Understanding Measurement

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Many Properties Can be Measured

The world and the objects around us have many common properties. Some of the obvious ones are shape, size, weight, volume, duration & length. Humans used these properties, among other things, to identify, trade and barter. They bartered goods on the basis of quality, shape, size and weight. They also realized that it would be advantageous to convert these properties into numbers. The science of measurement developed from these ideas.

One of the earliest property to be measured must have been the passage of time in terms of days & years. Humans measured time with reference to the Moon & Sun.

Measurement of Physical Dimensions

The three basic physical dimensions are length, area and volume. These correspond to space occupied by physical objects in one, two & three dimensional space.

Each of these dimensions are independent of one another. None of the can be reduced to any of the other two.

But how come we get area by multiplying 2 linear dimensions and volume by multiplying 3 linear dimensions. This has been made possible by choosing appropriate measuring units.

The unit of length is the basic unit, which is defined as 1cm.

The unit of area has been defined in terms of a "square" whose sides equal the basic unit of length. The unit of volume has been defined in terms of a "cube" whose sides equal the basic unit of length.

Through this definition the area in "square units" can be got by a product of two linear lengths. Similarly the definition if volume in "cubic units" can be got by a product of three linear lengths.

Precision & Accuracy

Only counting can yield an exact result. Measurements can never be "exact". There is always an error involved in the measurement.

These are two terms associated with any measurement - Accuracy & Precision

Accuracy is how close a measurement is to the true or accepted value. Precision is how close several measurements of the same entity are to one another.

Suppose we measure the weight of a student several times using a weighing machine. We know that the student weighs around 40 kgs.

Suppose the machine shows readings from 39.00 to 41.00 kg. Then we can say that the machine is accurate. Accuracy is how close the readings are to the true, here, the 40kg mark. But it is not precise.

Suppose all the measurements show a reading from 35.50 to 35.60kg. Then the weighing machine is precise. But all the readings are differ from 40 kg. Hence it is not accurate.

A good measuring instrument should both be precise as well as accurate.

Measurements Need a Number System

The development of measurements must have preceded and propelled the development of number systems. Counting was possibly the first measuring activity, possibly to get an estimate of their material possessions or to keep track of the passage of days.

Measurement Depends on Multiplicative Thinking

Measurement also depends on the idea of multiplicative thinking (Refer Chapter 18.4 & 18.5). To convert a property into numbers, a standard unit measure had to be adopted. The Kilogram for weight, Meter for length, Degrees for temperature are some examples of unit measures.

If we know the length of one meter, then the distance between 2 points can be expressed as a certain multiple number of meters. The number system gives us different types of numbers, like fractions &amp; decimals, to accurately express this distance.

Qualities Needed of Measuring Units

Further, any unit of measurement should be easily constructible as well as reliable. The unit should be such that it can be constructed anywhere using certain procedures.

The unit should also be reliable so that the numbers which result from the measurement are correct and easily verifiable. A weighing stone of 1 kg should be easily be "makeable" or available at all places and its weight should also be same as the standard.

Brief History of Measurement

The basic measurements that humans required were for discrete quantities, money, time, length, volume &amp; weight. Initially the units for all these measurements depended on events &amp; activities that humans could relate to.

Counting possibly developed to get a measure of discrete quantities. Time was based on the movements of the Moon &amp; the Sun. Length was based on the steps taken while walking. Volume depended on certain locally available standard sized containers and weight on certain stones. In the initial stages, groups of humans developed their own units as per their need and experience.

Slowly as groups got interlinked through trade &amp; social transactions, they evolved common units of measurement. Units also spread through wars for conquest of land & labor. The units used by the winners in their country were imposed on the conquered countries. Slowly units which were valid all over wider and wider areas were developed. Today we have units which have been adopted throughout the world.

The history of the development of various units of measurement is an interesting story of the problems faced by humans and their ingenuity in developing solutions to these challenges.

It is due to the development of accurate units of measurement that today design & manufacture of any product can be done in multiple locations and still adhere to single quality standard.

Some properties like temperature & speed became measurable with the advancement of science & technology.

Imperial System

The first documented efforts to develop measuring units started in England in the 12th century.

King Henry I of England fixed the yard as the distance from his nose to the thumb of his out-stretched arm and the inch as the distance between knuckles on his index finger. He also decreed that his foot would become the unit of measuring length. Hence they were called Imperial Units.

Confusion in Measuring Units can be Expensive

NASA's Mars Climate Orbiter

Confusion in the measuring systems caused a costly mistake of $ 125 million! And that too in the 20th century!!

In 1999, NASA’s Mars Climate Orbiter was lost in space due to a miscommunication between two teams working on the project. The engineers who made the orbiter used English linear units while the NASA controllers thought they were in the metric system! This caused the orbiter to fly too close to the planet and ultimately burn up in the atmosphere.

The Hubble Space Telescope

When the Hubble Space Telescope was launched in 1990, it was discovered that the telescope’s primary mirror had a flaw that caused the images to be blurry. The problem was traced back to a miscommunication between the telescope’s designers and manufacturers, who used different measurement units when building the mirror.

This mistake could have been avoided if the communication had been clearer and more consistent

All things cannot be measured

We must also remember that there are many properties which we value that cannot be measured. Some examples are beauty, taste etc.

We will now see the history of development of some of these units briefly.

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