Feeds:
Posts

## Bluebirds flying high

Even if the state of Welsh regional rugby is not good, the same cannot be said of Welsh football. Swansea City FC are doing very well in the English Premiership, lying mid-table and with several big wins this season. They have also just got through to the final of the League Cup, beating Chelsea 2-0 on aggregate last night. And Cardiff City FC are flying high in the Championship, the league below the Premiership.

The Cardiff City football club club badge.

The Championship table as it stood on Saturday (19th January 2013). Cardiff City are 10 points clear at the top of the Championship table with 28 of the 46 games played.

With 28 games played of the 46 in the season, Cardiff City have 60 points, 10 points clear of their nearest rivals. Of course, as anyone who has been following Cardiff City will know, they have failed to gain promotion to the Premiership several times in the last few seasons. Having grown up in Pembrokeshire I don’t have the same tribal loyalty towards Cardiff City that its die-hard supporters have. So most of them would not join me in saying how wonderful it would be to see both Cardiff and Swansea playing in the Premiership. But surely that can only be good for Welsh football and for Wales as a country.

## Murray in Melbourne

As I type this early on Wednesday morning (23rd of January 2013), half a World away in Melbourne Andy Murray is playing in the quarter final of the Australian Open Tennis tournament. He is playing against Jérémy Chardy of France, and Murray has just won the 1st set 6-4. Chardy is currenty ranked 36 in the World, Andy Murray is ranked 3rd. So, on paper at least, it should be a win for Andy Murray. Should he win, he has the unenviable prospect of facing Roger Federer in the semi final on Friday.

As those of you who follow tennins will know, Murray won his first Major a few months ago, when he won the US Open in September 2012. This came after his agonising defeat in Wimbledon, which I blogged about here, but also after his success one month later in August in the 2012 Olympics.

Andy Murray won his 1st Major, the US Open, in September 2012.

Prior to winning his first major, Murray had suffered an agonising series of 4 defeats in major finals. In particular, in Australia where he lost twice in a row. He lost to Roger Federer in the 2010 final, and in the 2011 final he lost to Novak Djokovic. Here is a summary of Murray’s records in Grand Slam finals.

Murray’s record in Majors
Year Tournament Opponent Score
2008 US Open Roger Federer 2-6, 5-7, 2-6
2010 Australian Open Roger Federer 3-6, 4-6, 6-7
2011 Australian Open Novak Djokovic 4-6, 2-6, 3-6
2012 Wimbledon Roger Federer 6–4, 5–7, 3–6, 4–6
2012 US Open Novak Djokovic 7–6, 7–5, 2–6, 3–6, 6–2

Now that Murray has finally won his first Major and got that monkey of his back, many are expecting him to go on and win many more over the next several years. Only time will tell. Certainly having Ivan Lendl as his coach seems to have made a big difference. Lendl won 8 Major finals in his career, but just like Murray he lost his first 4 Gland Slam finals. This experience has probably proved invaluable in advising Murray on how to improve his mental approach and start winning at the final hurdle. Should Murray win in Melbourne, he will be the first man in history to follow up his 1st major victory with a 2nd victory.

## +++++UPDATE+++++

Murray won easily, 6-4 6-1 6-2.

## The 22nd amendment to the US Constitution

This last Monday (21st of January 2013), the 44th president of the United States, Barack Obama, was sworn into his 2nd term in office. No matter how popular Obama is in 2016, he cannot stand for a 3rd term of office due to the 22nd Amendment to the United States Constitution. This was introduced in 1951, and as a consequence of this amendment to the Constitution, no US President since then has been allowed to be elected to more than 2 terms of office (strictly speaking they could serve 3 terms if they were Vice President and their first term came about through the incumbent President leaving office).

Barak Obama being sworn into office on 21st of January 2013.

In fact, of the 44 US Presidents, only one has served more than 2 terms of office, namely Franklin Delano Roosevelt, who was US President from March the 4th 1933 until his death on the 12th of April 1945, winning elections in 1932, 1936, 1940 and 1944. How many presidents have been elected to two terms of office rather than just one? And how many presidents have never been elected to office, but became President through the death or resignation of the incumbent?

The 2013 US Presidential inauguration.

## Presidents who have been elected to only one term

Here is a table of the presidents who have been elected to only one term. Note, in some cases they actually served two terms, e.g. Lyndon B. Johnson, who became President when John F. Kennedy was assassinated in November 1963, but then won his own election in November 1964 and served one full term as an elected President. Also note that this table does not include presidents who were never elected to the office but served a term as President due to the incumbent President leaving office through death or resignation.

Presidents who have been elected to one term
Name Year of inauguration after being elected Comments
John Adams 1797 2nd President of the U.S.A. Served his full term.
John Quincy Adams 1825 6th President of the U.S.A. Served his full term.
Martin van Buren 1837 8th President of the U.S.A. Served his full term.
William Henry Harrison 1841 9th President of the U.S.A. Died on his 32nd day in office from complications from pneumonia, the shortest presidential term in US history.
James K. Polk 1845 11th President of the U.S.A. Served his full term.
Zachary Taylor 1849 12th President of the U.S.A. Died 16 months into his term of office of natural causes.
Franklin Pierce 1853 14th President of the U.S.A. Served his full term.
James Buchanan 1857 15th President of the U.S.A. Served his full term.
Rutherford B. Hayes 1877 19th President of the U.S.A. Served his full term.
James Garfield 1881 20th President of the U.S.A. Was assassinated 200 days into his term of office. He was the 2nd US President to be assassinated.
Grover Cleveland 1885 22nd President of the U.S.A. Served his full term.
Benjamin Harrison 1889 23rd President of the U.S.A. Served his full term.
Grover Cleveland 1893 24th President of the U.S.A. The only US President to be elected to two non-consecutive terms of office.
Theodore Roosevelt 1905 26th President of the U.S.A. Came into office in September 1901 upon William McKinley’s assassination. Won the Presidency in his own right in 1904. The youngest US President in history, sworn into office when 42 years of age.
William Howard Taft 1909 27th President of the U.S.A. Served his full term.
Warren G. Harding 1921 29th President of the U.S.A. Collapsed and died in August 1923.
Calvin Coolidge 1925 30th President of the U.S.A. Came into office upon the death of Warren Harding, won the Presidential election in his own right in 1924.
Herbert Hoover 1929 31st President of the U.S.A. Served his full term.
Harry S. Truman 1949 33rd President of the U.S.A. Came into office upon the death of Franklin Delano Roosevelt in April 1945. Won the Presidential election in his own right in 1948.
John F. Kennedy 1961 35th President of the U.S.A. The youngest President to be elected to office, 43 years old when inaugurated. Was assassinated by Lee Harvey Oswald in November 1963.
Lyndon B. Johnson 1965 36th President of the U.S.A. Came into office upon the assassination of John F. Kennedy. Won the Presidential election in his own right in 1964.
Jimmy Carter 1975 39th President of the U.S.A. Served his full term.
George H. W. Bush 1989 41st President of the U.S.A. Served his full term.

As you can see from the above table, there are 23 presidents who have been elected to only one term. [note: I have put Grover Cleveland in this table even though he was elected to two terms of office, as he served two non-consecutive terms. He counts twice in the list of the 44 Presidents to-date.]

## Presidents who have been elected to two terms

The following is a list of the Presidents who have been elected to two terms. Note, this list does not include presidents like Theodore Roosevelt, who served two terms but was only elected to his 2nd term, his 1st term as President arose through the death of William McKinley.

Presidents who have been elected to two terms
Name Years of inauguration after being elected Comments
George Washington 1789 and 1793 The 1st President of the United States. Served his full two terms.
Thomas Jefferson 1801 and 1805 3rd President of the U.S.A. Served his full two terms.
James Madison 1809 and 1813 4th President of the U.S.A. Served his full two terms.
James Monroe 1817 and 1821 5th President of the U.S.A. Served his full two terms.
Andrew Jackson 1829 and 1833 7th President of the U.S.A. Served his full two terms.
Abraham Lincoln 1861 and 1865 16th President of the U.S.A. Assassinated in April 1865, just over 1 month into his 2nd term of office, by John Wilkes Booth.
Ulysses S. Grant 1869 and 1873 18th President of the U.S.A. Served his full two terms.
William McKinley 1897 and 1901 25th President of the U.S.A. Was assassinated in September 1901, 6 months into his 2nd term of office. He was succeeded by his Vice President, Theodore Roosevelt, who became the youngest person to serve as US President.
Woodrow Wilson 1913 and 1917 28th President of the U.S.A. Served his full two terms.
Dwight D. Eisenhower 1953 and 1957 34th President of the U.S.A. Served his full two terms.
Richard M. Nixon 1969 and 1973 37th President of the U.S.A. Resigned in August 1974 after the Watergate scandal, some 18 months into his 2nd term.
Ronald Reagan 1981 and 1985 40th President of the U.S.A. Served his full two terms.
William Jefferson Clinton 1993 and 1997 42nd President of the U.S.A. Served his full two terms.
George W. Bush 2001 and 2005 43rd President of the U.S.A. Served his full two terms.
Barack Obama 2009 and 2013 44th President of the U.S.A. Just starting his 2nd term.

As you can see from this table, there are 15 presidents who have been elected to two terms.

## Presidents never elected to the office of President

There are also presidents who have never been elected to office. They are Vice Presidents, who are made President when the incumbent leaves office (usually through death, but once in the case of Richard Nixon, through resignation).

Presidents who have never been elected President
John Tyler 1841 The 10th President and the 1st President to never be elected as President, he was made President when William Henry Harrison died in office and served only 1 term.
Millard Fillmore 1850 The 13th President and the 2nd President to never be elected as President, he was made President when Zachary Taylor died in office and served only 1 term.
Andrew Johnson 1865 17th President, was made President upon the assassination of Abraham Lincoln. Also the 1st President to be impeached, he was acquitted by 1 vote. He is generally considered the worst President in US history.
Chester A. Arthur 1881 21st President, came to office upon the assassination of James A. Garfield.
Gerald Ford 1974 The 38th President, and so far the only President to come to office due to the resignation of the incumbent (Richard Nixon).

There are 5 presidents in this final list.

## Franklin Delano Roosevelt

Franklin Delano Roosevelt (FDR) is unique amongst US Presidents in that he was elected to office a record 4 times. It was this that led to the Constitution being amended to limit presidents to only being allowed to be elected a maximum of two times.

Franklin Delano Roosevelt at his 1st inauguration in 1933.

So, in summary, 23 presidents elected once, 15 elected twice, 5 never elected and FDR elected 4 times, which makes a total of 44.

Who do you consider to be the greatest US President? And the worst?

## How will Wales do in the 2013 Six Nations?

In Wales, our National rugby team is either playing fantastically or playing dreadfully. In 2012 we saw both extremes. After winning the 2012 Six Nations Championships with a Grand Slam in March, Wales went on tour of Australia in June and lost all 3 tests against the Wallabies. All 3 were close, but particulary the 2nd and 3rd ones, two games Wales should really have won.

Wales win the 2012 6 Nations Championships with a Grand Slam, beating France in the final match.

Wales went into the annual Autumn Tests series with high expectations amongst her supporters, including myself. I blogged about my hopes here. Well, the reality was very different, Wales lost all four tests, the first time this has happened in the Autumn Test Series since it started in about 2002. I guess, in hindsight, that it was not a big surprise to lose to Argentina in our opening game. Wales traditionally start the Autumn Series very badly, and so to have such a tough team as Argentina to play in our opening test was always going to be a challenge.

But, before Wales could recover from the disappointment of losing to Argentina, we lost to Samoa the following Friday. Again, Samoa are a tough team, and we have lost to them before, even in Cardiff. But coming on the back of such successes earlier in the year, it was a tough defeat for the Welsh rugby public to bear. The following week came our annual beating by the All Blacks, whom we have not defeated since 1953!

Our final match was against Australia, our 4th against them in 2012. Just like the 2nd and 3rd Tests in Australia in June, Wales were in a match winning position as the 80 minutes were up. In fact, with 80 minutes on the clock Wales were actually in the lead. But, bizarrely, we kicked possession away and Australia counter attacked, and scored a last minute try to steal victory. The narrowness of the defeat, and the nature of it happening in the dying seconds, made this the hardest defeat of the Autumn series, and maybe of the entire year.

So how will Wales get on in the impending 2013 Six Nations? My fear is – not very well. We are coming off the back of 7 (seven) straight defeats, so confidence in the squad has to be pretty low. Also, we will be without our inspirational team manager Warren Gatland, who has been appointed the Lions coach for the summer tour of Australia, and so is on sabbatical from his Wales duties.

It is also the year when we play 3 games away from home, and only 2 at home, which of course makes it a slightly tougher proposition. Our fixture list is

Wales’ 6 Nations games, 2013
Date Country Kick-off time (GMT) Home/Away Record in all competitions (Played/Win/Loss/Draw)
Saturday 2nd February Ireland 13:30 Home 118/65/47/6
Saturday 9th February France 17:00 Away 92/45/44/3
Saturday 23rd February Italy 14:30 Away 19/16/2/1
Saturday 9th March Scotland 14:30 Away 117/66/48/3
Saturday 16th March England 17:00 Home 123/55/56/12

It may surprise readers to see that the only nation in the 6 Nations that Wales have lost more than won against is England, with the games standing at 55 wins to Wales and 56 to England. The game against England in March provides an opportunity to equalise the series of games between the two countries. On the other hand, the game against France in February provides France with the opportunity to equalise the series between the two countries, currently Wales have 45 wins to France’s 44.

Of course, how players across all 4 home nations perform will determine who gets picked by Warren Gatland and his team to go on the Lions tour of Australia in June, so this year the players are playing for more than just their country.

Who do you think will win this year’s 6 Nations?

## Vector basics

I wanted to get back to explaining Maxwell’s equations, which I mentioned in this blog of the statue to James Clerk Maxwell that is in Edinburgh. Before I do that I thought I would cover some very basic mathematics, namely the basic idea of vectors.

In physics and mechanics, a vector is something which has both size (magnitude) and direction. If the quantity has only a size, we call it a scalar. So, for example, in physics we differentiate between speed and velocity, even though in everyday language they are used interchangeably.

If we say a car is moving at 50 km/h, that is a speed, and hence is a scalar. But, if we were to say it is moving at 50 km/h due North, that is a velocity, and hence a vector as we have given it both a size and direction.

Vectors are very important in physics, and one of the most important and widely used vectors is force. We measure force in Newtons (named after Sir Isaac Newton), but a force has both a size and a direction. We usually denote a vector by either putting a line or arrow above the symbol, or by using a bold font. I will use an arrow above the symbol, so for example $v$ would be a scalar, but $\vec{v}$ would be a vector.

Any vector in 3-dimensional space can be split into 3-components. This is often useful, as unlike scalars which add simply, when we add vectors we need to take into account their directions. As an example, suppose we have two forces $\vec{F_{1}}$ which has a size of 7N in the x-direction, and $\vec{F_{2}}$ which has a size of 5N at $25^{\circ}$ to the x-axis. The combined force is not 12N, as the two forces are not acting in exactly the same direction.

A 7N and a 5N force at 25 degrees to each other, with the 7N force acting along the x-direction.

To find the combined (resultant) force, we need to split the two forces up into their x and y-components. To do this we simply use trigonometry, and note the unit vectors $\hat{x}$ and $\hat{y}$, which are vectors with a size of unity (1) in the x and y-directions respectively. We can then split each of the forces $\vec{F_{1}}$ and $\vec{F_{2}}$ into their respective x and y-components.

$\vec{F_{1}} = 7\cos(0) \hat{x} + 7\sin(0) \hat{y} = 7\hat{x} + 0\hat{y}$

$\vec{F_{2}} = 5\cos(25) \hat{x} + 5\sin(25) \hat{y} = (5 \times 0.9063)\hat{x} + (5 \times 0.4226)\hat{y} = 4.53 \hat{x} + 2.11 \hat{y}$

From this we can write that the total force in the x-direction is $7 + 4.53 = 11.53 \hat{x}$ and the total force in the y-direction is $0 + 2.11 = 2.11 \hat{y}$. To then find the resultant force, we need to combine these two components as follows

The size of the resultant force R can be calculated using Pythagoras’ theorem, its direction using trigonometry.

To calculate the size of the resultant vector we just use $R^{2} = x^{2} + y^{2}$ so here $R^{2} = (11.53)^{2} + 2.11^{2} = 157.0 + 4.45 = 137.39$ so $R=\sqrt{137.39}=11.72 N$. To calculate the angle $\theta$ we note that $\theta = \arctan \left( \frac {2.11} {11.72} \right) = 10.2^{\circ}$.

So, as we can see, the resultant of these two forces is a force of size 11.72N which is at an angle of $10.2^{\circ}$ to the x-axis.

In a series of future blogs I will go on from these basic ideas of vectors to talk about vector fields, which we need to understand in order to understand Maxwell’s equations.

A vector field. The length of each arrow represents the strength of the field at that location, the direction is given by the orientation of the arrow.

## Cardiff turns white

On Friday (18th January 2013) Cardiff woke up to a blanket of white. This was the first snow of the winter, and as usual in Wales, with a light dusting of snow chaos ensued. Even the M4 motorway was closed for several hours because of an accident. It’s very different from my 6 years in Wisconsin. I moved to Wisconsin in the summer of 1995. I remember waking up in November 1995 at about 2am on a Sunday morning, woken by the sound of snow ploughs out clearing the roads. By the time I got up on that Sunday morning, despite over 30cm of snow having fallen, all the roads were clear. Wales, on the other hand, shuts down if we have more than 2cm!

Here are some of the photographs I took of the snow on Friday, mainly in Bute Park.

What is the heaviest snow fall you’ve experienced?