Fractal dimension, effective mass and Tamil grammar: at first, the three things look very odd. Hey, what connects the three? In the following I ll try to justify as possible as I can.
Fractal dimension: We know the dimension of a line is one, that of surface is two and that of volume is three. Can we imagine a dimension of 2.4?. At first, it seems meaningless. But, there are systems carrying non integer values. Indeed, those systems are majority! They are called fractals. A fractal is a rough or fragmented geometric shape which can be subdivided in parts, each of which is reduced size copy of the whole [1] i.e. it has the property of self similarity.
In terms of Euclidean geometry, the dimension of fractal surface is two. But it is not a simple surface like a plane. It possesses self similarity. So, to include the self similarity property, mathematically the dimension is modified. Infact, now fractal dimension become more general and Euclidean dimension is now become a subset (special case) of fractal dimension!
Effective mass: In a crystal lattice in the presence of external electric field, the motion of electrons is very complex as the electrons have to face frequently the lattice ions. Because of this, at some regions the velocity of electrons is high and some regions it is less. To explain this complexity, the entire burden is put on the mass of electron! When the electrons move faster inside the lattice, it is assumed that the mass is reduced and when they move slow it is assumed that the mass is increased. But in reality, the mass of electron has not changed at all. We know that there is no scope for the mass of electron to increase as there is no relativistic speed associated with it. But in order to explain the complexity, it is assumed that electron mass changes!
In Tamil grammar: One type of tamil rhetorics, there is an usage. The poet can portrait his own thought to a naturally occurring event. That is called “thar kurippetra ani”. For eg let us take 5th century Tamil epic Silappadikaram. Kovalan and Kannaki are husband and wife. They travelled from Kaveripoompattinam to Madurai. After reaching Madurai, both the couple suffered a lot and finally Kovalan was killed. The poet wanted to indicate this to the readers during their arrival to Madurai. For that, he had taken the waving of flags.
When the couple was travelling towards Madurai, the flags on the top of the fort wall waved because of wind. Here, the poet interpreted that the flags waved in such a way that they warned the couple not to enter Madurai! The poet tries to interpret that the flags foreseen the bad things and expressed them not to enter Madurai.
The basic theme is the same. To a naturally occurring event/property, the existing parameters are altered/interpreted to include that property/event. In the first case there is a need to include self similarity, in the second case, one need to include distribution of speed of electrons and in the third case to interpret the future, the waving of flags is used as a signal.
Finally, another interesting feature is buried in these arguments. The first one happens in Real space, the second one in Fourier space (K-space) and the third one in poet’s Imaginary space!
[1] http://www.math.nus.edu.sg/aslaksen/gem-projects/maa/World_of_Fractal.pdf