Erdős-Bacon-Sabbath (EBS) number

 

 

To have an Erdős -Bacon-Sabbath (EBS) number, you must have: co-written a scientific paper with someone who eventually connects to Erdős; appeared in a film with someone who eventually connects to Kevin Bacon; and performed musically with someone who eventually connects to Black Sabbath. The sum of those three numbers is the EBS.

Erdős number

 

The Erdős number (Hungarian: [ˈɛrdřːʃ]) describes the "collaborative distance" between mathematician Paul Erdős and another person, as measured by authorship of mathematical papers.  See https://en.wikipedia.org/wiki/Erd%C5%91s_number and https://oakland.edu/enp/compute/ .

 

The Erdős number of the following three authors in bold are 1, 2, and 3, respectively.

1.       P. Erdős, J. H. van Lint, On the number of positive integers<= x and free of prime factors >y, Simon Stevin, 40th year, nr. 11, p. 73-76, Oct 1966.

2.       J.I. Hall, A.J.E.M. Janssen, A.W.J. Kolen, J.H. Van Lint, Equidistant codes with distance 12, Discrete Mathematics, Volume 17, Issue 1, pp. 71-83, 1977.

3.       A.J.E.M. Janssen (‘Guido’ aka dr. Janssen, see https://nuhagphp.univie.ac.at/janssen/) coauthored over a dozen papers with Ronald M. Aarts one of those is:
R.M. Aarts, A.J.E.M. Janssen, Approximation of the Struve function H1 occurring in impedance calculations, The Journal of the Acoustical Society of America 113, 2635, 2003; see https://doi.org/10.1121/1.1564019 or https://www.sps.tue.nl/rmaarts/RMA_papers/aar03c2.pdf This Struve paper is followed by another Struve paper on Hn (see https://www.sps.tue.nl/rmaarts/RMA_papers/aar16pu20.pdf) which is cited by the NIST Digital Library of Mathematical Functions, see https://dlmf.nist.gov/11.13

Like the Erdős number, the distance with another author can be measured. E.g the mathematician Nicolaas Govert (Dick) de Bruijn. He covered many areas of mathematics, see https://en.wikipedia.org/wiki/Nicolaas_Govert_de_Bruijn . He is especially noted for:

·      the discovery of the De Bruijn sequence,

·      discovering an algebraic theory of the Penrose tiling and, more generally, discovering the "projection" and "multigrid" methods for constructing quasi-periodic tilings, see e.g. https://core.ac.uk/download/pdf/82022369.pdf and https://link.springer.com/chapter/10.1007/978-1-4614-7258-2_29

·      the De Bruijn–Newman constant,

·      the De Bruijn–Erdős theorem, in graph theory,

·      a different theorem of the same name: the De Bruijn–Erdős theorem, in incidence geometry,

·      the BEST theorem in graph theory,

·      and De Bruijn indices.

·      Making the work of the Dutch artist M.C. Escher known to mathematicians e.g. R. Penrose and H.S.M. Coxeter. In 1954, the International Congress of Mathematicians was held in Amsterdam. For the occasion, a special Escher exhibition was organized in the Stedelijk Museum. Professor N. G. de Bruijn (1918) was one of the people involved, see https://www.nieuwarchief.nl/serie5/pdf/naw5-2008-09-2-134.pdf

·      He wrote one of the standard books in advanced asymptotic analysis (1958).

·      He did many other important works, see https://www.nieuwarchief.nl/serie5/toonnummer.php?deel=14&nummer=1&taal=0

He wrote papers together with the above-mentioned Jack van Lint, e.g.:
Bruijn, de, N. G., & van Lint, J. H. (1964). Incomplete sums of multiplicative functions. I. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen: Series A: Mathematical Sciences, 67(4), 339-347.

Hence, the de Bruijn number of: van J.H. van Lint, A.J.E.M. Janssen, and Ronald M. Aarts is 1, 2, and 3, respectively.

 

Jack van Lint was a former rector of the Eindhoven University of Technology, see https://en.wikipedia.org/wiki/J._H._van_Lint and https://mathgenealogy.org/id.php?id=51426. A.J.E.M. Janssen was one of de Bruijn’s PhD students, see https://mathgenealogy.org/id.php?id=49968 . See https://www.win.tue.nl/debruijn90/ for movies on Sept. 5 2008, with the Bruijn at festivities for his 90th birthday.

 

Likewise other distances can be measured, with a.o. the papers below, as listed in Table I.

 

E.R. Berlekamp , J.H. Van Lint, J.J. Seidel, A Survey of Combinatorial Theory, Chapter 3 - A Strongly Regular Graph Derived from the Perfect Ternary Golay Code, pp. 25-30, 1973.

 

C.E. Shannon, R.G. Gallager, E.R. Berlekamp, Lower bounds to error probability for coding on discrete memoryless channels, Information and Control, Volume 10, Issue 1, pp. 65-103, January 1967.

 

N.G. de Bruijn, D.E. Knuth, S.O. Rice, The average height of planted plane trees, Graph Theory and Computing, , pp. 15-22, 1972.

 

E.R. Berlekamp, J.H. Conway, R.K. Guy, Winning ways for your mathematical plays.

 

E. R. Berlekamp, R. L. Garwin, D. E. Knuth, et al., Report of the ARPA study group on advanced memory concepts, Defense Advanced Research Projects Agency ARPA Order No. 288, 1976.

 

Table I Distance between various authors

                        RA    AJ    JvL   EB    NdB   PE    JC    DK    CS

R.M. Aarts              0

A.J.E.M. Janssen        1     0

J.H. van Lint           2     1     0

E.R. Berlekamp          3     2     1     0

N.G. de Bruijn          3     2     1     2     0

P. Erdős                3     2     1     2     1     0

J.H. Conway             4     3     2     1     3     1     0

D. Knuth                4     3     2     1     1     2     2     0

C.E. Shannon            4     3     2     1     3     2     2     2     0

 

Departing from authors from the table above, new paths can be formed:

 

Erdős->Gutti Jogesh Babu->Paul Sommers->Roger Penrose

Erdős->Terence Tao

Erdős->Ernst Gabor Straus->Albert Einstein->David Hilbert

Erdős->Stanisław Marcin Ulam->Nicholas Metropolis->Richard Feynman

Erdős->Stanisław Ulam->Nicolas Metropolis->Edward Teller

Erdős->Vance Faber->Emanuel Knill->Raymond Laflamme->Stephen Hawking

Erdős->Godfrey H. Hardy->Srinivasa Aaiyangar Ramanujan

Erdős->Andrew Odlyzko->Chris M. Skinner->Andrew J. Wiles

Erdős->…->……-> Antoine Lavoisier->Pierre-Simon Laplace   see https://sites.google.com/a/oakland.edu/jerry-grossman-home-page/home/the-erdoes-number-project/some-famous-people-with-finite-erdoes-numbers

 

Albert Einstein->Marie Curie

Albert Einstein->Hendrik Antoon Lorentz

Albert Einstein->Paul Ehrenfest->J. Robert Oppenheimer

Albert Einstein->Wolfgang Pauli->Hendrik A. Kramers->Niels Bohr

 

Paul Ehrenfest->Heike Kamerlingh Onnes

 

Heike Kamerlingh Onnes->Antoine Henri Becquerel

 

J.H. van Lint->Ronald L. Graham

 

N.G. de Bruijn-> Christoffel Jacob Bouwkamp

 

C.J. Bouwkamp->Hendrik Brugt Gerhard (Henk) Casimir->Dirk Polder

 

Example of a small world map of some authors in physics, discrete mathematics, geometry, tessellations, and recreational mathematics.


                                H. Casimir

                                   ↑

                                C. Bouwkamp

                                   ↑

                     R. Graham   N. de Bruijn  Gutti Jogesh Babu → Paul Sommers → Roger Penrose

                           ↑      ↑     ↑     ↑

R. Aarts→ A. → Janssen → J. van Lint → P. Erdős →B. Grünbaum → Tomaž Pisanski→ D. Schattschneider

                                   ↓     ↓     ↓         |

                      D. Knuth →E. Berlekamp →J. Conway   |

                                   ↓            ↓        ↓

                             Claude Shannon    H.S.M. Coxeter

 

 

Bacon Number

Similar to the Erdős number, Six Degrees of Kevin Bacon or Bacon's Law is a parlor game where players challenge each other to arbitrarily choose an actor and then connect them to another actor via a film that both actors have appeared in together, repeating this process to try to find the shortest path that ultimately leads to prolific American actor Kevin Bacon.

Via https://oracleofbacon.org//movielinks.php the following path can be established:

Ronald Aarts in VPRO’s Waskracht -> Sunny Bergman in Een Maand Later-> Renée Soutendijk in Eve of Destruction -> John M. Jackson in A Few Good Men -> Kevin Bacon

Which means that Ronald has a Bacon number of 4, and an Erdős-Bacon number of 3+4=7