The point that all change leverages

So here is a busy scene

Despite its busyness there is a particular point that unifies all the movement: it is the centre. It doesn't need to be centre every transformation whose range is within the domain has such a fixed point. I've spoken at length on fixed points, this is a revision.

The fixed point remains unchanged under a transformation. Certainly if we refer to the set of everything then this must have a fixed point, since by definition the range is within the domain. And all transformations on infinite sets the same. This is the basis of Diagonalisation.

But its also the basis of Spirituality too. Which is much more why this blog spends so much time on SRH. Millennia ago people were talking about the hole in a wheel into which the axle fits, and around which the wheel turns. They spoke of rotation around the centre as referring to the world moving around an unchanging truth. The Enlightened Mind observes change fully because it itself is still.

"The point that all change leverages" is a good description of the Truth. In the picture above it is quite easy to see that all the zooming in and out and the cross hairs moving in are all aimed at or occurring round the single centre point. We can discover this special point quite easily here. But in the complex changing world of our Lives with everything changing from the weather to the news to the people and events around us to our own bodies, thoughts, emotions and minds: the World IS most definitely Changing! All of it is changing. They say in Buddhism it is a burning house. But all this change is swirling around a singularity of perfect peace and calm that is never-the-less not separate from the world. The Point that forms the special centre of the picture above, of any affine transformation is part of that domain and range. It is not "outside" the picture. The Peace of Truth Enlightenment and Wisdom is not outside the world, but is created through the very swirling of all the transformation that make up the change all around and in us.

One unfortunate thing is that the processes of education like explaining and showing people things are all part of the world's change. If one considers a student before standard education and after they hopefully have changed. The fixed-point of Peace is thus even a fixed point of the education system. You can't change to a state of Peace because obviously the new state would be itself be changeable and so not Peaceful. We must find the Peace that lies even in the states of change that regard education. Even while reading this the world and our minds are in Flux (to use Heraclitus' word): observing all this change closely so we can see where it has its unchanging centre is all we need to do. 

An algorithm you can use to find the centre of rotation is to take a point of reference that is outside the rotation. So for example on a computer screen with a rotating complex shape if we place our finger on the screen we can see that this point traces out a circle on the rotating image. If we then move our finger inside this circle and do again we will eventually arrive at the centre. Of course with the World it is harder to get a reference point that is "outside" the World, and so harder to get a reference point. However you can have two systems in different states of rotation. From the perspective of one the other traces a trajectory, and vice versa. This is like looking at the orbit of planets from a planet that is itself orbiting. No one can stand on the Sun so we effectively have no way of viewing from the fixed point, we cannot get a finger outside the picture. But we can look at these trajectories. Originally with Epicycles (a predecessor of Fourier Transform) and then we a Heliocentric solar system. we did eventually work out the fixed point of all these changes especially the bizarre behaviour of retrograde planets (which turned out to be just parallax). The process of spiritual progress is very analogous, comparing chaotic and changing systems looking for the centre. 

I won't go as far as Fritjof Capra in Tao of Physics to suggest that there is anything more here than just a nice analogy joining fixed points and spiritual peace. But it is uncanny how these ideas are so similar. It is almost as though through meditation and reflection we slow down the change enough to see the point that is not effected by the world's transformations. The point of Peace. Once found obviously all the changes make sense and have a centre and a grounding. And the more the world changes the more we see the point around which it all changes. This is quite different from the view of change which is trying to stop the world. This type of Peace is disturbed the moment change occurs again.

So regarding SRH. A quick stub to remind me to look at Fixed Points and Russel's Paradox. Excellent summary here in Scientific American