Are there limits to what we can know?


These days, there’s no shortage of scientific optimism, that this or that problem, even though it cannot be solved today will one day be solved. One day we will understand the nature of consciousness and, yes, it will be shown to be material in origin. One day we’ll prove why the universe contains something rather than nothing. We’ll be able to upload our consciousness to a computer and become immortal. Yet every now and then nature reminds us that there are limits to what we can know or do; when our research runs into a brick wall that seems totally intractable. The earliest example is the Second Law of Thermodynamics that opens with the statement, It is not possible that…

A recent paper published in Nature, called The Undecidability of the Spectral Gap is the latest case demonstrating that there may be limits to what we can learn about macroscopic structures based on what we know about their atomic constituents. This is nothing to do with the well-known Heisenberg Uncertainty Principle. The team of physicists led by Toby CubittDavid Perez-GarciaMichael M. Wolf demonstrated that no matter how much we know about an atomic system, there are some properties of the structures they form that we will never be able to compute. The word “never” is used in the same sense as Kurt Godel used it when in 1931 he published a paper demonstrating that in mathematics there are classes of problems that do not have algorithmic solutions, results that the most powerful computer can never prove. Godel’s theorem, and its corollary derived by Turing was also the principal argument used by Roger Penrose in his book, The Emperor’s New Mind as to why computers will most probably never be intelligent, at least in a human sense.

What is at issue is whether we can ever derive the behaviour of a complex physical system from the properties of the atomic particles that underlie it.

Co-author Michael Wolf said, From a more philosophical perspective, this also challenges  the reductionists’ point of view, as the insurmountable difficulty lies precisely in the derivation of macroscopic properties from a microscopic description