Tuesday, September 6, 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.
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.
Digital Counters, Flummoxations.
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.