CHAPTER 2 - AXIOMS
“Knowledge is power, power is dangerous, therefore knowledge is dangerous. That’s just the transitive property.” Introduction to the Second Charter of the Galilean Conspiracy, by Sir Issac Newton
After a truly arduous examination of what was covered over the entire course, a very simple question was put to him as the last one on the physics test.
‘Assuming the small angle approximation, what is the equation governing the period of a simple pendulum?’ It was odd that such a simple question would be the last one on the test. Owen jotted down the answer and walked up to the front of the room to submit his examination.
Equation [https://miro.medium.com/v2/resize:fit:512/format:webp/1*N9FHVhiXXGoWF5MLfeGhcg.png]
Then professor M‘Laurine said, in a whisper, “You may have noticed that the last question was a bit odd, we’re having a little contest between students.” He pointed to the weight suspended by a string and asked “Look hard at that pendulum there, please approximate the period? You have 30 seconds.” and handed Owen a slip of paper, then started the timer. Owen looked at the pendulum and pictured the equation from his test in his mind, ‘I’ve got to do this fast’ Owen thought. ‘I’ll just estimate 2π as 6, and that string is about 2 feet long, and …. damn, what was the value for g?... I know it has 3, 2, and 1 in that order’ Owen stared at the pendulum ‘Okay, 3.21 ft/s2 for g, 2/3.2 is the same as 20/32 which equals 5/8 or 0.625 that’s close to 0.64 and √0.64 is 0.8 and 0.8 x 6 is 4.8 seconds’
Owen wrote 5 seconds down on the slip of paper, figuring his low approximation for π meant he should round up, and handed it to the professor.
Outside the test room, other students were discussing the surprise contest at the end of the test. One student, Charles was working it out in detail out to 3 decimal places, and when Owen saw 2/32.1 under the radical, his heart fell as he realized his mistake, the gravitational constant was 32.1 not 3.21 . That meant that his answer was off by a factor of √10, over 3 times too large. Other than that factor, he had done surprisingly well, as his answer of 5 divided by √10 was 1.58 which was very close to the “exact” answer of 1.567 that Charles had just painstakingly computed by hand.
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Symbol confusion is what his father had called it. Owen would often mix up the order of letters or numbers in his mind. This affected his reading, spelling, and arithmetic as well. Owen had learned to cope with the problem, but he would often need to slow down or check his work to be sure that he didn’t make one of those mistakes. Misplacing a decimal point by one was a common mistake for him to make, mixing up whether it was before or after a particular digit.
The aide outside asked everyone to stay close by for the results of the contest, and since there were only 12 of them, the students didn’t have to wait much longer as, after Owen, there were only two more students who were still taking their tests.
It was difficult for Owen knowing that he had failed this particular test. He did not think that he would have won but he surely wanted to. The professor said "congratulations goes to James Harper with the guess of 1.55 seconds".
The professor took him aside and said “Do you know what your mistake was?”
“Yes I was off by the square root of 10 because I didn't remember what the gravitational constant was. I misplaced the decimal.”
“Please stay after class.” he said, “I wish to speak with you and two of the other students as it seems you each made the same mistake.” When the rest of the students were gone, he asked us all to confer with each other. It seems we had all made the same error in the decimal point.
The professor then proceeded to start the pendulum in motion. This time, the pendulum went much much slower, and Owen noticed that the estimate of 5 seconds was actually very close to the truth. He puzzled over what was going on, however the clock didn't lie. It was indeed five seconds for the pendulum to swing. ‘This was impossible’, thought Owen. The length of the pendulum hasn't increased, and changing the mass of the pendulum would have no effect on the period. Which only left that the gravitational constant itself must have changed. But you couldn't change the gravitational constant any more than you could change the mass of the Earth. Something very funny was going on here.
“I have kept you after class because you all seem to have the ability of insight. Since you have this ability you will have the opportunity to develop into prestidigitators and join the Galilean conspiracy, congratulations.”