A Paradox

 There is some unknown process whereby the structure of reality at the very small is ordered. We constantly are reminded of this today as the weird illogical realm of quantum physics. Apparently events are somehow connected by what we imagine to be instantaneous communication of these infinitesimal parts of the physical world.

At the other largest scale of the structure of our universe we can view enormous networks of skeins of galaxies. But these very structures are organized somehow as a whole, even though there is the fact that any method of communication among its parts would need to be faster than the speed of light. 

Herein lies the paradox that in the extremes of the very, very small and large our version of how the macroscale world of sense certainty functions breaks down. The notion that we can be certain that the universe is energetically winding down toward a final sort of heat death seems awfully presumptuous of us given how little we actually know about its constituent processes. For example, about what constitutes so called dark matter and dark energy.

Bernard Riemann, among the greatest creative thinkers of the last two millennia put it this way:

 "Questions concerning the immeasurably large, are, for the explanation of Nature, useless questions. Quite otherwise is it however with questions concerning the immeasurably small. Knowledge of the causal connection of phenomena is based essentially upon the precision with which we follow them down into the infinitely small. The progress of recent centuries in knowledge of the mechanism of Nature has come about almost solely by the exactness of the syntheses rendered possible by the invention of Analysis of the infinite and by the simple fundamental concepts devised by Archimedes, Galileo, and Newton, and effectively employed by modern Physics. In the natural sciences however, where simple fundamental concepts are still lacking for such syntheses, one pursues phenomena into the spatially small, in order to perceive causal connections, just as far as the microscope permits. Questions concerning spatial relations of measure in the indefinitely small are therefore not useless. 

 "If one premise that bodies exist independently of position, then the measure of curvature is everywhere constant; then from astronomical measurements it follows that it cannot differ from zero; at any rate its reciprocal value would have to be a surface in comparison with which the region accessible to our telescopes would vanish. If however bodies have no such non-dependence upon position, then one cannot conclude to relations of measure in the indefinitely small from those in the large. In that case the curvature can have at every point arbitrary values in three directions, provided only the total curvature of every metric portion of space be not appreciably different from zero. Even greater complications may arise in case the line element is not representable, as has been premised, by the square root of a differential expression of the second degree. Now however the empirical notions on which spatial measurements are based appear to lose their validity when applied to the indefinitely small, namely the concept of a fixed body and that of a light-ray; accordingly it is entirely conceivable that in the indefinitely small the spatial relations of size are not in accord with the postulates of geometry, and one would indeed be forced to this assumption as soon as it would permit a simpler explanation of the phenomena.

 "The question of the validity of the postulates of geometry in the indefinitely small is involved in the question concerning the ultimate basis of relations of size in space. In connection with this question, which may well be assigned to the philosophy of space, the above remark is applicable, namely that while in a discrete manifold the principle of metric relations is implicit in the notion of this manifold, it must come from somewhere else in the case of a continuous manifold. Either then the actual things forming the groundwork of a space must constitute a discrete manifold, or else the basis of metric relations must be sought for outside that actuality, in colligating forces that operate upon it. 

 "A decision upon these questions can be found only by starting from the structure of phenomena that has been approved in experience hitherto, for which Newton laid the foundation, and by modifying this structure gradually under the compulsion of facts which it cannot explain. Such investigations as start out, like this present one, from general notions, can promote only the purpose that this task shall not be hindered by too restricted conceptions, and that progress in perceiving the connection of things shall not be obstructed by the prejudices of tradition.

 "This path leads out into the domain of another science, into the realm of physics, into which the nature of this present occasion forbids us to penetrate."

I would add here that since the time of Riemann, we have made incredible advancements in expanding our knowledge of the universe in the "immeasurably large" with revolutionary viewing technologies across the spectrum of electromagnetic wavelengths.  Therefore the question of continuous versus discrete manifolds can now be appropriately investigated in this domain as well. 

Cosmic web.