M^{8}H duality maps the preferred extremals in H to those M^{4}× CP_{2} and vice versa. The tangent spaces of an associative spacetime surface in M^{8} would be quaternionic (Minkowski) spaces.
In M^{8} one can consider also coassociative spacetime surfaces having associative normal space. Could the coassociative normal spaces of associative spacetime surfaces in the case of preferred extremals form an integrable distribution therefore defining a spacetime surface in M^{8} mappable to H by M^{8}H duality? This might be possible but the associative tangent space and the normal space correspond to the same CP_{2} point so that associative spacetime surface in M^{8} and its possibly existing coassociative companion would be mapped to the same surface of H.
This dead idea however inspires an idea about a duality mapping Minkowskian spacetime regions to Euclidian ones. This duality would be analogous to inversion with respect to the surface of sphere, which is conformal symmetry. Maybe this inversion could be seen as the TGD counterpart of finiteD conformal inversion at the level of spacetime surfaces. There is also an analogy with the method of images used in some 2D electrostatic problems used to reflect the charge distribution outside conducting surface to its virtual image inside the surface. The 2D conformal invariance would generalize to its 4D quaterionic counterpart. Euclidian/Minkowskian regions would be kind of Leibniz monads, mirror images of each other.
 If strong form of holography (SH) holds true, it would be enough to have this duality at the informational level relating only 2D surfaces carrying the holographic information. For instance, Minkowskian string world sheets would have duals at the level of spacetime surfaces in the sense that their 2D normal spaces in X^{4} form an integrable distribution defining tangent spaces of a 2D surface. This 2D surface would have induced metric with Euclidian signature.
The duality could relate either a) Minkowskian and Euclidian string world sheets or b) Minkowskian/Euclidian string world sheets and partonic 2surfaces common to Minkowskian and Euclidian spacetime regions. a) and b) is apparently the most powerful option information theoretically but is actually implied by b) due to the reflexivity of the equivalence relation. Minkowskian string world sheets are dual with partonic 2surfaces which in turn are dual with Euclidian string world sheets.
 Option a): The dual of Minkowskian string world sheet would be Euclidian string world sheet in an Euclidian region of spacetime surface, most naturally in the Euclidian "wall neighbour" of the Minkowskian region. At parton orbits defining the lightlike boundaries between the Minkowskian and Euclidian regions the signature of 4metric is (0,1,1,1) and the induced 3metric has signature (0,1,1) allowing lightlike curves. Minkowskian and Euclidian string world sheets would naturally share these lightlike curves aas common parts of boundary.
 Option b): Minkowskian/Euclidian string world sheets would have partonic 2surfaces as duals. The normal space of the partonic 2surface at the intersection of string world sheet and partonic 2surface would be the tangent space of string world sheets so that this duality could make sense locally. The different topologies for string world sheets and partonic 2surfaces force to challenge this option as global option but it might hold in some finite region near the partonic 2surface. The weak form of electricmagnetic duality could closely relate to this duality.
In the case of elementary particles regarded as pairs of wormhole contacts connected by flux tubes and associated strings this would give a rather concrete spacetime view about stringy structure of elementary particle. One would have a pair of relatively long (Compton length) Minkowskian string sheets at parallel spacetime sheets completed to a parallelepiped by adding Euclidian string world sheets connecting the two spacetime sheets at two extremely short (CP_{2} size scale) Euclidian wormhole contacts. These parallelepipeds would define lines of scattering diagrams analogous to the lines of Feynman diagrams.
This duality looks like new but as already noticed is actually just the old electricmagnetic duality seen from numbertheoretic perspective.
For background see chapter Some questions related to the twistor lift of TGD or the article with the same title.
