[AntonioLao]

There is a way using mathematics to show that the real number axis and the imaginary number axis could never have intersected. Nevertheless, the real and the imaginary or the complex domain and the real domain share common solutions at the integral values of unity and infinity simultaneously.

The images below represent the two distinct topologies for the linkings of the space axes (real axes) and the time axes (imaginary axes). Please note that the loops never touch each other no matter how infinitesimally small they are.



acknowledgment goes to subversion for educating me in acquiring URL for the insertion of these images into this post.

[Guille]

Thanks for the image, it really helps to visualzie a lot.


I have one question: What if the spirals can move, and so, they could end up touching each other, would anything happen?

[AntonioLao]

Originally Posted by GUILLE What if the spirals can move, and so, they could end up touching each other, would anything happen?

The spirals are forbidden to touch each other due to the conservation of LIM (local infinitesimal motion) and the duality of interconnectivity that only two points are allowed to connect. The image below will clarify that

[AntonioLao]

The duality of interconnectivity of space-time points allows various different configurations at the global scale. However, at the local scale there are three fundamental metrics, which minimize distances: the unity metric (black lines), the square root of 2 metric (orange lines) and the square root of 3 metric (red lines).

[Guille]

Originally Posted by AntonioLao the unity metric (black lines), the square root of 2 metric (orange lines) and the square root of 3 metric (red lines).

Thanks again for the images.

I have inmediatelly recognised what differentiates the three kind of lines, my trigonometry is quite good.

Now, from what you say in the above qoute, then: The multiplication of the squares of two unity metric (black lines) is equal to the sqaure of a 2 metric (orange line). Or at least this is what my pythagorean knowledge tells me.

[Guille]

From my above post, I have thought something:

Is the connectivity between two sqaures energy?

If so, then I have thinked, that if pythagoras' theorem is valid as I predicted in my other post, then we would be dealing with sqaure of energies, which have a lot to do with your theory.

Please tell me if these posts are valid (at least they are logical) or if I'm going along a wrong road.

[AntonioLao]

Originally Posted by GUILLE then we would be dealing with sqaure of energies

You are absolutely right! And thanks for this extra profound thought. However, the Pythagorean theorem seems to be applicable only for n-dimensional Euclidean space-time not for Riemann space-time of Gaussian space-time. I still think that the time axis and space axis do not intersect at all at the local infinitesimal region of space-time. I am proving this using math and have done so. Will send you the email file as soon as finish this post. In the meantime, look at the image of graph of the rational function a=b/(1-b).

[AntonioLao]

The following is the graph of rational function b=a/(1+a).

[Guille]

Originally Posted by AntonioLao However, the Pythagorean theorem seems to be applicable only for n-dimensional Euclidean space-time not for Riemann space-time of Gaussian space-time.

It's always glad to help others. Thanks for the images again.

I have done no math in school to do with gauss or riemann's geometries, so I'm quite lost in these. I understand some things of them that you ahv tought me, like the curve types, etz... Now, does each of these two geometries have a special theorem such as pythagorean theorem is to euclidean geometry, but for them?

I'll read your e-mail tomorrow morning first thing (It's 1 in the morning an dI'm jsut back from whaching real madrid's horrible football match in the stadium).

[AntonioLao]

Originally Posted by GUILLE I'm jsut back from whaching real madrid's horrible football match in the stadium).

In any kind of game, somebody wins and somebody loses but there is always a next game to hope for and next time the losing team might win.

About the Riemann, it is just like Pythagoras, except for the middle term
Pythagoras is x²+y² but Riemann is x²+2xy+y². Note the middle term 2xy for the Riemann. As for Gauss it's like this x²-y². Note the minus sign replaces the plus sign.