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## Connecting classical Maxwell´s equations to the S4 view

I have claimed now for years that the true equations of electromagnetism result from taking the square root of the wave equation on differential forms on a four sphere with radius $1/h$ where $h$ is Planck´s constant.  If $M$ is an embedded three dimensional manifold with a local orthonormal coframe $\omega_1, \omega_2, \omega_3, \omega_4$ with $\omega_4 = 0$ defining $M$, and if $D$ is the Dirac operator on forms on the ambient four-sphere and $H = D\omega_4$ then the restriction of the square root of the wave equation is the square root of the operator $(D_M + H)^2 + \partial_t^2$.

If we are able to fully connect the observed electromagnetism with this picture, we would have given justification for the naturality of electromagnetism as a feature of the shape and other attributes of our universe and remove theories that posit any supernatural designer of the universe.  An eternal stationary (unless $h$ changes) universe cannot have been created by a creator-God either.

The analysis here of the differential form version of Maxwell´s equations can be used to fill the link between the claims in the last paragraph and the way in which Maxwell´s equations are considered in actual use.

## My reading of Eliot´s The Waste Land

Eliot himself puts the image of Tiresias as the center of the poem, but I will give a reading centering on the passage:

What are the roots that clutch, what branches grow

Out of this stony rubbish?

Son of Man, you cannot guess for you only know

A heap of broken images where the sun beats and the dead tree gives no shelter, the cricket no relief and the dry stone no sound of water

This is the Antichrist speaking to Christ, and the knowledge of broken images is passed.  On one hand these broken images are the pride of modernity built on the destruction of whole images from perhaps a distant and a wholly mythical past, and perhaps a pre-Christian past.  This pitiless description of the present, for in the historical scale of myth, there is not much difference between 1922 and 2012.

But who is this Antichrist?  From the lament of April as the cruellest month mixing memory and desire, an intolerable form of torture of a longing that cannot be fulfilled, stirring dull roots with spring rain.  April 6 was the death-date of Richard the Lionheart who was Duke of Aquitaine and the identity of this specific Antichrist is revealed in the last lines as the Prince of Aquitaine enters the ruined tower, written in the French with which Richard of Angevins was far more familiar and comfortable than English.  The speaker-narrator makes a direct identification with Tiresias a few times but otherwise we would not be badly in error if we posited that the voice of the entire poem is that of the Antichrist-Richard the Lionheart who can say ¨These fragments I have shored against my ruins¨ with ´fragments`both emphasizing the broken images in the center of the poem and the fragments of the poem itself.

The dream-mythic fragments of the remaining poem form a prophesy of the Antichrist.  The ´sacred content´ of the poem, the return of the king is most vibrant in the declaration of Ón Margate sands I can connect nothing with nothing, Broken fingernails of dirty hands, my people humble people who expect nothing.´

Hamlet never became a king because he was stuck in the bifurcation of suffering the slings and arrows of outrageous fortune and taking up arms against a sea of troubles and by opposing ending them.  In contrast, the three virtues of Datta, Dayadhvam, and Damyata guide our Antichrist, the reborn or perhaps not-yet-reborn Richard the Lionheart.  They might be even seen to be performing a ritual incantation to revive him in a manner wholly different from the return of Lazarus

Datta:  What have we given?

My friend, blood shaking my heart,

The awful daring of a moment´s surrender

That an age of prudence can never retract

By this, and this only, we have existed,

Which is not to be found in our obituaries

Or in memories draped by the beneficent spider

Or under seals broken by the lean solicitor

In our empty rooms

This awful daring of a moment´s surrender can of course have devastating practical consequences in an age of prudence and yet the virtue of Datta cannot exist without this for there is nothing substantial to be given without this courage and what is given is not the abandonment of the room that is empty for that is not found easily, not even in memories draped by the beneficent spider, who weaves a web and a tapestry perhaps of courage.