Alfred Moebius and Views of a Self

DN1:3.74.3: “Well, then, Ānanda, you may remember this exposition of the teaching as ‘The Net of Meaning’, or else ‘The Net of the Teaching’, or else ‘The Prime Net’, or else ‘The Net of Views’, or else ‘The Supreme Victory in Battle’.”

Alfred Ferdinand Moebius was an astronomer and a mathematician who taught us many things, including the lovely experience of cutting a piece or paper through and through to end up with…one piece of paper. Alfred Moebius developed a deep understanding of views and transformations. In fact, the Moebius Transformation is named after him.

Let’s take a little journey into Moebius’s world of transformations and views. And for that little journey, just for fun (FUN!), let’s take the view that the following image is the SELF. And for all those Buddhists raising their fingers to type an outraged response to this “affirmation of self”, let’s hold off a bit on that judgement. Let’s play a little and see where Moebius takes us…

The Self

Let there be variable, “Self”, that labels the following image:


Grasping that view (softly, patiently!), let’s take a little journey…

Now watch this video about Moebius transformations


OK. Now that you’ve watched the video, we can notice some very interesting things about our nice colorful square:

  • we can move it about (translation) :running_man:
  • we can rotate it around a center (rotation) :icecream:
  • we can make it big or small (scaling) :moneybag:
  • and most amazingly, we can transform the finite Self into and out of the Infinite Atman Cosmos (inversion) :infinity: :open_mouth:

The Moebius transformation maps every point in an Infinite Atman Cosmos to a point in the unit circle. Specifically, the Moebius transformation can map an infinite span to a finite span with a simple rotation. And that very strange transformation provides a concrete example for understanding a teaching about how we might understand each other.

DN34:1.7.87: They understand the minds of other beings and individuals, having comprehended them with their own mind.

The Moebius transformation demonstrates that view inversion is quite natural and versatile. In fact, it is the stubborn Euclidean plane that confines us with its limited assumptions, its fanatically stubborn, orthogonal and dictatorial grid.

Not self

At this point, one might wonder at the request to consider the square as self as posed earlier in this post. And let’s pause here to ask a question.

As you watched the video clinging to a square grid known as self, was there a moment of wild disorientation perhaps? Was that moment the inversion of the square into infinity?

If it was disorienting, then simply watch the video again without grasping at the square as self. And on this second viewing, perhaps the viewing might be more peaceful.


DN1:3.72.4: In the same way, all of these ascetics and brahmins who theorize about the past or the future are trapped in the net of these sixty-two grounds, so that wherever they emerge they are caught and trapped in this very net.
DN1:3.73.1: The Realized One’s body remains, but his attachment to rebirth has been cut off.
DN1:3.73.2: As long as his body remains he will be seen by gods and humans.
DN1:3.73.3: But when his body breaks up, after life has ended, gods and humans will see him no more.