Cricket – bat and ball game

Many young British Pakistanis play cricket for...
Many young British Pakistanis play cricket for recreation (Photo credit: Wikipedia)

That’s how Wikipedia describes cricket – as a bat and ball game. Since the Cricket World Cup is currently being staged in Australia and New Zealand, I thought that I would choose cricket as the topic for the week.

The roots of cricket are in England, though it so happens that the mother country of cricket has been eliminated from the Cricket World Cup (CWC). Cricket has spread to a number of other countries as a result of colonial and other influences and 14 teams have been taking part in the 2015 CWC.

List of ICC cricket member nations. Orange mar...
List of ICC cricket member nations. Orange marked countries are test teams, yellow are associate and purple are affiliate member nations. (Note: Certain island nations may not be shown.) For those who may not be able to make out the colours: Shade used for Australia is orange Shade used for United States is yellow Shade used for Mexico is purple (Photo credit: Wikipedia)

Cricket playing nations are either full members of the International Cricket Council or associate or affiliate members. The CWC contestants are the 10 full members and 4 other members who are required to qualify for the tournament. The ‘minnows’ as the associates and affiliates are often referred to rarely trouble the full members in matches, but upsets are not unknown.

Of the bat and ball games, cricket is of the class where a batsman defends a target from a ball thrown (“pitched” or “bowled”) by a player from the other team. Points (referred to as runs) are scored by running from one end of the pitch to the other, or by hitting the ball out of bounds.

Sri Lankan bowler Muttiah Muralitharan, the hi...
Sri Lankan bowler Muttiah Muralitharan, the highest wicket taker in both Test and ODI forms of cricket bowls to Adam Gilchrist. (Photo credit: Wikipedia)

Cricket is similar to baseball and softball and the informal game of rounders in the sense that the members of the batting team take turns ‘at bat’. The target area is a physical target in cricket (“stumps” and “bails”) but is a virtual box in baseball and softball. There is no specific target in rounders, where the ball just has to be hittable by the batter.

Cricket has two “targets” or wickets, and I can’t think of any other bat and ball sport that has two wickets or the equivalent. The wickets are one chain apart in the old Imperial measures, and the person who delivers the ball to the batsman throws or bowls the ball from one wicket to the other. The game switches around after every 6 balls, with a second bowler bowling at the batsman at the other end of the pitch. This is termed an “over” as the supervising official, the umpire, calls “Over” when six balls have be bowled.

English: Wicket, the stumps being hit by a ball
English: Wicket, the stumps being hit by a ball (Photo credit: Wikipedia)

In informal or backyard cricket it is common to have just one wicket and a single pole (or stump) for the bowler to deliver the ball from. Other rules are ignored or modified as appropriate from the much smaller space available. In recent years, there has been a move to formalise at least some games of backyard or beach cricket and to institute competitions in the formalised code. These are still considered “fun” games though.

There are variants of cricket played in some Pacific Islands, The rules of these variants are also informal, team sizes are variable, and the bat often resembles a war weapon. Teams can contain both men and women and people of all ages. The Wikipedia article mentions that there have been attempts to formalize the rules of this variant of the sport.


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The original format of the formal game of cricket is multi-day, multi-innings. Even the Island form of the game runs to several days, but that may be related more to the social nature of island cricket than anything else. As in any formal game the equipment and the uniform is closely specified and in particular the uniform is white – known as “cricket whites”.

The multi-day format is unusual in sports and arises from the fact that each team has eleven players and each may have to have their time at bat twice in a game. Shorter forms are often played at a semi-formal or provincial level, many being completed in one innings in one day. Cricket is not a quick game in terms of time taken, as each batsman may face upwards of one hundred balls. The semi-formal “village green” cricket is a leisurely affair, in spite of the fact that the ball may be bowled at speeds of up to 150kph.

A family playing cricket on the Village Green
A family playing cricket on the Village Green (Photo credit: Wikipedia)

A new form of cricket has developed where the number of overs or sets of six balls is restricted to 50 for each team. The uniforms are not restricted to white and some other minor changes have been made to the rules. These changes have led to a more exciting, quicker form of the game and the matches are over in one day. This is the form that is being played for the Cricket World Cup.

There is an even shorter version of the game called Twenty20, which is a fast paced version with only 20 overs per side. Both the 20 over and (slightly less so) 50 over versions of the game result in fast scoring and more excitement than the standard version of the game as teams, both fielders and batsman take a  more highly charged attitude.

Turner slides to prevent a boundary during a T...
Turner slides to prevent a boundary during a Twenty20 Cup match against Gloucestershire. (Photo credit: Wikipedia)

The sport is professional at the top level, and the top players are treated as celebrities. Since the sport is international these days players get to play in many countries. In particular many overseas players play in the Indian Premier League, a very rich Twenty20 competition based, as the name implies, in the Indian sub-continent.

The stance of a batsman in cricket is side on, with the bat grounded before the bowler start his delivery and raised backwards in preparation for the stroke. Consequently there are left hand and right batsmen (and bowlers). Since the game has been around there are unique terms for various matters to do with the game.

Collins's batting stance
Collins’s batting stance (Photo credit: Wikipedia)

For example, the field positions have traditional names which might seem whimsical. “Silly Mid On” is one of them. It certainly is “silly” as it is close to the batsman in the natural line of a stroke on the on or leg side. The position is intended for a close in catch and is obviously dangerous as the ball is hard, much like a baseball. Some Silly Mid On fielders wear protective helmets and other gear.

One field position that I had not heard of until recently is “Cow Corner”. A fielder at Cow Corner is in much the same line from the bat as Silly Mid On, but much further away, almost on the edge of the field (the “boundary”). The name seemly relates to the rustic roots of the game where the field was indeed a field or paddock that had to be cleared of livestock before a game could commence.


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Of course, the cattle would most likely have left deposits behind them which could trouble the fielders during the game.


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Why Pi?

Based on Image:P math.png
Based on Image:P math.png (Photo credit: Wikipedia)

If you measure the ratio of the circumference to the diameter of any circular object you get the number Pi (π). Everyone who has done any maths or physics at all knows this. Some people who have gone on to do more maths knows that Pi is an irrational number, which is, looked at one way, merely the category into which Pi falls.

There are other irrational numbers, for example the square root of the number 2, which are almost as well known as Pi, and others, such as the number e or Euler’s number, which are less well known.

Illustration of the Exponential function
Illustration of the Exponential function (Photo credit: Wikipedia)

Anyone who has travelled further along the mathematical road will be aware that there is more to Pi than mere circles and that there are many fascinating things about this number to keep amateur and professional mathematicians interested for a long time.

Pi has been known for millennia, and this has given rise to many rules of thumb and approximation for the use of the number in all sorts of calculations. For instance, I once read that the ratio of the height to base length of the pyramids is pretty much a ratio of Pi. The reason why this is so leads to many theories and a great deal of discussion, some of which are thoughtful and measured and others very much more dubious.

Menkaure's Pyramid
Menkaure’s Pyramid (Photo credit: Wikipedia)

Ancient and not so ancient civilisations have produced mathematicians who have directly or indirectly interacted with the number Pi. One example of this is the attempts over the centuries to “square the circle“. Briefly squaring the circle means creating a square with the same area as the circle by using the usual geometric construction methods and tools – compass and straight edge.

This has been proved to be impossible, as the above reference mentions. The attempts to “trisect the angle” and “double the cube” also failed and for very similar reasons. It has been proved that all three constructions are impossible.

English: Drawing of an square inscribed in a c...
English: Drawing of an square inscribed in a circle showing animated strightedge and compass Italiano: Disegno di un quadrato inscritto in una circonferenza, con animazione di riga e compasso (Photo credit: Wikipedia)

Well, actually they are not possible in a finite number of steps, but it is “possible” in a sense for these objectives to be achieved in an infinite number of steps. This is a pointer to irrational numbers being involved. Operations which involve rational numbers finish in a finite time or a finite number of steps. (OK, I’m not entirely sure about this one – any corrections will be welcomed).

OK, so that tells us something about Pi and irrational numbers, but my title says “Why Pi?”, and my question is not about the character of Pi as an irrational number, but as the basic number of circular geometry. If you google the phrase “Why Pi?”, you will get about a quarter of a million hits.

Animation of the act of unrolling a circle's c...
Animation of the act of unrolling a circle’s circumference, illustrating the ratio π. (Photo credit: Wikipedia)

Most of these (I’ve only looked at a few!) seem to be discussions of the mathematics of Pi, not the philosophy of Pi, which I think that the question implies. So I searched for articles on the Philosophy of Pi.

Hmm, not much there on the actual philosophy of Pi, but heaps on the philosophy of the film “Life of Pi“. What I’m interested in is not the fact that Pi is irrational or that somewhere in its length is encoded my birthday and the US Declaration of Independence (not to mention copies of the US Declaration of Independence with various spelling and grammatical mistakes).

Pi constant
Pi constant (Photo credit: Wikipedia)

What I’m interested in is why this particular irrational number is the ratio between the circumference and the diameter. Why 3.1415….? Why not 3.1416….?

Part the answer may lie in a relation called “Euler’s Identity“.

e^{i \pi} + 1 = 0

This relates two irrational numbers, ‘e’ and ‘π’ in an elegantly simple equation. As in the XKCD link, any mathematician who comes across this equation can’t help but be gob-smacked by it.

The mathematical symbols and operation in this equation make it the most concise expression of mathematics that we know of. It is considered an example of mathematical beauty.


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The interesting thing about Pi is that it was an experimental value in the first place. Ancient geometers were not interested much in theory, but they measured round things. They lived purely in the physical world and their maths was utilitarian. They were measuring the world.

However they discovered something that has deep mathematical significance, or to put it another way is intimately involved in some beautiful deep mathematics.

English: Bubble-Universe's-graphic-visualby pa...
English: Bubble-Universe’s-graphic-visualby paul b. toman (Photo credit: Wikipedia)

This argues for a deep and fundamental relationship between mathematics and physics. Mathematics describes physics and the physical universe has a certain shape, for want of a better word. If Pi had a different value, that would imply that the universe had a different shape.

In our universe one could consider that Euler’s Relation describes the shape of the universe at least in part. Possibly a major part of the shape of the universe is encoded in it. It doesn’t seem however to encode the quantum universe at least directly.

English: Acrylic paint on canvas. Theme quantu...
English: Acrylic paint on canvas. Theme quantum physics. Français : Peinture acrylique sur toile. Thématique physique quantique. (Photo credit: Wikipedia)

I haven’t been trained in Quantum Physics so I can only go on the little that I know about the subject and I don’t know if there is any similar relationship that determines the “shape” of Quantum Physics as Euler’s Relation does for at least some aspects of Newtonian physics.

Maybe the closest relationship that I can think of is the Heisenberg Uncertainty Principle. Roughly speaking, (sorry physicists!) it states that for certain pairs of physical variables there is a physical limit to the accuracy with which they can be known. More specifically the product of the standard deviations of the two variables is greater than Plank’s constant divided by two.

English: A GIF animation about the summary of ...
English: A GIF animation about the summary of quantum mechanics. Schrödinger equation, the potential of a “particle in a box”, uncertainty principle and double slit experiment. (Photo credit: Wikipedia)

In other words, if we accurately know the position of something, we only have a vague notion of its momentum. If we accurately know its velocity we only have a vague idea of its position. This “vagueness” is quantified by the Uncertainty Principle. It shows exactly how fuzzy Quantum Physics.

The mathematical discipline of statistics underlay the Uncertainty Principle. In a sense the Principle defines Quantum Physics as a statistically based discipline and the “shape” of statistics determines or describes the science. At least, that is my guess and suggestion.


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To return to my original question, “why Pi?”. For that matter, “why statistics?”. My answer is a guess and a suggestion as above. The answer is that it is because that is the shape of the universe. The Universe has statistical elements and shape elements and possibly other elements and the maths describe the shapes and the shapes determine the maths.

This is rather circular I know, but one can conceive of Universes where the maths is different and so is the physics and of course the physics matches the maths and vice versa. We can only guess what a universe would be like where Pi is a different irrational number (or even, bizarrely a rational number) and where the fuzziness of the universe at small scales is less or more or physically related values are related in more complicated ways.


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The reason for “Why Pi” then comes down the anthropological answer, “Because we measure it that way”. Our Universe just happens to have that shape. If it had another shape we would either measure it differently, or we wouldn’t exist.


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