1. Measurement ©2013 Robert Chuckrow

2. Low-Level Estimation Do we have too little? Do we have enough? Do we have more than enough?

3. Making a One-to-One Correspondence Using a vine or stick of the same length as the object in question.

4. Laying off Smaller Units and Counting them or Fractions Thereof Use of body parts Cubit = distance from elbow to tip of middle finger (standardized to 18.24").Cubit = distance from elbow to tip of middle finger (standardized to 18.24"). Span = distance from thumb to last finger of outstretched hand (9").Span = distance from thumb to last finger of outstretched hand (9"). Palm = width of four fingers (3").Palm = width of four fingers (3"). Digit = width of middle finger (3/4").Digit = width of middle finger (3/4"). “Foot” = length of the foot (12.16").“Foot” = length of the foot (12.16"). “Inch” = width of the thumb at the nail root (1/12 of a foot).“Inch” = width of the thumb at the nail root (1/12 of a foot). Fathom = distance from fingertip to fingertip of outstretched arms (6').Fathom = distance from fingertip to fingertip of outstretched arms (6'). Half Fathom = distance from nose to thumb of outstretched arm (1 yard).Half Fathom = distance from nose to thumb of outstretched arm (1 yard). The Shaftment = length of fist with thumb protruding (6").The Shaftment = length of fist with thumb protruding (6"). Nail = length of forefinger from tip to second joint (standardized to 1/16 yard = 2.25").Nail = length of forefinger from tip to second joint (standardized to 1/16 yard = 2.25").

5. Systems of Measurement English System (based on halves, quarters, eighths, etc.). Examples are length: inches, feet (standard), yards; volume: ounces, pints, quarts, gallons; weight: ounces, pounds; and temperature: degrees Fahrenheit. Even today, inches are divided up into halves, quarters, eights, sixteenths, and so on. Metric System (based on tenths). Examples are length: millimeters, centimeters, meters (standard), kilometers; volume: milliliters, liters; mass: grams, kilograms; and temperature degrees centigrade.

6. Advantages of the Fractional System Dividing things in 1/2, 1/4, 1/8, etc., is very easy to do. Fractions of amounts are more convenient for human needs. For example, milk comes in the following size containers: 1 gallon, 1/2 gallon, quart (1/4 gallon), pint (1/8 gallon), and 1/2 pint (1/16 gallon).

7. Disadvantages of the Fractional System A measurement consisting of the fractions one-half plus one eighth plus one thirty-second is quite inconvenient to add and then express as single number.

8. Advantages of the Metric System By comparison, expressing a measurement using a system using divisions of ten (metric system) is easy. For example, one-tenth plus three hundredths plus 7 thousandths equals 0.137.

9. Disadvantages of the Metric System The metric system is awkward for human needs. If, for example, milk containers were sized according to a metric breakdown, there would be 10-liter, 1-liter, and 1/10-liter sizes. Few families would find such sizes convenient.

10. The Best of Both Worlds U.S. currency comes in $100, $10, $1, 10¢, and 1¢ (metric breakdown). Interestingly, U.S. currency also comes in $50 (half of $100), $20 (twice $10), $5 (half of $10), 50¢ (half of $1), 25¢ (half of 50¢), and 5¢ (half of 10¢) (fractional breakdown).

11. Questions What are the advantages and disadvantages of using body parts for measurement? What are the relative advantages and disadvantages of the two main systems, English and metric, (a) for human needs and (b) for scientific work?