This article of mine was published in The Malaysian Insider Oct 22, 2013. To read from the source click HERE
We are all familiar with Pi, the mathematical constant and its glorious treatment by scientists to the extent we have movies about it; the most famous one would be The Contact starring Jodie Foster. The movie was about Pi being the constant claimed to be understood universally even by the extraterrestrial. It was featured in the movie that, if the aliens want to communicate with us, they would send us the number 3.1416.....
But why is this? Why such claim? Why Pi is treated and accepted by scientists, mathematicians and engineers alike as so fundamental? These questions are what we about to answer.
To start with, Pi is the ratio of a circle's circumferential to its diameter. It is a constant having the value of 3.14 accurate up to two decimal places for all circles.
As a number, Pi is irrational thus has infinite decimals without any repeating pattern. This means, the decimal places will never end but weirdly though, there will be no repetition whatsoever in the occurring decimals. Meaning, there will be no repetition such as, Pi=3.14......676.......676.....676...infinity.
You got me?
So this Pi is but we also want to know why Pi is so fundamental, right? To know this, we must discuss the purpose of having the constant in the first place.
Well, if we want to talk about the purpose of Pi, we must hold to the concept that measurement only has meaning if it is referred to a point or frame of reference and usually this reference is a constant; a value that is applicable to all conditions.
In the context of a circle, Pi is the circle's property; a constant that is applicable to all circles regardless of size. Having established or accepted this constant, other properties of circle such as area, perimeter/circumferential and angle can now be defined based on this constant. Thus the reason why the area of a circle is given as Pi*r^2 and the perimeter as 2*Pi*r.
Accordingly, those entities that are circle-related such as the harmonic motion which can be described geometrically by the path of a circle can then be described using Pi, for example through Fourier series which components are An*sin(n*2*Pi*t/T) and Bn*cos(n*2*Pi*t/T).
I purposely mention Fourier series so that now we have at our disposal some mathematical expression (other than the circle) which can be used in answering question about the practicality of Pi such as "when Pi appears in physical use?"
For example, since the solution of the differential equation of a buckling strut can be given by a Fourier series, the buckling load of the strut is thus given as Pi^2*EI/L^2.
See the inclusion of Pi in the formula? This is an immediate demonstration of the use of Pi in physical problem beyond its use in just defining a circle's properties.
It is all come back to differential equation isn't?
This is an example of the building of mental construct which progress is built consecutively upon prior knowledge/concept.
The same mental construct (i.e the need for a "constant" frame to progress) is applied in other scientific arguments, for example, in Einstein's Special Relativity where the constant nature of light speed has been chosen as the point of reference for which other motions are relatively measured.
So it is the mental construct of science to:
1. First establish a constant which later to be taken as point/frame of reference
2. Define other entities relative to this point of reference
3. To apply the same mental construct to other problems hence its consecutive progress
(Point 3 in fact, highlights the limitation of science and human "brain").
This is why Pi is so "great". The mental construct that is built upon it what makes Pi so fundamental thus "great".
This is why it is claimed by those scientists that if the alien do exist, they would transmit this number so as to telling us their existence and that they comprehend the same universal laws.
We should not stop here as the understanding on the importance of a constant will increase our appreciation towards the standard way of scientific thinking, works and evolution. We have a glance at it already so we should say more so as to nail our understanding especially on the progressive building of a mental construct.
It would allow us to understand better, for example, why Newton's Law is insufficient. It turns out that, the insufficiency of Newton's Law is due the dependency of the law on space and time as the absolute (constant) entities resulting in the failure to describe the phenomenon of electromagnetism.
Extending the discussion would then increase our appreciation towards Einstein's theory who has resorted to the idea of taking the speed of light as the new constant (no longer space and time as in Newton's, in fact these entities change according to a transformation known as Lorentz's transformation) and solved Newton's deficiency.
And we should by now able to appreciate the search for TOE (Theory of Everything) as scientists believe that there should be a more fundamental constant than the speed of light that would define all physical phenomenons and omit the need to have separate laws for the macroscopic level (relativity) and microscopic level (quantum).
In other words, there should be (as they believe) a constant that will exist in all future mathematical statements, just like Pi appears in the circle's area formulation of Pi*r^2.
This is the example of the mental construct of math and science and if we look carefully, it is philosophical in nature, as philosophical as Immanuel Kant's, Friedrich Nietzsche's and others but with objectivity.
This is the reason why Stephen Hawking stated that "philosophy is dead". What he meant was, whilst a present scientist can understand the arguments of a philosopher, the latter cannot do the same to the former, on top of the latter's lack of objectivity.
Anyway, these are the mathematical and scientific mental constructs I emphasized in my previous articles, both in The Malaysian Insider, Let PPSMI be bygone but its spirit come alive in our universities (October 4) and NST (October 9).
And if someone ask me whether I can explain all these in Bahasa Malaysia, I will say yes but then remind him that this ability of mine only come after I read tens of English written textbooks. So it is a kind of chicken-egg condition. You see, what I wrote above cannot be found in a single writing or book but is a cross-reference from one book to another in providing relations, patterns and reasons; a mental construct. – October 22, 2013.
* Dr Airil Yasreen Mohd Yassin is a senior lecturer and computational mechanicist at the Faculty of Civil Engineering, UTM Johor Bahru.
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