Story of Measurement 1

Counting

One of the earliest inventions were numbers which helped compare collections of discrete objects. Initially each group may have had its own system of counting.

The words calculus comes from “calculi” which mean pebbles in Roman. In English, pebbles were called counters.

Time

The measurement of time is intimately involved with the history of humans. We would deal with this in detail in the next chapter.

Temperature

Feeling change temperatures is one of the universal & early experiences of humans. But it has been a very difficult entity to measure.

Until 3 centuries ago, the measurement of temperature was very crude and qualitative. It was only in the 18th century that thermometers could be accurately calibrated.

The modern invention of the unit of measurement of temperature depends on the physical fact that pure water freezes of boils anywhere in the world (at the same altitude/ atmospheric pressure) at the same temperature. The freezing temperature of pure water at sea level was taken as 0 and the boiling temperature was taken as 100. These are purely arbitrary numbers given keeping the decimal number system in mind. The unit was called Degrees Centigrade, the name referring to its relation with the decimal system.

Another unit to measure temperature unit had been developed earlier, to measure the temperature of the human body called Fahrenheit.

Temperature is also the only physical entity which has a zero value, in the real sense. Absolute zero is the lowest possible temperature a physical body can have. It is a "hypothetical" temperature at which the thermal motion of the particles stops completely. Hypothetical because such a temperature is unattainable physically.

Absolute zero is the start of the measure of temperature called Kelvin. In the degrees Celsius we are used to, this temperature is -273.15 degrees.

Length

Various civilizations developed various measures of length related dimensions of body-parts and speeds of walking and riding on animals. The name "foot" & "cubit" are reminders of this relation.

In the 19thcentury, most countries decided to accept the meter as a unit for length. A meter was defined as a fraction of the distance between the pole and the equator. The circumference of the Earth was assumed to be 40000 km.

There are a few things the teacher needs to keep in mind while teaching linear measurements.

Distance measured with a ruler

Students need to realise that the distance between two points is actually the "total of the number of spaces on the ruler between the readings". Keeping the 0 mark of the ruler at the starting point of the distance just makes the "difference/ distance" easy to calculate because one of the values is 0.

This concept can be tested with the idea of measuring with a "broken ruler".

Distance on the road

Students also need to realise that this can cause 2 variations in problems involving travel along routes with km stones.

The distance covered is always the difference between the "starting reading & the "ending reading".

But if the problem asks for the number of km stones crossed from the starting point & the ending point, they need to add 1 to the distance answer. A distance of 5 km will have 6 km stones including the one at the starting point.

Stellar Distances

Today astronomy has advanced tremendously. But the human brain, used to terrestrial distances, finds it difficult to comprehend the mind-boggling distances in the universe, even the shortest such distance; from the Earth to the Moon.

Area

Area was initially defined possibly in terms of a land measure related to ploughing.

Initially are was seen as an independent idea. Terms like "ground" & "acre" are remnants of this idea. It was only later that area was seen as an extension of length. The unit of area was taken as the area of a square with its side being a unit of length.

The square shape was probably chosen because it could be drawn given just one dimension; that of the side. Any 2-dimensional surface has only 2 directions which can be called up/ down, left/ right etc. Squares provide these 2 directions and only these directions. It is a shape which can be replicated anywhere very easily.

Square is also a shape which tessellates any area without leaving any gaps. Hence a definitive answer can be got for any area.

Any polygon could be divided into triangles, which in turn can be converted to rectangles of the same area and the rectangles could be expressed in terms of unit squares. It was natural to call the area units in terms of "squared" & SqCm, SqM etc. We will see more about measuring areas in the section on mensuration.

Volume

Volume was possibly defined in terms of the quantity of water which a normal person could drink. Terms like Pint & Gallon possibly came out of this understanding.

Later the definition of volume was seen as a natural extension of the measurement of area. The unit of volume was taken as the volume of a cube whose side is one unit of length. The unit of volume was a Cubic Mt which is a cube with 1m edges. They were subdivided into Cubic Cms.

Since a cubic mt was too large a volume for daily transactions, the common unit of volume was a Litre. A litre was equal to 1000 cubic cms. A cubic mt was equal to 1000 litres. A cubic cm was a milli litre.

Volume & Capacity

In our daily life we also need to differentiate between volume and capacity. Volume is that of the material out of which an object is made. Capacity refers to the volume of solids or liquids that an object can hold.

For example, a cylinder made of solid iron cannot be used as a container. Hence it has volume but no capacity.

But a hollow cylinder has volume and also has the capacity to hold a liquid. Its capacity is nearly equal to the total volume of the cylinder. But in most cases the term volume is used to denote capacity. For example, a math problem may just ask for calculation of the volume of a cylinder. The exact meaning has to be understood from the context of the problem.