Posts Tagged ‘limits to knowledge’
“The Universe is not only queerer than we suppose, but queerer than we can suppose”*…
Complex nature
Albert Einstein said that the “most incomprehensible thing about the Universe is that it is comprehensible.” He was right to be astonished. Human brains evolved to be adaptable, but our underlying neural architecture has barely changed since our ancestors roamed the savannah and coped with the challenges that life on it presented. It’s surely remarkable that these brains have allowed us to make sense of the quantum and the cosmos, notions far removed from the ‘commonsense’, everyday world in which we evolved.
But I think science will hit the buffers at some point. There are two reasons why this might happen. The optimistic one is that we clean up and codify certain areas (such as atomic physics) to the point that there’s no more to say. A second, more worrying possibility is that we’ll reach the limits of what our brains can grasp. There might be concepts, crucial to a full understanding of physical reality, that we aren’t aware of, any more than a monkey comprehends Darwinism or meteorology. Some insights might have to await a post-human intelligence…
Abstract thinking by biological brains has underpinned the emergence of all culture and science. But this activity, spanning tens of millennia at most, will probably be a brief precursor to the more powerful intellects of the post-human era – evolved not by Darwinian selection but via ‘intelligent design’. Whether the long-range future lies with organic post-humans or with electronic super-intelligent machines is a matter for debate. But we would be unduly anthropocentric to believe that a full understanding of physical reality is within humanity’s grasp, and that no enigmas will remain to challenge our remote descendants…
Martin Rees (Lord Rees of Ludlow), cosmologist and astrophysicist, Astronomer Royal since 1995, past Master of Trinity College, Cambridge, and former President of the Royal Society, on the limits of human understanding (and how we might transcend them): “Black holes are simpler than forests and science has its limits.”
For a “companionable” take on the character of the knowledge that we do (seem to) have, see “Is Quantum Theory About Reality or What We Know?“; and for an argument that we should stop worrying about the limits of human knowledge, and start worrying about wasting the knowledge we already have, see here.
* J. B. S. Haldane, Possible Worlds and Other Papers (1927)
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As we prepare to call (an artificially-intelligent) friend, we might send acutely observant birthday greetings to an astute student of the human animal, anthropologist Margaret Mead; she was born on this date in 1901. Best-known for her studies of the nonliterate peoples of Oceania, she was 23 when she first traveled to the South Pacific, to conduct research for her doctoral dissertation. The book that resulted, Coming of Age in Samoa, was– and remains– a best-seller.
Knowing what’s unknowable…
We’ve known for quite awhile that there’s a limit to what we can know… Werner Heisenberg discovered that improved precision regarding, say, an object’s position inevitably degraded the level of certainty of its momentum. Kurt Gödel showed that within any formal mathematical system advanced enough to be useful, it is impossible to use the system to prove every true statement that it contains. And Alan Turing demonstrated that one cannot, in general, determine if a computer algorithm is going to halt.
Now David Wolpert, a physicist working as a computer scientist at NASA Ames, has elaborated on that limit. As Scientific American reports, Wolpert’s work show’s that
…the universe lies beyond the grasp of any intellect, no matter how powerful, that could exist within the universe. Specifically, during the past two years, he has been refining a proof that no matter what laws of physics govern a universe, there are inevitably facts about the universe that its inhabitants cannot learn by experiment or predict with a computation. Philippe M. Binder, a physicist at the University of Hawaii at Hilo, suggests that the theory implies researchers seeking unified laws cannot hope for anything better than a “theory of almost everything.”
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Wolpert proves that in any such system of universes, quantities exist that cannot be ascertained by any inference device inside the system. Thus, the “demon” hypothesized by Pierre-Simon Laplace in the early 1800s (give the demon the exact positions and velocities of every particle in the universe, and it will compute the future state of the universe) is stymied if the demon must be a part of the universe.
Researchers have proved results about the incomputability of specific physical systems before. Wolpert points out that his result is far more general, in that it makes virtually no assumptions about the laws of physics and it requires no limits on the computational power of the inference device other than it must exist within the universe in question. In addition, the result applies not only to predictions of a physical system’s future state but also to observations of a present state and examining a record of a past state.
The theorem’s proof, similar to the results of Gödel’s incompleteness theorem and Turing’s halting problem, relies on a variant of the liar’s paradox—ask Laplace’s demon to predict the following yes/no fact about the future state of the universe: “Will the universe not be one in which your answer to this question is yes?” For the demon, seeking a true yes/no answer is like trying to determine the truth of “This statement is false.” Knowing the exact current state of the entire universe, knowing all the laws governing the universe and having unlimited computing power is no help to the demon in saying truthfully what its answer will be.
Read the full story here.
As we reconcile ourselves to incompleteness, we might console ourselves that it was on this date in 1929 that the Hollywood Sign was officially dedicated in the hills above Hollywood, Los Angeles. It originally read “Hollywoodland ,” but the four last letters were dropped after renovation in 1949. Recently threatened with demolition for want of maintenance funds, the icon was saved by a donation from Hugh Hefner.
The sign in it’s original form, as seen from Beachwood Canyon (source)
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