The Outer Limits of Reason by Noson S. Yanofsky


Humans seem to be driven by a desire to understand the world they live in, what we call “reality.” Jacques Monod, Nobel Laureate and co-discoverer of the gene, considered this desire to be genetic in origin. Perhaps it is the result of neurological development that favored cohesion among groups of hominids that shared a common desire for “understanding.” The neuropaleontologist Harry J. Jerison argued that reality itself is a mental construct and that living organisms create their own realities that provide them with just enough information to survive. Indeed, he suggested that the various senses of living organisms sent just enough information to their brains so that they could survive and that additional information was not sent, lest it actually contribute negatively to survival. For example, the frog’s eye only sent the frog’s brain a target for its tongue if that target was in motion. A stationary insect was not ignored, it literally wasn’t there.
Professor Noson S. Yanofsky, in his most fascinating and eminently readable treatise The Outer Limits of Reason, tells the story of how humans have developed the faculties and tools of reason with which to describe and understand their reality. Unfortunately for those readers who seek comfort in a belief that these tools and faculties will suffice to bring us complete understanding, Yanofsky reaches a somewhat depressing conclusion. Fortunately, the journey to that conclusion is exciting and thoroughly enjoyable. For Yanofsky, as powerful as these tools of logic, abstract mathematics, physics, and computation are, they are fraught with ambiguities, paradoxes, and ill-defined concepts that hinder their ability to bring understanding. Moreover, what we have already learned about the physical world (our reality) by using these tools indicates that it is a strange place indeed. Quantum mechanics tells us that there is a separation between the observer and the observed (“wholeness”), which leads to a vast array of conundrums. In the quantum mechanical description of things, knowledge of certain pairs of descriptive variables cannot be obtained simultaneously with equal degrees of exactness. Such knowledge is called “complementary,” meaning one or the other is to be used depending on the circumstances. In the more familiar “classical” reality, knowledge might be called “supplementary,” meaning that each new determination adds to what is already known.

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