change and invariance

[AntonioLao]

The more things change the more they stay the same. This principle of change and permanence is still being revered by eleatic philosophers, religious Buddhists, cubic painters, and last but not least, mathematical topologists.

The concept of dynamic invariance is fundamental in natural laws. From the absolutes to the relatives and then from the relatives back to the absolutes, the cyclic process continues. From zero to infinity and from infinity back to zero, the calculation proceeds over and over again, abstractly disguising as numerous cycles of change and permanence but as realistically as the cycle of life and death and rebirth.

To the experimentalists, a widening circle represents dynamic change, e.g., the observed expansion of the universe. To the theorists, a widening circle represents dynamic invariance. The experimentalists see the circumference increases in length, while the theorists see the circle as a simple closed curve bounding an inside and an outside whose topological soul remains an unchanging essence.

[Guille]

This confuses me. For me, if thigs change, they variate, not stay invariance.

[AntonioLao]

GUILLE,

the technical name of change is transformation. The technical name for invariance is topological equivalence. For example, given a circle and if there are no markings on the circumference there is no way to tell that the circle has actually rotated which it might well be and at different rates.

[Guille]

GUILLE,

the technical name of change is transformation. The technical name for invariance is topological equivalence. For example, given a circle and if there are no markings on the circumference there is no way to tell that the circle has actually rotated which it might well be and at different rates.

Oh I see...

Things can have transformations still being topologically equivalent.

[AntonioLao]

GUILLE,

That's correct. Each of us is growing older and wiser. However, our memory cells are gradually dying. In the end we forget that we are ever here. I have already forgotten some of the things I posted in this forum. My physical body now is topologically equivalent to the body I had 50 years ago.

[Guille]

GUILLE,

That's correct. Each of us is growing older and wiser. However, our memory cells are gradually dying. In the end we forget that we are ever here. I have already forgotten some of the things I posted in this forum. My physical body now is topologically equivalent to the body I had 50 years ago.

Humm.....

This post of yours has given me an incredibel thought! Thanks! If you see, change to occur requiers time, but if there is trully no change, i.e. there is invaraince, then there is no time.

HAHA! Let's see who can solve this one! I will post it in my time paradox thread.