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Ayer, escribí un primer post sobre Matemáticas y Realidad (ver ahí como nació el tema en Twitter). Hoy, preparando un email DIARIO (jeje... lo mío es un apostolado) que envío a una lista privada de un cliente sobre temas que me interesan, decidí enviar enlaces sobre matemáticas y filosofía. Fue una sorpresa encontrarme con la European Mathematical Society Newsletter y sus artículos de filosofía (citados en el primer enlace de la lista de abajo).
A todos los que les interesa el tema, les recomiendo la lectura de estos artículos (los primeros de la lista). Vean cómo David Mumford define platonismo:
The belief that there is a body of mathematical objects, relations and facts about them that is independent of and unaffected by human endeavors to discover them.
Vean cómo Barry Mazur hace la misma pregunta que comenté en el post de ayer:
Is mathematics discovered or invented?
Muchos conocemos a Mazur por el gran rol que jugaron sus ideas y papers en la demostración de Wiles del último teorema de Fermat. Pero vean que tiene un ancho campo de intereses, incluso la filosofía de su propia actividad matemática.
Al leer el principio del artículo de Mazur, me pareció conocida su cita del Huckleberry Finn. Y sí, ya había escrito post! ;-) Estrellas desde la balsa donde cité:
... Teníamos el cielo sobre nuestras cabezas, todo moteado de estrellas, y solíamos tendernos boca arriba y discutir si alguien las había hecho o habían salido solas. Jim decía que las habían hecho, y yo, que habían salido por azar; yo pensaba que se habían salido por azar; yo pensaba que se habría necesitado mucho tiempo para hacer tantas.
Otra gran pregunta que estoy tratando de comentar en mi serie ¿Qué está haciendo el Universo?
Si les gustan las matemáticas, vean los newsletter de EMS que cito abajo. Vean los títulos, las publicidades de libros y conferencias, busquen las biografías de los autores. Es un mundo fascinante y asombroso, de conocimiento y actividad humana.
Philosophy in the European Mathematical Society Newsletter
http://golem.ph.utexas.edu/category/2010/03/philosophy_in_the_ems_newslett.html
Platonism
http://www.math.chalmers.se/~ulfp/Platonism/platonism.pdf
a context of Gromov's program
http://ideafoundlings.blogspot.com.ar/2010/01/context-of-gromovs-program.html
http://www.ems-ph.org/journals/newsletter/pdf/2010-03-75.pdf
Applied Platonism Zvi Artstein
Nominalism versus Realism
David Corfield
http://www.ems-ph.org/journals/newsletter/pdf/2008-12-70.pdf
Why I am a Platonist
David Mumford
The belief that there is a body of mathematical objects, relations and facts about them that is independent
of and unaffected by human endeavors to discover them.
http://www.ems-ph.org/journals/newsletter/pdf/2007-06-64.pdf
Let Platonism die
E. B. Davies (King"s College London, UK)
Over the last few years I have noticed that a number of Fields medallists and other famous mathematicians are being asked by interviewers whether they are Platonists. Many are quite unprepared for this question and try to evade it, or give answers which indicate that they have not thought seriously about it.
http://www.ems-ph.org/journals/newsletter/pdf/2008-06-68.pdf
On Platonism
Reuben Hersh (University of New Mexico, USA)
"Platonism" can mean a lot of different things. Even "Platonism in mathematics" can mean a lot of different
things. In my writings on the philosophy of mathematics, I have been concerned about the philosophical stance or preconceptions of practicing mathematicians, whether explicitly formulated
or not. As I have written, this usually involves some choice or combination or alternation
of "formalism" and "Platonism", both of them in rough-and-ready, naïve versions. Their "Platonism" says
mathematical objects exist independently of our knowledge or activity, and mathematical truth is objective,
with the same status as scientifi c truth about the physical world. This may be boiled down to the phrase "out there." That"s where mathematical entities are, meaning, not "in here."
…
Mathematical
Platonism and
its Opposites
Barry Mazur (Harvard University, Cambridge MA, USA)
We had the sky up there, all speckled with stars, and we used to lay on our backs and look up at them, and discuss about whether they was made or only just happened – Jim he allowed they was made, but I allowed they happened; I judged it would have took too long to make so many. mused Huckleberry Finn.
The analogous query that mathematicians continually fi nd themselves confronted with when discussing their art with people who are not mathematicians is:
Is mathematics discovered or invented?
I will refer to this as The Question, acknowledging that this fi ve-word sentence, ending in a question mark
– and phrased in far less contemplative language than that used by Huck and Jim – may open conversations, but is hardly more than a token, standing for puzzlement regarding the status of mathematics.
If you engage in mathematics long enough, you bump into The Question, and it won"t just go away.1 If we wish to pay homage to the passionate felt experience that makes it so wonderful to think mathematics, we had better pay attention to it.
http://www.ems-ph.org/journals/newsletter/pdf/2008-03-67.pdf
An interview with Alain Connes, part II
I have no doubt that mathematical reality is something which exists, that it exists independently of my own brain trying to see it, and has exactly the same properties of resistance as external reality. When you want to prove something, or when you examine if a proof is correct or not, you feel the same anguish, the same external resistance as you do with external reality. Some people will tell you that this reality does not exist because it is not "localized" somewhere in space and time. I just fi nd this absurd
(ver también sus comentarios sobre Mathematics and Physics, Heisenberg, standard model...)
What is a Theory? | The n-Category Café
http://golem.ph.utexas.edu/category/2010/07/what_is_a_theory.html
El Amor a las Matemáticas.Relación entre la vida y los números.
http://viajeaitacaconmanoli.blogspot.com.ar/2010/07/el-amor-las-matematicasrelacion-entre.html
The language of explanation
http://www.math.harvard.edu/~mazur/papers/Utah.3.pdf
Newton's Principia : the mathematical principles of natural philosophy
http://www.archive.org/details/newtonspmathema00newtrich
Mathematical Problems by David Hilbert
http://aleph0.clarku.edu/~djoyce/hilbert/problems.html
Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries? What particular goals will there be toward which the leading mathematical spirits of coming generations will strive? What new methods and new facts in the wide and rich field of mathematical thought will the new centuries disclose?
Hilbert, 1900
Random Reality
http://sprott.physics.wisc.edu/pickover/pc/random_reality.html
"Randomness generates everything," says Cahill. "It even creates the sensation of the 'present', which is so conspicuously absent from today's physics."
Science historian cracks the 'Plato code'
http://phys.org/news196943667.html
La autoconsistencia matemática, posible indicio de la existencia de Dios
http://www.tendencias21.net/La-autoconsistencia-matematica-posible-indicio-de-la-existencia-de-Dios_a2602.html
Sigue impulsando la imaginación filosófica del creyente científico
BABAB.COM - De cómo las matemáticas pueden enderezar tu torcida existencia.
http://www.babab.com/no19/matematicas_19.php
In Quest of Truth and Justice « Algorithmic Game-Theory/Economics
http://agtb.wordpress.com/2010/04/07/in-quest-of-truth-and-justice/
LA MATEMÁTICA Y LA COSMOVISIÓN DEL MUNDO. (INFORME PRELIMINAR)
http://www.fcecon.unr.edu.ar/investigacion/jornadas/archivos/spenglerycicerchia.PDF
Lo que hoy se entiende por matemática ¿es lo que siempre se entendió por
ello? ¿Qué elementos fundamentales contempla una disciplina como esta para adquirir
Climate Scientists and the Riemann Hypothesis « Climate Audit
http://climateaudit.org/2008/07/07/climate-scientists-and-the-riemann-hypothesis/
el status científico? La matemática ¿demuestra o verifica? ¿Es una ciencia que avanza
por ruptura o por revolución?
Logicomix: An Epic Search for Truth
http://www.amazon.com/Logicomix-Search-Truth-Apostolos-Doxiadis/dp/1596914521
This exceptional graphic novel recounts the spiritual odyssey of philosopher Bertrand Russell.
Alfred North Whitehead (Stanford Encyclopedia of Philosophy)
http://plato.stanford.edu/entries/whitehead/
Conocer Ciencia: Matemáticas: Forma y Contenido
http://pepascientificas.blogspot.com.ar/2010/03/matematicas-forma-y-contenido.html
The Two Cultures Again | The n-Category Café
http://golem.ph.utexas.edu/category/2010/03/the_two_cultures_again.html
The Two Cultures of Mathematics
http://golem.ph.utexas.edu/category/2007/04/the_two_cultures_of_mathematic.html
Two cultures
http://www.dpmms.cam.ac.uk/~wtg10/2cultures.pdf
Two Cultures in David Corfield
http://ncatlab.org/davidcorfield/show/Two+Cultures
The n-Category Café
http://golem.ph.utexas.edu/category/
What is math? : Good Math, Bad Math
http://scienceblogs.com/goodmath/2009/12/what_is_math.php
Why is physical intuition possible?
http://sbseminar.wordpress.com/2009/11/16/why-is-physical-intuition-possible/
Emmy Noether NY Times obituary
http://www-history.mcs.st-andrews.ac.uk/Obits2/Noether_Emmy_Einstein.html
Free Online Course Materials | Godel, Escher, Bach: A Mental Space Odyssey
http://ocw.mit.edu/OcwWeb/hs/geb/VideoLectures/
Scientific Commons: Simon Colton
http://de.scientificcommons.org/simon_colton
Scientific Commons: Lakatos and machine creativity (2008)
http://de.scientificcommons.org/40850155
Por qué Pascal iba a misa todos los domingos ? « Martin Mendez blog
http://martinmendez.com/2009/02/24/por-que-pascal-iba-a-misa-todos-los-domingos/
Principia Mathematica - Wikipedia, the free encyclopedia
http://en.wikipedia.org/wiki/Principia_Mathematica
The sum of human emotion
http://news.bbc.co.uk/2/hi/uk_news/magazine/7790253.stm
Lakatos and Machine Creativity
http://www.doc.ic.ac.uk/~sgc/papers/pease_ecai02workshop.pdf
Our thesis in this paper is that Lakatos"s Proofs and Refutations [17]
has important and exciting implications for the field of machine creativity.
Mis Enlaces
http://delicious.com/ajlopez/mathematics+philosophy
Nos leemos!
Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez
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