Saturday, July 9, 2016

How Do You Measure?

          In ancient times, measurements were made using local standards which varied from one country to another depending on the person whose biometrics defined what the standard would be. In Egypt, a cubit was about the distance from the elbow to the fingertips. In some areas the width of a thumb was considered to be an inch. In the 14th century, King Edward II of England decided the official inch should equal the length of 3 grains of barley placed end to end. A foot closely approximated the 12 inches we now call a foot. A yard was determined by the distance from the tip of a different king’s nose to his thumb on his out-stretched hand. The height of horses was measured by the number of hand-widths from the hoof to the withers.
As commerce increased and expanded beyond a country’s borders, it became advisable to develop a system of weights and measures which would be the same regardless of the origin and destination. A pound or a foot or a gallon should be the same in country B as they are in country A. In the 1790’s, France recognized the value of uniformity and began developing what became the International System of Weights and Measures abbreviated “SI” units. (SI for the French Systeme Internationale.) They began with the meter for length and the kilogram for mass (weight). Ultimately the SI system established five additional standards: the second for time, the ampere for electric current, the kelvin for temperature, the mole for amount of a substance, and the candela for intensity of light.

Before the 1790's the framers of our Constitution recognized the value of regulating weight sand measures:
“The regulation of weights and measures is necessary for science, industry, and commerce. The importance of establishing uniform national standards was demonstrated by the drafters of the U.S. Constitution, who gave Congress in Article 1, Section 8, the power to "fix the Standard of Weights and Measures."
Until 2013, the United States of America shared the distinction with two other world powers, Liberia and Myanmar (formerly Burma), of resisting the adoption of the Metric System. We are one of the last holdouts. (In 2013, Myanmar began the transition.) Why have we resisted the change? Because we don’t like change. In 1866, Congress authorized the use of the metric system but our resistance for the past 150 years has resulted in only small steps in the metric direction.

With an early interest in the Sciences, the Metric System seemed almost natural after a very short time. For those unfamiliar, the internet offers many conversion tools but for easy daily use some units become so familiar that an official converter is not necessary. Weights: A Kilogram is equal to 2.2 pounds. A Pound is equal to 454 grams. An Ounce is 28 Grams. A Gallon is 3.8 liters. A Liter is 0.26 Gallons (that’s very close to a quart). These equivalents are quite satisfactory for everyday use. On the other hand, in a laboratory, measurements to several decimal places are absolutely crucial – micrograms, milliliters and so on. If you work in a lab, you already know that.

Two units of daily concern to most are miles per hour/kilometers per hour. Most vehicles now come with double numbering on the speedometer. Mph on top of the display, Kph underneath the display. Digital speedometers have a push button switch allowing the driver to switch to the applicable units. If a vehicle doesn’t have this luxury, two equivalencies are easy to remember: 100 kilometers per hour is the same as 62 miles per hour. The ratio is very close to the decimal equivalent for five-eighths which is 0.625. Kilometers per hour times 5/8 yields miles per hour. (Converting in the other direction is the inverse operation – eight-fifths or 1.6).

 The only other regularly occurring concern might be temperature readings. The United States and most of its territories remain the only ones to continue using the Fahrenheit scale (Named for Daniel Gabriel Fahrenheit, a German physicist) which marks the melting point of ice at 32 degrees and the boiling point of water at 212 degrees. The rest of the world since the end of the 20th century is using the Celsius scale (previously known as the centigrade scale until named for the Swedish astronomer Anders Celsius) which marks 0 degrees as the freezing point of water and 100 degrees as the boiling point of water. 

In daily life, how crucial is it to know the temperature to a precise number? Can you feel the difference between 72 F and 74 F? Or 33 F and 35 F? It’s funny that a 2 degree difference between Fahrenheit temperatures is about equal to a one degree difference in the Celsius temperature. The major difference is the starting point. Remembering a few equivalencies might make the transition easier.
Celsius degrees                        Fahrenheit degrees                 How they feel                     

Minus 10                                 Minus 14                                 Frigid
0                                              32                                            Freezing
10                                            50                                            Chilly
20                                            68                                            Comfy
30                                            86                                            Hot
40                                            104                                          Too hot
50                                            122                                          Danger

If you really have to exactly translate Celsius to Fahrenheit, an easy method is to multiply 
the Celsius temperature by two. Reduce that result by ten percent. Add 32 and you will have the Fahrenheit temperature. For example, 25 Celsius times two is 50, minus 5 is 45, plus 32, equals 77 Fahrenheit degrees. 

77 degrees. 

Now all you need is a bit of shade, a comfortable chair and a well made Margarita. 

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Tuesday, July 5, 2016

Rube Goldberg Meets William of Ockham

            New math; old math? I have no children and I am not in frequent contact with any parents of school-age children but with what I’ve seen about so-called Common Core math I see a parallel to Rube Goldberg (1883-1970) who created devices deliberately over-engineered to take 20 or more steps to accomplish a two-step task. Goldberg was an American cartoonist and inventor. His “cartoons” humorously described a complicated series of steps to achieve a very simple result. Just like the “New Math” in which I see no humor.
            Enter William of Ockham, an English friar, philosopher and theologian. Ockham (c. 1287-1347) is credited with developing a problem-solving principle which held, generally, that when there are multiple hypotheses, the one needing the fewest assumptions is likely the correct one. The fewer assumptions, the greater the likelihood of repeating the same result which is related to the empirical nature of The Scientific Method – testability and repeatability. This is the “Old Math”.
            Educators tout the value of Common Core as bringing to students a broader exposure, immediately, to the underlying principles of Mathematics. My bias will show when I say there’s absolutely nothing wrong with the old way. Even the best Forensic experts in any field learned their craft by starting with the basics progressing layer by layer to broader knowledge and understanding.
            Writers are advised to begin their stories in medias res (in the middle of things). In medias res is definitely not the best way to teach math. Even Euclid of Alexandria, the Greek mathematician regarded as the father of geometry, determined that a straight line is the shortest distance between two points. Start at the beginning point and progress to the next without swerving. To dapple in arithmetic, algebra and perhaps calculus, simultaneously, before mastering the basics seems ludicrous.
            I learned math the old way – arithmetic, geometry, algebra, trigonometry, logarithms, and calculus. I can solve most math problems easier than I can open pilfer-proof plastic packaging. I can see the product but I can’t get to it before employing tools and cutting myself on the sharp plastic edge.
            Sometimes an old dog’s old tricks are more valuable than the new tricks you’re trying to teach it.
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