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.
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
↑ ↑ ↑ ↑
↓ ↓ ↓ |
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