The rule conjectured from the movie “Money Ball” and its outside

I watched a movie starring Brad Pitt, Money Ball that is based on a true story. The General Manager (GM) struggles over the victory of championship.

It is now commonplace, but at that time, it is rare to use statistics for baseball games with the method of finding new strategies from data that no one has never used.

It is so-called data mining, but some of strategies are deviating from conventional thinking such as “a player can frequently walk to the first base is good.” The statistics gives a proposal to raise the probability of winning.

In professional sports, there is a disparity among the teams. There are rich teams and poor teams. Of course, if you have money, you can take as many excellent players as you want.

However, the poor team can not afford it. If you try to get a good player, much money will be concentrated on that player. Therefore, the rest of money will not be used for other players.

So, with the data and statistical methods, even though we did not match the slugger, we came up with the idea that in the long run we can win the race. We can make a team that can win the victory without spending too much money.

Actually, this story is not limited to baseball. Many people, such as companies, organizations and schools, think of that in existing “boxes”; then, they repeat the same mistake again and again.

After all, no matter how you think, you can only come up with a similar way, and even if you do it over and over, the result will not change.

In the movie, the scouter of the old stock said to the GM, “Baseball is what human beings do, so I can not think that mathematics predicts the outcome of baseball.  Sports always make things happen unexpectedly.

I certainly think so. However, he was just looking for a nearby player to compensate for the number of home runs and hitting average of the traded players. He is actually the one who gets stuck with the existing “mathematics.”

In the US, people say “Think outside the box.” However, it is easy to say, but it is difficult to do.

Perhaps the essence of this movie is universally teaching people who can not get out of existing ways of thinking. We can learn the importance of communication, patience, and calmness to manage organizations.

Discrete dynamics and its applications to our daily lives

Math, physics, engineering, and our lives are closely related. Physics formulates the nature’s motion with mathematics. This provides applications to creating a convenient system for our living.

Let us introduce a two dimensional discrete mapping:
x_(n+1) = 0.6x + y + 5.2/(1.0 + x^2)
y_(n+1) = -0.9999x
The plot is shown as a picture above.

The above equation is a mathematical example, but such model can be used to analyze population growth, radioactive decay, pollution control, medication dosages, robotics, etc.

Complicated waves made from a simple equation

Speaking of waves, we come up with ocean. Wind creates complicated shapes of waves as you know.

Waves have an interesting property that is called principle of superposition. Each wave oscillates up and down. When an up-wave and a down-wave collide at a point, the both waves appear to be vanished if both waves have an equal amplitude.

Sounds and electromagnetic waves also have the same property.

The picture is expressed by the equation, sin(x^2)-cos(y^2)-sin(x*y).