Few thoughts

I was in the hospital's administrative office today. This is a hall where there are about 5 to 6 counters. A few chairs in the waiting room. As I walked in, I noticed that there is a token dispenser. I took one and sat down and waited for my number to be called. I had a few minutes completely for myself. I decided to just shut down my own thoughts of my little world and focus on people around me. At "counter 1" was a young lady. She was discussing with clerk animatedly. The clerk was trying to placate her that the particular rule is not applicable to her. The young lady was throwing up her hands in the air, in exasperation. It felt like she is still young and had some arrogance that goes with that age. A middle-aged very mellow lady was at the next counter. She was worried about her insurance benefits. Counter clerks seemed genuinely helpful. I saw another old Chinese man waiting patiently for his turn. He had a band-aid across his cheek bone. I wondered what had happened to him. There must be a story behind that. He looked serious, lost in his thoughts. I glanced around.. there was another old African American gentleman- in a call with his insurance company. I unintentionally eavesdropped on the call. He was saying, " I read in your documentation that you wont insure people over 80. I am a bit concerned about that. I am expecting to live beyond that. Are you going to cut-off health insurance for me when I get older?". Hmm. Just then, another old lady who was being wheeled in by a relative was approaching the token machine. An elderly man was ahead of her. However, when he picked the token, he gave his to the old lady and took the next one for himself. It is such a nice gesture. I feel it is not so common to see such kindness in daily life. This is what everyday looked like here. Real people with real unique worries. Each person at a different stage of life. It was like a scene out of a Hollywood movie- just before something unexpected happens. After I finished the paperwork, as I walked out, some local musicians had setup a band to play some soft soothing music in the hospital lobby. Must be volunteer work. It was a beautiful "everyday". In the age of continuous fear-causing 24x7 news reporting, it feels nice to report about a single beautiful day in human life.

Channel Capacity - Heuristic proof

Quick recap of the channel capacity heuristic proof. Reference here: https://www.eecs.berkeley.edu/~dtse/Chapters_PDF/Fundamentals_Wireless_Communication_chapter5.pdf Assume we are transmitting a codeword in N dimensions. The dimension could represent time or any other signal characteristic. Assume it is corrupted with a noise vector (also N dimensions). Now each of the codewords can be represented as a point in N dimensional space. Assume also that we have a power constraint P (total power transmitted must not exceed P)- so all the received codewords must lie in an N-dimensional sphere of radius sqrt(N(P+sigma^2)). For error free decoding, all the received vectors (transmitted point + noise vector) should lie inside non-overlapping spheres inside this large sphere of radius sqrt(N(P+sigma^2)). The radius of this non-overlapping noise spheres has to be sigma^2 (noise variance) for a large N. Thus, max number of codewords that can be transmitted in this scenario can be geometrically deduced as sqrt(N(P+sigma^2))^N/sqrt(sigma^2)^N or equivalently the max number of bits that can be conveyed is log2(max_num_codewords). This yields the famous shannon expression for channel capacity. I.e no more information can be transmitted with the given power constraint on an AWGN channel with arbitrarily small error rate.

Today, while going through all the documents that have collected dust over the years, I started organizing them in to separate folders-by category. Bank related, income tax related, Visas, passport, stock certificates, real-estate investments, rental agreements, insurance etc.. the usual stuff. In the process, I came across my marks sheet from my under-grad. I stared it for a while. Most people hold themselves to some simple expectations. The expectation is that, one has to do what one is good at... regardless of the area of the job. "Well" here means whether one can do or has done new and innovative work in that area. For me, it is a bit late in life. However, to repeat a cliche, one should keep exploring. I am trying to recollect what I really-really enjoyed doing. What was I really-really good at? Should we all ask ourselves this question? May be the answer could even change from time to time. If you ask yourself that question often enough and you get an answer- I feel you are probably living a more fulfilling life. Let me know what u think.

What a wonderful day!

We choreographed a dance for dad's birthday. It was almost childish. In our conservative family environs, dancing itself was a big deal - so getting it right was not that important. The bigger part of "self growth" was for the first time in my life, I coordinated with people on the organization of an event. It felt so wonderful. We worked without taking ourselves too seriously but just wanted to make it fun for a bunch of people around us. The outcome was beautiful- none of us were perfect- but it was fun, nevertheless. I think the "key" learning that day was to not worry about getting things right- but just doing something different. My daughter was one of the best dancers.