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Monday 19 September 2011

सरणार कधी रण?



Im posting a poem after many many days. Its one of my most favourite poems, and everytime I read it or listen to it, it brings a tear to my eye. We are all familiar with the heroics of and the ultimate sacrifice by Baji Prabhu Deshpande for laying the foundations of Swarajya. Somehow I feel that the spirit in which he gave up his life for the Hindu Rashtra is being forgotten amidst the political turmoil. These political parties, making caste a basis are divisive forces at work which weaken our nation. We just need to look at Shivaji Maharaj and see how effectively he established and defended a kingdom- a kingdom which grew like the waxing moon. He made no descrimination amongst his rayat. Everyone was awarded position according to merit. Todays politicians need to set Shivaji Maharaj as a role model for governance.(More on this later)

Anyway, coming back to the point, the other day, I was travelling from Pune to Mumbai and was listening to Shivakalyanraja- a legendary musical album describing the important events of Shivajis life. One song in the album is especially touching- सरणार कधी रण?.. . The story told in the poem bought a tear to my eye. Such sacrifices for ideals and principles are rare. Relationships such as these are even more rare. I wont say much, im getting overwhelmed by the sacrifice just thinking of the poem. Here is a link to a video I came across on youtube, which I am sure will definitely touch your heart. Also presented is the poem, written by Kusumagraj.



सरणार कधी रण प्रभू तरी
हे कुठवर साहु घाव शिरी?

दिसू लागले अभ्र सभोती
विदीर्ण झाली जरी ही छाती
अजून जळते आंतरज्योती
कसा सावरू देह परी

होय तनुची केवळ चालन
प्राण उडाया बघती त्यातून
मिटल्या झाले अधीर लोचन
खड्ग गाळले भूमिवरी

पावनखिंडीत पावूल रोवून
शरीर पिंजे तो केले रण
शरणागतीचा अखेर ये क्षण
बोलावशील का आता तरी?

सरणार कधी रण?

Let us rekindle the spirit in which Baji Prabhu gave up his life for the establishment of Swaraj. Let us channelize his spirit as we strive to build a strong India.

Thursday 15 September 2011

On Rajanikants 4th Law of Motion


Title of the Paper:
On Rajankikants 4th Law of Motion.

Authors:
Chinmay Datar 1.

Special Thanks:
Taniya Bapat 2.


Abstract:
The paper is written with a view of calculating the Rajani Radius(Rajanitrijjya) based on Rajanikants 4th Law of Motion. The Law itself deals with the movements of superheroes such as Rajinikanth and Flash amongst others. The Law, and its following derivations should not be attempted by normal mortal human beings such as ourselves, for the force that would be exerted is beyond the biological capacity that the body is designed to handle. Superhumans (Heroes) with modified DNA and Superpowerful(and as of yet undiscovered) subatomic particles are the only things to whom the law may apply . The inspiration for this research was provided by a Taniya Bapat SMS forward, for which the author duly recognizes her inputs.

Index Terms:
Rajinikanth, Rajanitrijjya, Highspeed circular motion, 4th Law of Motion, Persistence of vision.

Introduction:
Newton is credited to have formulated the first three laws of motion on which the whole universe is based. Well, the whole universe follows these laws except for some nutcases termed as superheroes (Rajani, Flash, Green Lantern, Superman, etc). To fit these heroes’ deeds scientifically, Rajani, the great, came up with a new Law- one that shook the earth beneath the feet of Shri Shri Isaac Newton.
Rajani states in his 4th Law: “If you run at 100 km/sec around a tree, you can see your own back” [1]
While physically, it may seem impossible that this can be true, scientifically and mathematically it is quite possible. 100km/s roughly equals 100000m/sec, which is about 0.0003333 times the speed of light, and hence, speed which can be easily achieved by fast things, such as superheroes. This rules out the problem that heroes would need to travel faster than light. Also as the speed is quite fractional and nominal compared to the speed of light "c", relativistic effects and Lorentzian transformations can be ignored.

On Persistence of Vision and field vision of a human eye:
An important concept in this derivation is that of “Persistence of Vision”. Our eyes, for a short duration, store the image that it catches on its retina. The effect lasts for a very short time, however, if a body moves at that rate, it appears to our eyes that the object is in continuum.  An application for the same is the television, where about 25 frames per second and shown so that the picture appears continuous. From here we can calculate that per frame, 1/25 second is needed for it to be stored on the retina. i.e if the eye sees something even for a minuscule period of time, due to persistence of vision our mind “reads it” for 1/25th of a second.

The second important concept is field of vision. Looking forward, humans usually have a field vision of 95 degrees as shown in the fig below:


Calculation of the Rajanitrijjya.
(Trijjya, Sanskrit for Radius) Rajanitrijjya, literally, the Rajani radius is the maximum radius that can be used by a superhero to run in a circle to see his own back. Certain assumptions about speed and radius were made to achieve the results.
Rajani 4 says that you need to run at 100km/sec which gives a speed of 100000m/s. The velocity will be linear velocity. V=100km/s. ω would be v/r, and will depend on the radius. 

Scenario 1:
The superhero only sees forward, and has no field of vision while running:
In this case, the superhero need to be at the same spot that he started from in (1/25) of a second. Only then, will he be able to see his own back.
The distance covered by the superhero would be equal to the circumference of the circle on which he is running.
Thus, we have,
D= s*t;
2*π*r = 100,000 (m/s) *(1/25)(s)
2* π *r= 4000m;
r= 4000m/(2* π);
r= 636.66 m, which is roughly 637 m.
However this will be true only if the Superhuman only looks straight ahead.

Scenario 2:
The superhero possesses a human field of vision
The superhuman, at the end of the day is a human, and thus, possesses a field of vision, which Wikipedia states is 95 degrees.
Using this, the human may be able to see his back at a position which is not at the exact same spot on the circle from where he started running, but rather on a point much earlier to that.
A quick glance at the following circle will help answer our doubts.
 
Total field vision is 95 degrees. Assuming symmetry, and assuming the superhero is not cross-eyed (rather doubt it) field of vision per side along the line of symmetry will be: 95/2 = 47.5 degrees.
At any point on the circle, the superhero is running tangentially to the radius at that point. He thus makes an angle of 47.5 degrees with the point from where he started (A) from a point say B. this means that the angle between the furthest vision and the radius is 42.5 degrees. Reminding the reader that the circle has a constant radius (Polar r=a), an isosceles triangle will be formed, subtaining an angle of 95 degrees on the center.
Thus, the superhero would need to run a distance equal to the arc length equivalent to 265 degrees.
Thus, distance covered will be:
(265/360)*2* π *r.
This will be equal to s*t
(265/360)*2* π *r = 100000*1/25
(265/360)*2* π *r= 4000;
R= 4000 *360/(265*2* π)
r= 864.8 m.
Thus if the superhero runs at a radius of roughly 865 m from the centre of the tree, he should be able to see his back.
Now, the widest tree has a diameter of 32 m(from wiki). Thus, radius is 16m. For his own safety, let the superhero run around the tree at a distance of 20m.
Thus,
(265/360)*2* π *20 = s* (1/25)
Thus, s= 2312.5 m/s.
This equals 2.3125km/s
This is just the 1/50th the speed at which Rajani can run. No wonder he easily sees his own back!
Superhumans having such capabilities have been discovered. The wait is for the discovery of the fundamental units that build up these superhumans. These fundamental particles, although as of now only imaginary have been assigned the term Rajanions by VERN (Vadheev Engineers Research Network)- the Research branch of IVEE.

References:
[1] SMS, received on 14th Sept, [Taniya Bapat].

Acknowledgements:

The author would thoroughly like to thank Taniya Bapat- still a student for inducing a thought process to formulate the concept of seeing your own back while running.

All material is copyrighted to the IVEE. Any person imitating any research or stealing it (especially non-members) and using it for ridicule, will be given 50 whiplashes. The author or for that matter anyone at IVEE shall not entertain questions regarding how Rajanikant reaches speeds of 100km/s- Go ask Rajanikant himself. 
People wishing to promote fun side of Science and Math can contact IVEE chairmen- Chinmay Datar or Sumedh Dhabu to obtain and a lease to use the vadheev proofs.

Tuesday 6 September 2011

Digital Counter Paradox

Title of paper:
On Chinmay Datars Digital Counter Paradox

Authors: Chinmay Datar 1
Special thanks: Sumedh Dhabu 2 Shreyas Bhaban 3.

Abstact:
A reverse thought experiment generated out of the idea to mathematically model a situation of a couple moving into a locked house and generating an offspring and leaving the house only for another person to enter the house.

Index terms:                                                                                                           
Digital Counters, Flummoxations.
Introduction:
Completing work related assignments is kind of boring. Especially if its an assignment that does not make you think out of the box. IT assignments are mostly of such non-creative types. I guess they strive to stifle your imagination and creativity. My new job, though interesting, is making me lose my creativity to a certain extent. To not go completely mad, I try to come up with mathematical formulations and spoofs, to keep thinking and not get engrossed in the world of IT.(I have no idea why its called technology here). Ive come up with some very interesting theories- one about complex numbers has already been shared.. Today, early in the morning, when I have nothing to do, I was thinking of a thought experiment. The experiment is leaving me flummoxed. Why me, it has even left the Grab-all and gobble scientist Shreyas Bhaban (who works not coz he loves his work, math and science, but coz he wants to grab all the money around) dumbstruck.


Assume a room where there is a single door for entry and exit. The room has no other possible entry or exit points.Just the one entrance/exit. Whats inside the room is unknown, so basically its a black box. On outside of the door, there is a digital counter which can count anything real from -infinity to +infinity. Whenever anything enters the room, the counter is automatically incremented by one. When anything leaves the room, the counter is decremented by 1. All elements are counted individually. Elements enter the room when the door is opened at 2n-1 opening and elements exit when door is opened at 2n opeing.( n =1 to infinity)

Although the inside of the room is unknown, what we do know is that the room performs a simple operation of square rooting anything inside at even numbered door opening.

Let us assume that we push the number "1" in the room. The counter will increment to show that there is 1 entity in the room. Now when we open the door again, it will be the 2nd opening, so the square root rule will be applied on "1". This will result in two results: +1 and -1. as it is the 2nd opening, the elements inside will exit. As two elements will come out, the counter will decrement twice, and show -1 as the number of entities inside. Now if we open the door again for a 3rd time, and force "1" inside again, the counter will increment by 1, and show the number of entities inside as "0". Practically this is not possible as we ourselves have pushed "1" inside the door, and definitely know that physically there is an entity that exists inside. 

So, now, a paradox has been generated about the number on entities inside the room. Mathematically, the counter reads zero, but practically, we know it should read 1. This paradox has been labeled the Digital Counter Paradox or DC paradox.

The paradox has been generated for exclusive use for IVEE. Any reproduction will be charged with 50 whiplashes and brain-washing. The paradox is created to confuse people. People attempting to solve the same with mass-energy-momentum conservation or any other methods shall be deemed too nerdy to be vadheev and be permanently disqualified to visit IVEE blogs and posts.