(Roughly) Daily

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.”

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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