Accomplishing the Impossible The movie Star Trek II, The Wrath of Khan, opens with the Kobayashi Maru test being administered to an aspiring starship captain. This test is a simulation of an attack on the student's ship, to test the student's responses to the various calamities resulting from the attack. As each difficulty is dealt with, the simulation computer issues a new, even more difficult, problem until it is no longer humanly possible to handle the situation. It was impossible to win the simulation game. And yet one person, James Kirk, had won it. It was impossible, but he did it. How? He hacked into the simulation computer the night before the test and reprogrammed it. He cheated, but he won. Anything that seems to be impossible is only impossible within the conditions, rules, laws, hypotheses, assumptions, that limit the means that may be taken to accomplish the desired effect. This set of conditions define the paradigm, or “box”, that restricts the mental act...
Inabel One of the more interesting characters that I met during those hard years at Roanoke college was a girl named Inabel. She had a glaring physical defect. Her nose had a prominent hook, and on that hook there was a wart. In other words she was the living embodiment of a fairy tale witch. But her bright happy character was just the opposite of that of a witch. And she had a natural sense of humor that clearly overrode any anxiety she may have had about her appearance. The students who lived in Roanoke and did nor participate in dorm life were assigned a study room for those who did not have 8 o'clock classes, and it even extended to the 9 o'clock hour for those returning from an 8 o'clock class. These were hours of heavy study. We asked each other questions, some of which were anticipated test questions, and some real need-to-know questions as we struggled to keep our heads above water in the oner...
Dr. McShane But now I want to return to those first days of my introduction to graduate level mathematics, specifically to one course with the intimidating title, “Functions of a Real Variable”. The lecturer was Dr. E. J. McShane. He was the acting head of the department, in the absence of the permanent head who was on a sabbatical. I think that I may have made a slight impression on him by sitting on the front row in class, looking at him as he lectured, and attempting, with some success, to explain a theorem that he had assigned for study. But he definitely made an impression on me. He had enrolled all of the new graduate math students in this class. Apparently he wanted to give us a proper introduction to abstract mathematics, because he spent the first six weeks of the course teaching us logic in considerable depth – far beyond the basic logic of my high school course in Euclidean geometry. This logic utilized an extensive system of symbols that was appropria...
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