One day one of my friends wanted some company while going for the health centre, and I decided to do that, just that I also came out with my camera, and started taking videos of him. I was just sharpening my video skills, and after I came back and watched what I had shot, I found out that it compiled into a nice sequence. Hence, I made it up, and posted it in Youtube.
The friend featured in this video is Prabaha Gangopadhyay, of the blog "Through a Convex Lens".

Random thought on probability

Suppose you are given a coin, and told to check whether its a biased coin or not. What would you do? How would the coin be determined whether it is biased or not?
To understand the whole essence of biasing, we must first understand what is bias actually. And the answer for this case can be stated as:
1>Which has two faces, one as a head, and another as a tail.
2>Satisfies the probability of outcome of 50% of any of the face.
3>The event is random.
Now, point 1itself satisfies our calculation that the outcome SHOULD be 50%. But is it really possible to achieve an exact 50% outcome? If not, then the second point mentioned is not satisfied, which means we cannot say what biasing is.
Now, what actually happens is this. The fact that we cannot obtain the exact outcome is quite many. The major reason is that we cannot produce exactly the same condition every time we toss the coin. The angle at which the coin is initially inclined, the torque applied to our thumb while releasing the coin, etc, cannot be exactly reproduced by us. And neither can we exactly record and measure these settings exactly. I mean, the angle of inclination can be measured if tried, but the force produced by our thumb, which is actually produced by the internal muscles, is not possible in the current technological scenario. Hence we are certainly to obtain some errors.
Thankfully, the margin of this error is finite and small, and the error magnitude doesnt significantly increase with the increase in the number of trials taken. SO, If we take trials of 4 tosses, and for the sake of the explaination, let us consider the given coin is unbiased, there is quite a chance that we might obtain 4 heads, and hence, we might not be able to verify the biasness of the coin. But if we take it to 100 times, and keep on increasing to 1000, 10000...... , we might see that the probability of any face is closing to somewhat 50%, and for a really very large number of trials, the probability will tend to 50%. Using this concept in the other way round, if even for a large number of trials, the probability of a particular face is significantly more, then it will be termed as biased.
Now notice the words“significantly more” that I have used in the last line of the previous paragraph. How do we determine this “significant” limit, crossing which we will term the coin as biased? There is no fixed value. The crude manner by which we can differentiate is by comparing the graphs of the two outcomes. We take a graph for the number of heads and the number of tails obtained in the experiment. The more the graphs look similar, the more with assurance we can say that the coin is unbiased. Now, nature says these graphs will never be exactly mirror image, there will be some difference, because of what I have said previously. Here, on the basic level, we apply our trivial judgemental fuzzy logic, and determine whether the error in any case is negligible or not, because that “significant” value depends on the total number of trials taken.
Hence, we can say, the coin is not biased, when the error in between the practical results and the theoretical results is as small as possible, when tested in very high number of trials, and we can define bias as “the Boolean logic of yes and no, which returns 'a positive response'(or 'is yes')if a random event is unrandomized, ie the outcomes don't have the equal theoretical probability they should have had. "
Again,a coin can also said to be not biased when 50% probability of any of its face is achieved in an infinite number of trials.
Now here is the interesting fact. If a coin is tossed by, say, a robot, which can replicate exactly the same condition with which it has tossed before, and in a sealed box, so that the outer environment cannot effect the experiment, and say the coin is measured to be as perfect as possible, ie the mass distributed about its centre of mass is exactly the same, even then, the practical probability cannot be achieved to exactly 100% of the head. No matter how small, and how negligible may the error be, still we will obtain error. The reason is, our perfection is limited to the least number of significant values our current machines can use, and as we know, there are no limit to the number of significant values a machine might have. A perfect measurement tool is a tool which has in trial finite number of significant digits in its measurement. And since there is no limit to perfection, this also implies error will always creep in, no matter how small. Hence, the calculated value will be somewhat like 91%, or 99.99% (depending on the number of trials) or something. And the pattern in which the errors will come will be unique in each cases, providing the number of trials is large. But this comes under non linear dynamics and chaos, which is a different story, also, the situation mentioned here is not random, its parameters are fixed by the robot. And in computer, there is no exact thing as random. The random programs so created are repeating numbers which comes in a particular function provided, whereas when we toss the coin, we dont know anything judgmental about the position of our thumb, etc, and hence, this can be said to be random.
Again, how can we say that, for example, that the umpire(or referee) tossing the coin during a cricket(or football) match, is a random event? Because, the umpire (or referee)does this toss trivially, and has no knowledge whatsoever about the parameters such as angle of inclination, height of the coin, how the wind will effect the coin turning or trajectory path, where will it land, torque provided by his thumb muscles, etc. Even the face of the coin facing upwards before tossing is trivial. Hence, the event is random.
Now if the umpire had full knowledge about these parameters, not only can he predict the outcome with a 100% probability, but can become a millionaire, because such a person can predict just anything, so why not the stock markets???(okay, may be I went off too much!)
And now back to the coin biasing argument. Now suppose that the coin is made such that the head side is weighed more, and it is a fixed parameter. So, the coin is said to be biased, as it will have the tendency to show heads more. But that also, can be considered to be a random event, provided the decision makers doesnt know about the biasing, as the decision makers will have the same probability of choosing either head or tail, and that is 50%, Hence, it is quite random. The choice is random, but not the outcome. Hence, the coin might be biased, but the experiment still has its validity.
This is what I think about biasness in coin. If anyone can share anything about the biasness regarding any other experiment, feel free to comment in. Also, comment in about any mistakes you find.

My thoughts on Genetic Imprinting

One of the most interesting things present in animals. This is called genetic imprinting.
Have you ever imagined why a kangaroo baby always reaches for her mother's pouch just after it is born? I mean how does it even know that her mother is sitting outside him/her? Its all imprinted in its brain. Its an evolutionary tactics which developed over the years. And when I say years, it means centuries of centuries or even more!
Also, the best remarkable example of genetic imprinting can be seen in an episode of the cartoon of Tom and Jerry, where the famous duckling(i forgot its name) hatches out of the egg, and follows Tom throughout the episode. Thats what ducks do. They consider the biggest moving object they first see as their mother, and will follow it all the time, even if its a robot. It is also seen in chicks(pun not intended).
Now, as we say it developed by evolution, how? I mean, it just didnt happen suddenly, and all became just like that. Evolution can be explained in many different theories. It is simply logical and mathematical.
One of the theories for the ducks can be considered as follows: Genetic changes happens sometimes, ie genetic characteristic in an offspring may shift from their parental characteristic to a new one, or they might show some new behavior, which after generations, becomes imprinted on the genes. The probability of this happening(sudden change in behaviour) is very low. Now, suppose in one of them, the offspring tends to follow her mother just after it is born. And it is seen that due to some reasons, it had more chance of surviving, and does survive, whereas other dies. So, the offspring with such behaviors survive, and others die. Or we can say, to be more accurate, the rate of the 'offspring with behavior dying' is more than that of which doesnt have it. Hence, its genes strives, and this is now common in every offspring. Even now, some ducklings might not show this behavior, and hence, it wont become a healthy adult, or may be eaten by a predator before. So, its modified gene will not be included in the gene pool. Hence, the words "Survival of the fittest."
Now what happens if, by any situation, the offspring with the tendency of following its mother faces the threat of dying more than the counter behavior? Then two thing can happen:
1>Either the whole duck family will go in the verge of extinction
2>Or luckily, if any offspring with the counter tendency shows up, and can multiply, that previous known behavior will be completely reversed.
You can even take the first cry of a baby as a genetic imprinting. Those babies, who after being born, cried for air, survived, and those who didnt, didnt. But now that medical science has advanced so much, such a child who doesnt breathe can be made to live. This is the reason why earlier, humans, or homo erectus, or any of our earlier ancestors, were healthy, and now, our gene pool is polluted as such unhealthy child survives.
But, on the sunny side, this is a primary difference between the homo sapiens and the rest of our ancestors. We now have evolutionary advantage by our mind, and not by our strength. Hence, survival of such a child doesnt really hamper our development. We dont require peak physical fitness any more, we require human resource. And thats partly why, slowly, homo sapiens have developed such a large cerebrum.
PS: If you can carefully care a duck or hen egg and can hatch it, you will find yourself a true best friend, who follows you even to death! (As for the offspring, it will see you as its mother!)