Friday, February 26, 2016

EDDINGTON CONSTANTS

The natural constants are just about as mysterious as the constants of math. To my knowledge there are no infinite series representations of the natural constants. Eddington identified several dimensionless constants formed out of combinations of the natural constants. I wonder if their is some limiting expression or series expression that gives any of these dimensionless numbers. I will look in to that some time. Eddington was active at the time of Ramanujan........they may have met each other in England or at the Royal Society. I wonder if Eddington asked Ramanujan to try to come up with some formulas for the dimensionless constants. Ramanujan may be the one and only human being who could do that. Hardy did not take care of Ramanujan very well in England, or some Aryan poisoned Ramanujan while he was glorified in England. Ramanujan was in England for 3 or 4 years then mysteriously boards a boat back to India and dies in his wife's arms (Janaki) near Madras at the age of 32 from some intestinal ailment. I think the people in England including Hardy should have had an investigation in to the untimely death of Ramanujan. 

Saturday, February 20, 2016

TRANSCENDENCE

There are various approximations for the constants of mathematics. There are the rational approximations, like 22/7 for pi.........or 355/113 for pi, these come to within 3 or more 9's of the absolute truth. There are others.........60/7 for (e)x(pi) and 96/7 for (phi)x(e)x(pi)............then there are the Ramanujan formulas..............these formulas are "exact" out to any number of decimal places for the constants of mathematics. Transcendental numbers should be defined as those numbers that can be represented as an infinitely non-repeating continued fraction...............that you can generate a transcendental number out to any number of decimal places from a closed form expression in a series expansion is a miracle. Ramanujan's formulas are used by the big number crunchers to calculate the mathematical constants like pi to arbitrary accuracy.......billion of digits of pi for example. My point is that transcendence is expressible in closed form by human beings, including possibly the transcendence of the languages and human forms in to some eternal truth. This is what faith is all about among human beings, that transcendence is accessible from and on the stage of the everpresent played out on the Earth.