Minimax Decision Theory

Minimax – Decision Rule 

Minimax is referred to a decision rule which is used in decision theory, statistics, game theory and philosophy, in reducing the possible loss for a worst case scenario. It is a principle for decision making when presented with two various and conflicting strategies with the use of logic and determine using the strategy which will minimize the maximum loss that may occur.

Formulated earlier for two players zero sum game theory covers both cases wherein players make alternate moves. Those that make simultaneous moves have been extended to more complex games with general decision in the presence of uncertainty. In the case of theory of simultaneous games, a minimax strategy is considered to be a mixed strategy that is part of the solution to a zero sum and in zero sum games; the minimax solution is the similar to the Nash equilibrium.

There is a minimax algorithm for game solutions in combinatorial game theory. With games like tic-tac-toe, simple version of the minimax algorithm is used where individual player can win, lose or end up in a draw. Minimax algorithm is considered to be a recursive algorithm in choosing the next move in a game which usually has two players participating in a game.

Combinatorial Game Theory

It is associated with a value for each position or state of the game and the value is computed by a position evaluation function, indicating how good it would be for a player to reach a particular position. The player on his part tends to make the maximum moves thereby minimizing the value of the position from the opponent’s following moves.

 An allocation method comprises of assigning a certain win for one play as +1 and for the other player as -1 which leads to combinatorial game theory developed by John Horton Conway. Using a rule is an alternative if the result of a move is an immediate win for one player, it is considered positive infinity and if it is an immediate win for the other player, then it is a negative infinity. Value of the first player of any other move is the minimum values resulting from each of the second players possible moves. Due to this the first player is called the maximizing player while the second player is called the minimizing player; hence it is given the name minimax algorithm.

Heuristic Evaluation Function 

This algorithm assigns a value of positive as well as negative infinity to any position since the value of every position will be the value of some final winning or losing position. Generally this is often possible at the end of a complicated game like chess because it is not feasible to know about the result before the completion of the game which could lead to one of the player winning.

We could extend this if we supply a heuristic evaluation function which gives values to non final game status without taking into account all possible following complete sequences and then limit the minimax algorithm to note only a certain number of moves coming up. The number is known the `look-ahead’, which is measured in `plies’. For instance, the chess computer `Deep Blue’ looked forward to at least 12 plies and then applied a heuristic evaluation function.

Western Wall Tunnel

Image Credit:shalomisraeltours.com

Western Wall Tunnel – Underground Tunnel 

The Western Wall Tunnel is an underground tunnel portraying the full length of the Western Wall and the tunnel is adjacent to the Western Wall, located under the buildings of the Old City of Jerusalem.

It is Judaism’s most sacred site and revered as the last remnant of the Second Temple and because of the invitation for everyone by King Solomon, visitors of all faith and cultures can come here and pray and experience specialpeace.

 The open air area of the Western Wall is around 60 metres long while the major part of its original length seems to be hidden underground and the tunnel enables access to an additional 485 metres of the wall. Day and night one will find worshippers here though on Bar Mitzvah days which is Mondays, Thursdays and Saturdays; families around the world and from Israel assemble at this place to celebrate their son’s first public Bible reading which is at the age of 13 together with the Jews from every destination.

Each of them assembles with their own respective customs, dress, music and liturgy creating a colourful as well as an unforgettable cultural event. Placing a traditional prayer within the ancient stones by the visitors is a memorable incident.

Image Credit: Generationword.com

Various Arches Side by Side 

The tunnels have been created by various arches side by side which supports staircases going to the Temple Mount from the city and in ancient times had shallow valley known as the Tyropaean running along the Western area of the Temple Mount which is now filled because of the constant demolition and rebuilding.

This separates the rich Herodian quarter from the Temple and the need to bridge it gave rise to the building of the arches. While the pathways continue to hold up the streets presently, the tunnel goes directly underneath the Muslim quarter.

King Herod had come up with a project to double the area of the Temple Mount in Jerusalem, in 19 BC by incorporating a portion of the hill on the Northwest and in order to do so; four retaining walls were constructed while the Temple Mount was expanded on top. The retaining walls were left standing, together with the platform after the Temple was destroyed by the Romans in 70 CE.

Western Stone – Largest and Heaviest Stone 

The tunnel besides exposing the 485 metre of wall also reveals the system of construction together with the various activities within the Temple Mount.

The excavations comprises of several archaeological discoveries from the Herodian period like the streets, monumental masonry, with parts of reconstruction of the Western Wall which dates to the Umayyad era together with variety of structures dating back to the Ayyubid, Hasmonean and Mamluke periods which were constructed to support the buildings in the vicinity of the Temple Mount.

The largest stone in the Western Wall called the Western Stone is also exposed within the tunnel, ranking as one of the heaviest piece ever lifted by anyone without the help of powered machinery. Its length is 13.6 metres, 3 metres high and the width is estimated between 3.5 and 4.5 metres while estimated weight is 570 short tons

Kadal-Katti – Shark Charmers of Ancient South India as Observed by Marco Polo

Image credit:1990 Painting by Kozyndan

Shark Charmers – Main feature of Fisheries

Till 1885, the main feature of fisheries in Asia was the services of the shark charmers or binders of sharks and their presences were considered essential by the superstition of Indian divers. The fishermen relied on the supernatural powers of these imposters and would refrain from diving without their supervision. It is not known which period influenced this idea but in 1294 when Marco Polo paid a visit, they were in full bloom of their authority and received one twentieth of the total catch of oyster amounting to a very considerable sum of money.

Being a very alert observer, Marco Polo had related some interesting details with regards to Tamil customs of his contemporary times. It seems that he was in South India on two occasions and the second time was during his journey to Persia on the way back to Venice. He mentioned about the charming of sharks by the use of mantras. He states`and they must also pay those men who charm the great fishes, to prevent them from injuring the divers, whilst engaged in seeking pearls under water, one twentieth part all that they take. Their charm hold good for that day only, for at night they dissolve the charm so that the fishes can work mischief at their will’.

Sharks – Dangers to Divers 

These shark charmers existed till about fifty years ago and were known as `kadal-katti. Sharks were the main occupational dangers to divers and being superstitious the divers would consult the shark charmers before starting their expedition underwater.

The divers would not venture out at sea till they would receive an assurance from the shark charmers that the mouth of the sharks remains close at their command.At every fishery, there were at least two or three shark charmers in attendance where one would go out at sea with the fleet while the other would recite mantras, performing some rituals on the shore.

The shark charmer would lock himself in a closed room and would sit before a brass basin which would be filled with magic water obtained from a secret well in which were silver replicas of male and female sharks. With this the shark charmer would get to know if there would be shark attack on a diver for one shark in the basin would bite the other.

By midday a signal would be made to stop work and the boats would head for the coast lining up close to the shore in front of a huge enclosure which was called as the kottu or oyster store.

Three Equal Heaps – Division of Ancient Origin

This comprised of nine open huts which were divided into compartments where the divers carried their catch into them depositing them in the compartment in three equal heaps which was a division of ancient origin.

Two heaps were chosen by the British official as the Government’s share while the third was left for the diver. While the divers took their oysters to sell or open, the Government’s share was counted and auctioned to the merchants.

Thereafter the oysters were placed in small pits along the sea and allowed to decompose where the final remains were rinsed and the pearls were picked out and graded, The haul of the pearls which were of great value for their golden hue made their way to Bombay where they were perforated and tied into ropes and later on sent to dealers and brokers all across the globe.

Ball Lightning

Ball Lightning – Rare Weather Phenomenon

A rare weather phenomenon known as ball lightning has been observed for the first time in nature by Chinese scientists. Ball lightning is an unexplained electrical phenomenon which occurs during thunderstorm, is unpredictable and is the reason why the researchers do not know much regarding it. It tends to last for more than a second that is considered long lived for lightning but hard to capture and study.

Some reports state that the ball would explode sometimes with fatal consequences and would leave behind the odour of sulphur. Several scientific hypotheses have been proposed down the centuries about the ball lightning. A report published in The Journal of Physical Chemistry, last year, has made researchers at the U.S. Air Force Academy in Colorado, to figure out how to reproduce ball lightning in the lab. Electrodes were used partially submerged in electrolyte solution in order to create high power electric sparks which resulted in bright white plasmoid balls.

According to layman’s term, ball lightning seems to be a big flash of light which looks circular and appears during a storm in the sky. Sometimes it tends to have a blue glow and emanates from objects like lightning rods or ship masts.

Few Scientific Data – Infrequency/Unpredictability

Till 1960, several scientists debated that ball lightning was not a real phenomenon inspite of numerous sighting throughout the world and laboratory experiments could produce effects which seemed to be visually similar to the reports of ball lightning.

 Many are speculating whether these were related to the natural phenomenon. The scientific data with regards to ball lightning are few due to its infrequency as well as unpredictability. Its existence is presumed on basis of reported public sightings which has produced some inconsistent findings. Based on inconsistencies and the lack of reliable data, the true nature of ball lightning is yet unknown.

The first optical spectrum which appears to be a ball lightning event was published and included a video at high frame rate in January 2014.According to historical account it is considered that the ball lightning to be the source of the legends which describe luminous balls like the Mapuche Anchimayen of mythology and some have claimed that it is harmless and small while others state that it is dangerous and large.

Mike Lindsay/US Air Force Academy

Various Theories

A study done in 1960 shows that 5% of the population of the Earth witnessed ball lightning while another study analysed reports of around 10,000 cases. One such description was reported on 21st October 1638, during the Great Thunderstorm near a church in Widecombe-in-the-Moor, Devon, England, where four people died with around 60 injured during a severe storm when an 8 foot ball of fire struck, entered the church and destroyed it.

The huge stones from the walls of the church were hurled to the ground and through the large wooden beams and the ball of fire smashed the pews as well as several windows filling the church with the odour of sulphur and dark thick smoke. It was reported that the ball of fire had been divided into two parts with one exiting from the window by smashing it open while the other disappeared in some area in the church.

The conclusion at the time was that the ball of fire was the `devil’ or the `flames of hell’ and the fire had sulphur smell. Others blamed it on two people who had been playing cards in the pew during the service which aroused God’s wrath.

Fringe Theory

Fringe theory - Viewpoint of Idea 

Fringe theory is a viewpoint or an idea held by a small group of supporters and includes the theories as well as the models of fringe science together with identical ideas in different areas of scholarship like humanities. It is used in a sense as a pejorative which is synonymous with pseudo-scholarship. Exact definition which classifies between the viewpoints, fringe theories and pseudo-scholarship may not be easy to construct due to the demarcation problems and issue of false balance could occur when these theories are presented as being same to the already accepted theories. Fringe theories are considered to be ideas which depart significantly from the existing or mainstream view in a specific field of study and are not the majority opinion or of the respected minority.

 According to Alexander Davidson, Financial journalist, he states that `such ideas as peddled by small band of staunch supporters’ though not necessarily without any merit. The theories tend to meet with varying levels of academic acceptance.

According to Daniel N, Robinson’s description he considered it as occupying `a limbo between the decisive dead end with the ultimately credible productive theory and though some fringe theories may comprise of work done to the much needed level of scholarship in respective field or study, the general term is close to the popular meaning of the word `theory’.

Discussed in Diverse Areas of Scholarship

Margaret Wertheim recommend that they should be considered in a manner which is similar to outsider art, curated at the Santa Monica Museum of Art, an 2003 exhibition which was dedicated to the work of Jim Carter, a fringe physicist.

 Fringe theories are discussed in diverse areas of scholarship including Biblical criticism, history, law, finance, medicine and politics, when the phrase is used in the context of fringe science. The theories also exist relative to fields of study which are beyond the mainstream like the cryptozoology.

Some ideas which were considered as fringe theories pejoratively were dismissed as out of touch with reality, cranks or crackpots by their advocates and are also at times considered to be interchangeable with or overlap, more disparaging categories like pseudoarchaeology, pseudohistory or pseudoscience.

Besides this, the term also describes conspiracy theories in derogatory sense and according to Richard Hofstadter, isan explanations of historical as well as political events for accomplishments of unrealistically powerful, secretive groups, `a vast insidious preternaturally effective conspiratorial international network.

Part of Established Scholarship

As described by Esther Webman it could also be conspirators of all superhuman power and cunning though the naming ideas as fringe could be less pejorative than to describe them as pseudo-scholarship and it is unlikely that it would identified as their own work as pseudoscience by anyone.

Most of the fringe theories tend to be part of an established scholarship and rejected ideas could help to refine mainstream thought. However external theories do not attempt it and they tend to be incorrect though some of the ideas tend to gradually receive wider acceptance till they are no longer considered as fringe theories and at times these theories tend to become the mainstream view and the known examples is Alfred Wegener’s theory of continental drift which served as the basis for a model of plate tectonics.