Science and Common sense

by Nikolai V. Shokhirev

Contents

• What is scientist?
• What is science?
• Measurements
• Examples
• More Examples

Up (Popular science) 
Previous (Crazy scientist, Common sense, Science is a refined common sense, Back to crazy scientist)
    Science is measurement, Great Discovery, How to make the right angle, From Alchemy to Chemistry, Science is purified and extended measurement
Next (Measurements: Everyday measurements, Direct and indirect measurements, Incomplete measurements, How to fool customers, How to handle indirect measurements)

Science is measurement 

Currently science is a very complex phenomenon. There are many definitions of science. Some of them are very broad, the other are specific. Trying to keep things simple, the essence of all the definitions is: science is a measurement. 

The seven stages of research in the previous section can be combined into three major stages: 

Notion of measurement

Starting with Ancient Egyptians, Babylonians, Indians and Greeks, the necessity of the second stage in solving problems was understood. Performing actual measurements is usually not an easy task. However, the most fundamental scientific result is the introduction of the notion of measurement. From then on, it was considered unacceptable to make up a conclusion without  measurements (direct ones or derived from previously established facts). Without this notion there is no science. This give us a reason to say that science is measurement. 

Examples

The oldest science is mathematics. It began with the measurement of the quantity of objects or counting (one, two, many). Later it developed into arithmetic and then calculus. 

Another old branch of mathematics is geometry. This Greek word (γεωμετρία) literally means "land measurement". 

Greatest discovery

Pythagoras's theorem is one of the great scientific discoveries of mankind. It is know from the work of the famous Greek mathematician Pythagoras of Samos (Born: about 569 BC in Samos, Ionia; Died: about 475 BC). However, the theorem itself was discovered much earlier probably in the Old Babylonian Empire, which flourished in Mesopotamia (modern Iraq) between 1900 BC and 1600 BC (http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Babylonian_Pythagoras.html). 

A translation of a Babylonian tablet which is preserved in The British Museum goes as follows:

4 is the length and 5 the diagonal. What is the breadth ?
Its size is not known.
4 times 4 is 16.
5 times 5 is 25.
You take 16 from 25 and there remains 9.
What times what shall I take in order to get 9 ?
3 times 3 is 9.
3 is the breadth.

in the modern mathematical notation it is  .

This theorem also was a great technological tool widely used in the ancient civilizations.

How to make the right angle

This theorem allows us to make a 90° angle using only a rope and a stick. 

1. Take a rope and a stick so that the rope is longer than 12 sticks
2. Using the stick for control, tie 12 equidistant knots
3. Tie the ends to make a loop
4. Make the triangle with the sides 3, 4 and 5
5. This is the right-angled triangle:

a rope and a stick	right-angled triangle

Now you can start building a pyramid, a temple, a palace or just a house.

This methods provides us with a mathematically exact 90° angle. Of course, the actual accuracy depends on the implementation.

From Alchemy to Chemistry

Chemistry is another interesting example. For a long time, it was a sort of art or magic in Ancient Egypt and Babylon, and later in Europe. At that time, it was called Alchemy. 

It became a science when the precise measurement methods were developed (for measuring mass, volume and temperature). To distinguish from the pre-scientific Alchemy, the name of the new science was changed to Chemistry. 

Science is a purified and extended measurement

In fact, science is something bigger than just measurement. Measurement and Science are in a relation similar to the relation of Common sense and Science: Science is a purified and extended measurement.

Extended measurements are concepts based on the primary measurements. For example, the first level of abstraction for ordinary counting are the natural numbers (1, 2, 3, . . ). The higher levels are fractions, negative numbers (abstraction of debts), zero, complex numbers, irrational numbers and infinitely small and infinitely large numbers in increasing order of abstraction level. The concepts of the higher level extend the lower level abstractions and they are all ultimately based on a simple counting.

Measurements summary

Scientists must be very experienced with measurements. What is actually known about the measurements? Here is a short summary.

• Measurements require units of measures (otherwise a measurement is pretty much useless)
• Measurements always have errors (nothing and nobody is perfect)
• Any particular tool or instrument has a limited interval of measurement (e.g. an ear cannot hear very low or very high sounds) 
• Usually the measurements are incomplete (a single measurement cannot give all properties of a complex system)
• Usually the measurements are indirect (the properties of interest are estimated from the properties that can be measured)
• The indirect measurements have additional processing error

To minimize these problems one should:

• Develop standards for the units of measurement 
• Get the correct estimation for errors (this is very important:: making measurements without knowing their accuracy makes no sense)
• Use tools with different measurement intervals (e.g. different kinds of spectroscopy)
• Use complementary measurements
• Since indirect measurements are usually incomplete and require additional processing, treat them accordingly.
• Get the correct estimation of the accuracy and resolution of the processing procedure 

All this can be applied to our everyday life. This will be considered in more detail in the next section.

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ŠNikolai V. Shokhirev, 2002-2005