A fundamental feature of the scientific revolution of 1700-1800 was the concept that the forces on earth were similar to the forces that drive the universe. This led to the drive for laws that explained these relationships. As science has progressed it has become increasingly difficult to find universal relationships between physical forces and the forces that rule the celestial spheres. This is brought to a head in the inability for quantum mechanics to include gravity in its theoretical embrace. The most fundamental celestial element is the very element that cannot be explained by ever finer descriptions of physical forces. This is a particularly revealing problem.

Prior to the widespread use of reductionist mathematical techniques it was implicitly understood that it was possible to identify locations on earth that had particular resonances to celestial positions. The placement of observatories at particular places on the earth was a mysterious feature of many ancient cultures.

1 Stone Henge

Why would the ancient peoples spend so much time and effort to create observatories to predict the rising and setting of planets and the motions of the fixed stars? To some researchers not only were there observatories to look out to the heavens but the placement of temples, shrines, and holy places was determined through even more mysterious techniques for finding resonance between celestial coordinates and terrestrial positions. These activities known as geomancy were mystically inspired attempts to link the earth to the movements of the planets and stars. Through time there have been many versions of these techniques but none of them could be used as a basis for scientific inquiry except for the increased observational skill of the astronomers.

However, to measure the exact position of a star or planet is quite within the realm of computation. To project this position onto a spinning earth and be able to say with confidence that Jupiter will be over the central Pacific for most of 2006 is counter to rational thought. And yet this is just what is needed if the field properties of the subtle interplay between the motions in arc of Jupiter and the unfolding of an El Nino is to be tracked in a scientific way. To do that requires two things. The first is that some rational, mathematical and reproduceable system of projection be used so that experiments can be set up. The second is some sort of empirical, phenomenological, data rich information source is readily available to track and record the results of the mathematical experiments.

2 Edward Lorenz

The computer offers much of this however the climate problem is unique. Edward Lorenz the father of chaos theory originally found his insights by trying to model weather systems. Lorenz eventually concluded that in certain ways climate patterns defy mathematical modeling even with enhanced computer power. Lorenz worked on slower analog computers and found that the slower more organic processing of these early machines could come closer to modeling the intangible interfaces that climate study requires. Even with the slower computational rhythms Lorenz eventually had to concede that even the tiniest error in the formation of the modeling algorithm got magnified exponetntially through the process of iterating it in the computer many hundreds of times. At some point chaos ensued as the system sought a higher level of integration. The chaos made it very difficult to model these systems in flux.

3 attractor-the Lorenz butterfly

The third image is the famous Lorenz butterfly. It depicts the polar states all processes go through in order to integrate the energies in the whole system. One side of the butterfly is the positive levels of energy where the system is functioning and active then the middle point between the two wings is the chaos point where the system loses integrity in order to begin unfolding on the other side of the butterfly in the negative side of the energy economy of the system. This model is used to visualize everything from storms and hurricane development to population explosions and collapses.

4 Blaise Pascal

There is however a division of mathematics that can offer modeling potentials for tracking the almost organic or morphological transformations http://www.christianhubert.com/hypertext/analogy___homology.html#13 of weather systems and climate patterns. That discipline is known as projective geometry. This system of geometry was invented by Blaise Pascal http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Pascal.html who lived between 1623 and 1662. This work has led to some of the most recent advances in present day geometry but at the time of its discovery it was an outgrowth of the perspective studies of the artists of the Renaissance coupled to the new investigations into optical systems.

To make an enormous subject painfully simple, projective systems need a projector. The simplest projector is a point. The point is not just located in space but is active in interacting with the fields of activity around it. It helps a lot when thinking projectively to use images rather than numbers so the following image is of an optical system interacting with a human eye. Projection was originally developed as a geometric discipline with the rise of optics..

5 lens system

In this optical system there are several projectors. The vanishing point at the horizon is one. Between that projector and the screen of the world there is an expanding perspective of light rays that are the field of the projector of the vanishing point. This thinking comes from the work of the artist that first discovered the optical laws of perspective in the Renaissance. These researches set the stage for the later developments of the higher levels of projective space that was the seed for Riemann and Einstein. The world or in this instance the tree has countless points of light on it that reflect in all directions. In the center of the lens of the eye there is another point where light rays are gathered. Here a reversal happens in the direction that the light rays are moving. The top of the tree is projected down and the bottom of the tree is projected up upon the new screen, the retina. The now upside down image is gathered once again and moved back towards the brain by the action of the nerves. There another point like projector, the ganglia of nerves in the area of the hypothalamus / pituitary gland, receives the impulses and once again up becomes down and vice versa as the visual nerves split and merge in new combinations as the nerve impulses flow back towards the visual center in the back of the brain.

The condensation of the image into a point and the polar reversal of the image on the expanded field or screen is the most fundamental operation in projection. In the image of the Lorenz butterfly, the two wings are the opposite fields or phases of activity of the system being studied and the center in the point of chaos where they reverse is the attractor or projector depending upon which side you are on. This is true for sand flowing in an hourglass or the activity around a black hole in astrophysics. The power of projective geometry to model such disparate systems is a sign of its effectiveness for modeling climate. For an in depth and absolutely brilliant and very approachable website on projective geometry please go to the following link for the work of Nick Thomas. http://www.nct.anth.org.uk/

The true challenge in climate study is to work with a modeling technique that least intrudes into the chaotic realm of the attractor or projector. There are two possible approaches to forming such a model. The first is to find an algorithm that when iterated in a computer will be able to replicate the observed phenomenon. This is the approach Lorenz used when he discovered the phase butterfly with the attractor in the center. His conclusion was that the slightest bit of error in the formation of the algorithm leads to great distortion when the algorithm is iterated. That is essentially the difficulty with a computational approach to climate study. Lorenz came to the conclusion that modeling in this was next to impossible because of the sheer amplitude of variables that could modify the algorithm.

The other approach to climate research is to let the phenomena themselves form the iterative patterns and instead seek to find a filter that can allow the significant aspects of the system to emerge as the system goes through the complete set of parameters on both sides of the phase butterfly. The problem here is that the chaos of the manifest phenomenon (climate) is too complex for computational mathematics to model it. One possible solution is to use as a modeling algorithm mathematical tables (log period tables) that already are predictable and then reference the natural phenomenon to the periods and fluctuations of the existing table and see if there is a statistical relationship. The most elegant log period tables available to humans are the periods and harmonic phase relationships found in an ephemeris or table of planetary motions. It is the work done by Copernicus, Galileo, Kepler and Newton to understand these most fundamental time phenomena that led to the scientific revolution that we celebrate today. Today the drive for technological advancement has replaced wonder at the incredible richness and precision of the motion in arc events of the celestial spheres that was the very focus of the work of the founders of current science. Perhaps we have thrown the baby out with the bathwater. Or better said, we have kept the bathwater but have forgotten that there ever was a baby.

The ClimaTrends research protocol is designed to form a phenomenology that can allow the variables in the system to form the algorithms that drive the model.

To study climate patterns in a context of using projective geometric concepts requires finding a point that can serve as a projector that could somehow provide a coincident link between the rhythms of planetary motion in arc events and the unfolding of particular weather or climate patterns. The two most fundamental planets to the unfolding of weather events on earth are the sun and the moon. The single most important point in the relationship between the sun and the moon is an eclipse point. Using an eclipse point for the projector it is possible to see that often on the day of either a solar or lunar eclipse significant geometric patterns arise in the placement of lows and highs in the northern hemisphere. These relationships are explained in detail in the article on projective fields http://docweather.com/4/show/45/ on the Doc Weather site.

This article is not intended to be an explanation of geodetic projection. The links provided below are to the Doc Weather website where more aspects of this geometrical technique are gone into in detail.

For an explanation of the basic chart http://docweather.com/2/show/161/

For help in reading the charts http://docweather.com/2/show/65/

For an article on the details of the jet curves http://docweather.com/4/show/20/ used to predict disturbance zones