much ado about e

[AntonioLao]

The development of logarithms in 1594 by Napier and independently by Bürgi about 1600 marked the beginning for discovering the natural base of logarithms, the special irrational transcendental constant e, numerically equals 2.71828 18284 59045 23536 0287 … by Euler in 1728, in an unpublished manuscript (Opera Posthuma, 11, 800-804).

It was well known by many mathematicians which include Newton, Leibniz, and Euler that the theory of convergent infinite series could be of service for working with differential and integral calculus and for finding special constants and quantities, such as p, e, as well as logarithmic and trigonometric functions. However, the ultimate exponential power of e lies within its differentiable manifolds, both real and complex domains.

Since then this number appeared practically everywhere: from the growth of financial bank accounts to the radioactive decays of matter, from calculus to probability theory, from Maxwell’s electromagnetism to the wave equation of quantum mechanics, and now as the complex phase factors of quantum field theory.

More recently, 1984, Cahn, at the University of California in Berkeley, wrote (http://www-physics.lbl.gov/~rncahn/book.html) semi-simple Lie algebras and their representations by re-introducing finite rotation as exponentials of negative complex 3 by 3 matrices. The reason for the negative complex exponentials is the fact that they are cyclic differentiable with increasing powers of the modulus analogous to an outward spiral. All these are done for the purpose of preserving the local gauge invariance of vector representations of infinitesimal rotations. However, the commutative invariance of infinitesimal rotations could still be achieved by alternatively using real Hadamard matrices, which could also describe quantum of spacetime, quantum of charge (electric, weak, and color) as well as quantum of mass.

[mkirkpatrick]

If we fully understand the total implication of e,will it unlock the doorway for the TOEs
discovery,or will it be another blind-alley.a willothewisp!


regards michael.

[theunify]

Great ideas Antonio and Michael to answer your question about the number is it trancendental, irrational? I think when we discover the TOE we will realise it's not irrational or trancendental but our understanding have been simply limited and close minded. How can a number diverge or approach? This is irrational thinking numbers don't have a mind of their own and we simply state what we cannot understand using language we can understand...I am not debating that e, or pi are trancendental without a pinpoint but that these numbers are hard to understand because of our number system not because of where they lie on the number plane.... What if we had base e, or base pi systems... it would "normalize" the number to a pinpoint...in other words what is the number "ten" why can we locate it on the number plane so easily? It is because we have given it preferential status which limits the other numbers from being so easy to read....if this system were reverse "ten" would be trancendental and "e" would be prefered... I hope you realize I am connecting numbers to forms... in the physical realm so that if we had a sphere of volume 10 it would be finite and rational, and if we had a sphere of volume e it would be finite and rational...this is only the case if we do not make sense of e from base ten, and we do not make sense of base ten from e.

One common explanation is that C^2 = 1 in the famouse equation E=mc^2, Einstein used a base C system to make sense of velocities that "approach" a certain point. Do those velocities have finite and rational values, the answer has to be yes if we believe in a fundemental universe in a base C system.... The problem is when we use an incorrect base to interpret arbitras numbers such as base ten explanation of trancendental e.

How many apples does it take to build an apple tree? That is much like how many base ten units does it take to build e...it's irrational and transcendental in that light.

[AntonioLao]

If we fully understand the total implication of e,will it unlock the doorway for the TOEs discovery,or will it be another blind-alley.a willothewisp!

Often physicists use a number without complete understanding, a job for mathematicians per se. But the Euler's number is used practically everywhere in the advancement of science.

[mkirkpatrick]

Often physicists use a number without complete understanding, a job for mathematicians per se. But the Euler's number is used practically everywhere in the advancement of science.

Will they then Antonio,use this number to discover the TOE,and why is it taking them
so long,what is the"missing equation" that would bridge the gap of ignorance,and open
the door of discovery?


regards michael.

[theunify]

Will they then Antonio,use this number to discover the TOE,and why is it taking them
so long,what is the"missing equation" that would bridge the gap of ignorance,and open
the door of discovery?


regards michael.

Your questions open many doors, those doors open many more, and so it goes.

[mkirkpatrick]

Your questions open many doors, those doors open many more, and so it goes.

May those continue to open,and may we recieve an inrush and a upwelling of profound
knowledge and wisdom,may the snow crystal,glink towards that doorway?



regardsmichael.

[AntonioLao]

use this number to discover the TOE,and why is it taking them
so long,what is the"missing equation" that would bridge the gap of ignorance,and open
the door of discovery?

Euler's number is not the one and only transcendental irrational numbers found by mathematicians. The TOE might have to explain all of them and instead of an equation it is more like an inequality as in attractive secondary forces while equality is for repulsive primary forces.

[mkirkpatrick]

Euler's number is not the one and only transcendental irrational numbers found by mathematicians. The TOE might have to explain all of them and instead of an equation it is more like an inequality as in attractive secondary forces while equality is for repulsive primary forces.

As the Buddist way of the middle road seems attractive,and the way of repulsion seems
to suggest rejection of offered aid?Then maybe in the eqilibrium will be found an oasis
where the water will be sweet,and on drinking,will intuit the mind with the formula for
the TOE s revelation!


regards michael.

[AntonioLao]

Then maybe in the eqilibrium will be found an oasis

In chaos theory it is possible to reach a state of dynamic equilibrium.