This series of posts will have four parts. Part one will deal with definitions (needed for accuracy and precision) and an examination of Pi. Part two will look at our spherical universe and the fundamental units we have for measurements. Part three will consider how much is enough. And part four will look at how we measure ourselves as a community, both individually and collectively.
Accuracy and precision are tough terms to visualize or internalize. For example, the Merriam-Webster Dictionary defines precision as the quality or state of being precise. Really clear, isn’t it? Or is it simply not precise? Precision also is used to describe accuracy with witch a number can be represented in decimal places. From the same source, accuracy is freedom from mistake or error, conformity to truth, or to a standard or model, or degree of conformity of a measure to a standard or a true value. Simplify. Consider a target being shot at by a gun. If the bullets, bb’s, or darts all hit the target closely together, the gun is said to be precise. But if the cluster of bullets, bb’s, or darts is far from the bulls eye (or aim point), the gun is not accurate.
Closely related to accuracy and precision is randomness. In the context of this column, randomness or a random event is totally unpredictable. Consider a pair of “fair” dice, that is a pair of “perfect,” unbiased cubes with from one to six dots on each side. When they are tossed, the sum of the dots on the upper surfaces will be a number ranging from two through twelve. The possible outcomes can be calculated and a probability distribution defined. The roll of the dice, however, produces a random event within the defined possible numbers. Before the roll of the dice you cannot say with certainty what number will result.
A few years ago, my granddaughter, Chloe, had to do a science project in the fifth grade. She had a new laptop computer with the Basic programming language loaded. So I suggested she might want to determine the value of Pi using random numbers. After an extended blank stare, we finally got started. With some teaching of Pi being the ratio of the circumference of a circle to its diameter and programming a computer, Chloe wrote a simple program that used the computer’s random number generator. After using 200 million random numbers, the value of Pi was determined to be 3.14054898.
When I was a lad, I learned that the value of Pi was 3.1416 except when my mother was around. Then Pi was equal to 3.14159. Did it make a difference? For my interests at the time, probably not. If I needed a circle with a radius of three inches, I got a compass, adjusted it using an available ruler, drew the circle, and cut it out using a coping saw. Was it accurate? Probably not. Was it precise? Probably not. Did it do the job? Most of the time.
When I went away to college, I was issued Keuffel and Esser slide rule for use in my engineering courses. When carefully used, you could get an answer accurate to two decimal places. Was it precise? It depended on how well you used the slide rule. It was manufactured to a “high” degree of precision and two decimal place accuracy, but did you use it the night before or the morning after?
Returning to Pi, it is an irrational number, which means the number of digits beyond the decimal point go on forever. As an interesting side note, starting at the 762nd decimal point is a string of six consecutive nines, known in mathematical folk lore at the “Feynman point.” And, according to the BBC, Pi has now been calculated to 2 quadrillion digits. Yet according to Jorg Arndt and Christoph Haenel in Pi Unleashed, only 39 digits are needed to calculate the circumference of the universe to one atom. So how accurate do we have to be? Or should we be simply precise?
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