Science and Engineering

Science and engineering disciplines are characterized by their objective studies of the material universe.  An objective study,  in contrast to a subjective one, is a study whose premises, methods, and particularly results are independent of the mood, beliefs,  taste, and other dispositions of the  subject conducting it. (Do not take this to mean that no errors are made in science). In  science and engineering, the ultimate judge of what is true or correct is not  an individual scientist  or engineer, but rather the physical reality, its dynamics and laws.  Indeed, we accept as scientific fact, theory, or process that which has been  proven, established, or verified using premises and methods accepted by the scientific community!  Note well that this means that science and engineering are evolving; they are  getting closer and closer to a deeper understanding of the physical or material realities or processes. In general, a scientific fact or theory is not accepted if it does not "agree" with physical reality or phenomena.  For instance, the physics law of gravity is well accepted because scientists conducted several experiments in which the law was proven to agree with physical reality or process of attraction between any two masses.

Distinction between science and engineering disciplines, on one hand, as compared to Arts, Humanities, Philosophy, and others, on the other, hinges in part on the following.
 

a) Scientific facts, theories, and findings are expressed by using quantities, definitions, principles, laws, and methods that are objective.

b) Experiments and measurements are made, using proven methods, to test the validity or correctness of scientific facts , laws, or theories.

From b. above note well that a hallmark of science and engineering is the fact that theory and experiment support and check on one another.

Measurements and Experiments

To measure a scientific quantity like time, mass, area, weight, etc. is to compare it to another.  If the same quantity is measured by several scientists and engineers at different places and different times, they may find different results unless they compare the quantity to be measured to the same reference!  The yard stick is one such reference for the measurement of the length of objects.  The meter stick is another reference more widely used for the measurement of length. A length in yards can be converted to meters and vice versa.  Properly working clocks constitute a reference for the measurement of  the time elapsed between two events.

Experiments are simple or elaborate set-up and processes utilized to measure, directly or indirectly, physical quantities. Properly run experiments give results that characterize the physical reality or processes under study.  We noted above that experiment and theory check on and support one another.  In general, a theory is a coherent set of propositions (definitions, postulates,principles, laws, etc.) that a) explains some physical phenomena and b) correctly predicts others. While experiments measure physical quantities, theory general establish some mathematical relations between scientifically well defined quantities.  One can therefore see how experiment and theory check on and support one another.
 

A theory  says: weight = mass x acceleration of gravity. Experiment  measures  weight, mass, and acceleration of gravity of a person   at a given point.  If the product of the measured mass by the measured value   of the acceleration of gravity equals the measured weight, then experiment   agrees with this theory.

The selection of the references needed in the section above is the subject addressed below. Indeed, there are hundreds of physical quantities. Do we define a  reference  of  the measurement of each one of them or not? The scientific community said no, we do not.  The reasons for this answer were simple: the area (S) of a rectangle is the product of its length (a)  by its height or width (b),  S=ab. So, we do not need a reference for length and one for area. Once we have the reference for length, then we can always measure surfaces by using length multiplied by length.  Similarly, if we decide to define a reference for area, then we can measure length by using the square root of area.  In conclusion, we only need to select a small number of physical quantities for which a reference - called a standard - must be defined.  These quantities are referred to as base quantities.  A base quantity is one for which a standard of measurement  is defined.  A standard of measurement is in general an object or a phenomenon. Unit of measurement, defined by using a standard of measurement, are called base units. A base unit is a measure of a property of a standard of measurement.

From the above paragraph, it is clear that a standard of measurement is not a unit. It is also clear that a base unit is a measure of a property of a standard.  This is made particularly clear by the following example.

Mass is one of the few base quantities in many systems of measurement. The standard of measurement for mass, in the International System of Units, is a platinum-iridium cylinder in  the  Pavilion of Weights and Measures in a town near Paris, France.  The base unit of mass used to be defined as the mass of that cylinder.  What property of this standard served to define the base unit of mass?  Answer: its mass. We did not used its height or volume.

In the above example, the standard of measurement was an object. The standard of measurement for time, another base quantity in the International System of Units (SI), is the cyclic or periodic emission of a particular radiation (light - not necessarily visible) by  a particular atom of cesium (Cs). In this case, the standard is a phenomenon.  The base unit of time, in SI units, is the measure of the duration of  a cycle of the selected emission of a particular isotope of the cesium atom.  (The nuclei of two isotopes of an element have  the same number of protons and different numbers of neutrons).

We answer below the question relative to the number of base quantities. We also illustrate additional standards of measurement and the related base units.  What needs to be clearly learned about a standard, in addition to the above points, is that
 

a) A standard must be invariable, constant.

b) A standard ( or a very good representation of it) must be accessible.

Systems of Units

A system of unit is defined when

a) a (complete and) coherent set of base quantities has been selected ,

b) a standard has been selected for each one of these base quantities, and

c) a base unit has been defined, from these standards, for each base quantity.

The International System of Units (SI)

In 1971,  the 14th General (and International)  Conference on Weights and Measurements selected seven (7) quantities as the base quantities in the International System of Units .   These base quantities, along with the base units and their symbols are listed below. The International System of Units is complete, i.e., using its seven (7) base units, we can express any of the currently known scientific quantities. This is accomplished by using laws and formulas to derive the units for quantities that are not base quantities.  For instance, the derived unit of area is meter multiplied by meter, i.e. m^2.  The derived unit of volume is m^3.
 

Meter-  "....the length of the path traveled by light in vacuum in of a second" shall define the meter (1983).

Kilogram-  "....the mass of this prototype [a certain platinum-iridium cylinder] shall henceforth be considered to be the unit of mass." (1889)

Second-  "....the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom."(1967)

Ampere-  "....the constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and
placed 1 meter apart in vacuum, would produce between these conductors a force equal to  Newton per meter of length." (1946)

Kelvin-  "....the fraction  of the thermodynamic temperature of the triple point of water." (1967)

Mole-  "....the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12." (1971)

Candela-  "....the luminous intensity, in the perpendicular direction, of a surface of 1/600000 square meter of a blackbody at the temperature of freezing platinum under a pressure of  101,325 Newton per square meter."  (1967)

Some derived SI units are listed in the table below.  One is not expected to memorized these units.  One is rather expected to understand and learn the definitions, principles, and basic laws of physics and of other science and engineering as one meets them.  From them one can instantly derive a needed unit. For instance, a key law of physics (mechanics) says that the sum of the external forces acting on an object is equal to the time rate of change of the linear momentum of that object. From this Newton's Second  Law and related definitions, one can derive the SI unit for force, i.e. kg.m/s2.  This unit is called the Newton (N) in honor of Sir Isaac Newton who discovered the above law of motion. Similarly, we can get the SI unit for the gravitational constant G.  According to the law of universal gravitation,

and G = (force x length x length)/(mass x mass) , the unit of force is kg*m/s^2 ,that of length is m, and that of mass is kg.  The SI unit for the gravitational constant G is therefore m^3/s^2*kg.
 

Quantity	Definition Formula	Name of Derived Unit	Symbol	In terms of Base Unit
area	A = x*x	meter-squared	m^2	m^2
volume	V = A*x	cubic meter	m^3	m^3
speed		meter per second
acceleration		meter per second squared
force		newton	N
pressure		pascal
work or energy		joule
power		watt
mass density		kilogram per cubic meter

As noted above, there potentially exist an infinite number of systems of units. We defined a system of units called the Lower Canonical System of Units (LCSU) by selecting as base quantities and as standards the same ones that are used by the International system. But, We defined our base units to be the base SI units divided by the golden ratio that is equal to 1.618.  Hence, to find the length  of an object is LCSU units one has to multiply its length in meter by 1.618, given that 1 LCSU unit of length equals 1m/1.618.  We similarly defined the Upper Canonical System of Units  where the base units are those of the International system multiplied by 1.618.

1 unit of length in UCSU= 1m x 1.618.

In particular, the MKS units is extensively used in mechanics. MKS stands for Meter, Kilogram, and Second.  Please look at the above table of derived units in the International System to understand that m, kg, and s are enough to express numerous mechanical quantities.  Note, however, that the original MKS system was not a complete system.  One could not express quantity of substance (in units of moles in SI),  luminous intensity (in units of candelas in SI), or electric current (in units of Amperes in SI) used only MKS. MKS is very often taken nowdays to be synonymous with SI.

Another mechanical system that was popular in the past was the CGS system. CGS stands for Centimeter, Gram, and Second.   In this system, the unit of length is the centimeter, those  of mass and of time are respectively the gram and the second.  Unlike the MKS system, the CGS system cannot be synonymous with SI.  Because its units of length and of mass are not those of the SI system.

Consult encyclopedia,  handbooks, and CD-ROMs to read about other systems of units.  In particular, we need you to find out the system of units in which lengths are measured in feet, masses in slugs, and forces in pounds!  Caution: be very careful with the word pound.  In the supermarket, you are essentially using it as a unit of mass. In most textbooks, however, pound is a unit of force not of mass!
 

Unit Conversion

Unit conversions are extremely common in science and engineering. This partly explain the reason that several systems of units are currently in use. Whenever quantities are needed in a given system of units in which they have not been measured, one simply finds a system of units in which they have been measured and convert them to the units one wants.  Note well, however, that most scientific journals and many publishers of serious scientific books require that quantities be expressed in the International System of Units (SI).   Metric System is another named of the International System of Units (SI).