Oddly evenly

[AntonioLao]

In the theory of Fourier analysis a function f is said to be odd if f(-x)=-f(x). A function gis said to be even if g(-x)=g(x). For examples: the circular functions or trigonometric functions of sine and cosine. Since cos(-x)=cos(x), the circular function cosine is an even function. Since sin(-x)=-sin(x), the circular functions sine is an odd function.

However, applying a biortho test to these two circular functions does not give negative unity. There is no such value of the circular argument x that would satisfy the requirement that the product of their derivatives must be negative unity or equivalently that sin(x)cos(x)=1. In degrees, the value of x that give ½ of unity is 45° or p/4 in radians of angular measurements. At best, there is a missing factor of 2. On the other hand, the squares of these circular functions namely sin²x and cos²x satisfy the biortho test for value of the circular argument that is equal to 45° or p/4 radians. Its significance will be discussed later.

[mkirkpatrick]

In the theory of Fourier analysis a function f is said to be odd if f(-x)=-f(x). A function gis said to be even if g(-x)=g(x). For examples: the circular functions or trigonometric functions of sine and cosine. Since cos(-x)=cos(x), the circular function cosine is an even function. Since sin(-x)=-sin(x), the circular functions sine is an odd function.

However, applying a biortho test to these two circular functions does not give negative unity. There is no such value of the circular argument x that would satisfy the requirement that the product of their derivatives must be negative unity or equivalently that sin(x)cos(x)=1. In degrees, the value of x that give ½ of unity is 45° or p/4 in radians of angular measurements. At best, there is a missing factor of 2. On the other hand, the squares of these circular functions namely sin²x and cos²x satisfy the biortho test for value of the circular argument that is equal to 45° or p/4 radians. Its significance will be discussed later.

It amazes me how even all things are when understood
fully.

regards michael.

[AntonioLao]

Thanks for your comments. Everness implies the indistinguishable attributes of positive and negative or good and evil or left and right or up and down or forward and backward or past and future. All these are parts of the attributes that fully describe a directional invariance.

[mkirkpatrick]

Thanks for your comments. Everness implies the indistinguishable attributes of positive and negative or good and evil or left and right or up and down or forward and backward or past and future. All these are parts of the attributes that fully describe a directional invariance.

Yes,it seems that balance is inbuilt into the very fabric of
reality.


regards michael.

[AntonioLao]

perfect dynamic equilibrium implies a perfect symmetry but not a true directional invariance.

[mkirkpatrick]

perfect dynamic equilibrium implies a perfect symmetry but not a true directional invariance.

That seems to imply an oddity,is that so!



regards michael.

[AntonioLao]

oddity is the attribute for the universe to create matter while evenity is the attibute for the universe to create energy. Together they create square of energy.

[mkirkpatrick]

oddity is the attribute for the universe to create matter while evenity is the attibute for the universe to create energy. Together they create square of energy.

I really liked that answer Antonio,great way of putting it,
and of course so inline with how it seems to be!



regards michael.

[AntonioLao]

Thanks again. Could this mean that we cannot extract energy out of square of energy?

[mkirkpatrick]

Thanks again. Could this mean that we cannot extract energy out of square of energy?

Yes I think it does,after all,we are within it,how then could we be without?


regards michael.