A stock operator's thoughts and ideas about market principles
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Jun/23/2007
Lagrangian Points
The Lagrangian points are the five positions where a small object, affected only by gravity, can be stationed relative to two larger objects. The history behind the discovery, the lack of stability of these points, and the modern use of them, give insights into the development of the fields of finance and economics too. An intuitive explanation of the theory can be obtained at Wikipedia, and a more advanced mathematical description is provided by the Montana state University.
The History
These points seem quite intuitive, at least after having read about them. Yet, Isaac Newton himself did not see them. Where everyone else saw chaos, Lagrange used used a few lines of mathematics and re-formulated classical mechanics. He even got a new field named after himself.
I'm pretty confident new theories explaining pricing will greatly structure the chaos of present economics. Every aspiring scientist out there should learn from the example above.
Unstable Points
The Lagranigian points are very unstable out of several reasons. Paths are elliptic, not circular, which make the points more like areas than just points. Gravity from other objects, like other planets in the solar system, will disturb any object in one of the points. And L1-L3 are only forced back toward equilibrium if the object drifts away in the two dimensions on a plane perpendicular to the two bodies.
Theory that is, well just theory, and not observed in reality is something economists are way too familiar with too. Still, the improved insight a theory offers will often come in handy at some way or another.
Space Exploration
Although no parallel Earth has been found on L3, asteroids have been found on Sun-Jupiter L4 and L5 and all are given names associated with the Trojan War. In space missions are for instance Sun-Earth L1 and L2 very useful. Orbits around these points are used by a number of spacecrafts.
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