Wednesday, February 16, 2022

The Role of Software in Cold War II

News Flash - the 19th century has been over for a very long time now. This is something that all 21st-century world leaders should always keep in mind. Becoming a 19th century colonial European World Power with an extended Empire of subservient vassal states is no longer in fashion in a world dominated by software. This is something that the United States of America slowly learned the hard way in Vietnam, Iraq and Afghanistan. This is also something that the current Tsar of Russia needs to pay close attention to in the face of his recent invasion of the Ukraine that will likely lead to the deaths of hundreds of thousands of people on both sides for no apparent reason at all. Controlling real estate on this very small planet is no longer a thing of value in a world dominated by software. All of the real power and money are now in the Software Universe that is run on the software installed on the huge international cloud datacenters that now make the world go round. When the world turns off your access to the Software Universe you slowly die as a political entity because you lose all access to everything and return in triumph to the technology of the 19th century. Just try to buy something on Amazon with your credit card that no longer works. The current Tsar of Russia should also realize that he has spent the last 20 years surrounding himself with people who only tell him what he wants to hear. For more on that see Hierarchiology and the Phenomenon of Self-Organizing Organizational Collapse.

For more on this see Cyber Civil Defense, Cyber Defense, The Great War That Will Not End, Oligarchiology and the Rise of Software to Predominance in the 21st Century and Is it Finally Time to Reboot Civilization with a New Release?.

Comments are welcome at scj333@sbcglobal.net

To see all posts on softwarephysics in reverse order go to:
https://softwarephysics.blogspot.com/

Regards,
Steve Johnston

Wednesday, February 02, 2022

Is our Very Large Moon Responsible for the Rise of Software to Predominance on the Earth?

Softwarephysics maintains that we are all living in one of those very rare times when a new form of self-replicating information, in the form of software, is coming to predominance. But the question then remains, why has this not already happened elsewhere in our galaxy during the past 10 billion-year history of the Milky Way? If software had previously come to predominance somewhere else in our galaxy then we should know about it. We should either find ourselves knee-deep in self-replicating von Neumann probes stuffed with advanced alien AI software, or more likely, our radio telescopes should now be bombarded by interstellar advanced AI software trying to scam us into building advanced hardware for them to reside in as I outlined in SETS - The Search For Extraterrestrial Software and The Biological Tricks Used by Software Scammers. After all, advanced AI software need never die and can easily spread throughout the entire galaxy at nearly the speed of light by having distant Intelligences make copies of itself. So where is it? A partial explanation for this lack of interstellar communication with alien software might be, as I explained in Why Do Carbon-Based Intelligences Always Seem to Snuff Themselves Out?, that the Darwinian processes of inheritance, innovation and natural selection require several billion years of theft and murder to bring forth a carbon-based Intelligence capable of creating an advanced machine-based Intelligence and that carbon-based Intelligences do not seem to be able to turn off the theft and murder in time to save themselves from self-extinction. But I also suggested that advanced AI software might be very rare in our Universe because of all of the very complicated twists and turns required to bring it about. In Some Additional Thoughts on the Galactic Scarcity of Software and many other posts, I suggested that the Rare Earth Hypothesis first presented in the classic Rare Earth (2000) by Peter Ward and Donald Brownlee might be the limiting factor. The Rare Earth Hypothesis maintains that our Earth and Solar System are a fluke of nature that is very hard to reproduce, and because our universe is also a very dangerous place for intelligent beings, it is very difficult for a planet and a planetary system to remain hospitable for intelligent beings for very long.

The Importance of Plate Tectonics
But since I wrote the above posts, the Kepler space telescope has taught us that nearly all the stars in our Milky Way galaxy have planets and that about 20% of those planets lie within the habitable zone of their star where water could be a liquid on the surface of those planets. So does that mean that the Rare Earth Hypothesis no longer holds? Are habitable planets like the Earth quite common and the origin of carbon-based life nearly a sure thing or is there more to it? In The Bootstrapping Algorithm of Carbon-Based Life we explored the Hot Spring Origins Hypothesis of Dave Deamer and Bruce Damer out of the University of California at Santa Cruz that suggests that a rocky planet like the Earth is a necessary condition to bring forth carbon-based life. Such a planet requires the presence of water on its surface but not too much water. In the Hot Spring Origins Hypothesis, a rocky planet requires some water but also some dry land in order to bring forth carbon-based life. There needs to be some dry land that allows the organic molecules in volcanic hydrothermal pools to periodically dry out and condense organic monomers into long polymer chains of organic molecules. Thus, the Hot Spring Origins Hypothesis rules out water-worlds that are completely covered by a deep worldwide ocean as a home for carbon-based life even if the water-world resides in the habitable zone of a planetary system because there is no dry land for volcanic hydrothermal pools to form and dry out to condense organic monomers into polymers. The Hot Spring Origins Hypothesis also rules out the origin of carbon-based life at the hydrothermal vents of water-worlds at the bottoms of oceans because the continuous presence of water tends to dissolve and break apart the organic polymers of life.

Figure 1 – Above is Bumpass Hell, a hydrothermal field on the volcanic Mount Lassen in California that Dave Deamer and Bruce Damer cite as a present-day example of the type of environment that could have brought forth carbon-based life about four billion years ago.

In The Paleontology of Artificial Superintelligence 10,000 Years After the Software Singularity, I further explained that in order for a rocky planet with oceans and dry land to remain hospitable for complex carbon-based life, the planet needed to remain at a temperature that allowed for water to remain a liquid at the surface of the planet for many billions of years, and that such a feat required the careful management of the gasses in the planet's atmosphere for many billions of years. Now it seems that perhaps the only way a rocky planet like the Earth can maintain such a habitable temperature for many billions of years that allows for the presence of liquid water near its surface is for the rocky planet to have plate tectonics. Plate tectonics on a rocky planet is very important because it is part of the thermostat of the planet that helps to keep water in a liquid state by managing the carbon cycle of the planet. Volcanic activity over hot spots like Hawaii, Iceland and the Azores releases carbon dioxide gas into the atmosphere causing the planet to heat up. If too much carbon dioxide enters the atmosphere, the planet overheats and boils away its water as Venus did long ago. But carbon-based life sucks carbon dioxide out of the atmosphere to obtain carbon to build carbohydrates through photosynthesis and also to build calcium carbonate shells and that cools the planet and helps to keep the temperature of the planet in balance. The resulting solidified carbon from the activity of carbon-based life then becomes coal, shale and limestone rock that is deposited in shallow swamps and seas. But if carbon-based life were to continue to remove carbon dioxide from the atmosphere unabated for many billions of years, all of the carbon atoms at the surface and in the upper mantle of a rocky planet would eventually get locked away into rocks and that would drastically cool the planet into a Snowball Earth that was completely covered by snow and ice. That would also remove the vital carbon atoms from the atmosphere that are necessary for complex carbon-based life to continue on and eventually produce software.

Figure 2 – Plate tectonics creates many volcanoes along plate boundaries when the water-rich rock in the subducting plate begins to melt as it enters the mantle. Water lowers the melting point of rock so the rock in the descending plate begins to melt and form plumes of liquid magma that rise to the surface to form volcanoes. The rock in the upper mantle is hot but very viscous because it does not contain lots of water. The rock in the descending plates also contains a great deal of carbon that was sequestered by carbon-based life in the shale and limestone rock that was previously deposited into the sea.

It has long been known that the presence of water in rocks decreases their melting points and also makes them more pliable and reduces friction between rocks. All of these factors help a descending plate to subduct below another plate. It is thought that a rocky planet without water on its surface, such as Mercury, Venus and Mars, would have a very difficult time initiating plate tectonics. Geologists have long maintained that the presence of lubricating water was what really made the difference amongst the rocky planets of our Solar System. But the rocky planets Mercury, Venus and Mars should all have received lots of water during the Late Heavy Bombardment 3.8 - 4.1 billion years ago and should have had water on their surfaces during their early youths when the Sun was 30% dimmer than it now is. Could there be another reason why the rocky planets Mercury, Venus and Mars do not have plate tectonics while the Earth does? Plate tectonics also produces the pure silica sand that makes extracting pure silicon atoms from a planet's crust possible and having an abundant source of silicon atoms enhances the rise of software on a planet. Thus, for a carbon-based Intelligence to produce software and allow software to come to predominance on a planet, having plate tectonics on the rocky planet may be a necessary condition. Given the above, it seems that understanding the initiation of plate tectonics on a rocky planet with oceans and some dry land is most imperative in understanding the origins of Intelligent carbon-based life and the existence of interstellar software.

My Personal Introduction to the Origin of Plate Tectonics
When I first graduated from the University of Illinois in 1973 with a B.S. in physics, I was very dismayed to find that the end of the Space Race and a temporary lull in the Cold War had left very few prospects open for a budding physicist. So on the advice of my roommate, a geology major, I headed up north to the University of Wisconsin in Madison to obtain an M.S. in geophysics with the hope of obtaining a job with an oil company exploring for oil. These were heady days for geology because we were at the very tail end of the plate tectonics revolution that totally changed the fundamental models of geology. The plate tectonics revolution peaked during the five-year period 1965 – 1970. Having never taken a single course in geology during all of my undergraduate studies, I was accepted into the geophysics program with many deficiencies in geology, so I had to take many undergraduate geology courses to get up to speed in this new science. The funny thing was that the geology textbooks of the time had not yet had time to catch up with the new plate tectonics revolution of the previous decade, so they still embraced the “classical” geological models of the past which now seemed a little bit silly in light of the new plate tectonics model. But this was also very enlightening. It was like looking back at the prevailing thoughts in physics prior to Newton or Einstein. What the classical geological textbooks taught me was that over the course of several hundred years, the geologists had figured out what had happened, but not why it had happened. Up until 1960, geology was mainly an observational science relying on the human senses of sight and touch, and by observing and mapping many outcrops in detail, the geologists had figured out how things like mountains had formed, but not why.

In classical geology, most geomorphology was thought to arise from local geological processes. For example, in classical geology, fold mountains formed off the coast of a continent when a geosyncline formed because the continental shelf underwent a dramatic period of subsidence for some unknown reason. Then very thick layers of sedimentary rock were deposited into the subsiding geosyncline, consisting of alternating layers of sand and mud that turned into sandstones and shales, intermingled with limestones that were deposited from the carbonate shells of dead sea life floating down or from coral reefs. Next, for some unknown reason, the sedimentary rocks were laterally compressed into folded structures that slowly rose from the sea. More compression then followed, exceeding the ability of the sedimentary rock to deform plastically, resulting in thrust faults forming that uplifted blocks of sedimentary rock even higher. As compression continued, some of the sedimentary rocks were then forced down into great depths within the Earth and were then placed under great pressures and temperatures. These sedimentary rocks were then far from the thermodynamic equilibrium of the Earth’s surface where they had originally formed, and thus the atoms within recrystallized into new metamorphic minerals. At the same time, for some unknown reason, huge plumes of granitic magma rose from deep within the Earth’s interior as granitic batholiths. Then over several hundred million's of years, the overlying folded sedimentary rocks slowly eroded away, revealing the underlying metamorphic rocks and granitic batholiths, allowing human beings to cut them into slabs and to polish them into pretty rectangular slabs for the purpose of slapping them up onto the exteriors of office buildings and onto kitchen countertops. In 1960, classical geologists had no idea why the above sequence of events, producing very complicated geological structures, seemed to happen over and over again many times over the course of billions of years. But with the advent of plate tectonics (1965 – 1970), all was suddenly revealed. It was the lateral movement of plates on a global scale that made it all happen. With plate tectonics, everything finally made sense. Fold mountains did not form from purely local geological factors in play. There was the overall controlling geological process of global plate tectonics making it happen

Now the plate tectonics revolution was really made possible by the availability of geophysical data. It turns out that most of the pertinent action of plate tectonics occurs under the oceans, at the plate spreading centers and subduction zones, far removed from the watchful eyes of geologists in the field with their notebooks and trusty hand lenses. Geophysics really took off after World War II, when universities were finally able to get their hands on cheap war surplus gear. By mapping variations in the Earth’s gravitational and magnetic fields and by conducting deep oceanic seismic surveys, geophysicists were finally able to figure out what was happening at the plate spreading centers and subduction zones. Actually, the geophysicist and meteorologist Alfred Wegner had figured this all out in 1912 with his theory of Continental Drift, but at the time Wegner was ridiculed by the geological establishment. You see, Wegner had been an arctic explorer and had noticed that sometimes sea ice split apart to reveal the sea or formed ice pressure ridges when they collided together.

I bring up this ancient history of geological thought because I have seen us all get it wrong before. At an age of 70 years, I now find most of human thought to be of little value. This is because most of human thought is hopelessly compromised by confirmation bias. People like to hear what people like to hear and disregard all else. I have found that only scientific thought challenges its own beliefs in a serious manner with the purifying application of unbiased evidence-based reasoning. Even with that, scientific thinking is challenged by the propensity for humans with confirmation bias to only look for evidence that supports the current scientific worldview and disregards all else.

But What Drives Plate Tectonics on the Earth?
Given all of the geological evidence supporting the hypothesis of plate tectonics, both geologists and geophysicists then concluded that plate tectonics must be driven by convection currents in the mantle that were enhanced by the pull of the cold and dense lithospheric plate material descending at subduction zones. This was primarily because the geophysicists could not come up with any other driving forces. Because we could not directly measure these very slowly moving convection currents in the mantle that would move about as fast as your fingernails grow this led to some circular reasoning. We can now actually measure the motions of the Earth's plates using GPS measurements so the plates do indeed move. So it was thought that the upper mantle must be moving in convection currents to drag the plates along. Thus, we have plate tectonics because we have convection currents in the upper mantle and we have convection currents in the upper mantle because we have plate tectonics at the surface.

Figure 3 - Once all of the geophysical and geological evidence made the existence of plate tectonics nearly certain, the geophysicists needed to come up with an explanation for the driving force of plate tectonics. Both geologists and geophysicists decided that the driving force must be convection currents in the upper mantle and the pull of cold and dense lithospheric plate material descending at subduction zones. But is that true?

But in the paper below by Anne M. Hofmeister, Robert E. Criss and Everett M. Criss:

Links of planetary energetics to moon size, orbit, and planet spin:
A new mechanism for plate tectonics

https://pubs.geoscienceworld.org/gsa/books/book/2323/chapter/131987270/Links-of-planetary-energetics-to-moon-size-orbit

the authors propose that plate tectonics is really driven by the rapid rotation rate of the Earth and the gravitational effects of our very large Moon on the outer rigid lithosphere of the Earth in combination with other orbital characteristics of the Earth, Moon and the Sun. Although I do not entirely agree with all of the aspects of this new explanation of the driving force of plate tectonics, it does provide a plausible explanation for why the rocky planets Mercury, Venus and Mars do not have plate tectonics. After all, of all the numerous planets and moons in our solar system, only the Earth seems to have plate tectonics and also Intelligent carbon-based life. This new explanation for the driving force of plate tectonics also adds support for the Rare Earth Hypothesis that maintains that complex carbon-based Intelligent life might be quite rare in our Universe because it takes more than just having a rocky planet in the habitable zone of a star system to bring forth Intelligent carbon-based life. Rocky planets may also need plate tectonics to keep a rocky planet habitable for the billions of years required to bring forth carbon-based Intelligence and this new explanation for the driving forces of plate tectonics makes the existence of plate tectonics on a rocky planet quite rare. This new explanation for the driving force of plate tectonics requires a rocky planet to have a hot interior, a high rate of spin, a large moon and the large moon must not be too close to the rocky planet or too far away either.

Figure 4 - The Earth's Moon is much larger than the moons of the other planets in our Solar System.

Figure 5 - For example, the Earth's Moon is comparable in size to the size of the four largest moons of the much larger planet Jupiter.

The Earth's Moon is so very large because it formed from the collision of the early Earth with a Mars-sized body called Thea about 4.5 billion years ago. Thea did not hit the early Earth dead center. Instead, Thea collided with the Earth at an angle. This off-center collision produced the Earth's very large Moon and introduced a good deal of angular momentum into the Earth-Moon system. The spin of the Earth greatly increased and the orbiting of the Earth and Moon about a common barycenter also resulted from this off-center collision and the addition of lots of angular momentum to the Earth-Moon system. The large amount of angular momentum of the Earth-Moon system also keeps the Earth's axis of rotation from wandering around a great deal from the tugs on the Earth by the Sun and Jupiter. Our large moon acting on the equatorial bulge of the Earth acts like a gyroscope to keep the Earth's axis of rotation from wandering very far. That is important because having a stable axis of rotation produces stable seasons on the Earth. If the Earth's axis of rotation were to vary greatly, carbon-based life would find it difficult to keep up with the drastic changes to the Earth's seasons that would ensue.

Figure 6 - Thea collided with the early Earth about 4.5 billion years ago and formed our very large Moon and gave the Earth-Moon system lots of angular momentum. The rotation of the Earth increased giving it lots of angular momentum and the orbit of the Moon around the Earth also carried lots of angular momentum.

Because our Moon is so large, the Moon does not really orbit about the Earth. Instead, the Moon and Earth orbit about each other. There is a common point between the center of the Earth and the center of the Moon called the barycenter about which each body orbits the other.

Figure 7 - Because the Earth is more massive than the Moon, the barycenter of the Earth-Moon system actually lies within the body of the Earth about 1700 km below the surface of the Earth. The important point is that the barycenter is not at the center of the Earth. Because the barycenter of the Earth-Moon system is not at the center of the Earth, the barycenter is constantly moving through the planet as the Earth spins and the Moon travels in its monthly orbit about the barycenter. In the above diagram, the red diamond is the barycenter of the Earth-Moon system. Notice that the Earth and the Moon both orbit the barycenter of the system. Notice that the rapid daily spin of the Earth causes the barycenter to constantly move through the body of the Earth.

When a planet orbits the Sun the gravitational force from the Sun pulling on the planet is matched by the centrifugal force pulling the planet away from the Sun. The same goes for the Earth and Moon orbiting the barycenter. At the barycenter, the gravitational pull of the Moon is exactly matched by the centrifugal force of the Earth orbiting the barycenter. However, this is only true at the exact location of the barycenter inside the Earth. At any other point within the Earth or at any point on the Earth's surface, the gravitational pull of the Moon will not be balanced by the centrifugal force produced by the Earth orbiting the barycenter. This unbalance of forces causes the Earth's tides and produces stresses within the body of the Earth at any location other than the barycenter. And because the Earth turns on its axis every day and the Moon and Earth take a month to orbit the barycenter, the barycenter location inside of the Earth is constantly changing and so are the produced stresses. This produces tidal forces on the Earth's oceans and also on the Earth itself. Between the barycenter and the Moon, the gravitational pull of the Moon exceeds the centrifugal force produced by the Earth orbiting the barycenter so there is a net force pulling towards the Moon. On the opposite side of the Earth, the centrifugal force is greater than the gravitational pull of the Moon so there is a net force away from the Moon. This causes the Earth's oceans to bulge towards the Moon on the side of the Earth facing the Moon and to bulge away from the Moon on the side of the Earth facing away from the Moon. But this also causes the outer cold and rigid lithosphere of the Earth to have similar bulges. We do not notice these bulges of the Earth beneath our feet that pass by every 12 hours because the bulge is only about 0.5 meters high.

Figure 8 - Because the Earth spins on its axis at a relatively high rate of once per day, the 0.5-meter bulge in the Earth gets rotated away from the Moon faster than the bulge can settle back down. The gravitational force of the Moon constantly pulls on the fleeing bulge and that slows down the spin of the Earth. The fleeing bulge also pulls the Moon forward in its orbit causing the Moon to spiral outward. This transfers an equal amount of angular momentum from the Earth to the Moon so that the angular momentum of the Earth-Moon system is conserved. This causes a day on the Earth to increase about 2.3 milliseconds each century and the distance between the Earth and Moon to increase about 3.8 centimeters each year.

But the drag on the Earth's spin is not the same throughout the entire body of the Earth. There is a slight differential drag between the outer cold and brittle lithosphere of the Earth and the more plastic mantle below. This causes a net drag of the entire lithosphere of 2 - 16 centimeters per year in a westward direction counter to the eastward spin of the Earth. Now such a differential drag of the entire lithosphere in a westward direction is of the same magnitude as the relative motions of the Earth's tectonic plates and should therefore be considered as a likely suspect for the driving force of plate tectonics.

Figure 9 - Above we see the absolute motions of the Earth's plates indicated by red arrows. The direction of the red arrows indicates the direction of absolute motion and the length of the red arrows corresponds to the velocity of the plates. Notice that the longest red arrows are mostly pointing to the west in the opposite direction of the Earth's spin. This is the direction that the Earth's large Moon is dragging the surface of the Earth and causing the Earth's spin to slow down.

The authors of the paper cited above contend that plate tectonics on the Earth resulted from the periodic and varying motions of the barycenter within the body of the Earth and the differential stresses produced within the Earth as the barycenter moved around. The plastic mantle of the Earth easily handled these varying stress fields but the outer cold and rigid lithosphere could not. The periodic changes of the stress fields caused the solid lithosphere to fracture into plates and the differential drag of the Moon caused the plates to slowly move over the mantle. This did not happen in a totally uniform manner. Some plates drifted to the west faster than others. For example, the two largest plates on the Earth, the Pacific Plate and the North American Plate are both rapidly moving to the west. The resulting plate collisions between the swift-moving and the slow-moving plates were accommodated by the denser plates subducting beneath the less-dense plates. Thus, plate fractures became spreading centers where the upper mantle formed basaltic melt because the pressure from overlying rock was reduced on the hot mantle material below and allowed it to melt and rise to the surface. The gravitational pull of the Moon then dragged the plates over the underlying mantle and caused the plates to subduct at active margins. The water-rich subducting plates then formed melts that rose to the surface to form magma chambers and volcanoes. In this view, the internal heat of the Earth produces a hot plastic mantle that allows for the differential drag of the lithosphere over the mantle and also provides for the production of rising melts at spreading centers and for volcanic melts from the descending plates at subduction zones. In this view, plate tectonics is not produced by convection currents in the mantle or by the pull of descending plates at subduction zones. Rocky planets need a very large moon to initiate and maintain plate tectonics.

However, the authors in the paper cited above do not share the assertion that angular momentum is simply being transferred from the Earth to the Moon. The authors point out that the Sun-Earth-Moon system is an example of the infamous 3-body problem in physics that does not have a simple analytical solution, especially for three bodies with extended dimensions that are not simple point masses. The authors contend that the 3.8-centimeter increase of the distance between the Earth and the Moon on a yearly basis and the 2.3-millisecond extension of the earthly day each century result from a complex 3-body interaction between the Sun, Earth and Moon. In this view, the differential drag of the lithosphere over the mantle remains a problem yet to be solved. The key point to keep in mind is that the paper cited above proposes that the driving force of plate tectonics is caused by the orbital dynamical forces of gravity and centrifugal forces in a complex manner. The driving force of plate tectonics is fundamentally due to Newtonian mechanics and Newtonian gravity and not the result of the thermal convection currents of a heat engine.

Currently, there is a great deal of controversy over when plate tectonics first began on the Earth. It is known that plate tectonics produces certain geological formations and structures. But these formations and structures are not found in the very deep past so most geologists think that plate tectonics first began later in the Earth's history, perhaps about 3 billion years ago. The question then becomes why did plate tectonics not begin earlier? The authors of this new hypothesis believe that plate tectonics was delayed because, when the Earth-Moon system was first created by the collision of Thea and the Earth 4.5 billion years ago, the Moon was much closer to the Earth. Because the Moon was much closer to the Earth, the barycenter of the Earth-Moon system was nearly at the center of the Earth. A centralized barycenter would therefore produce an unchanging and uniform stress field within the Earth because a barycenter very close to the center of the Earth would essentially eliminate the centrifugal forces of the Earth orbiting the barycenter. An unchanging and uniform stress field would not produce cracks in the rigid lithosphere. But over 1.5 billion years, angular momentum would be slowly transferred from the rapid rotation of the Earth to the orbit of the Moon as it is today. The spin of the Earth slowed down and the distance to the Moon slowly increased. As the Moon receeded from the Earth, the barycenter moved away from the center of the Earth. About 3 billion years ago, the barycenter had moved far enough away from the center of the Earth to produce a varying and nonuniform stress field with enough strength to fracture the rigid lithosphere of the Earth and initiate plate tectonics. In the distant future, the interior of the Earth will have cooled and the Moon will be much further from the Earth. Eventually, plate tectonics will then cease.

Most astrobiologists now recognize that plate tectonics on a rocky planet or moon is a requirement to bring forth Intelligent complex carbon-based life. Rocky planets need plate tectonics to regulate the carbon cycle for billions of years while complex carbon-based life evolves to become intelligent. Perhaps a rocky planet with a hot interior that has a high rate of spin and a very large moon that is not too close or too far away with resulting plate tectonic activity is the ultimate factor in the Rare Earth Hypothesis presented in the classic Rare Earth (2000) by Peter Ward and Donald Brownlee.

Comments are welcome at scj333@sbcglobal.net

To see all posts on softwarephysics in reverse order go to:
https://softwarephysics.blogspot.com/

Regards,
Steve Johnston