Friday, December 30, 2011
Lt. General Satish Nambiar
THE BANGALORE CANTONMENT
I see a particular part of Bangalore and find it quite different if not special from the many other parts,the large area of land around the Ulsoor lake. The view of this lake cannot but help me make various presumptions and according to me the heart of Bangalore city is this lake. Adjacent to the Ulsoor lake is a rock and a temple which I have not visited but appears to me very historically significant. Kempe Gowda must have been drawn to this rock and set up some kind of a tower there and when upon this rock a breath taking view of the surroundings were possible. The lake and the rock combined must have been some sort of an abode for various communities since time immemorial. There is a similar rock inside lalbagh and i have seen one more at hebbal. These rocks are sacrosanct and possibly provided refuge from enemies and acted as a watch tower to identify invaders.Bangalore city needs to reinvent its roots and in these structures ly embedded the past in various forms.
When the British take control of India I think the MEG or what is called the Madras Engineering Group find the ulsoor lake ideal for providing aquatic training of various kinds to its recruits as such military training begins to become more and more relevant for the british troops and there could be no other place than the Ulsoor lake. Ulsoor must have been the anglicised version of Halasuru and Halasu must be some vegetable or fruit in the colloquial. Note that troops of various kinds were probably routed to this point for training there by ceating military outfits and residenes and laying for ever the foundation for the "Bangalore Cantonement"..how logical , crucial and eternal. What must have looked worse than a hamlet becomes a key breeding ground for various activities of a world class nature and the modern day M G Road owes its existence to these events. One can see the Bangalore Cantonment railway station very close to the ulsoor lake as with time supplies to the MEG centre were becoming increasingly larger necessitating the use of railway and as more and more of the english making settlements around this area there began the need for another railway station the "Bangalore East" not far away. Thus this lake and its hillock proved a central attraction for english settlers and their activities from whence grew this city of Bangalore - how resplendant. As a child growing not more than ten kilometers from this point never knew to myself or appreciated the fact that I was reared and lived in the vicinity of history which was a judicious combination of the western and the local... I realise it very much now and how different and suave a place I spent childhood for largely good in many ways and may be bad in very miniscule ways.
An area of a radius of around 15 kilometers around the ulsoor lake is the Bangalore Cantonment which had military parade grounds; residences for trainee military men; residences of British serving officers;churches; railway and road systems; recreation centers ; cricket grounds; auditoriums; public offices not to mention schools and the British brought them all converting to the exclusion of its immediate environment a formidable patch of land which could be called little-england into which only a secluded few could make entry and to the best of my knowledge there is no other place in India which could have had a large scale and concentrated British influence as this stretch and every english- man of these times enjoyed his tryst with this belt as we did many decades later as children mutely appreciating the aura of some kind around us.
The Richmond Road, The Residency Road; South Parade;Cavalry road and the Infantry road formed key roads of the official part part of the Cantonement and note the military linguistics that formed part of the names of these roads. There were many inter connecting roads of a criss-cross kind like the Brigade road and the Lavelle road. The Infantry road probably housed the offices of the Infantry who were possibly trained and paraded near by and so was the cavalry which means mounted soldiers and note that all these key roads are almost parallel to each other. During the world wars there was need for an airport and hence the old airport some where close by sums up this part of the city in those times. All these roads were on the left side of the lake and to the right side of the lake and yonder came various residences and the Coles Park which we call Bangalore East today.
THis is Bangalore Cantonement of the past and any one who comes to Bangalore of today must identify and associate oneself with this distinct past and this patch or stretch or periphery or domain or whatsover one may wish to attribute to it is an un-erasable stamp of the British on the lives of a common Bangalorean or a common Indian of today ; everything commencing from a hillock and a lake nearby called the Ulsoor Lake.
Friday, December 16, 2011
THE GREENS THEOREM
When I was a student at a technical school I had real problem with this theorem and thought to myself why not try to simply this theorem to any present day student who would be having difficulty at understanding this theorem.
I have seen many people who forcibly digest these theorems with no understanding what so ever of what they are doing. Mathematics and its many variants have been confused profusely by humanity in some form or another so much so that many practitioners fail to assimilate or atleast ponder to give many things a thought.
They say Greens theorem is another version of the stokes theorem about which I have no idea but will dwell upon it some time in the future.
At the center of the greens theorem is the cartesian co-ordinates which can be treated both as a vector or scalar co-ordinate. Note that scalars do not have direction as against thevectors. When some one uses the cartesian co=ordinates in a polar form it becomes vector co-ordinates and is defined by r and theta..r signofying the magnitude and theta signifying the direction. Whenever we define and treat the cartesian co-ordinates by x and y they are scalar co-ordinates. Hence we have both scalar and vector algebra arising from the cartesian plane.
What are the basic components of the Greens Theorem;
1. A closed curve chosen to be traversed in the counter clockwise direction also called positive direction.
2. Another function defined by X and Y components called F which is integrated upon the above curve which can be smooth or piece-wise smooth.( A circle is smooth whereas a triangle is piece wise smooth).
3. Greens theorem like many simple theorems says that the line integral over the curve is equal to a partial double integral over the plane.
The theorem goes something like this;
Closed Intregral of f.dx + g.dy along the curve mentioned
Double Integral of the function resulting from the subtraction of PD of g with respect to x and PD of f with respect to y.
(the above will be mathematically described by any text)
PD means partial derivative
f is the x component of the plane F which will be a function in x and y
g is the y component of the plane F which will be a function of x and y
Example : Let F be defined as ( -y x) and let the curve in question be a circle x^2 + y^2 = 4 which would be a circle centered at the origin with radius 2.
Note that at the end of the day "What does Green's theorem do ?" that is very simple. A line integral of a function over a closed loop is calculated easily using a partial differential equivalent.
In the above problem suggested f is -y and g is x and please compute the partial integrals and you get 8 phi which is twice the area of the circle.
IF YOU ARE A STUDENT OF MATHEMATICS YOU MIGHT HAVE TO GO MORE INTO THE DETAIL OF THIS THEOREM. IF YOU ARE A STUDENT OF ENGINEERING GET THE ABOVE IDEA WHICH I HAVE GIVEN AND ALSO LEARN THE MATHEMATICAL PROOF AND SOLVE SOME SIMPLE PROBLEMS. THIS AREA IS SOMETIMES CALLED COMPLEX ALGEBRA NOT TO BE CONFUSED AND FRIGHTENED ABOUT..THIS IS JUST AN ALGEBRA OF TWO FUNCTIONS ON THE CARTESIAN PLANE.