October 26, 2009

Monastery Coffee

- to the memory of Dimitri Egorov (1869-1931)
October 26, 2009 - St. Demetrius of Thessaloniki

by Mihai Caragiu

Tiny surface waves emerge
in the cup of dark monastery coffee.
A great and bitter saga,
fourteen billion years in coffee-cup time,
a time convoluted with our fall, bearing the smell of skin cloth.

The old monk returns to the prayer corner
in front of the icon placed right in the middle of his heart
for a dialogue with a different kind of time,
liturgically-shaped,
bearing the sweetness of the Name.

October 20, 2009

The Axiom of Choice

Three useful links dealing with the Axiom of Choice: The Axiom of Choice - Stanford Encyclopedia of Philosophy entry by John L. Bell, the University of Western Ontario; The Axiom of Choice (a short paper by Prof. John L. Bell) ; The Relative Consistency of the Axiom of Choice - Mechanized Using Isabelle/ZF by Lawrence C. Paulson, Computer Laboratory Univ. of Cambridge. An important result, in a categorical setting linked to intutionistic set theory, was obtained by Radu Diaconescu (Axiom of choice and complementation, Proc. Amer. Math. Soc. 51, 1975, 176-178): a topos satisfying the axiom of choice must be boolean (in short... the axiom of choice implies the law of the excluded middle).

La mormantul parintelui Ghelasie Gheorghe




















Imagine preluata de pe blogul Parintele Ghelasie de la Frasinei - © Florin Caragiu (pentru permisiunea de a reproduce materiale de pe acel blog, contactati administratorul).

October 12, 2009

Dialogic

"For Bakhtin, all language - indeed, all thought - appeared dialogic. This means that everything anybody ever says always exists in response to things that have been said before and in anticipation of things that will be said in response. We never, in other words, speak in a vacuum. As a result, all language (and the ideas which language contains and communicates) is dynamic, relational and engaged in a process of endless redescriptions of the world" (also see Corporeal Worlds: Mikhail Bakhtin's Theology Discourse - by Alexandar Mihailovic, Northwestern University Press (1997) ; @ google books). On this blog we already mentioned the work done by Prof. Stefan Trausan-Matu on Bakhtin's dialogism, its connections with Orthodox Christianity (addressing them in the recent volume "Repere Patristice în dialogul dintre teologie şi ştiinţă") and relevance to the area of artificial intelligence (computer-supported collaborative problem solving, human-computer interaction, etc).

Ferdinand Eisenstein (1823 – 1852)

Ferdinand Eisenstein died of tuberculosis at the age of 29, on October 11, 1852. Carl Friedrich Gauss once said: "There have been only three epoch-making mathematicians: Archimedes, Newton, and Eisenstein"... Ph.D. Universität Berlin 1845 (advisor: Gustav Dirichlet).
Eisenstein's Mac Tutor Biography
The life of Gotthold Ferdinand Eisenstein - by M. Schmitz (Res. Lett. Inf. Math. Sci., 2004, Vol. 6, pp 1-13 - provides an English translation of the "Curriculum Vita" written by him when he was 20 years old)
Eisenstein series ; Eisenstein series in string theory ; (2002) E.S. bibliography.

October 5, 2009

Arsenie Praja the hermit and Petre the elder


A photograph from the monastery cell of Fr. Ghelasie Gheorghe (1944-2003).


© Florin Caragiu.
Original post on Parintele Ghelasie de la Frasinei blog.

Dimitrie Pompeiu (1873-1954)

Dimitrie Pompeiu (October 4, 1873, Broscǎuţi, Botoşani – October 8, 1954, Bucharest) - orthodox christian, and one of the greatest Romanian mathematicians. He is remembered in the mathematical world for numerous contributions such as: the set distance [1] that he introduced in his 1905 Université de Paris dissertation published in the same year in the Annales de la faculté des sciences de Toulouse (a set distance was introduced in a slightly different form in 1914 by Hausdorff, who credited Pompeiu's definition though), his contributions in complex analysis, including the areolar derivative [2] and the seminal Cauchy-Pompeiu's formula (higher dimensional analogues of the Cauchy-Pompeiu formula are topics of current research, while the formula was used in the theory of functions of several complex variables by Dolbeault and Grothendieck [5]), and for the celebrated Pompeiu's Conjecture that he formulated in his 1929 C. R. Acad. Sci. Paris article [4], a conjecture not fuly proved yet. Still, elegant analogues of Pompeiu's Conjecture continue to be proved in other areas [6] - this is an indicator of the fertility of the idea.

REFERENCES

[1] T. Bârsan and D. Tiba. One hundred years since the introduction of the set distance by Dimitrie Pompeiu. Institute of Mathematics of the Romanian Academy.
[2] D. Pompeiu. Sur une classe de fonctions d'une variable complexe. Rendiconti del Circolo Matematico di Palermo, t. XXXIII, Ist sem. 1912, pp. 108-113.
[3] Pompeiu's biography from the The MacTutor History of Mathematics archive.
[4] D. Pompeiu. Sur certains systèmes d'équations linéaires et sur une propriété intégrale des fonctions de plusieurs variables, Comptes Rendus de l'Académie des Sciences Paris Série I. Mathématique, 188, 1138 –1139 (1929).
[5] R. Remmert. Theory of Complex Functions. Graduate Texts in Mathematics, Springer Verlag, 2nd Edition (1989).
[6] D. Zeilberger. Pompeiu's problem on Discrete Space. Proc. Natl. Acad. Sci. USA, Vol. 75 (8), 3555-3556 (1978).