Dixit: Una inaudita sección de corte político, social, políticosocial, antropológico, erótico o misceláneo, de frencuencia semanal, que corre a cargo de Jorge Sierra. Está pensada para ser escuchada:
Dixit #7a
Dixit: Una inaudita sección de corte político, social, políticosocial, antropológico, erótico o misceláneo, de frencuencia semanal, que corre a cargo de Jorge Sierra. Está pensada para ser escuchada:
Aquel que esté libre de pecado, que tire la primera piedra
Figúrese que es usted el Mesías y quiere salvar a una adúltera de ser lapidada. Según la Biblia, Jesús dice "Aquel que esté libre de pecado, que tire la primera piedra". La frase es ingeniosa, pues todos se preguntan si están libres de pecado, y como predeciblemente no lo están, o no creen estarlo, o no quieren que los demás piensen que tienen la arrogancia de creer estar libres de pecado, nadie tira la primera piedra.
Pero la relación entre tirar la piedra y estar libre de pecado no tiene por qué darse. En efecto, como afirma el filósofo medieval Ibn Hazm:
"Si sólo prohibiese el mal aquel que nada de éste tiene y si sólo ordenase hacer el bien aquel que en sí lo contiene cumplidamente, entonces a nadie se le prohibiría hacer el mal ni se le ordenaría practicar el bien tras la muerte del Profeta".
O, en otras palabras, "No tengo que estar libre de pecado para castigar a un criminal", lo cual en lo referente al adulterio, dentro de la lógica interna del judaismo salomónico, tiene sentido. Esta respuesta simplemente cuestiona la asunción de la pregunta que la precede, de la misma forma que ante "¿Has dejado de pegar a tu mujer?" la respuesta no es ni sí ni no, sino "Nunca he pegado a mi mujer", o "Mu". Combinando ambos, "Aquel que quiera dejar de pegar a su mujer, que tire la primera piedra"
En otras palabras, el Mesías temporalmente toma control de las mentes de sus adversarios mediante un virus lingüístico. Esta es exactamente la habilidad que caracteriza al proverbialmente peligroso Loki. ¿Y qué tiene Tor contra esto? ¿un martillo? La pluma, metonimia, palabra es más poderosa que la espada.
Addendum: Véase la teoría del master persuader de Scott Adams, creador del comic Dilbert: http://blog.dilbert.com/
Otros ejemplos:
"Linara hat mir von ihr erzählt, vor allem was ihre Groẞzugigkeit betrifft. Bezuglich dessen, gestatten Sie mir doch sicher das Vergnügen eines Tanzes mit ihr [mit Linara]" . - Firefly.
Otros ejemplos:
"Linara hat mir von ihr erzählt, vor allem was ihre Groẞzugigkeit betrifft. Bezuglich dessen, gestatten Sie mir doch sicher das Vergnügen eines Tanzes mit ihr [mit Linara]" . - Firefly.
Paradox Party
1. (*) Carmen Sandiego is equally likely to be anywhere on the surface of the Earth. Since lines of latitude are longer near the equator, it’s more likely for her to be near the equator than near the poles. So if we learn that she is somewhere on the prime meridian, then it’s still more likely for her to be near the equator than near the poles. But by the symmetry of the problem, we should expect her to be anywhere on the prime meridian with uniform probability
2. (**) You have the opportunity to play the following game: Flip a coin until you get tails, and receive 2n dollars where n is the number of times you flipped the coin. Since the expected value of this game is infinite, you should be willing to pay any price to play this game. But clearly this is absurd.
3. (*) Let P be the claim “all ravens are black”. Observing a single black raven is evidence that P is true. P is equivalent to “all non-black things are non-ravens”. Therefore observing a single non-black thing that is not a raven is also evidence of P. But this is absurd.
4 (**). You have a friend to whom blue objects appear red and vice versa (and pink objects appear light blue and so on). But since your friend has always had this condition, they believe that the word “red” refers to what they experience as blue and they use that word to refer to objects you experience as red. Thus you are unaware of your friend’s condition. How do you know you don’t have this condition? Could everyone in the world have this condition? Is there no way to know, even in principle? What is going on here?
5. (*/**) There are two envelopes full of money, and you may choose and keep one. All you know is that one contains twice as much money as the other. Suppose the envelope you choose contains n dollars. The other envelope is equally likely to contain 2n dollars as n/2 dollars, for an expected value of 3n/2 . So whichever envelope you choose, you should expect the other one to be better. How can this be?
6. (**) An instructor chooses one one of two buckets at random (50% / 50% chance): one containing 5 green and 20 red balls, and one containing 5 red and 20 green balls. Then all participants draw a ball from the selected basket (while being separated in different rooms). They are proposed the following bet:
Everyone gets 50 chips if the selected bucket was the “mostly red”
Everyone loses 100 chips if the selected bucket was the “mostly green”
The game master then asks all those who have a red ball if they want to accept the bet. If everyone says “yes”, the bet is on. A person who drew a red ball should conclude that it’s much more likely that the drawing was from the “mostly red” bucket, as the likelihood of them getting a red ball is 0.8 in that case, and only 0.2 in the “green” case. SO their expected payoff is 50*0.8 – 100*0.2= 20. The bet is favorable and they accept it
But, on the other hand, in advance you should conclude that your expected payoff in such a game is
50*0.5 – 100-*0.5 = -25 and you should reject the bet
7. (***) A stranger comes up to you on the street and asks you for $5. In exchange, the stranger claims they will use magical powers to cause a fantastic number (say N) of people in a different world to be very happy and lead rewarding lives. You don’t believe the stranger has magical powers, but surely there is an N such that your subjective probability of the stranger being able to carry out their promise is greater than 1/N. Then since the stranger can give you more expected happiness and well-being than you can otherwise buy with $5, you should give the stranger the money. But this is absurd.
8. (**) A person who does not know Chinese sits alone in a room with a big book of instructions. The person receives letters written in Chinese through a slot in the wall and, following the book’s instructions, manipulates the symbols to produce responses in Chinese. The instructions do not require the person to do anything creative or intelligent, but this process results in perfectly coherent Chinese responses to the input, as if a person had written those. So responses to the letters are being written without anyone involved understanding the letter. But how can that be?
9. (*/**/***) We expect healthy grass to be green tomorrow because we have always observed it to be green in the past. Define the adjective grün to mean “green if the date is before January 1, 2020, and blue otherwise”. We have always observed living grass to be grün, so we should expect grass to always be grün . So grass will be grün in 2020
10. (**) Discovering a cure for a disease provides an infinite stream of benefits, since people get health benefits of not having the disease in every generation. Therefore we should allocate our entire health budget to research. But clearly this is absurd.
11. (**) You are blindfolded and transported to an unknown city. You do not know how many taxis there are in the city. The only thing you know is that the taxis in the city are numbered 1,2,3,…,n, for some value of n with each number occurring exactly once. You stand on the street corner and wait until you see a taxi. The taxi is numbered k. What probability should you assign that there are at least 2k taxis in the city?
A person might argue:
(I). The probability is 50%. Because if we get dropped again and again into new cities, and always put 50% on this claim, the claim will be right half the time (because the taxi will be 50% of the time in the first half of all taxis, and 50% of the time in the second half), and this is what 50% means.
Alternatively, a person might argue:
(II). The probability cannot be determined unless you have a probability distribution over city-size (or rather, over city-taxi numbers). Imagine, for example, any specific set of cities, e.g., that there is a 1/3rd chance of 100 taxis, a 1/3rd chance of 200 taxis, and a 1/3rd chance of 300 taxis. Then, given any particular k, you can determine the chance that n > 2k using standard conditional probability. And the answer you get depends on your distribution over cities. So the person claiming (I) would be incorrect, since they are claiming an answer that does not depend on the distribution over cities.
12. (**/***) Modern cosmology teaches that the world might well contain an infinite number of happy and sad people. Aggregative ethics implies that such a world contains an infinite amount of positive value and an infinite amount of negative value. You can affect only a finite amount of good or bad. In standard cardinal arithmetic, an infinite quantity is unchanged by the addition or subtraction of any finite quantity. So it appears you cannot change the value of the world.
13. (**) Imagine that there's a very, very large population of people in the world, and that there's a madman. What this madman does is, he kidnaps ten people and puts them in a room. He then throws a pair of dice. If the dice land snake-eyes, then he simply murders everyone in the room. If the dice do not land snake-eyes, then he releases everyone, then kidnaps 100 people. He now does the same thing: he rolls two dice; if they land snake-eyes then he kills everyone, and if they don't land snake-eyes, then he releases them and kidnaps 1,000 people. He keeps doing this until he gets snake-eyes, at which point he's done. So now, imagine that you've been kidnapped.
So you're in the room. Conditioned on that fact, how worried should you be? How likely is it that you're going to die? One answer is that the dice have a 1/36 chance of landing snake-eyes. A second reflection you could make is to consider, of people who enter the room, what the fraction is of people who ever get out. Let's say that it ends at 1,000. Then, 110 people get out and 1,000 die. If it ends at 10,000, then 1,110 people get out and 10,000 die. In either case, about 9/10 of the people who ever go into the room will die. Independently on when the experiment stops, if each prisoner guesses that the chance of them dying is 1/36, because most will die, most will be wrong.
2. (**) You have the opportunity to play the following game: Flip a coin until you get tails, and receive 2n dollars where n is the number of times you flipped the coin. Since the expected value of this game is infinite, you should be willing to pay any price to play this game. But clearly this is absurd.
3. (*) Let P be the claim “all ravens are black”. Observing a single black raven is evidence that P is true. P is equivalent to “all non-black things are non-ravens”. Therefore observing a single non-black thing that is not a raven is also evidence of P. But this is absurd.
4 (**). You have a friend to whom blue objects appear red and vice versa (and pink objects appear light blue and so on). But since your friend has always had this condition, they believe that the word “red” refers to what they experience as blue and they use that word to refer to objects you experience as red. Thus you are unaware of your friend’s condition. How do you know you don’t have this condition? Could everyone in the world have this condition? Is there no way to know, even in principle? What is going on here?
5. (*/**) There are two envelopes full of money, and you may choose and keep one. All you know is that one contains twice as much money as the other. Suppose the envelope you choose contains n dollars. The other envelope is equally likely to contain 2n dollars as n/2 dollars, for an expected value of 3n/2 . So whichever envelope you choose, you should expect the other one to be better. How can this be?
6. (**) An instructor chooses one one of two buckets at random (50% / 50% chance): one containing 5 green and 20 red balls, and one containing 5 red and 20 green balls. Then all participants draw a ball from the selected basket (while being separated in different rooms). They are proposed the following bet:
Everyone gets 50 chips if the selected bucket was the “mostly red”
Everyone loses 100 chips if the selected bucket was the “mostly green”
The game master then asks all those who have a red ball if they want to accept the bet. If everyone says “yes”, the bet is on. A person who drew a red ball should conclude that it’s much more likely that the drawing was from the “mostly red” bucket, as the likelihood of them getting a red ball is 0.8 in that case, and only 0.2 in the “green” case. SO their expected payoff is 50*0.8 – 100*0.2= 20. The bet is favorable and they accept it
But, on the other hand, in advance you should conclude that your expected payoff in such a game is
50*0.5 – 100-*0.5 = -25 and you should reject the bet
7. (***) A stranger comes up to you on the street and asks you for $5. In exchange, the stranger claims they will use magical powers to cause a fantastic number (say N) of people in a different world to be very happy and lead rewarding lives. You don’t believe the stranger has magical powers, but surely there is an N such that your subjective probability of the stranger being able to carry out their promise is greater than 1/N. Then since the stranger can give you more expected happiness and well-being than you can otherwise buy with $5, you should give the stranger the money. But this is absurd.
8. (**) A person who does not know Chinese sits alone in a room with a big book of instructions. The person receives letters written in Chinese through a slot in the wall and, following the book’s instructions, manipulates the symbols to produce responses in Chinese. The instructions do not require the person to do anything creative or intelligent, but this process results in perfectly coherent Chinese responses to the input, as if a person had written those. So responses to the letters are being written without anyone involved understanding the letter. But how can that be?
9. (*/**/***) We expect healthy grass to be green tomorrow because we have always observed it to be green in the past. Define the adjective grün to mean “green if the date is before January 1, 2020, and blue otherwise”. We have always observed living grass to be grün, so we should expect grass to always be grün . So grass will be grün in 2020
10. (**) Discovering a cure for a disease provides an infinite stream of benefits, since people get health benefits of not having the disease in every generation. Therefore we should allocate our entire health budget to research. But clearly this is absurd.
11. (**) You are blindfolded and transported to an unknown city. You do not know how many taxis there are in the city. The only thing you know is that the taxis in the city are numbered 1,2,3,…,n, for some value of n with each number occurring exactly once. You stand on the street corner and wait until you see a taxi. The taxi is numbered k. What probability should you assign that there are at least 2k taxis in the city?
A person might argue:
(I). The probability is 50%. Because if we get dropped again and again into new cities, and always put 50% on this claim, the claim will be right half the time (because the taxi will be 50% of the time in the first half of all taxis, and 50% of the time in the second half), and this is what 50% means.
Alternatively, a person might argue:
(II). The probability cannot be determined unless you have a probability distribution over city-size (or rather, over city-taxi numbers). Imagine, for example, any specific set of cities, e.g., that there is a 1/3rd chance of 100 taxis, a 1/3rd chance of 200 taxis, and a 1/3rd chance of 300 taxis. Then, given any particular k, you can determine the chance that n > 2k using standard conditional probability. And the answer you get depends on your distribution over cities. So the person claiming (I) would be incorrect, since they are claiming an answer that does not depend on the distribution over cities.
12. (**/***) Modern cosmology teaches that the world might well contain an infinite number of happy and sad people. Aggregative ethics implies that such a world contains an infinite amount of positive value and an infinite amount of negative value. You can affect only a finite amount of good or bad. In standard cardinal arithmetic, an infinite quantity is unchanged by the addition or subtraction of any finite quantity. So it appears you cannot change the value of the world.
13. (**) Imagine that there's a very, very large population of people in the world, and that there's a madman. What this madman does is, he kidnaps ten people and puts them in a room. He then throws a pair of dice. If the dice land snake-eyes, then he simply murders everyone in the room. If the dice do not land snake-eyes, then he releases everyone, then kidnaps 100 people. He now does the same thing: he rolls two dice; if they land snake-eyes then he kills everyone, and if they don't land snake-eyes, then he releases them and kidnaps 1,000 people. He keeps doing this until he gets snake-eyes, at which point he's done. So now, imagine that you've been kidnapped.
So you're in the room. Conditioned on that fact, how worried should you be? How likely is it that you're going to die? One answer is that the dice have a 1/36 chance of landing snake-eyes. A second reflection you could make is to consider, of people who enter the room, what the fraction is of people who ever get out. Let's say that it ends at 1,000. Then, 110 people get out and 1,000 die. If it ends at 10,000, then 1,110 people get out and 10,000 die. In either case, about 9/10 of the people who ever go into the room will die. Independently on when the experiment stops, if each prisoner guesses that the chance of them dying is 1/36, because most will die, most will be wrong.
Hablar o no hablar
A raíz de una faringitis y de una apuesta que en último término perdí, y cuyos términos no serán revelados, y aprovechando que mis distintos círculos sociales no convergen en absoluto, pasé el año pasado un mes sin hablar en mi universidad. Esto significa, fuera de un "oye" accidental y de otra excepción adicional, no dije ninguna otra palabra, si bien sí he escribí, gesticulé, moví los labios, y demás.
Al comentar esto entre conocidos y amigos, una reacción frecuente es el asombro. En mi experiencia, no obstante, callar el pico no supone un gran esfuerzo; frecuentemente no tenía nada que decir. No obstante, cuando sí tenía algo que decir, cuando hablar me hubiera sido útil, me hubiera sido útil en extremo. Por ejemplo, una guapa chica me devolvió mi móvil tras yo haberlo perdido, y acto seguido me pregunto mientras se iba si era el mismo Nuño que tenía un blog. Qué rabia no poder responder.
Curiosamente, mediante la gesticulación todavía podía tomar en cierta medida parte en muchas otras, en la mayoría de las conversaciones, lo cual sugiere tanto que el nivel de complejidad de una conversación típica era ínfimo, como que el gesto puede transmitir mensajes inusitadamente elaborados. Sobre lo segundo, llegué a comunicar en pocos segundos a un profesor "No, no es que esté haciendo un voto de silencio, es que estoy enfermo y ellos son tontos" de la siguiente forma: hacía algunos gestos, él me dice lo que cree entender y yo le corrijo, matizo o rechazo su interpretación. Finalmente, cuando ha dado en el clavo, hago un gesto de afirmación.
El contexto por supuesto ayudaba, complementado por un factor x: la inteligencia o intuición social de aquel con el que hablaba. De ser elevada, casi me podía comunicar de manera fluida, y en el caso contrario me estrellaba contra muro tras muro y tenía que recurrir a sacar mi cuaderno. Por otro lado, en ningún caso encontré una forma exitosa de transmitir lo relacionado con el tiempo: hoy, ayer, mañana; mis símbolos eran como un cumpleaños feliz interpretado con los nudillos en la mesa: obvios para el emisor e indescifrables para el receptor.
Extraído de: https://mathwithbaddrawings.com
N.B: Puede existir una relación entre esta entrada y:
De filosofía y matemáticas he adquirido la manía de dividir y analizar en casos. Hasta ahora he considerado la combinación no hablar pero sí comunicarse. Queda todavía la combinación trivial: hablar y comunicarse. También está hablar pero no comunicarse, como se hace con aquellos que no te caen bien pero a los que no puedes evitar. Y finalmente no hablar y no comunicarse, que es lo que hacía una chica que conocí este verano, tímida timidísima y que me destrozó al ajedrez 12-0 (luego "remonté" 17-6). Por otro lado está el identificar comunicarse con hablar, como hago y se hace en Whatsapp al decir "hablamos luego", en vez de "nos escribimos luego".
El menú de niños, por si alguien quiere probar un aperitivo, es un juego llamado "Person do thing" (Persona hace cosa: https://www.persondothing.com/), en el que se tiene que transmitir una palabra, p.ej. "esqueleto" utilizando 36 palabras simples predeterminada. Esto me lleva a una idea cuyo esquema recibí hace unas semanas: Frente a comunicar un mensaje totalmente, también se pueden simplemente transmitir las instrucciones para que el lector lo reconstituya en su cabeza, como un mueble de Ikea o como el lector avispado habrá hecho al leer "hablar o no hablar" y completar con "esa es la cuestión". Los chistes que disfruto tienen algo de esto y por esto a veces dejo frases sin terminar.
Retomando el tema del lenguaje corporal, merece la pena la siguiente entrevista con el humorista George Carlin: https://www.youtube.com/watch?v=QirDGt2t9X0. Recomiendo o bien dedicar al menos media hora al siguiente ejercicio o bien ignorarlo completamente. En el primer caso, véase primero el vídeo con y luego sin sonido, tomando apuntes; a mi esto me hizo pillar, hizo clic el lenguage corporal, donde incluyo tanto el tono y el ritmo de la voz como las frondosísimas cejas, con las cuales continuamente interpela al presentador, en oposición al lenguaje verbal, donde incluyo solo el mensaje. El contraste entre las barbaridades que suelta y su cándida actitud es, por otra parte, muy gracioso. Vale.
Freud: Sobre la conquista del fuego
En una acotación a mi estudio sobre El malestar en la cultura aludí, aunque sólo incidentalmente, a cierta conjetura que el material psicoanalítico nos ofrece respecto de la forma en que el hombre primitivo habría conquistado el dominio sobre el fuego. Véome ahora inducido a volver sobre el mencionado tema por las opiniones discrepantes de la mía que expuso Albrecht Schaeffer y por la sorprendente referencia de Erlenmeyer, en su reciente estudio, acerca de la prohibición de orinar sobre las cenizas que rige entre los mogoles.
Creo que mi hipótesis -de que la condición previa para la conquista del fuego habría sido la renuncia al placer de extinguirlo con el chorro de orina, placer de intenso tono homosexual– puede ser confirmada mediante la interpretación de la leyenda griega de Prometeo, siempre que se tenga debida cuenta de la obvia deformación que media entre los hechos históricos y su representación en el mito. Estas deformaciones son de la misma índole -y no más violentas- que las que toleramos a diario cuando reconstruimos, a partir de los sueños de nuestros pacientes, sus vivencias infantiles reprimidas, tan extraordinariamente importantes. Los mecanismos aplicados en esta deformación consisten en la representación simbólica y en la sustitución por lo contrario. No me atrevo a interpretar de tal manera todos los rasgos del mito, pues bien podría ser que en su trama se hubiesen agregados a los hechos primitivos otros sucesos más recientes. Pero los elementos que admiten interpretación analítica son precisamente los más notables e importantes: la manera en que Prometeo transporta el fuego, la índole de su acto (sacrilegio, robo, engaño de los dioses) y el sentido del castigo que se le impone.
El titán Prometeo -un héroe cultural aún dotado de carácter divino; quizá en la versión original un demiurgo y creador de seres humanos- trae pues, a los hombres, oculto en un bastón hueco, en una rama de hinojo, el fuego que ha robado a los dioses. Si nos hallásemos ocupados en la interpretación de un sueño, de buen grado entenderíamos aquel escondrijo como un símbolo fálico, pese a que nos molesta un tanto la insólita acentuación de su oquedad. Pero, ¿cómo relacionar este tubo fálico con la conservación del fuego? He aquí una conexión que nos parece infructuoso establecer, hasta que recordamos el proceso de la transformación o sustitución por lo contrario, de la inversión de las relaciones mutuas, tan frecuente en el sueño y tantas veces revelador de su sentido oculto. No es el fuego lo que el hombre alberga en su tubo fálico, sino, por el contrario, el medio para extinguir la llama, el líquido chorro de su orina. De este vínculo entre fuego y agua surge al punto un material analítico que ya nos es familiar.
En segundo lugar, nos hallamos con que la conquista del fuego es un crimen sacrílego, pues se obtiene mediante el robo, la sustracción. Henos aquí ante un rasgo constante e invariable de todas las leyendas sobre la conquista del fuego, presente en los pueblos más dispares y distantes, y no sólo en la leyenda griega de Prometeo, el portador de la llama. Aquí debe hallarse, pues, el elemento nuclear de esta deformada reminiscencia humana. Pero, ¿por qué aparece la obtención del fuego indisolublemente ligada a la idea de un sacrilegio? ¿Quién es aquí el perjudicado, el engañado? En la versión de Hesíodo la leyenda nos ofrece una respuesta directa, pues en otra narración, no vinculada directamente con el fuego, Prometeo engaña a Zeus en favor de los hombres, al preparar los sacrificios que le son ofrendados. ¡De manera que los engañados son los dioses! Como se sabe, la mitología concede a los dioses el privilegio de satisfacer todos los deseos a que la criatura humana debe renunciar, como bien lo vemos en el caso del incesto. En términos analíticos, diríamos que en la vida pulsional, el ello, es el dios engañado con la renuncia a la extinción del fuego, de modo que en la leyenda un deseo humano se habría transformado en un privilegio de los dioses, pues en este nivel legendario la divinidad de ningún modo tiene carácter de superyó, sino que aún representa a la omnipotente vida pulsional.
La sustitución por lo contrario llega a su grado máximo en el tercer elemento de la leyenda, en el castigo que sufre el conquistador del fuego. Prometeo es encadenado a una peña y un buitre le roe diariamente el hígado. También en las leyendas ígneas de otros pueblos interviene un ave, de modo que ha de tener en el conjunto alguna significación que por el momento me abstengo de interpretar. En cambio, nos hallaremos en terreno seguro al tratar de explicar por qué se eligió el hígado para aplicar el castigo. Para los antiguos, el hígado era asiento de todas las pasiones y de los deseos; así, un castigo como el sufrido por Prometeo era el más adecuado para un delincuente pulsional, para un delito cometido bajo el impulso de deseos ofensivos. Pero en el demiurgo del fuego nos encontramos precisamente con lo contrario: ha renunciado a sus pulsiones, demostrando cuán benéfica, pero también cuán imprescindible para los fines culturales es semejante renuncia. Así, ¿qué podía inducir a la leyenda a considerar semejante hazaña cultural como un delito digno de castigo? Pues bien: si en todas las deformaciones se transparenta la circunstancia de que la obtención del fuego tuvo por condición previa una renuncia pulsional, entonces la leyenda expresa sin ambages el rencor que la humanidad pulsional hubo de sentir contra el héroe cultural. Y, por otra parte, esto concuerda con lo que sabemos y esperábamos. Sabemos que la invitación a la renuncia pulsional y la imposición de ésta despiertan la misma hostilidad y los mismos impulsos agresivos que sólo en una fase ulterior de la evolución psíquica llegarán a expresarse como sentimiento de culpabilidad.
La impenetrabilidad de la leyenda prometeica, así como la de tantos otros mitos ígneos, es acrecentada por el hecho de que a los primitivos el fuego debe haberles parecido algo similar a las pasiones amorosas; nosotros diríamos: un símbolo de la libido. El calor que el fuego irradia despierta la misma sensación que acompaña el estado de la excitación sexual, y la llama, con su forma y movimiento, nos recuerda el falo activo. No puede cabernos la menor duda con respecto a que la llama era en sentido mítico un falo, pues aun la leyenda genealógica del emperador romano Servio Tulio lo atestigua. Cuando nosotros mismos hablamos del «fuego de la pasión» y de las llamas que «lengüetean» o «lamen» un combustible, es decir, cuando comparamos la llama con la lengua, no nos hemos alejado mucho, por cierto, del pensamiento de nuestros antepasados primitivos. En nuestra derivación del mito ígneo también aceptábamos que para el hombre primitivo la tentativa de extinguir las llamas con su propia agua representó una lucha placentera con un falo ajeno.
Por la puerta de esta asimilación simbólica pueden haber penetrado al mito otros elementos puramente fantásticos que luego se habrían entretejido con los primitivos, históricos. Así, es difícil rechazar la idea de que siendo el hígado asiento de las pasiones signifique simbólicamente lo mismo que el fuego, de manera que su cotidiana consunción y regeneración describiría con fidelidad la fluctuación de los deseos amorosos que, diariamente satisfechos, se renuevan diariamente. Al ave que sacia su apetito en el hígado le correspondería entonces una significación fálica que, por otra parte, no le es nada extraña, como nos lo demuestran las leyendas, los sueños, los giros del lenguaje y las representaciones plásticas de la antigüedad. Un pequeño paso más nos lleva al ave fénix, que renace rejuvenecida de cada muerte en las llamas y que, con toda probabilidad, aludió primitiva y preferentemente al falo reanimado después de cada relajación, más bien que al sol, ocultado en el crepúsculo vespertino para renacer cotidianamente.
Hemos de preguntarnos si es lícito atribuir a la función mitopoiética el propósito frívolo de representar, disfrazados, procesos psíquicos dotados de expresión corporal, por todos conocidos, pero sumamente interesante, sin ser animada por ningún otro motivo, fuera del mero placer representativo. Seguramente es imposible responder a esta pregunta sin penetrar antes en la esencia del mito, pero para nuestros dos casos es fácil reconocer este contenido y con ello una tendencia determinada. Ambos ilustran la reanimación de los deseos libidinales después de haberse consumido en una satisfacción, es decir, representan su perennidad, y el consuelo contenido en este tema predominante está plenamente justificado, ya que el núcleo histórico del mito trata una derrota de la vida pulsional, una renuncia a las pulsiones que ha sido imprescindible aceptar. Viene a ser como la segunda fase de la comprensible reacción que presentaría un hombre primitivo ofendido en sus pulsiones: una vez castigado el delincuente, se le asegura que en el fondo nada malo ha cometido.
En un punto inesperado de otro mito, que al parecer muy poco tiene que ver con el fuego, nos topamos con la sustitución por lo contrario. La hidra de Lerna, con sus innumerables y agitadas cabezas de serpiente entre -ellas hay una inmortal-, es, como su nombre lo atestigua, un dragón acuático. Heracles, el héroe cultural, la destruye cortándole las cabezas, pero éstas vuelven a crecer, y sólo logra dominar al monstruo después de haberle quemado con fuego la cabeza inmortal. ¡Un dragón acuático dominado por el fuego!: he aquí algo que no da sentido. Pero sí lo tiene, como en tantos sueños, la inversión del contenido manifiesto. En tal caso, la hidra es una hoguera; las cabezas de serpientes son sus llamas, y como prueba de su índole libidinal presentan, igual que el hígado de Prometeo, el fenómeno de la regeneración, de la integridad restablecida luego de su intentada destrucción. Ahora bien: Heracles extingue este incendio con… agua. La cabeza inmortal es, sin duda, el propio falo, y su destrucción representa la castración. Pero Heracles también es el libertador de Prometeo, el que mata al ave cebada en su hígado. ¿Acaso no se habría de aceptar una relación más profunda entre ambos mitos? Vendría a ser como si el acto de uno de los héroes fuese anulado por el otro. Prometeo había prohibido extinguir el fuego -igual que el precepto de los mogoles-, pero Heracles lo permitió en caso de incendios amenazantes. El segundo mito parece corresponder a la reacción de una época ulterior de la cultura contra el motivo primitivo de la conquista del fuego. Tenemos la impresión de que desde aquí podríamos penetrar profundamente en los misterios del mito, pero, naturalmente, la sensación de seguridad no nos acompañaría muy lejos.
Hemos de preguntarnos si es lícito atribuir a la función mitopoiética el propósito frívolo de representar, disfrazados, procesos psíquicos dotados de expresión corporal, por todos conocidos, pero sumamente interesante, sin ser animada por ningún otro motivo, fuera del mero placer representativo. Seguramente es imposible responder a esta pregunta sin penetrar antes en la esencia del mito, pero para nuestros dos casos es fácil reconocer este contenido y con ello una tendencia determinada. Ambos ilustran la reanimación de los deseos libidinales después de haberse consumido en una satisfacción, es decir, representan su perennidad, y el consuelo contenido en este tema predominante está plenamente justificado, ya que el núcleo histórico del mito trata una derrota de la vida pulsional, una renuncia a las pulsiones que ha sido imprescindible aceptar. Viene a ser como la segunda fase de la comprensible reacción que presentaría un hombre primitivo ofendido en sus pulsiones: una vez castigado el delincuente, se le asegura que en el fondo nada malo ha cometido.
En un punto inesperado de otro mito, que al parecer muy poco tiene que ver con el fuego, nos topamos con la sustitución por lo contrario. La hidra de Lerna, con sus innumerables y agitadas cabezas de serpiente entre -ellas hay una inmortal-, es, como su nombre lo atestigua, un dragón acuático. Heracles, el héroe cultural, la destruye cortándole las cabezas, pero éstas vuelven a crecer, y sólo logra dominar al monstruo después de haberle quemado con fuego la cabeza inmortal. ¡Un dragón acuático dominado por el fuego!: he aquí algo que no da sentido. Pero sí lo tiene, como en tantos sueños, la inversión del contenido manifiesto. En tal caso, la hidra es una hoguera; las cabezas de serpientes son sus llamas, y como prueba de su índole libidinal presentan, igual que el hígado de Prometeo, el fenómeno de la regeneración, de la integridad restablecida luego de su intentada destrucción. Ahora bien: Heracles extingue este incendio con… agua. La cabeza inmortal es, sin duda, el propio falo, y su destrucción representa la castración. Pero Heracles también es el libertador de Prometeo, el que mata al ave cebada en su hígado. ¿Acaso no se habría de aceptar una relación más profunda entre ambos mitos? Vendría a ser como si el acto de uno de los héroes fuese anulado por el otro. Prometeo había prohibido extinguir el fuego -igual que el precepto de los mogoles-, pero Heracles lo permitió en caso de incendios amenazantes. El segundo mito parece corresponder a la reacción de una época ulterior de la cultura contra el motivo primitivo de la conquista del fuego. Tenemos la impresión de que desde aquí podríamos penetrar profundamente en los misterios del mito, pero, naturalmente, la sensación de seguridad no nos acompañaría muy lejos.
En lo que se refiere a la contradicción entre el fuego y el agua que domina estos mitos en toda su amplitud, podemos demostrar, junto a los factores históricos y fantástico-simbólicos, un tercero, un hecho fisiológico que el poeta Heine describió en los siguientes versos:
Con lo que le sirve para mear,
el hombre puede a otros crear
[Was dem Menschen dient zum Seichen
Damit schafft er Seinesgleichen]
El miembro viril del hombre posee dos funciones, cuya reunión orgánica es para muchos motivo de indignación. Está encargado de evacuar la orina y de realizar el acto sexual que satisface las necesidades de la libido genital. El niño aún cree reunir ambas funciones y, según sus teorías, los niños se producen al orinar el hombre en el vientre de la mujer; pero el adulto sabe que ambos actos son en realidad mutuamente incompatibles; en efecto, tan incompatibles como fuego y agua. Cuando el falo llega al estado erecto que le ha valido la equiparación con el pájaro y durante el cual se perciben aquellas sensaciones que recuerdan el calor del fuego, es imposible orinar, por el contrario, cuando el falo sirve a la evacuación de la orina (el agua del cuerpo), parecen extinguidas todas sus vinculaciones con la función genital. La contradicción entre ambas funciones podría llevarnos a afirmar que el hombre extingue su propio fuego con su propia agua. Y el hombre primitivo, que se veía obligado a tener que captar el mundo exterior con ayuda de sus propias sensaciones y condiciones corporales, seguramente no dejó de advertir y de utilizar las analogías que le reveló la conducta del fuego.
Sobre el problema de las parejas estables
Planteamiento. Explicación cultivada en Wikipedia.
Podemos modelizar el problema poblacional de encontrar una pareja aceptando las asunciones de El problema de las parejas estables (Stable Marriage Problem). Estas son: que la población se divide en hombres y mujeres, y que todo hombre y toda mujer prefieren a los individuos del sexo opuesto en un orden concreto.
Por supuesto, la población es plenamente heterosexual. Además, nadie tiene estándares, es decir, todos prefieren mejor estar mal acompañados que estar solos. A pesar de estas asunciones, me sigue pareciendo interesante presentar qué pasa si se sigue el siguiente algoritmo:
En la iteración 1,
a) Cada hombre no emparejado se declara a la mujer que más prefiere
b) Cada mujer dice "tal vez" al pretendiente que más prefiere y "no" a los demás.
En la iteración n+1 / n+1 > 1
a) Cada hombre que todavía no está emparejado se acerca a la mujer que más prefiere de entre las que todavía no le han rechazado.
b) Cada mujer dice "tal vez" al nuevo pretendiente que más prefiere, si y solo si prefiere a este sobre su pareja actual. Si elige a alguien para reemplazar a su pareja, la expareja está ahora desemparejada y en la siguiente ronda participa en a).
Esto se repite hasta que todos quedan emparejados. Además, cuando el proceso se termine no existirá ninguna pareja {A,B} tal que A y B preferirían al otro sobre su pareja actual y no estén ya juntos. Esto pasa por razones fáciles de entender y que están fácilmente disponibles en Wikipedia
{https://en.wikipedia.org/wiki/Stable_marriage_problem}
Un ejemplo
Si hay tres hombres, H1, H2 y H3, y tres mujeres M1, M2 y M3, representamos sus preferencias respectivamente por:
Si se implementa el algoritmo,
Ronda 1) H1 -> (se declara a) M1; H2 -> M2; H3 -> M1. H1 y H2 son aceptados, H3 es rechazado.
Ronda 2) H3 -> M3. H3 es aceptado.
Fin.
Las parejas finales son {H1,M1}; {H2, M2}; {H3,M3}
Los Hs han terminado, de media, con su opción: (1 + 1 + 2) / 3 = 4 / 3, pues H1 termina con su primera opción, H2 también y H3 con su segunda.
Las Ms han terminado, de media, con su opción (1 + 1 + 3) / 3 = 5 / 3, pues M1 termina con su primera opción, M2 también y M3 con su tercera.
Nomenclatura: Podemos llamar a 4/3 la "distancia al ideal" de los Hs, y a 5 / 3 la "distancia al ideal" de las Ms. Cuanto más bajo es el número, mejor para ellos.
Fin del ejemplo
{https://en.wikipedia.org/wiki/Stable_marriage_problem}
Un ejemplo
Si hay tres hombres, H1, H2 y H3, y tres mujeres M1, M2 y M3, representamos sus preferencias respectivamente por:
Preferencias(H1)={M1,M2,M3};
P(H2)={M2, M1,M3};
P(H3)= {M1, M3, M2}
P(M1) = {H1, H3, H2};Esto "significa" que el H1 prefiere a la M1, luego a la M2, y finalmente a la M3, mientras que la M1 prefiere al H1 seguido del H3 y del H2.
P(M2) = {H2, H1, H3};
P(M3) = {H1, H2, H3}
Si se implementa el algoritmo,
Ronda 1) H1 -> (se declara a) M1; H2 -> M2; H3 -> M1. H1 y H2 son aceptados, H3 es rechazado.
Ronda 2) H3 -> M3. H3 es aceptado.
Fin.
Las parejas finales son {H1,M1}; {H2, M2}; {H3,M3}
Los Hs han terminado, de media, con su opción: (1 + 1 + 2) / 3 = 4 / 3, pues H1 termina con su primera opción, H2 también y H3 con su segunda.
Las Ms han terminado, de media, con su opción (1 + 1 + 3) / 3 = 5 / 3, pues M1 termina con su primera opción, M2 también y M3 con su tercera.
Nomenclatura: Podemos llamar a 4/3 la "distancia al ideal" de los Hs, y a 5 / 3 la "distancia al ideal" de las Ms. Cuanto más bajo es el número, mejor para ellos.
Fin del ejemplo
Dicho lo cual, Wikipedia menciona que el algoritmo descrito resulta óptimo para los pretendientes. Me interesa cuantificar esa afirmación anto para preferencias aleatorias y no aleatorias. Para ello, he escrito varios programas en Python, que se pueden acceder aquí: {https://github.com/NunoSempere/Stable-marriage-problem}. Incidentalmente, estimo que la complejidad del asunto es similar a la la chicha de este proyecto de fin de carrera: {Algoritmo de Gale-Shapley. Variaciones y alternativas; Documento archivado}, que trata de algo similar.
Resultados:
En las gráficas que siguen, un punto representa un nivel de "distancia al ideal" de un sexo, donde el rojo representa a los hombres y al azul a las mujeres. El que el punto esté más arriba implica que ese "nivel de distancia" es más común, y si está cerca del cero, que es menos frecuente. Frecuente entre el resultado final de preferencias inciales elegidas o bien aleatoriamente o bien cercanas un orden canónico. Si quisiéramos que todos fuesen felices, querríamos que los puntos estuviesen arriba a la izquierda. (Tal vez quieras leer este párrafo otra vez).
a) Preferencias elegidas aleatoriamente.
Para experimento con 20 personas de cada sexo, repetido 100 veces, obtenemos la siguiente gráfica✝:
Hay un patron, que se va discerniendo a medida que aumentamos el número de repeticiones.
Para 10^3 repeticiones:
Para 10^4 repeticiones:
Y para 2*10^4 repeticiones:
Para una población de 100 de cada sexo, obtenemos resultados similares.
Para 1000 repeticiones:
Para conseguir resultados "bonitos" podemos o bien reducir el número de personas o bien aumentar el número de experimentos. Si hacemos ambas cosas, con 10 sujetos de cada sexo y 10^4 experimentos, obtenemos lo siguiente:
b) Preferencias elegidas no aleatoriamente.
Modelamos el asunto de la siguiente manera: Hay una preferencia platónica [H1, H2 , H3, H4, H5,...], es decir, el hombre n es más deseable que el n+1, y lo mismo con las mujeres. Sobre esta lista platónica, los sujetos tienen un número variable de variaciones, donde una variación es intercambiar la persona n con la n+1. Daré la magnitud de la variación el % sobre la población, es decir, si hay n personas de cada sexo, v% variación se corresponde con floor(n*v/100) variaciones, donde floor(x) es el redondeo hacia abajo de x.
Es directo que para 0% variación la curva se corresponde con una campana centrada en n/2, donde n es la población✝✝.
Para un 10% de variación y 2000 repeticiones:
Para una población de 20 de cada sexo, obtenemos:
Y para una población de 100:
Y se ven por donde van los tiros. Como sabemos que estamos hablando de campanas más o menos de Gauss, podemos pasar a contemplar solamente la media, que será el eje de simetría de la campana. En la siguiente gráfica se muestran las medias de diferentes variaciones aplicadas a una población de 20 sujetos de cada sexo. Es un poco diferente:
- El punto (a,b) representa dos medias de un experimento repetido 100 veces, donde a (eje x) es la media de los hombres y b (eje y) es la media de las mujeres.
- El color representa la variación; cuanto más azul, más variación. La variación va de 0% a 1000%, en intervalos de 20%.
Nótese que los ejes no están centrados. La línea azul es y=x, por lo que mayor azar (más variaciones) benefician a ambos sexos, pero más rápido a los hombres. Recordamos que para una población de preferencias aleatorias tendríamos puntos en torno al (2.12, 4.98), respectivamente la media de hombres y de mujeres.
El punto negro flotando por encima de la recta es la media de una población aleatoria.
Moraleja
La moraleja, no obstante, depende de en qué medida nuestras asunciones se cumplan en la realidad, y estas no son robustas. Es, entonces, una cuestión de criterio personal si una validez parcial de los principios implica una validez parcial de las conclusiones.
Dejo como ejercicio al lector y como preguntas a mí mismo:
- ¿Cuantas variaciones son necesarias para llegar a una lista decentemente pseudoaleatorio?
- ¿Qué pasa si solo hay un sexo, d.h., si todos son bisexuales? Demuestra que la existencia de una configuración estable de matrimonios está garantizada, o da un contraejemplo.
- ¿Se pueden construir casos patológicos en los que todos los hombres terminen con su última opción y todas las mujeres con su primera?
- N.B.: Parece que esto ya ha sido estudiado, véase Improving Man-Optimal Stable Matchings by Minimum Changeof Preference Lists, Takao Inoshita et al, extraído de:
- Demuéstrese que las campanas de Gauss se van separando a medida que n aumenta. ¿A qué es proporcional esa separación?
✝ El lector perspicaz se habrá dado cuenta de que en las gráficas hay puntos en el intervalo [0,1]. Esto se debe a que, en Python, la primera posición de una lista es la posición cero. No se preocupen; réstenle 1 a los números utilizados en el ejemplo.
✝✝ Realmente (n-1)/2, porque el más deseado es el 0, no el 1. Pero
da igual. Aunque ahora que lo pienso, tal vez tenga un error por uno
(off by one error) en algún sitio.
Elitismo: Una anécdota inverosímil.
Fragmento de mi correspondencia personal con una pen pal nativa alemana.
"Es tut mir ehrlich mega leid, aber wenn jemand auf dieser komischen Sprachaustauschseite so eine Beschreibung aufstellt, wie du und zusätzlich behauptet, er studiere Mathematik und Philosophie, ruft dies bei mir die Befürchtung aus, dieser sei entweder einfach bloß irgend ein von Umgebung unverstandener Hochbegabter, der den Prozess des Lernens einer Sprache mit etwas inhaltlich sinnvollem füllen will, oder (Hochbegabung nicht ausgeschlossen) irgend ein arroganter abgehobener pseudo Snob, der nach seinesgleichen sucht."
"Lo siento de verdad mega mucho, pero cuando alguien de ese extraño sitio de intercambio de idiomas tiene una descripción como la tuya, y además afirma estudiar matemáticas y filosofía, me entra la sospecha de que este sea o bien simplemente algún tipo de superdotado incomprendido que quiera llenar el proceso de aprender un idioma con algún contenido sustancial, o bien (sin excluir a la superdotación), algún tipo de pseudo Snob arrogante y estiradillo que busca a gente de su misma calaña".
El contexto de este fragmento es, omitiendo algunos detalles, que tras seis correos de discusión protofilosofica, ella escribiendo entorno a 1000 palabras y mis respuestas de entre 400, se pica tras preguntarle yo si había reflexionado antes de escribir una idea (revelación: no), y revela que siempre ha tenido sospechas acerca de mi carácter (Una vez más, comienza el drama).
Esto apunta a un fenómeno interesante: tras dos años de bachillerato rodeado de gente de mente afilada he y hemos desarrollado unos estándares intelectuales despiadados; recuerdo una discusión en la que alguien que vino sin preparación se rompió y terminó llorando. Si presentas una idea claro que va a ser atacada. Sin cuartel. Incluso si se está de acuerdo con ella. Y la gente lee mucho, y recuerda miscelánea, que se utiliza como contrajemplo inesperado, al que se debe responder, si uno puede, pensando rápido, lo cual nunca es excusa para meter de contrabando una falacia, porque eso solo conduce a la crucifixión. En este sistema tiene sentido la libertad de expresión, la metáfora del "mercado de ideas", y en este sistema se espera que si alguien está equivocado lo esté de forma interesante, es decir, no trivial, o bien que esté aprendiendo algo nuevo, en cuyo caso se espera que se planteen preguntas perspicaces.
Frente a ello, la alemana me acusa de no ser tolerante y de carecer de empatía. Una innovación a la forma del ya cliché "es mi opinión", "debes respetar las opiniones de los otros". Algo diplomático, y pronuncio esa palabra con las mismas connotaciones con las que un nazi diría judío. Estas dos actitudes se oponen de forma similar a como la "cultura del preguntar" y la "cultura del adivinar" lo hacen: cuando un acólito de una y uno de otro se juntan surgen chispas.
Por otra parte, tampoco creo que haya forma alguna de decir con tacto a alguien: Tengo unos estándares intelectuales, y tú no llegas, ya sea de forma explícita, ya no verbal, o bien proponiendo una conversación para cuya participación se requiere una maquinaria de la que carece. Hacer esto último genera odio, y el odio lleva a la ira. Por eso me parece necesario un cierto elitismo. No por principio, sino como fruto de mi experiencia, y por descontado evitando cualquier virus de descalificación total.
Esto apunta a un fenómeno interesante: tras dos años de bachillerato rodeado de gente de mente afilada he y hemos desarrollado unos estándares intelectuales despiadados; recuerdo una discusión en la que alguien que vino sin preparación se rompió y terminó llorando. Si presentas una idea claro que va a ser atacada. Sin cuartel. Incluso si se está de acuerdo con ella. Y la gente lee mucho, y recuerda miscelánea, que se utiliza como contrajemplo inesperado, al que se debe responder, si uno puede, pensando rápido, lo cual nunca es excusa para meter de contrabando una falacia, porque eso solo conduce a la crucifixión. En este sistema tiene sentido la libertad de expresión, la metáfora del "mercado de ideas", y en este sistema se espera que si alguien está equivocado lo esté de forma interesante, es decir, no trivial, o bien que esté aprendiendo algo nuevo, en cuyo caso se espera que se planteen preguntas perspicaces.
Frente a ello, la alemana me acusa de no ser tolerante y de carecer de empatía. Una innovación a la forma del ya cliché "es mi opinión", "debes respetar las opiniones de los otros". Algo diplomático, y pronuncio esa palabra con las mismas connotaciones con las que un nazi diría judío. Estas dos actitudes se oponen de forma similar a como la "cultura del preguntar" y la "cultura del adivinar" lo hacen: cuando un acólito de una y uno de otro se juntan surgen chispas.
Por otra parte, tampoco creo que haya forma alguna de decir con tacto a alguien: Tengo unos estándares intelectuales, y tú no llegas, ya sea de forma explícita, ya no verbal, o bien proponiendo una conversación para cuya participación se requiere una maquinaria de la que carece. Hacer esto último genera odio, y el odio lleva a la ira. Por eso me parece necesario un cierto elitismo. No por principio, sino como fruto de mi experiencia, y por descontado evitando cualquier virus de descalificación total.
Mathematicians under the Nazis: Notes & quotes.
INTRO
The history of mathematics as an academic discipline in a time of intense political and ideological pressure.
There were psychologists like E.R. Jaensch and mathematicians like Ludwig Bieberbach who saw Mathematics as a fruitful area in which Nazi ideology could be exemplified and play a significant role.
“There is no attempt in this book to fit the narrative to a procrustean bed of underlying interpretation”
When evil is present it is tempting to see things only in starkly contrasted black and white
Deutsche Mathematik: ethnic styles in the doing and teaching of mathematics (while not denying the validity of any particular fact)
Indeed, its supporters argued that the universal validity of mathematical fact is precisely what makes mathematics most suitable for discerning such different styles.
CHAPTER 1: WHY MATHEMATICS
Relation between extra-scientific culture and pure science.
Image of science proceeding in a vacuum.
Truth is necessary but not sufficient for real mathematics.
“They argued that exactly the apparent culture-free nature of mathematical abstraction and mathematical causality makes mathematics the ideal testing ground for theories about racially determined differences in intellectual attitudes”
Rassenseelekunde: theory of the racial soul.
The mode of intellectual discovery → feeling and attitude towards the world
Associate the political argument with various philosophical differences within mathematics
Put succinctly, a Nazi argument promoted by Bieberbach was that because Jews thought differently and were suited to do mathematics differently, they could not be proper instructors of non-Jews. Indeed, their presence in the classroom caused a perversion of instruction. Thus, an elaborate intellectual rationale for the dismissal of Jews was established, discussed and defended.
Biological reductionism
Irrationalism
Philip Lenard (Deutsche Physik, Nobel): it was important for students to avoid studying too much mathematics. Mathematics was the “most subordinate intellectual discipline” because, under Jewish influence, it had lost its “feeling for natural scientific research”
matiz: p. 10
The Nazi typology cannot be dismissed out of hand
Other researchers, say in America, were attempting to recognize Jewish students by their writing style (A. A. Roback, pro-Jewish bias)
// In an expert, absence of evidence may be evidence of absence
CHAPTER 2: THE CRISIS IN MATHEMATICS
Uncomfortable axiomatic procedures: anomalies, paradoxes, but seemingly essential for ordinary analysis
Banach-Tarski
ZFC does not assume that, for every property there is a set of things satisfying that property
Type theory: every term has a type and operations are restricted to terms of a certain type.
Mathematiker oder Jongleur mit Definitionen?
Hilbert: Wir mussen wissen – wir werden wissen: Debemos / necesitamos saber, sabremos.
Comte: The chemical composition of stars will never be known
Some other guy: Temperature is unmeasurable
For the Nazi mathematician, the issue was the ability of mathematics to relate to real objects.
For Ludwig Bieberbach, the distinction was between defining pi as the ratio of the perimeter of a circumference to its diameter or, f.ex. As twice the smallest positive 0 of the cosine.
Jews attempt to create, true Germans discover.
Undeutsch
Categorization of method according to racial and national boundaries.
What is mathematics and what should it be? The conflict is deep, but precisely because it is so fundamental and so removed from everyday practice, many working mathematicians could simply get on with the job.
Intellect has no necessary connection with the ability to reason
CHAPTER 3: THE GERMAN ACADEMIC CRISIS
There was no Nazi party line on mathematics or science, and mathematicians who espoused similar cultural politics might disagree on how that politics affected mathematics.
The German professor was generally a conservative establishment figure who, under Weimar, had largely lost his establishment status.
Part of the academic culture was the notion of the professor as a prestigious state servant who had been declassed by the collapse of the empire.
“German academic freedom as defined by the government in 1898 did not include the right to be a politically active Social Democrat; thirty-five years later it did not include the right to be a Jew”.
Kulturstaat: The state would support learning in a widely humanistic sense; in return, the educated would become the trained civil servants and defenders of the state
Manifesto of the 93
„Fort also mit dem landfremden und abstoßenden Schlagwort »demokratisch«!”
“Away with the repugnant motto “democratic”, foreign to our country!” - Thomas Mann
Salonkommunist – Salonbolschewist
Emil Gumbel.
The majority of German academics simply “went along”, neither supporting nor condemning the regime.
Anti Semitism
Jews were represented in German universities far out of proportion to their numbers in the population
Promotion for Jews was the exception
Heinrich von Treitschke: Jews as the eternal foreigners within the people.
Elitist, genteel anti-Semitism: condemn the rabble rousing anti-Semitic agitator Herman Anwardt while understanding and condoning his position.
Refugee scientists from Germany were not always welcome in the USA.
Harvard began to restrict Jewish admissions in 1926, and Jewish quotas at Harvard, Princeton and Yale persisted until well after WWII.
The dismissal of the Jews meant more academic posts available for those not so tainted
Stennes-Putsch: by crushing the more violent elements of the S.A. (Stennes) and embracing the legality principle (z.B. forbidding street fights with the communists), the Nazis gained respectability in the eyes of conservative businessmen: Posible investigación histórica.
Hitler’s speech of Jan 27, 1932 to Düsseldorf industrialists.
“Nothing gives more credence to the correctness of our idea than the triumph of National Socialism at the University”, Adolf Hitler, July 8, 1930
Thus, it was natural that the parliamentary Weimar Republic was viewed as a corrupt and deceitful intrusion into the naturally Germanic order of things.
Jews, as outsiders, took posts away from real Germans
The mathematician, whose work basically involves self-generated mental constructions.
During the Nazi regime, mathematicians not only exhibited the same range of behaviours as their colleagues, but shared the same fundamental attitudes and reactions.
Phenomenon of initial enthusiasm followed by serious second thoughts, when it was “too” late
CHAPTER FOUR: THREE MATHEMATICAL CASE STUDIES
Politicization of Mathematics: Struggle among individuals, each purporting that they represented the true aims of the Nazi state in their actions
Once adherence to the state was established and its pariahs were eliminated, the system, with its overlapping bureaucracies, not only allowed conflict but was even said to encourage it. Mathematics was no exception.
For Doetsch, a law of nature was a description of a causal connection, not an explanation thereof
“That the two men became somewhat close may perhaps be indicated by a letter written by Kamke to Süss on February 24, 1943, which ends “Mit freundlichem Grüss – Ihr” instead of the mandated “Heil Hitler”
niggard: avaro
Such symbolic appointments were presumably quite important. But absent these, once the regimes basic demand – elimination of all Jews and political undesirables from academic posts – was satisfied, no one seems to have cared much about academic mathematics, including even its role for military purposes.
A decree existed by which inadequate academic performance could be compensated for by political service.
What Hasse did not understand was that national socialism meant the politicization of all life according to its Weltanschauung. This effectively was his irremediable and unredeemable flaw in Weber’s eyes.
Infighting between shades of Nazi, each striving to prove itself the true participant in standard bearing for the “national will”.
In the Nazi bureaucracy, if an initial approach somewhere had failed, there were always other ways, other completing agencies to which one could turn.
Given the positions to fill in Göttingen, especially the institute directorship, which was arguably the most important mathematical position in the entire country, the political demands of the Nazi regime could be met in two ways: seek the best politically acceptable mathematicians or seek the best mathematically acceptable true Nazi believer. Weber seems to have oscillated between both antipodal options, leaning towards the second and finally adopting it.
“the completely judaized mathematics institute at Göttingen had been waiting for over two semesters for National Socialist leadership”.
Questions of academic value only rarely played a significant role in academic placement under the Nazis.
“Sometime after that September, Mohr apparently told a female friend he thought Hitler was a megalomaniac and the German situation hopeless. He was led to this by the overthrow of Mussolini and the illegal listening to English radio broadcasts. She denounced him. On may 17, 1944, the Gestapo arrested him”. He was sentenced to death.
“English public opinion seems to be badly prejudiced against Germany. The papers pick up every bit of bad news they can get hold of about Germany, but they hardly think it worthwhile to write about good things brought about by National Socialism. One would not expect enthusiasm, since the whole movement has a certain and very outspoken tendency against the allies because of the Versailles Treaty. But one would expect a certain detachment and aloofness, otherwise so strong in the English. It is not their business after all.”
The only condition was that all activity, all struggle, as carried on in the name of ideology.
CHAPTER 5: ACADEMIC MATHEMATICAL LIFE.
Hannah Arendt
Dictatorial regimes: Merely insisted on enforced obedience to the dictator or monarch
Totalitarianism: Revolt of the masses that ended with all individuals being portions of the state machinery, in which each individual’s connections to the others was mediated by the state.
Thus the life of the mathematician was replete with intrusions of non-academic nature intent on making each individual a subservient member of the state, without connections to others except as mediated by the state. Academics had always been civil servants; such intrusions were easy.
~Under the Nazis, academic life became a progression of increasing restrictions and continual evaluations. No respect for academic rank: it was enforced from the bottom
Gradually all able bodied men who were not over-age were drawn into the armed forces.
The conservative Catholic atmosphere in which the university of Munster dwelled kept it from excesses prior to Hitler’s ascension to power.
“One often learned of one’s own dismissal from the newspapers”
he had to go back to Germany because he could go back to Germany, to make room for those who could not do so.
Cleansed of Jews, the remaining faculty needed only worry about the students who, inspired by the “new order”, might consider them “calcified”.
One consequence for mathematics was that the number of female students, originally discouraged by the Nazi government, increased.
Decline in effective secondary school instruction ⇒ decline in student quality
Bohn book burning on May 10.
Incidentally, anyone physically unable to raise his or her right arm was instru8cted to use the left if possible.
Three protected exceptions: WW1 veterans who had served at the front / Those who had been in civil service since 1/09/1914 continuously / Those who had lost a father or son in WW1.
Führerprinzip.
Rektor, and thus, in the Nazi interpretation, effectively Führer of the University.
“What a benefit, to find a pure German in such a hopelessly judaized discipline”
The Nazi believed in a sort of scientific reductionism, but for them the basic science was biology.
July 1933: All civil servants were ordered while on the job or inside their place of work to greet one another with the Hitler salute.
All servants of the state had to take a civil service oath. Under the Nazis, this was transformed into a personal oath to Adolf Hitler.
Dozentenschaft: Zumo de docente
All organizations were replaced by National Socialist ones.
Assistent – Ordinarien – Privatdozent – Extraordinarius.
People find their Nazi heart to climb in their Beruf.
No discussion, written or oral, was permitted about the reform of the Reich Government.
Inner emigration: Retreat into one’s work, holding all opinions to oneself.
The Nazi state was not satisfied with just having easily manipulable, atomized and terrorized individuals; it needed to weld them into a unified whole whose only bonds to each other were those binding them to the state.
An individual cannot answer to his Volk that mathematics is done because of the yearning for knowledge.
Pure mathematics (in the narrowest sense) has meaning only as a means of education to a formal character building that is consciously employed for service tot the entire people.
A characteristically German spiritual attitude to the doing of maths.
In March 36, all activity with League of Nations’ organizations was to cease.
“Is it really German to do something for its own sake?”
“Documentation cannot provide the “feeling” of a period by itself; while the personal narrative is subject to the strictures of subjectivity and the plague of an idiosyncratic point of view, it also provides the nuance of emotive detail that can only be inferred from documents. Thus, the two kinds of sources, when available, need to be used as complimentary to one another, providing symbiotically a clearer picture than either alone would.”
As Barbara Marshall has shown, in those years of late Weimar, Münster’s Catholic conservatism prevented it from becoming the hotbed of anti-Semitism and Nazi leaning nationalism that the town of Göttingen was.
While the onset of the war does not seem to have been greeted enthusiastically, the early German victories quickly changed this view.
There were deficits in instruction created by the many extracientific demands on the students.
Universities are depleted
“save qui peut”
Hitler, Mein Kampf: “A man of little scientific education but physically healthy, with a good, firm character, imbued with the joy of determination and willpower is more valuable for the national community than a clever weakling.”
[Thomsen] defends the fact that it takes perhaps decades for theoretical mathematics to find a practical utility by citing the length of time it took racial theory to develop, and “what is right for racial theory, for the benefit of our state, is also right for theoretical natural science and mathematics”.
“We need today a student youth that has ever so little fear of a murderous weapon in wartime as of the monster of a five-fold integral with singularities in the integrand”. [Sadly not taken seriously by the Nazi bureaucracy]
Secondary and elementary mathematics were corrupted: militarized, racialized and politicized.
To teach National Socialistially.
What does a bad achievement by an upper level student in Latin and Mathematics trouble him if he is loyal to his SA leader and comrades.
CHAPTER SIX: MATHEMATICAL INSTITUTIONS. (How mathematical journals were affected by the political pressures of Nazi Germany and how they responded)
The three directors of the three most important mathematical journals were intent on upholding mathematics and protecting it from chicanery and political inference
Distinction between a fact and the “style” that led to it
Law of August 17, 1938: Jews were only allowed to have distinctly Jewish first names, and those who did not had to append the name Israel if male and Sara if female.
The Lachman paper incident shows how difficult it was in the Nazi atmosphere for decent people to uphold various professional attitudes they thought appropriate, not just because of the pressure of the state and its ideology, but also because of the mephitic atmosphere brought ordinary decent actions into conflict with one another.
“It itself, I have nothing against German citizenship, however, at this moment, since Germany has occupied my homeland, I would not gladly give up my previous neutrality and throw myself in a certain measure publicly on the German side”
Bieberbach maintained that only through the recognition of the differences between different peoples could proper cooperation take place, and that mathematical style was racially determined (bluterfüllt)
Many people at first saw Hitler’s ascension to power as a means of reestablishing German honour and respect at a time when they felt Germany was still unfairly disdained and still unfairly placed under a burden of guilt, both financial and moral, for WW1.
Their rhetoric is not mere lip service to the reigning ideology. Many people believed the things that wre said. The early Nazi government had reawakened in many a German national pride that was felt to have been demeaned since the end of the war. Genuine feeling
Teleology must step into the place of pure logic.
There was much appeal to educating intuitive understanding of three dimensional space and the motion of objects in it.
November 15, 1938: The ministry of education issued the so called academy decree (Akademieerlass), which among other things decreed the Führerprinzip for scientific academics.
Führerprinzip: Cada Führer es instituido por un Führer superior y tiene poder y responsabilidad absoluta sobre sus subordinados. Pero no puede haber una cadena infinita de Führers: Adolfo Hitler es el Führer en última instancia superior.
Hitler’s “new Germany” at its outset held forth to many the promise of a new and justifiable respect for Germany and Germans.
Let it be mentioned that with the scientific emigrants into enemy foreign countries we have delivered to the opposition a not-insignificant potential gain.
Americans were much better at coordinating the sciences with the war effort.
“[…] This was possible only if the ideological fundamentals of the regime were not transgressed. It would have been in vain and only have brought suspicion on one to defend Jews, but it was possible to save a distinguished “Aryan” mathematician who was “Jewish-related” from being sent to labour camp because of the importance of his scientific activity. However, Süss was only enabled to behave in this way because he had established a reputation of being, in Nazi jargon, politisch zuverlässig”.
Though many Germans knew that Germany was irrevocably collapsing, the bureaucracy behaved bureaucratically, simply carrying on in the face of increased difficulty – the “alas, your letter took five weeks to reach me” sort of thing.
Defeatism was a capital offence.
The total collapse and ensuing occupation were not part of the German vision.
~One would have thought that in a militarising and then warring Germany, appropriate applied mathematics, at least, might have nurtured. But this did not happen until late in the war, with the intervention of Süss.
An academic-military-industrial-political complex was forged during WW2 in GB and the USA. No such complex was built in Germany. This failure provably stemmed from the deep suspicion of academe present in National Socialism, and its emphasis on emotion and intuition as opposed to intellect and abstraction. Añadir a causas de la derrota alemana en WW2.
One of the two leading aeronautical experts, Theodor von Karman, whose mother was a Hungarian Jew, was forced into emigration and became the chief scientific advisor to the US Army Air Force.
Mathematics in the Concentration Camps.
Mathematical Slave Labour
By the end of July 1944, not only had there been military computations completed, but also a set of mathematical tables, and translations of Russian mathematical papers.
The numerical solutions of parial differential equations connected to ballistics investigations under an industrial contract, as well as the computation of the emphemerides of Mars and Jupiter.
March 25, Heinrich Himmler wrote to a subordinate: “Among the Jews whom we have now received from Hungary as well as also among out concentration camp prisoners without doubt are a whole lot of physicists, chemists and other scientists”.
A scientific research establishment in which the disciplinary knowledge of this people could be applied to stressful and time consuming computation of formulas.
“Fischer claims in his memories that he realized political opponents and prisoners could not be expected to have the requisite inner drive for scientific activity on behalf of the Third Reich”.
It was established that then, if certain relief were granted, e.g. permission to work on ordinary clothing, the investigations were immediately more reliable.
Mathematical slave labour.
Originally the declared purpose of the camps was to arrest people for purposes of reeducation or for prophylactic security reasons. The first concentration camp opened, Dachau, was publicly celebrated. Conditions were never particularly good, however, and soon terror took over, as did the realization that the camps were an excellent source of slave labour. As slaves, the inmates could be worked to death and in general treated as human material, as for example, for the various medical experiments carried out in the camps. Thus the original purposes of indefinite preventive “detention” and “reeducation” became quickly subsumed by the better known and more permanent ones of terror and economic / scientific rationality.
The checking of computational work was not difficult. Just give the same task to two separate groups & then compare.
Mathematical intuitionism.
Importance of geometric intuition in mathematics, and mathematics should be more than just the surety of proof.
CHAPTER SEVEN: LUDWIG BIEBERBACH AND “DEUTSCHE MATHEMATIK”
Talented mathematician & leading proponent among mathematicians of Nazi ideology
“A man’s reputation has a very considerable coefficient of inertia”
Since the end of WW1, largely through the influence of the French, the Germans had been barred from international congresses.
After the ban was lifted, Germans at first chose not to attend: The first congress was sponsored by the Union Mathematique Internationale, an organization from which Germans had been excluded / The congress was to take place in Ledrousse, Austro-hungarian befor 1914, Italian after 1918.
“Suppose we had to fight a war to rearm Germany, unite with Austria, liberate the Saar and the German part of Czechoslovakia. Such a war would have cost us half a million young men. But everybody would have admired our victorious leader. Now, Hitler has sacrificed half a million Jews and has achieved great things for Germany. I hope some day you will be recompensed but I am still grateful to Hitler.”
There could and did develop a conservative right wing opposition to Hitler, which, e.g. prevented the Habilitation of a “deserving National Socialist” because his Habilitationsschrift was inadequate.
Geist als Wiedersacher der Seele: Intellect as adversary of the Soul.
There can be no self sufficient mathematical kingdom independent of human activity and intuition, therefore also none independent of the styles in which human racial membership expresses itself.
Generally I am of the opinion that the whole dispute over the foundations of mathematics is a dispute of contrary psychological types, therefore in the first place a dispute between races. The rise of intuitionism seems to me a corroboration of this interpretation.
An activity of an idiosyncratically German nature needs no further justification.
A new Journal: Deutsche Mathematik.
Thus mathematics is a mirror of the races, and proves the presence of racial qualities in the intellectual domain with mathematical, thus incontrovertible certainty
An international version: There are different incompatible racial styles, all of which produce mathematical truth.
A racial struggle did not imply a valuation of races. Each style was valid for its own people. “Thus German science relinquishes Jacobi and leaves it to Judaism to see in him one of its greatest sons”.
Philip Lenard: Trash mathematics!
[To rewrite history through taxonomy]
Copernicus was a German, not a Pole!
As soon as, however, the question arises whether the theorem concerned might be important, interesting or highly relevant, then one will hear the most various judgments, Opinion about it largely depends on the [Janeschian ≈ racial] type of the judge.
“I like mathematics as something organic”: una de las tipologías
For both the Heidelberg and Könisberg groups, the concept of force was particularly Germanic, and its elimination materialistic, whether French or Jewish. For both, religious grounding was Germanic. For both, Germanic attitudes were unitary and non-Germanic attitudes divisive, e.g. the cartesian mind body/dualism
“Only a people that, the danger known, allows the number of progeny to increase with the racial value of the parents can turn aside this danger of the erradication of fitness”
Students who wish to overthrow the status quo ante are a commonplace in universities at almost every time and place. In the Nazi context, however, the political establishment was on their side, and had provided a revolutionary ideology that had transformed the state/
The brilliant young mathematician and dedicated Nazi Oswald Teichmüller.
Nürnberg law: forbade sexual relations between Jews and non-Jews.
Even when dealing with intrinsically non-ideological material, such as book reviews, Weltanschauung could find its way in.
World Ice theory
Attack on acausality in physics and on those who want to introduce such acausal notions in biology (oh the heresy)
Science is not objective, and natural scientists should better understand this.
After WW2, Bieberbach apparently mantained to an Allied interrogator (who actually happened to know some mathematics) the validity of his views on ethnic personality types and mathematics – he was a true believer to this extent. […] On 1981, the ninety-five year old Bieberbach mantained that his distinction between a Jewish style and an Aryan style was valid but implied no comparative valuation of the styles.
CHAPTER 8: GERMANS AND JEWS.
Not only was the Nazi ideolog centered on nonrational processes as ideal, not only was it involved in a biologic reductionism of all learning to a fundament of racial genetics, but the general lay opinion of mathematics at that time was none too favorable.
The initial Nazi view of academia was a mixture of contempt and suspicion.
The speed of the nazification of the universities improved that view.
Most mathematicians simply wanted to be left alone with their mathematics.
The only reason professional resistance could be at all useful was that the regime did not care what happened in the academic world, provided that Jews and active troublemakers were expelled from their positions.
Someone like Erich Hecke could mantain his distinguished position despite his apparent refusal to say Heil Hitler.
“The sole Roman contribution to mathematics was teh negative one of murdering Archimedes”.
Process of denazification.
The argument made to me by Christoph Mass that Blaschke’s real concern was with what the Nazi regime could do for him rather than what he could do for them neglects the fact that a certain quid pro quo was involved. Obtaining what Blaschke wanted in prestige and position from the Nazis involved aiding them.
The nickname “Mussolinetto” [Musolinito]
Nazi political correctness
“Tietz was somewhat afraid of Zachenhaus, who always wore the insignia of a Nazi organization, but Hecke calmed him by saying that Zachenhaus was their trusted agent who behaved in a politically correct manner so as to protect them”
Teichmüller: The family was poor, but the son, with perhaps the sense of moving up in social class as a student, always listed his father’s occupation as factory owner rather than employee.
Party activity seems to have provided friends for Teichmüller.
The letter, the letter.
Jews unsuitable to teach German youth.
The Nazi education ministry dismissed Jews under the April 7, 1933 law because they were Jews, not because of any intellectual rationale about Jews being unfit teachers for Germans.
“You are a reactionary burgeois and don’t comprehend the Führer’s ideas”
Britain guaranteed the Polish borders on August 25, 1939, something it had refused to do fourteen years earlier at Locarno: Trabajo de historia.
Nothing necessarily connects a person’s brilliance in one area with a particular insight into politics.
Heidegger.
Ernst Witt: As a student in Göttingen, he had the naiveté to appear at Emmy Noether’s private seminar in her home in his SA Uniform // [someone] complained that he, despite being a party member, was “politically colorless” and had yet to understand that mathematics and natural science were also racially connected; he mistakenly thought them international. // He didn’t pay overly much attention to other’s opinions and so, for example, wore braids in his hair for a while [en la Alemania nazi]
Richard Courant, jewish mathematician: At the time of the planned Nazi boycott of Jewish stores on April 1, 1933, Courant thought the whole trouble was Einstain’s fault, and a recent speech of Hitler had made “a quite positive impression on him”
Landau: His father Leopold was both a nationalist patriot and someone politically engaged in Jewish issues – not a contradiction in the first decade of the century.
There is a story that reveals both Landau’s cynicism and his understimation of the Nazis: Once, on a visit in 1932, Fritzt Rathonau told Landau that he didn’t know whether the Nazis were going to win, but if they did, he had heard they planned to construct a concentration camp for Jews on the Lüneburg heath. Landau’s response is supposed to have been “In that case I should immediately reserve for myself a room with a balcony with southern exposure”.
Teichmüller recognized Landau’s genius and would have gladly studied advanced material with him (and Landau would have gladly taught him).
The yound Hausdorf was pirmarily interested in literature and philosophy and moved in those circles.
Ernst Pechl is a good example of the young mathematician who, in order to begin a career, was orced into at least a nominal political stance in which he apparently did not believe.
Hans Peterson had the courage to marry the woman he loved, despite her “tainted” status, to hide it succesfully, and to convincingly go through the motions of being an ardent nazi even when he was not.
It is hard not to respect Kähler as principled while abhorring his principles.
Süss’s efforts were only succesfull because the meaningful political ideological powers found mathematics unimportant.
It was easy for many to see the Nazi movement, for all its “plebeian excess”, aimed primarily at reestablishing Germany’s place among the nations.
The notion that training as a mathematician permits better analytical and logical thinking is a common belief.
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