Beyond Reason: Eight Great Problems That Reveal the Limits by A. K. Dewdney

By A. K. Dewdney

A mind-bending day trip to the bounds of technological know-how and mathematics
Are a few medical difficulties insoluble? In past cause, across the world acclaimed math and technological know-how writer A. okay. Dewdney solutions this query via analyzing 8 insurmountable mathematical and clinical roadblocks that experience stumped thinkers around the centuries, from historical mathematical conundrums similar to "squaring the circle," first tried via the Pythagoreans, to G?del's vexing theorem, from perpetual movement to the upredictable habit of chaotic platforms reminiscent of the weather.
A. okay. Dewdney, PhD (Ontario, Canada), used to be the writer of medical American's "Computer Recreations" column for 8 years. He has written a number of significantly acclaimed well known math and technological know-how books, together with A Mathematical secret journey

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Additional resources for Beyond Reason: Eight Great Problems That Reveal the Limits of Science

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In other words, all motion is perpetual in the absence of external forces. Paradoxically, type one perpetual motion is built into the very foundations of classical physics. As for type two, or true perpetual motion, one may analyze each device in turn and prove that it could not possibly be producing more energy than it consumes. Such proofs, because of the complexity of some devices, may involve considerable labor. In other cases, as below, the analysis is relatively straightforward. I will present an analysis of a device first described by the Dutch philosopher/mathematician Simon Stevinus at about the turn of the sixteenth century.

The clockwork motor concealed in the machine did not drive the birdcage gear, but the main axle itself, transmitting its force through friction that was barely sufficient with the weights in their cars. But with the weights removed, the friction dropped below the critical value, and the turning of the motor had no effect on the big wheel. Redheffer could not conceal his amazement at the device shown to him by these sober, respectable citizens. Privately he offered Sellers a great deal of money if only he would reveal the principle by which the machine operated.

On the other hand, the apparent directions of stars observed from the Earth were not affected by motion of the ether outside the Earth. Consequently, the ether outside material objects must be stationary, a fixed frame of reference that would have been heartily welcomed by the likes of Newton. The inconsistency arose from the assumption that the ether—whatever it was—actually existed. The speed of light would obviously be constant in the ether. An observer moving through the ether would be able to measure a slowing down or speeding up of light, depending on whether the observer was moving with the ether or against it.

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