The Edge of Knowledge

Exploring the limits of knowledge. This edition published by Corgi Books 1979.

Standing on the edge of a precipice is something which most of us find quite unnerving, especially if we cannot be certain what lies on the other side.  No matter whether that precipice is physical or conceptual, we may experience a fear of the unknown – or even the unknowable – beyond the edge.

Those of us watching the start of the long-running television series Doctor Who on first transmission in 1963 encountered such a sense of the unknown.  After initial serials back in the Stone Age, and then introducing the Daleks, two very strange episodes followed.  The Edge of Destruction and The Brink of Disaster, taking place entirely within the TARDIS, showed our heroes behaving oddly in peculiar conditions, apparently because they had been hurled back to the very beginning – or perhaps the end – of time.  They were on the edge of something potentially catastrophic.  After that, the next episode took them to a thirteenth century adventure with Marco Polo, and everything was back to normal – or relatively normal.  But we never really knew what they had been facing during that brief period at the limit of understanding.  That was really quite challenging back then.

The prize-winning science writer Timothy Ferris gave a sense of how far our areas of knowledge may be stretched in his 1977 book The Red Limit: The Search for the Edge of the Universe.  Describing theories in astronomy and cosmology as they were then understood, he explored discoveries on the origin and ultimate fate of the universe and, with regard to his title, on redshift-distance evidence for the true scale of the universe.  A key aspect was that we can understand what nature is telling us, and he emphasised that “nature is intelligible to us because we in some sense belong to it”.

In reality, there are some barriers which are erected by nature and, sadly, might never be crossed.  Marcus du Sautoy, Professor of Mathematics at Oxford University, provides a fascinating analysis in his 2016 book What We Cannot Know.  He takes us through various realms of knowledge to identify whether there are edges imposed only by our current technology or perception, and beyond which we may one day go.  Or whether some things will always remain beyond our comprehension.

He concludes that even questions on the vast scale, such as whether the universe is indeed infinite, may be proven through the use of mathematics: “although we may never explore or see beyond the finite bubble that encloses the universe we have physical access to, we may be able to know, using the power of minds alone, what is beyond.”

On the scale of the unimaginably small, though, it may be quite another matter.  Quantum physics suggests that we may never be able to investigate at a smaller scale than the Planck length, which represents the shortest possible distance between points and may be of significance in quantum gravity.  Space itself cannot be divided beyond this staggeringly tiny length – to use Professor du Sautoy’s description, if the full stop at the end of this sentence was scaled up to the size of the observable universe, then the Planck length would scale up to the size of the full stop before it was enlarged.  As he puts it, this is “an edge beyond which we cannot know.”

Even then, we can’t help wondering what exists there.  In his 2010 book The Edge of Physics, Anil Ananthaswamy explained how spacetime at that level “may not be smooth and infinitely divisible, as described in general relativity” but could be “possibly a roiling mess, a frothy concoction of black holes and virtual particles that pop in and out of existence.”  Now that’s worth investigating further.

Might the human race one day know everything?  It’s an intriguing thought, but our suspicion must be that, no matter how well informed we are, there’ll always be something else to discover.


Richard Hayes, Assistant Editor (Odyssey)

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