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RSS FeedJuly 22nd, 2010
An Old Physics Problem
Question: Three people – A, B and C – are standing at the three corners of an equilateral triangle. At time 0, A starts running towards B, B towards C and C towards A. At what time do they catch up and where? Assume each side of triangle is 1 unit, and speed of each person is 1 unit/hr.
Answer: By symmetry, they must meet at the center of the equilateral triangle. The center is at a distance of 0.5/cos(30) from each vertex of the triangle. The component of speed in that direction = 1 * cos(30). Therefore time = 0.5/cos^2(30) = 2/3 hr = 40 mins.
That used to be enough before I was a computer scientist. Now, of course, I must poison everything by simulating it and “testing it”. (Some test of a proof, huh?).
So, I wrote a small Java program which essentially simulates this scenario. A parameter it considers is the “step size” – that is, how long, will the person keep running before readjusting their direction. The smaller the step size, the closer the result should be to the theoretical answer. As a termination criteria, the simulator stops when the vertices are no more than the same “step size” away, since they will keep overshooting each other at that point.
So, here are the results:
Motion simulation started, stepsize: 0.1
Termination criteria reached.
p1: Point [x=0.549085637, y=0.3009455537], p2: Point [x=0.464830686, y=0.325049334], p3: Point [x=0.4860836758, y=0.2400305158]
Time: 0.7 hrsMotion simulation started, stepsize: 0.01
Termination criteria reached.
p1: Point [x=0.4945088945, y=0.2898249361], p2: Point [x=0.501749795, y=0.283344797], p3: Point [x=0.503741310, y=0.292855670]
Time: 0.68 hrsMotion simulation started, stepsize: 0.0010
Termination criteria reached.
p1: Point [x=0.4995170777, y=0.288533649], p2: Point [x=0.500363990, y=0.288327654], p3: Point [x=0.500118931, y=0.28916410]
Time: 0.668 hrsMotion simulation started, stepsize: 1.0E-4
Termination criteria reached.
p1: Point [x=0.4999632647, y=0.2886362474], p2: Point [x=0.500052044, y=0.2886627644], p3: Point [x=0.4999846904, y=0.2887263918]
Time: 0.666799 hrs
Motion simulation started, stepsize: 1.0E-5
Termination criteria reached.
p1: Point [x=0.500005073, y=0.2886767668], p2: Point [x=0.4999960499, y=0.288678711], p3: Point [x=0.499998876, y=0.288669925]
Time: 0.666689999 hrs
Motion simulation started, stepsize: 1.0E-6
Termination criteria reached.
p1: Point [x=0.500000347, y=0.2886754955], p2: Point [x=0.4999995134, y=0.2886752554], p3: Point [x=0.500000138, y=0.28867465]
Time: 0.666668999 hrs
Clearly, as the stepsize approaches 0, the time approaches the theoretical value of 2/3.
Maybe, some day, I will get around to putting a UI layer on it.
July 20th, 2010
iPad revisited
About a couple of months ago, I bought a netbook, even though the iPad was already out and I had already tried it at the Tysons Corner shopping store. Boy – did I regret that decision. I hated the netbook’s slow bootup time and the fact that you actually have to open it! Terrible. Still, it works better for me on the airplane than the 16in Dell I have, but I really want an iPad – look ma – no need to open!
But then, more recently, I visited Tysons corner again, and just for the sake of it, I started accessing NX applications (from my day job at NTELX) from the iPad. And really, some of these terrific applications didn’t work – of course, due to flash. So, now I have been wondering if my missing iPad is simply a case of grass being greener on the other side. I came across Jim’s scathing iPad review, and despite a very non-creative title, the author salvages himself by a very well written article. Jobs may have jumped the gun on the flash issue IMHO.
July 10th, 2010
Butterfly effect in congestion management
When dealing with congestion management, there are so many orders of effects, that it really helps to start with a simple change that people have consensus on. That change can enable other changes and those other changes can enable other changes, and situation can change drastically through a sequence of simple changes.
Many evolutionary changes, when looked through a different prism of time, may appear to be a revolution, even though they consisted of twenty evolutionary steps.
That, precisely, was my message during the ITSA 2010 executive session presentation.
July 6th, 2010
Don Norman, success, and the halo effect
Don Norman’s talk at Business of Software 2009 conveys yet another example of the Halo Effect
One of the great points that Don says is that good product need not be usable, understandable or emotionally satisfying. It need not be simple. Although these are all good qualities to have in general, they are not requirements, and have to be placed in the context of the actual product. A successful business is successful, and that is about it. Despite many books on this, there is no formula for it (at least not yet), and that is why there are at least 81 great business schools in the US alone that teach students and award award-winning MBA degrees. Cute short phrases and itemized lists have been inadequate to formulate success in the past, and Don’s words can serve as another reminder not to interpret the speakers’ pointers as bullet points.