To see that nature conspires to create dimensions and geometries that go far beyond any geometers have dreamed of one need only consider the human body and its many intricacies. Blood cells and hormones are generally limited to following prescribed paths dictated by blood vessels which themselves have their appointed routes. Similarly nerve impulses are confined to and limited by the branchings of the nervous system. Food ingested but not absorbed by body cells travels the circuitous, serpentine length of the digestive tract, once - - - in embryonic times - - - a straight undiverting tube, to appear once more at the anus as excrement. All of these convoluted paths and wanderings involve dimension and geometry, though not of the Euclidean kind, nor of any other described mathematical type.
Surgeons must study and master human anatomy and its many variants because when the knife is inserted within the human frame it may not follow any simple geometry as it makes its way through the integument into the subcutaneous tissues and onward to its ultimate destination, at the risk of serious and possibly permanent injury. If in fact dimension has to do with independent magnitudes that serve to define the location of an element within a given set, if dimension refers to the least number of independent coordinates required to specify uniquely the points in a space, and if this is to be interpreted functionally as well as structurally, then we must conclude that the human body has many more dimensions than three.
© 2013 Martin Hauser
Carlos Frenk, Director of the Institute for Computational Cosmology, Durham University
His offence was to be an ardent advocate of a then controversial idea - that most of the universe’s matter comes as a cold, heavy soup of invisible “dark matter”. Today that is the orthodoxy. [New Scientist]
See also WHERE IS THE MISSING MATTER?
Dark Energy and Quantum Mechanics
Quantum field theory predicts that each point in space has a vacuum energy, or a small amount of energy intrinsic to empty space, associated with it. We sometimes think of this as energy allowed by the Heisenberg uncertainty principle—if we know a point’s position in time well enough, we can’t know its energy. Originally, scientists hoped that the vacuum energy could explain the cosmological constant.
The vacuum energy of quantum field theory does indeed predict a “dark energy.” Unfortunately, it’s times more energy than we actually observe. Some people have called this “the worst theoretical prediction in the history of physics.” The current hope is that a fully developed theory of quantum gravity will resolve this discrepancy. The dark-energy problem is currently one of the biggest problems facing theoretical physics. If you can explain it, you’ll win a Nobel Prize.
Niels Bohr (1885 -1962)
Martin Rees (born 1942)
“A chimpanzee can’t understand quantum mechanics,” Rees points out.
That might sound like a statement of the obvious. After all, as Richard Feynman famously said, nobody understands quantum mechanics. The point, though, is that chimps don’t even know what they don’t understand. “It’s not that a chimpanzee is struggling to understand quantum mechanics,” Rees says. “It’s not even aware of it.” The question that intrigues Rees is whether there are facets of the universe to which we humans are similarly oblivious.
Martin John Rees, Baron Rees of Ludlow, OM, Kt, FRS is a British cosmologist and astrophysicist. He has been Astronomer Royal since 1995 and Master of Trinity College, Cambridge from 2004 to 2012. Wikipedia