No Silver line!

In all these years, I have never taken train to the Boston airport. I have only taken the car or the Peter Pan bus to airport for every trip from home. I have seen Silverline in the subway map connecting the airport and Boston South Station. I was curious for a long time to check out how convenient it is to take that train to airport or how I can get to South Station from the airport by the silver line. It will be good to know how train access worked. I wanted to find that out before I will have to use that option for any reason. It will be a hassle to explore it on a trip with the family. Anyway, I had that chance to find out about the Silverline today as I happen to be at South Station this evening and could afford to kill some time.

It was a busy Friday afternoon. I walk down the South station, buy a ticket, walk through the subway gate, couple of stairs down following the sign to airport and then I'm in front of the road standing on a bus stop! First of all I did not know that Silverline is a bus, not a train. That was a bummer. :)

It is kinda misleading to call it a Silverline (along with red line, green line, etc) and show it part of the subway map. Seemed to me like an elaborate plan by the city to mess with everyone. I'm guessing I am not the first person to be surprised at this experience. For a moment I wished to walk back and cancel my trip to airport and immediately realized it will just be a waste of the ticket. Imagine how the dialog would go with the guy in the ticket counter if I asked for a refund for disappointing me! That probably would be fun. So I ended up taking the bus to airport. It was uneventful. Took about an hour round trip.

No one seemed to check the ticket of passengers getting in at the terminals. I'm thinking may be the trip from airport to city is free...? I quickly snapped out and thought perhaps when we return back at South station you will need a ticket to get out. I had bought a round trip ticket so I wanted to make sure the return ticket is used up in my exploratory trip. However to my surprise I could walk out of the "subway" without paying again. Either Boston truly welcomes people from airport to town free of charge or I have missed something by not getting out at any terminal.

I have to find out about the trip from airport into the city. Now I'm planning to fly out somewhere alone, return to Boston airport and check out how the trip to South station works on the silver line :-)

Life and Alife

What is life? This question has haunted mankind for ever. Several axioms are listed to define life. None of them are entirely sufficient to describe life. The idea of soul or athma hasn't gained scientific acceptance mainly because there is no proof of its existence in any part of the body. The logic of indestructibility of soul, karma, rebirth are all beautiful religious concepts built to govern life. But let's say science hasn't caught up to those properties of life yet! So let's stick to understanding the definition of life scientifically.

From a material perspective, after the DNA structure was discovered mid 20th century it made sense how life expressed itself from primitive organisms to giant and intelligent life forms on earth. But then, DNA to life is like baking soda to cake. Apparently sufficient as constituents for most life forms, but not necessary! The fundamental atoms that form the proteins that constitute the DNA molecules can be replaced with non-carbon atoms. Through recent discoveries scientists have found that silicon, sulpher based life forms exist in acidic and hot environments under ground! Those life forms have not evolved to fit in the earth's atmosphere that is filled with oxygen and water at atmospheric temperature. So the ingredients of life need not be carbon based organic form. That left us sorta open ended. We don't know what other forms of life are possible beyond the well known four base (ACGT) based DNA that forms organic life.

Another definition of life went with the process of reproduction. Life is the process that is identified with the reproduction of species. Mathematician Von Newmann posed the following experiment and ended that definition. Imagine a robot in a warehouse with all parts required to make another robot and a storage tape that has instructions to build a robot. If the robot reads and executes the instructions from the tape, it can build a robot. In the end, if there is an instruction on the tape which says 'now replicate all the instructions in the storage tape to another tape, this time treating the instructions as simple text instead of executable instruction set', the robot can replicate the contents of the tape and stick it to the new robot. Now the new robot can be made to make another robot and so on. This thought experiment lead to the invention of self replicating software programs or Darwinbots. Software viruses are one such incarnations. Is that life? University of Michigan Professors call it ALife aka artificial life.

Well. Truth is, we are not even able to scientifically define life yet...let alone understanding its properties, transitions or indestructibility. So the pursuit continues!

Nature expressed in numbers

Historically people are fascinated by natural constants such as PI, the Pythagoras triples, e - the natural growth rate and such. In that series comes the sequence of numbers identified by a man who is known by his father's name as son of Bonacci, i.e. Fibonacci. He set out to solve the following problem and ended up with a surprisingly powerful sequence of numbers that has many expressions in nature.

"A certain man put a pair of rabbits in a place surrounded by a wall. How many pairs of rabbits can be produced by that pair in a year, if in every month, each pair begets a new pair, which from second month onward becomes productive? Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on."

Fibonacci solved it as follows and arrived at his famous sequence.

1, 1, 2, 3, 5, 8, 13,....and so on. Simply put, each number is the sum of two previous numbers.

There are many significance to this sequence of numbers. First of all the sequence expresses the natural phenomenon of physical growth with numbers. Plant and Animal cell divisions follow the Fibonacci sequence! Looks at the images below, the expressions of Fibonacci sequence.

There are more fascinating facts about the sequence.

Sum of 10 consecutive Fibonacci numbers is equal to 11 times the 7th number!
1+1+2+3+$+8+13+21+34+55 = 143
so is 11*13 = 143
5+8+13+21+34+55+89+144+233+377 = 979
so is 11*89 = 979

Here is another interesting property of the sequence.
Take any four consecutive Fibonacci numbers (a,b,c,d)
Pythagoras triples are ad, (2*bc) and (b2+c2)

Take 1,1,2 and 3 for a,b,c and d respectively,
ad=3, 2*bc =4 and b2+c2 = 5
i.e. 3,4,5 a well known Pythagorean sequence

Take 1,2,3 and 5
ad=5, 2*bc=12 and b2+c2 = 13
i.e. 5,12,13 another well known Pythagorean sequence!

and so on.

That is not all. Here is another interesting property. The ratio of nth number of the sequence to the (n-1)th number converges to the famous "Golden Ratio"

Interesting corollary is that Golden Ratio (Phi) is the number which when added with 1 gives the square of the number! i.e. (Phi)2 = Phi + 1

Fascinating facts indeed!

The book "Taming the Infinite" by Ian Stewart is a good read. Its about the history of Math. The book triggered renewed interest in Fibonacci sequence and a good journey into the fascinating facts around that set of numbers.