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Sachin Tendulkar, Kevin Bacon and Paul Erdos

Michael Jones | | Updated: October 7, 2015, 5:42 PM IST

An extension of Erdos and Bacon numbers is the combination of the two: a person's "Erdos-Bacon number" is the sum of their Erdos number and Bacon number. To possess a finite such a number, the individual in question must have both a chain of research papers linking them to Erdos, and a chain of films linking them to Bacon; numerous scientists and mathematicians have appeared in films, and a handful of actors have collaborated on scientific papers, so there are quite a number of people with both.

What about Bacon-Tendulkar numbers? Plenty of cricketers have appeared in films, so there are likely to be some with both numbers defined. For a start, Tendulkar himself appeared in Stumped (2003) alongside Alyy Khan, who appeared in A Mighty Heart (2007) alongside Demetri Goritsas, who appeared in X-Men: First Class (2011) alongside Kevin Bacon. Thus Tendulkar's Bacon number is 3, and since his Tendulkar number is 0 by definition, he has a Bacon-Tendulkar number of 3. Since Kevin Bacon is not known to have played cricket, the only way anyone could achieve a lower number would be to act with Bacon and play with Tendulkar; no-one has yet managed both, so Tendulkar's 3 appears to be the lowest such number of anyone.

Kapil Dev, Ravi Shastri, Rahul Dravid, Zaheer Khan and Yuvraj Singh all appeared in Stumped, so they have Bacon numbers of 3 by the same route as Tendulkar, and since they all played alongside him, they all have Bacon-Tendulkar numbers of 4. Other Indian players have also gone on to Bollywood: Salil Ankola, who made his Test debut in the same match as Tendulkar but never played another, has a Bacon number of 3 via his appearance in Silence Please... the Dressing Room (2004), as has Ajay Jadeja for Khel (2003)and Vinod Kambli for Annarth (2002). Mujhse Shaadi Karogi (2004) was another film featuring several Test players: Kapil Dev again, Navjot Sidhu, Javagal Srinath, Harbhajan Singh, Mohammad Kaif, Parthiv Patel, Irfan Pathan and Ashish Nehra. Rajpal Yadav, who was in Mujhse Shaadi Karogi, has a Bacon number of 2, so all those players have Bacon numbers of 3 and Bacon-Tendulkar numbers of 4.

Another value of 4 is obtained by someone better known for his exploits on the screen than on the pitch: Russell Crowe appeared alongside Burt Reynolds, who appeared alongside Bacon, giving him a Bacon number of 2 - and in between filming he's often turned out for the Crowe XI with his cousins Martin and Jeff, and thus has a Tendulkar number of 2 as well. As Martin Crowe confirmed in response to a query from a reader of the Ask Steven column on Cricinfo, he and Jeff dressed up as senators for the filming of Gladiator, but since their brief appearance didn't actually make it into the final film, they can't claim Bacon numbers.

The most prolific acting career of a Test cricketer is that of one Test wonder C. Aubrey Smith, and despite having been born 95 years before Kevin Bacon, thanks to his own lengthy career and that of one of his co-actors, he manages a Bacon number of only 2. At the age of 80, Smith appeared in The White Cliffs of Dover (1944), alongside June Lockhart, who was 18 at the time; 45 years later Lockhart appeared in The Big Picture with Bacon. Combined with his appearance for the British Born Film Stars against the 1932 Australian touring team featuring Don Bradman, this gives Smith a Bacon-Tendulkar number of 6. Bradman also tried his hand at acting: he was in The Queen in Australia (1954) and has a Bacon number of 3 to go with his Tendulkar number of 3, for a BT number of 6 (his link to Bacon is via the Queen, who has a Bacon number of 2 but unfortunately is not known to have played cricket).

Several films have centred on cricket, most with Test players appearing: That's Cricket (1931) featured Bradman, Bill Ponsford, Bill Woodfull, Stan McCabe, Alan Kippax, Clarrie Grimmett and Bert Oldfield; Cricket Story (1961) included appearances by Bradman again, Vic Richardson, Bill O'Reilly, Ray Lindwall and Keith Miller, giving Bacon-Tendulkar numbers (mostly 6, 7 or 8) to those players. In England, The Final Test (1953) saw Len Hutton, Cyril Washbrook, Denis Compton, Godfrey Evans and Jim Laker. More recently, Hit for Six (2009) gave Bacon numbers of 3 to Everton Weekes, Wes Hall, Gordon Greenidge, Desmond Haynes, Roland Butcher, Philo Wallace and Tino Best (and BT numbers of 4 to Greenidge, Haynes and Wallace; Best has never played a Test against India and only two ODIs, in a triangular tournament in Sri Lanka in 2005 when Tendulkar wasn't playing).

Plenty of actors have also tried their hand at cricket; Bollywood XIs have played a few charity matches in recent years, although in the absence of scorecards I have been unable to establish Bacon-Tendulkar numbers for any of them. Norman Wisdom appeared for the Lord's Taverners against an Old England XI at Lord's in 1962, and the presence of numerous Test players in the match gives him a Tendulkar number of 3, to go with his Bacon number of 2. Richard Hearne also has a Bacon number of 2, and was president of the Taverners; from playing alongside Fred Trueman he has a Tendulkar number of 4 and a BT number of 5.

Authors vs Actors was an annual fixture at Lord's in the early years of the 20th century, and while most of the actors involved faded into obscurity, they also included Gerald du Maurier, Hayden Coffin, Oscar Asche and Henry Ainley - all of whom have BT numbers of 7 (3 to Bacon via differing routes, and 4 to Tendulkar via their team-mate Aubrey Smith). Several of their opponents also became (or already were) household names - the cricketing Authors included Arthur Conan Doyle, PG Wodehouse and AA Milne.

Erdos-Tendulkar numbers are an altogether rarer breed; writing academic papers has not been quite as popular a second job for international cricketers as acting. Even Mike Brearley, whom Rod Marsh famously described as having "a degree in people", and who later became president of the British Psychoanalytical Society, can't claim an Erdos number. Edward Craig, who played alongside Brearley at Cambridge and has a Tendulkar number of 3, later became a professor of philosophy - but he only has one joint paper, Doubts About the Concept of Reason, written with JD Kenyon in 1985. Kenyon never wrote a paper with anyone other than Craig, so his chain reaches a dead end with no connection to Erdos. Tendulkar played in an exhibition match for Lashings against Cambridge University in 2006, giving 11 Cambridge players a Tendulkar number of 1; several of those players are now active researchers, but none in a discipline sufficiently closely related to pure mathematics to give them Erdos numbers.

Attempting to find a link starting from the other end doesn't look too promising, either: the leading lights of mathematics have not, in general, also been keen cricketers. GH Hardy, the early 20th century number theorist, certainly took an interest in the game: he categorised great mathematicians as being in "the Hobbs class" or "the Bradman class", and made it one of his New Year's Resolutions to "Make 211 not out in the fourth innings of the last Test Match at The Oval" (among an intriguing list which also included convincing the general public of the non-existence of God; becoming the first president of the USSR, Great Britain and Germany; and murdering Mussolini) - but he is not known ever to have played.

One who may fit the bill is Graham Sills, a Cambridge maths PhD and club cricketer. Sills co-wrote Local Solubility and Height Bounds for Coverings of Elliptic Curves with Tom Fisher, who wrote a paper with John Cremona, who wrote one with Barry Mazur, who wrote one with Andrew Granville, who wrote one with Paul Erdos - giving Sills an Erdos number of 5. When I contacted him regarding this, he told me he didn't have the scorebooks to check, but was fairly sure that he would either have played against one of the Cambridge team in the Lashings match, or against someone else who had - giving him a Tendulkar number of 2 or 3 and an Erdos-Tendulkar number of 7 or 8, the only person I have been able to trace with a finite such number.

Many thanks to Arnold D'Souza and Pete Church for their help in working out the above numbers, and to Graham Sills for humouring a complete stranger who contacted him out of the blue regarding some obscure distinction he might hold.

Addendum to the previous article: Thanks to Sreeram for drawing my attention to the case of Madhav Apte, who played against CK Nayudu in the final of the 1951-52 Ranji Trophy, and subsequently played against Tendulkar in the Purshottam Shield before the later made his Test debut. Thus Apte has a Tendulkar number of 1 and Nayudu 2, and all earlier players who link to Tendulkar via Nayudu have their numbers reduced by one (thus Frank Tarrant's becomes 3 and WG Grace's 4). It also gives a link connecting John Small and other 18th century players to Tendulkar in one step fewer: in 1918 Nayudu played for India against 'England' (in the days before India gained Test status, that meant a touring team comprised of miscellaneous county players - nowhere near a full strength England side), including the 48-year-old Gerald Weigall - who had been a regular for Kent since the early 1890s, and played against EM Grace several times. Thus the chain becomes Small - Billy Beldham - John Sherman - George Chatterton - EM Grace - Weigall - Nayudu - Apte - Tendulkar, reducing Small's Tendulkar number to 8.

Although John de Burgh never played Small, he did play the intriguingly nicknamed 'Lumpy' Stevens, who played Beldham, and therefore has a Tendulkar number of 9. Every first-class match before 1785 featured Small and/or Stevens, so every player in those matches links to Tendulkar in at most 9 steps; moreover, the few minor matches in the same period in which neither of them played all had at least one other player who also played Beldham. So it would seem that there is no recorded player with a Tendulkar number greater than 9.
First Published: May 11, 2013, 11:39 AM IST

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