489
applied in extinction-level models.
31
The lack of independent or co-precision is
qualified by an inexplicably vast multitude of such inconstant incisions in our perception of time. Precision is the illusion that biology stammers over, contends with
in every leaf, stoma, cell, and season. The history of statistics and probability
catches only a vague outline of the endless arrays and nuances.
32
Early probability
mavericks like Jacob Bernoulli (1655–1705), Thomas Bayes (1702–1761),
P. S. Laplace (1749–1827), and James Clark Maxwell (1831–1879) each concurred
that theories of probability were as much predicated upon chance as frequency, part
knowledge, part ignorance, part ratio.
33
52.2 Probability Theories
One of the earliest mathematical theories in the history of probability speculation
concerned a matter of some regard to Dostoevsky, as earlier referenced, named, “a
gambler’s dispute” which occurred in 1654 between two Frenchmen (of course);
the philosopher Blaise Pascal and his friend the mathematician Pierre de Fermat.
The details of the event in question concerned “an apparent contradiction concerning a popular dice game, during which a pair of dice would be tossed 24 times and
certain outcomes (that had always previously been interpolated as certain) were to
be tossed out the window. Not until the Russian mathematician Andrey Kolmogorov
(1903–1987) attended to it in 1933 was some clarity and predictability achieved.
34
Considered a modern father of probability, as well as algorithmic complexity, his
book Foundations of the Theory of Probability
35
elevated axioms of prediction such
31 See “Persistence and extinction in single-species reaction-diffusion models,” by Linda J. S.
Allen, Bulletin of Mathematical Biology, 45, 209–227, March 1983, Springer Link, https://link.
springer.com/article/10.1007/BF02462357, Accessed May 14, 2020. See also, “Persistence,
extinctions, and critical patch number for island populations,” by Linda J. S. Allen, Journal of
Mathematical Biology 24, 617–625(1987), February 1987, Springer Link, https://link.springer.
com/article/10.1007/BF00275506, Accessed May 15, 2020.
32 See “A Brief Look at the History of Probability and Statistics,” by James E. Lightner, The
Mathematics Teacher, Volume 84,, No. 8, November 1991, pp. 623–630, National Council of
Teachers Of Mathematics, JSTOR, https://www.jstor.org/stable/27967334, https://www.jstor.org/
stable/27967334?seq=1, Accessed May 14, 2020.
33 See “A short history of probability theory and its applications,” by Lokenath Debnath and
Kanadpriya Basu, International Journal of Mathematical Education, 46(1), January 2015, https://
www.researchgate.net/publication/271856948_A_short_history_of_probability_theory_and_its_
applications, Accessed May 14, 2020.
34 See “A Short History of Probability,” from Calculus, Volume II, by Tom M. Apostol, 2
nd edition,
John Wiley & Sons, New York, 1969, http://homepages.wmich.edu/~mackey/Teaching/145/probHist.html, Accessed May 14, 2020.
35 See Grundbegriffe der Wahrscheinlichkeitrechnung, Ergebnisse Der Mathematik; translated
as Foundations of Probability, New York: Chelsea Publishing Company, 1950. See also, Selected
Works of A. N. Kolmogorov, Vol.2, Probability Theory and Mathematical Statistics, Edited by
Albert N. Shiryaev, Springer Nature B.V., Springer Netherlands, 1992. See also, “On Logical
52.2 Probability Theories
applied in extinction-level models.
31
The lack of independent or co-precision is
qualified by an inexplicably vast multitude of such inconstant incisions in our perception of time. Precision is the illusion that biology stammers over, contends with
in every leaf, stoma, cell, and season. The history of statistics and probability
catches only a vague outline of the endless arrays and nuances.
32
Early probability
mavericks like Jacob Bernoulli (1655–1705), Thomas Bayes (1702–1761),
P. S. Laplace (1749–1827), and James Clark Maxwell (1831–1879) each concurred
that theories of probability were as much predicated upon chance as frequency, part
knowledge, part ignorance, part ratio.
33
52.2 Probability Theories
One of the earliest mathematical theories in the history of probability speculation
concerned a matter of some regard to Dostoevsky, as earlier referenced, named, “a
gambler’s dispute” which occurred in 1654 between two Frenchmen (of course);
the philosopher Blaise Pascal and his friend the mathematician Pierre de Fermat.
The details of the event in question concerned “an apparent contradiction concerning a popular dice game, during which a pair of dice would be tossed 24 times and
certain outcomes (that had always previously been interpolated as certain) were to
be tossed out the window. Not until the Russian mathematician Andrey Kolmogorov
(1903–1987) attended to it in 1933 was some clarity and predictability achieved.
34
Considered a modern father of probability, as well as algorithmic complexity, his
book Foundations of the Theory of Probability
35
elevated axioms of prediction such
31 See “Persistence and extinction in single-species reaction-diffusion models,” by Linda J. S.
Allen, Bulletin of Mathematical Biology, 45, 209–227, March 1983, Springer Link, https://link.
springer.com/article/10.1007/BF02462357, Accessed May 14, 2020. See also, “Persistence,
extinctions, and critical patch number for island populations,” by Linda J. S. Allen, Journal of
Mathematical Biology 24, 617–625(1987), February 1987, Springer Link, https://link.springer.
com/article/10.1007/BF00275506, Accessed May 15, 2020.
32 See “A Brief Look at the History of Probability and Statistics,” by James E. Lightner, The
Mathematics Teacher, Volume 84,, No. 8, November 1991, pp. 623–630, National Council of
Teachers Of Mathematics, JSTOR, https://www.jstor.org/stable/27967334, https://www.jstor.org/
stable/27967334?seq=1, Accessed May 14, 2020.
33 See “A short history of probability theory and its applications,” by Lokenath Debnath and
Kanadpriya Basu, International Journal of Mathematical Education, 46(1), January 2015, https://
www.researchgate.net/publication/271856948_A_short_history_of_probability_theory_and_its_
applications, Accessed May 14, 2020.
34 See “A Short History of Probability,” from Calculus, Volume II, by Tom M. Apostol, 2
nd edition,
John Wiley & Sons, New York, 1969, http://homepages.wmich.edu/~mackey/Teaching/145/probHist.html, Accessed May 14, 2020.
35 See Grundbegriffe der Wahrscheinlichkeitrechnung, Ergebnisse Der Mathematik; translated
as Foundations of Probability, New York: Chelsea Publishing Company, 1950. See also, Selected
Works of A. N. Kolmogorov, Vol.2, Probability Theory and Mathematical Statistics, Edited by
Albert N. Shiryaev, Springer Nature B.V., Springer Netherlands, 1992. See also, “On Logical
52.2 Probability Theories