Math Can Be Surprising Useful, If We Don’t Let It Scare Us
January 22, 2018 at 3:11 p.m.
By Max [email protected]
My library at home is filled with books of all descriptions about the history of mathematics, the birth of numbers, the joy of numbers, statistics, biostatistics, the science of measurement, calculus, precalculus and numerous others. I also have DVDs from Great Courses on the History of Mathematics. Despite this vast collection, I remain confounded by the subject but more appreciative of it. I view it as a lingering challenge despite my advanced age, and I encourage all people young and old to become more familiar with all of benefits derived from being more numerate.
A good way to start is to read "Innumeracy," a book by John Allen Paulos. Parents should also encourage their children to consider a career in mathematics, whether it be teaching, science, engineering, statistics, quality control or annuities. There will always be opportunities for work in any of these fields.
I thought about math recently because of the train derailment in Washington state where there were a number of fatalities. When it occurred, I wondered what calculations had been used to establish speed limits for trains negotiating curves. It was not difficult of find.
Not surprisingly, a study at the University of Florida considered maximum velocity, railway track embankment, track curvature, centrifugal forces, friction and other factors to establish derailment speed. All of the various factors were determined using mathematical formulas and proved once again the ancient wisdom that “Mathematics is the way to understand the universe.”
Since the days of Galileo and Newton, math has nurtured science. Unfortunately, the United States is far behind other nations in mathematics and math teachers are in short supply. Studies have shown that American students score significantly lower than students worldwide in math achievement, ranking 25th among 34 countries. One reason may be that many of us agree with Dave Barry. Therefore, I have included a few examples where simple math can actually be surprisingly useful. They may even provide the incentive to learn more about the essentials.
Probability
Probability involves weighing up the chances or likelihood of something or another taking place. It can become full of surprises. The birthday problem is a famously counterintuitive result. If 50 random people are in a room, there is a 97 percent chance that at least two of them will have the same birthday. In this case it is easier to compute the probability that all the people have different birthdays, as follows:
365/366 X 364/366 X 363/366 …. X 319/366 X 318/366 X 317/366 = 0.03
The product of all the fractions is about 0.03. Thus, the probability that no two people have the same birthday is about 3 percent. Hence, the probability that at least two people do have the same birthday is about 97 percent.
A similar calculation using 23 people rather than 50 yields one-half, or 50 percent, as the probability that at least 2 of 23 people will have a common birthday.
Anyone who gambles should be acquainted with probability theory and the notion of independence. Two events are said to be independent when the occurrence of one of them does not make the occurrence of the other more or less probable. If one flips a coin twice, each flip is independent of the other. If one rolls a pair of dice, the top face of one die is independent of the top face of the other. Calculating the probability of two events occurring is easy to do — simply multiply their respective probabilities.
As an example, the probability of obtaining two heads in a row in a coin flip is 1/4 — 1/2 X 1/2. The probability of rolling a 2 (1,1) with a pair of dice is 1/36 — 1/6 x 1/6, while the probability of rolling a 7 is 6/36 since there are six mutually exclusive ways [(1,6), (2,5), (3,4), (4,3), (5,2) and (6,1)] in which the numbers on the faces can add up to 7, and each of these ways has the probability of 1/36 or 1/6 x 1/6. You can bet accordingly.
Finally, while writing this article I came across a new book with a quotation about mathematics worth repeating: “The laws of nature are written in the language of mathematics. Math is a way to describe reality and figure out how the world works, a universal language that has become the gold standard of truth. Hence those who are fluent in this new language will be on the cutting edge of progress.”
Max Sherman is a medical writer and pharmacist retired from the medical device industry. He has taught college courses on regulatory and compliance issues at Ivy Tech, Grace College and Butler University. Sherman has an unquenchable thirst for knowledge on all levels. Eclectic Science, the title of his column, will touch on famed doctors and scientists, human senses, aging, various diseases, and little-known facts about many species, including their contributions to scientific research. He can be reached by email at [email protected].
My library at home is filled with books of all descriptions about the history of mathematics, the birth of numbers, the joy of numbers, statistics, biostatistics, the science of measurement, calculus, precalculus and numerous others. I also have DVDs from Great Courses on the History of Mathematics. Despite this vast collection, I remain confounded by the subject but more appreciative of it. I view it as a lingering challenge despite my advanced age, and I encourage all people young and old to become more familiar with all of benefits derived from being more numerate.
A good way to start is to read "Innumeracy," a book by John Allen Paulos. Parents should also encourage their children to consider a career in mathematics, whether it be teaching, science, engineering, statistics, quality control or annuities. There will always be opportunities for work in any of these fields.
I thought about math recently because of the train derailment in Washington state where there were a number of fatalities. When it occurred, I wondered what calculations had been used to establish speed limits for trains negotiating curves. It was not difficult of find.
Not surprisingly, a study at the University of Florida considered maximum velocity, railway track embankment, track curvature, centrifugal forces, friction and other factors to establish derailment speed. All of the various factors were determined using mathematical formulas and proved once again the ancient wisdom that “Mathematics is the way to understand the universe.”
Since the days of Galileo and Newton, math has nurtured science. Unfortunately, the United States is far behind other nations in mathematics and math teachers are in short supply. Studies have shown that American students score significantly lower than students worldwide in math achievement, ranking 25th among 34 countries. One reason may be that many of us agree with Dave Barry. Therefore, I have included a few examples where simple math can actually be surprisingly useful. They may even provide the incentive to learn more about the essentials.
Probability
Probability involves weighing up the chances or likelihood of something or another taking place. It can become full of surprises. The birthday problem is a famously counterintuitive result. If 50 random people are in a room, there is a 97 percent chance that at least two of them will have the same birthday. In this case it is easier to compute the probability that all the people have different birthdays, as follows:
365/366 X 364/366 X 363/366 …. X 319/366 X 318/366 X 317/366 = 0.03
The product of all the fractions is about 0.03. Thus, the probability that no two people have the same birthday is about 3 percent. Hence, the probability that at least two people do have the same birthday is about 97 percent.
A similar calculation using 23 people rather than 50 yields one-half, or 50 percent, as the probability that at least 2 of 23 people will have a common birthday.
Anyone who gambles should be acquainted with probability theory and the notion of independence. Two events are said to be independent when the occurrence of one of them does not make the occurrence of the other more or less probable. If one flips a coin twice, each flip is independent of the other. If one rolls a pair of dice, the top face of one die is independent of the top face of the other. Calculating the probability of two events occurring is easy to do — simply multiply their respective probabilities.
As an example, the probability of obtaining two heads in a row in a coin flip is 1/4 — 1/2 X 1/2. The probability of rolling a 2 (1,1) with a pair of dice is 1/36 — 1/6 x 1/6, while the probability of rolling a 7 is 6/36 since there are six mutually exclusive ways [(1,6), (2,5), (3,4), (4,3), (5,2) and (6,1)] in which the numbers on the faces can add up to 7, and each of these ways has the probability of 1/36 or 1/6 x 1/6. You can bet accordingly.
Finally, while writing this article I came across a new book with a quotation about mathematics worth repeating: “The laws of nature are written in the language of mathematics. Math is a way to describe reality and figure out how the world works, a universal language that has become the gold standard of truth. Hence those who are fluent in this new language will be on the cutting edge of progress.”
Max Sherman is a medical writer and pharmacist retired from the medical device industry. He has taught college courses on regulatory and compliance issues at Ivy Tech, Grace College and Butler University. Sherman has an unquenchable thirst for knowledge on all levels. Eclectic Science, the title of his column, will touch on famed doctors and scientists, human senses, aging, various diseases, and little-known facts about many species, including their contributions to scientific research. He can be reached by email at [email protected].
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