Bacon numbers were inspired by Erdős numbers, which Caspar Goffman introduced in 1969, 25 years before Bacon numbers. The brilliant, eccentric and prolific mathematician Paul Erdős authored or co-authored about 1400 published mathematical papers, more than anyone else in history. If you co-authored a paper with him, you have an Erdős number of one; if you co-authored a paper with someone who co-authored a paper with Erdős, you have an Erdős number of two, etc. Danica McKellar, who played Winnie Cooper on the TV series The Wonder Years (1988-93), has an Erdős number of 4 and a Bacon number of 2. For more on Erdős, I recommend the fascinating book The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth by Paul Hoffman, who later wrote King's Gambit: A Son, a Father, and the World's Most Dangerous Game.
Tim Krabbé was apparently the first to adapt the concept to chess, introducing Morphy numbers. Taylor Kingston then took up the cudgels in an article on chesscafe.com. Someone who played Morphy (in any sort of game, including an offhand game or simultaneous exhibition) has a Morphy number of 1 (MN1). Someone who played someone who played Morphy has a Morphy number of 2 (MN2), etc. For example, Emanuel Lasker played many games against Henry Bird, who played 12 games with Morphy in 1858 and 1859. Bird thus was an MN1, and Lasker an MN2. Anyone who played Lasker is an MN3.
As you might imagine, everyone who played Morphy died long ago. The lowest Morphy number held by anyone alive today is 3. Until very recently, it was thought that there were only a handful of living MN3s. Kingston in his article pointed out two: GMs Andor Lilienthal and Arturo Pomar. Lilienthal played R.P. Michell at Hastings 1934-35; Michell played the Rev. John Owen at Hastings 1895 (Amateur Section); and Owen played Morphy a number of games in 1858. Pomar played a match against Jacques Mieses in 1946; Mieses played Louis Paulsen at Nuremberg 1888 and Henry Bird at Hastings 1895; and both Paulsen and Bird played a number of games against Morphy. Leonard Barden, in his comments to another article about Morphy numbers, by Tim Harding, added three more living MN3s, all of whom played Mieses in the Premier Reserves section at Hastings 1948-49 or 1949-50: Dennis Horne, Peter Swinnerton-Dyer, and Barden himself.
Sadly, the great Lilienthal died earlier this year at age 99. That left only four living MN3s from the Kingston-Barden list. But wait, there's more! On April 28, 1938, 8-year-old Melvin Chernev (Irving's son), played a game against Emanuel Lasker (MN2) when the great man visited the Chernevs' home. Melvin Chernev lives near San Francisco; I spoke with him on the phone in June of this year. He is the fifth known living player with a Morphy number of 3.
Chicago's own Erik Karklins, age 95, recalls losing to Lasker in a simul in Riga, Latvia circa 1928. Karklins is thus the sixth known living player with a Morphy number of 3.
T.H. George of Essex, England may have been the last surviving player with a Morphy number of 2. The British Chess Magazine wrote in his 1971 obituary, "Essex chess players suffered a severe loss with the death of T.H. George on April 19th at the age of 85. He was the doyen of Essex chessplayers . . . . He was rather proud of having played a man who had played Morphy. This happened in his young days when he beat Jas. Mortimer in a club match; Mortimer had played friendly games with Morphy in Paris in the early sixties of the last century." British Chess Magazine, July 1971, p. 249. The claim that Mortimer played Morphy is corroborated by Chess Monthly, which had an article about Mortimer (1833-1911) in 1892. "In 1853, he was appointed attaché of the United States Legation in Paris, where he had an opportunity of renewing his acquaintance with Paul Morphy. The two countrymen thus became intimate friends. Both being passionately fond of chess, many hundreds of games were played by the master and pupil . . . ." Chess Monthly, Sept. 1892, p. 66.
Leonard Barden, in an e-mail to me yesterday morning, made a fascinating point:
Mortimer played Znosko-Borovsky and (most notably) Tartakover at Ostend 1907 which blows up Morphy 3 as a finite one-hand number[.]
Z-B played at London 1948 (two Penrose brothers), Tartakover met Gligoric, Benko, Bisguier, Fuderer (Bled 1950) , Matanovic, Ivkov, J Penrose and others[.] Tom George likely played Peter Clarke who was a young member of Ilford CC in the early 1950s when George was still active.
I reckon now the traceable living Morphy 3s number around 15-20.
Other opponents of Tartakower's who are still living include Fridrik Olafsson, Lothar Schmid, and possibly Gudbjartur Gudmundsson. In addition, Mortimer played Marshall at Monte Carlo 1902, and Marshall played Louis Levy in the 1941 Marshall Chess Club Championship. As far as I can tell from the USCF and FIDE websites, Levy is alive and living in California.
One wonders whether anyone alive today played Frederick Karl Esling (1860-1955). Esling, who became the first Australian champion in 1886, won an offhand game against Adolf Anderssen in 1878. Unfortunately, he does not seem to have played much in his later years; the last game of his that I have seen was from 1922. Since Anderssen of course played a match against Morphy, anyone who played Esling would have a Morphy number of 3 (and, incredibly, an Anderssen number of 2, even though Anderssen predeceased Morphy).
I played (and managed to draw) a 15-minute online game against Barden earlier this year, giving me a Morphy number of 4. But I also played two simul games against Bisguier around 1978, making me an MN4 through the Bisguier-Tartakower-Mortimer route as well.
In sum, here's an alphabetical list of known living MN3s: Leonard Barden, Pal Benko, Arthur Bisguier, Melvin Chernev, Andrija Fuderer, Svetozar Gligorić, Dennis Horne, Borislav Ivkov, Erik Karklins, Louis Levy, Aleksandar Matanović, Fridrik Olafsson, Jonathan Penrose, Oliver Penrose, Arturo Pomar, Lothar Schmid, and Peter Swinnerton-Dyer. Possibles include Peter Clarke (if he played T.H. George) and Gudbjartur Gudmundsson (if still alive).
ADDENDUM: Barden has pointed out on the English Chess Forum that Mortimer also played Ossip Bernstein at Ostend 1907. Bernstein lost to Frans Kuijpers at the 1961 IBM tournament. That apparently makes Kuijpers, now 69, the youngest living MN3. Bernstein also played Bent Larsen, who died earlier this month, twice at the 1954 Olympiad.