Posts Tagged ‘Panofsky’

Inside Knowledge: Why We’ll Never Know Everything

April 8, 2017

The title of this post identical to the title of an article by Richard Webb in the Features Section of the 1 Apr 2017 New Scientist.   There are many limitations, but let us just consider computational power.  One can argue that computational power is only a temporary limitation.  Webb notes, however powerful we make them, computers rely on human input to program them.

Webb goes on to comment “…human thought is a glorious, uproarious, complex mess. Statements like “this statement is false, hating someone yet loving them and yes, that small-yet-large jumbo shrimp, both compute and do not compute.”  Panofsky, an information scientist at the City University of New York says, “language is an expression of the mind, and my mind is full of contradictions.”

This flexibility allows us to think creatively, while remaining firmly grounded.  Webb says that “because we are predicated on contradiction, we see contradiction everywhere. But “the defining feature of reality is that it admits no contradiction.   Quantum objects apparently act as waves or as particles depending how we choose to measure them.”  Physicist Richard Feynman called this confusing duality “the only mystery” of the quantum world.  Webb conjectures, “In all probability, the basic building blocks of reality are neither wave nor particle, but something else entirely.  It’s just something that we lack the experience or cognitive ability to express.”

When HM was a naive undergraduate he did not want to waste time on philosophy courses where questions were raised, solutions were presented and argued about, but resolution or general agreement, was never achieved.  So he took courses in symbolic logic where, he thought, definitive conclusions could be reached.  Logic and mathematics is supposedly a cleaner, neutral language for a trained brain to describe in abstract terms what it cannot visualize.  What HM learned in symbolic logic was that there were logical limitations on both logic and mathematics.

For example, there is the well-known injunction that you should never divide a number by zero.  If you do, you can begin to do things like prove 1 = 2.  This can’t be allowed if mathematics are the language of a flawless universe.   Panofsky says, “if you want mathematics to continue without contradiction than you have to restrict yourself.”

Kurt Godel showed in the 1930s that any system of logic containing the rules of arithmetic is bound to contain statements that can be neither proved nor disproved.  It will remain “incomplete” , trapped in the same inconsistency as we are.  Model incompleteness is a mathematical expression of the logical-illogical statement “this statement is false.”  So there is no way for anything, be it a simple sentence, system of logic, or a human being to express the full truth about itself.

Webb continues “This problem of self-reference is endemic.  Godel’s contemporary Alan Turing showed that you cannot ask a computer program in advance whether it will run successfully.  Quantum mechanics sprouts paradoxes because we are part of the universe we are trying to measure.”

And Webb concludes, “So the sobering truth is that we can build the most powerful telescopes, microscopes and computers we want, we we will never overcome the limitations of our minds.  Our perspective on reality will always be skewed because we—and the jumbo shrimp—are part of it.”

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