[AntonioLao]

The analysis of the inverse function f(x)=1/x and the rational function g(x)=x/(1+x) suggests their natural golden connection to the natural base of logarithm, e. This base is used practically everywhere in the formulations of scientific discoveries for both field and particle theory even in the growth and decay of living things. In quadratic forms, the golden mean can be written as x+x-1=0 if x is less than unity or as x-x-1=0 if x is greater than unity. Equivalently, the first is given by equating (1/x)=x+1 and the second is given by equating (1/x)=x/(1+x). However, equating (x+1)= x/(1+x) would not make any sense unless x is complex. Nonetheless, (1/x)=x/(1+x) is simply the same as equating f(x)= g(x).

Further analyses give the following results: (1) the derivative of f(x) is -1/x (2) the derivative of g(x) is 1/(1+x) (3) the limit of f(x) as x®0 is undefined (4) the limit of g(x) as x®0 is zero (5) the limit of f(x) as x®infinity is zero (6) the limit of g(x) as x®infinity is unity (7) the integral of f(x) is ln|x| ( the integral of g(x) is x-ln|1+x|. Coincidently or maybe not, the clincher is that the natural base of logarithm is defined as the limit of the x-power of the reciprocal of g(x) as x®infinity.

[mkirkpatrick]

Originally Posted by AntonioLao The analysis of the inverse function f(x)=1/x and the rational function g(x)=x/(1+x) suggests their natural golden connection to the natural base of logarithm, e. This base is used practically everywhere in the formulations of scientific discoveries for both field and particle theory even in the growth and decay of living things. In quadratic forms, the golden mean can be written as x+x-1=0 if x is less than unity or as x-x-1=0 if x is greater than unity. Equivalently, the first is given by equating (1/x)=x+1 and the second is given by equating (1/x)=x/(1+x). However, equating (x+1)= x/(1+x) would not make any sense unless x is complex. Nonetheless, (1/x)=x/(1+x) is simply the same as equating f(x)= g(x). Further analyses give the following results: (1) the derivative of f(x) is -1/x (2) the derivative of g(x) is 1/(1+x) (3) the limit of f(x) as x®0 is undefined (4) the limit of g(x) as x®0 is zero (5) the limit of f(x) as x®infinity is zero (6) the limit of g(x) as x®infinity is unity (7) the integral of f(x) is ln|x| ( the integral of g(x) is x-ln|1+x|. Coincidently or maybe not, the clincher is that the natural base of logarithm is defined as the limit of the x-power of the reciprocal of g(x) as x®infinity.

You took the words right out of my mouth here,remarkable?
Now when this is "toned down will it reveal an opening?

regards michael.

[AntonioLao]

Originally Posted by mkirkpatrick will it reveal an opening

I'm still holding to the fact that there was never an opening. It is just our complicated thoughts that close them down and shut them up. The answers are right under our noses.

[mkirkpatrick]

Originally Posted by AntonioLao I'm still holding to the fact that there was never an opening. It is just our complicated thoughts that close them down and shut them up. The answers are right under our noses.

Prehaps we are already within it (our consciousness) and we see it not?



regards michael.

[AntonioLao]

Originally Posted by mkirkpatrick we are already within it

If it is a Moebius topology then there is no inside or outside. The convoluted topology makes it appears that there is inside and outside. But the linkage of the topology is mathematically real.

[mkirkpatrick]

Originally Posted by AntonioLao If it is a Moebius topology then there is no inside or outside. The convoluted topology makes it appears that there is inside and outside. But the linkage of the topology is mathematically real.

Then we need to somehow got into transcendant mode and gain access that way!




regards michael

[AntonioLao]

Originally Posted by mkirkpatrick into transcendant mode

That means you got to have the pie and eat it too since pi is the only irrational transcendental real number found in nature. Maybe I wrong but any professional mathematician would prove it otherwise.

[mkirkpatrick]

Originally Posted by AntonioLao That means you got to have the pie and eat it too since pi is the only irrational transcendental real number found in nature. Maybe I wrong but any professional mathematician would prove it otherwise.

In real terms though,many do just that,have the pie and eat it too?Prehaps there
is a fundamental error in the way we understand this? Think beyond maths-into
full and total unification.



regards michael

[AntonioLao]

Originally Posted by mkirkpatrick have the pie and eat it too

Can't remember this ever happened to me. On the other hand, if ever I ate a pie with the Golden Divine Proportion built-in then I should probably live forever and never get hungry again.

[mkirkpatrick]

Originally Posted by AntonioLao Can't remember this ever happened to me. On the other hand, if ever I ate a pie with the Golden Divine Proportion built-in then I should probably live forever and never get hungry again.

Ambrosia was the food of the Gods,I am sure if you ate that hunger would never
visit you again!



regards michael