, along with the science that inspired or explained them.

Any author, who puts himself into this position, should avoid displaying mistakes in history or in science/technology, or in the combination. The combination errors are often anachronisms, which may be trivial if the scale is a few years, but may be more serious if the scale is centuries. Of course, the author can also score successes, where everything fits perfectly.

For the readers, the opportunities are new inspirations to learn or re-learn science and technology. One can do a free association while reading, asking mental questions such as: Does this fit with what I already know?"; or "Would it really work that way?"; or "Did it actually happen that way?" For me, it has meant that I have read each one of these books several times, and I have learned something new every time. If fact, for some of the "case studies" I have considered for this blog, I have changed my mind about what I had learned, after a subsequent rereading. On a sobering side, I now wonder how many students I had managed to baffle, while trying to teach this stuff. But most importantly, I have enjoyed every one of Stephenson's books, every time I have read it.

As my UserName implies, I received a B.S. degree in Engineering Physics in 1951. In that era, introductory engineering courses typically included lots of historical material. I had also paid attention to things which happened during World War II. All of those memories were available as I did my own free associations. Unfortunately, I have disposed of my personal professional library, so that most of the analysis in these case studies is done "off the top of my head". Please feel free to catch me up in all the mistakes I may make here.

The subject matter in this blog will be at the introductory undergraduate level in physics, mathematics, astronomy, earth science, and branches of engineering. Specific topics will include optics, oscillatory systems, planetary motions, tides, surveying, deflections of beams, machinery, weapons, and units of measure.

I will cite pages in Stephenson's books as they become involved. To make it easy for me, I will refer to the editions which I happen to have. My copy of Cryptonomicon is in the first printing of Avon Books (HarperCollins) paperback. My copies of Quicksilver, the Confusion, and The System of the World, are all in first printings of First Editions of William Morrow (HarperCollins) hardcover.