Thursday, February 06, 2014

The Mathematics of Miracles

What is a miracle?

The word נֵס (nes),   נִסִּים (nee-SEEM) - plural of נס - is a miracle in Hebrew.

For observant people, a "nes" as an action, from G-d, that is supernatural. The word "nes" also means the sail of a boat. The sail enables the boat to move along, to travel in a path.  One can see that there is a force controlling which way the boat is traveling. When a person experiences a miracle, it becomes clear that there is a force controlling the direction of his life. Quoting Chabad web site resources:
What we refer to as nature is actually miraculous and “unnatural.” It is only because “natural” events happen all the time that we take them for granted.
In the words of the Talmud, “The one to whom the miracle is happening, does not recognize the miracle.”  Extraordinary miracles wake us up to the fact that all of life, down to the minute details, is one big miracle.

How do miracles work?

Maimonides, in his Guide for the Perplexed, (his philosophy treatise) writes that all supernatural events were “programmed” into the world at the time of creation. Thus, the Talmud says that G‑d “made a condition with creation” that when the Jews would arrive at the Red Sea on their way from Exodus from Egypt, it would split. 

Others see open miracles as G‑d “stepping in” and shattering the law of nature to change and defy it.

The latest and most unexpected explanation for miracles comes from David J. Hand, - a mathematician  and renowned statistician  - the author of a book "The Improbability Principle: Why Coincidences, Miracles and Rare Events Happen Every Day" . You can  pre-order the book from Amazon.

David J. Hand argues that extraordinarily rare events are anything but. In fact, they are commonplace. We should all expect to experience a miracle roughly once every month.

The Improbability Principle breaks this circular reasoning against
miracles,dispelling the myths that miracles are false and do not occur

Never Say Never

This is the title of an article written by David Hand for Scientific American on January 21, 2014

He defined a set of mathematical laws, - The Improbability Principle - that tells us we should not be surprised by coincidences.

The birthday problem

For example, how many people must be in a room to make it more likely that two people have exactly the same birthday?. More likely means there is 51% probability. At first , trying to answer the questions, one thinks of herself. How many people have the same birthday as I? But the question involves any two people who are in the room.

The answer is surprisingly low, 23. Only 23? Yes, only 23 and this completely unexpected for the majority of people

First we calculate the probability the none, zero people have the same birthday like me. For  1 person the probability  is 364/365 If there are "n" people in room, there are "(n-1)" people who must have a different birthday than mine. For 23 people, the probability that no one has the same birthday as me is ([364/365) *(23-1)]. The result is 0.94.

If there is a 94% probability that none share my birthday, then there is a 6% probability that someone is born on the same day and month as me.

This is very small and this is the wrong answer. We want to know if any pair among the 23 people in the room share the same birthday. We have in the room n*(n-1)/2 pairs of people. For 23 people we have 253 pair. The total probability that none of the pair share the same birthday will be:

(364/365)*(363/365)*(362/365).....*(343/365) =0.49

As the probability that none of the people in the room share the same birthday is 49%, then the probability that one pair shares the same birthday is (100%-49%) = 51%

Isn't this elegant?

Calculated miracles no one thought possible

On September 6 and September 10, 2009, four days apart, the Bulgarian lottery had exactly the same winning numbers; 4, 15, 23, 24, 35, 42 . The authorities ordered a fraud investigation and they found nothing. The probability for this event to happen, as calculated with the Improbability Principle is 1 in 13,983,816.  

Compared to nature,  - a 1  in 14 millions for the same consecutive winning numbers lottery - is a high probability. The probability for one sperm to fertilize the egg in humans is 1 in 280 millions, 20 times lower. Every person alive today, including of course everyone reading this blog, is the winner of a seemingly impossible to win lottery.

We are all a miracle and we do not know it

The World Wide Web

There are 2.5 billion users on WWW. This means there are  3*1018   pairs of people and 10750,000,000  possible groups of interacting members

Now this number is big, but quoting David Hand, this is good thing.
Even events with very small probabilities become almost certain if you give them so many opportunities to happen

Statistical mathematicians versus Data Scientists

Data Scientists

In  What a Data Scientist Does?  I wrote:
There is a big debate about who the Data Scientists are. Are they statisticians or are they computer science?
In another blog entry, GigaOm founder Om Malik says
The problem with data is that the way it is used today, it lacks empathy and emotion. Data is used like a blunt instrument..
The idea of combining data, emotion and empathy as part of a narrative is something every company — old, new, young and mature — has to internalize. If they don’t, they will find themselves on the wrong side of history.
The computer scientists in business  may use advanced the statistical methods where the math as a shield  tactic is used so "fewer critics are available to be properly skeptical." Their ideas of emotion is executing orders, in which they prove whatever the boss wants them prove.

The Improbability Principle 

The Improbability Principle has an elegance, depth and powerful metaphors to discover the world around us. The maths are simple to follow. Mathematicians don't analyze just data, that analyze the world we are in and, there a spirituality in their work. Their mere existence is נֵס (nes) by itself and it has a very profound human touch. From torah.org
The letter "nun,"  represents downfall, suffering, and misfortune. The letter "samech," which in the alphabet, and in the word "nes," follows "nun," represents uplifting, salvation, and redemption. A miracle, a "nes," is the combination of these two elements: we are faced with trials and tribulations, and our situation is perilous. Yet, through divine providence, a supernatural occurrence rescues us and provides us with salvation. The word "nes" is a reminder of the ups and downs in life. 

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