Sofía Alexandrovna Neimark Janovskaja
Sofía Neimark nació en el seno de una familia judía polaca, en un pueblecito que ahora es territorio bielorruso, donde la mayoría de la población era de esa raza. Cuando tenía 9 años su familia se trasladó a Odessa, donde estudió con Timchenko, relevante historiador matemático. A partir de ese momento se entusiasma con las Matemáticas y con su historia. También ingresa en la Cruz Roja, atendiendo a los presos políticos. Podríamos pensar que es en esa época cuando empiezan sus inquietudes sociales y políticas.
En 1915 ingresa en el instituto femenino de Odessa, dependiente de la universidad donde, de la mano de Shatunovsky, se aficiona por la Lógica Matemática. Pero aparca sus estudios cuando estalla la Revolución Rusa de 1917 y se vuelca en el partido comunista: primero en la clandestinidad y luego como editora del periódico Kommunist en Odessa.
En 1923 retomó sus estudios ocupándose de seminarios en la Universidad Estatal de Moscú, donde se doctora en 1935. En ese mismo año conoce al matemático y filósofo Wittgenstein.
Durante la segunda guerra mundial tuvo que huir de Moscú, regresando a su universidad en 1943 como Directora del Departamento de Lógica, impulsando fuertemente el desarrollo de esa disciplina en la Unión Soviética.
La historia de las matemáticas fue otro tema que trató Janovskaja e hizo diversas publicaciones. (Geometría de Descartes, Matemáticas Egipcias, Paradoja de Zenón de Elea…)
Recibió la orden de Lenin en 1951
La paradoja de Zenón
Zenón de Alejandría presentó una serie de paradojas para desmontar las teorías de Aristóteles. La más conocida es la de Aquiles y la tortuga.
Aquiles, el de los pies ligeros, es el corredor más veloz de toda Grecia. Y la tortuga… bueno, es una tortuga. Lenta. Ceremoniosa. Pesada.
Arreglan correr una carrera. Aquiles corre diez veces más rápido que la tortuga, por lo que decide darle diez metros de ventaja.
Empiezan. Aquiles corre esos diez metros, pero en ese tiempo la tortuga corre un metro. Aquiles corre ese metro y la tortuga, diez veces más lenta, corre un decímetro. Entonces Aquiles corre ese decímetro, pero la tortuga corre un centímetro. Cuando Aquiles corre ese centímetro, la tortuga corre la décima parte de un centímetro. Y así infinitamente.
Aquiles, el de los pies ligeros, jamás podría alcanzar a la tortuga, aunque la carrera durara por siempre.
Para resolver la paradoja hacen falta ciertos conocimientos de cinemática y tener claro que, cuando jugamos con el infinito, no vale el mismo razonamiento que cuando estamos en el mundo finito. Vamos a resolver una paradoja más simple. Supongamos que Aquiles recorre la mitad del camino, luego la mitad de lo que le queda, luego la otra mitad y así sucesivamente. Nunca llegará a su destino porque siempre quedará una mitad de recorrer.
Pero echemos mano de lo que sabemos de las progresiones: si el camino mide 1, al principio recorre ½, luego la mitad de ½, que es (½)2
Cuando lleve n mitades, recorrerá (½)n
¿Cuánto llevará recorrido? La suma de todas las mitades
½ + (½)2 + —— + (½)n
Tenemos una progresión geométrica de razón ½. La suma de los infinitos términos de una progresión geométrica es
Si cambias r por ½ y el primer término también, verás que Aquiles ha recorrido el camino.
Juegos de lógica
Como has leído en su biografía, Sofía fue Directora del Departamento de Lógica e impulsó el desarrollo de esta disciplina en la Unión Soviética.
Te proponemos los siguientes juegos en homenaje a ella.
- Descubrir el número secreto.
- Una versión con colores del juego anterior llamada Mastermind.
- EL juego de los tres cofres.
A nosotros nos parece una mujer fascinante porque con solo 9 años ya empezo a interesarse por la matematicas.
Ademas no solo estudiaba matematicas sino que tambien estudiaba otras cosas como la filosofía etc.Esta mujer llegó a ser profesora de universidad que requiere un gran esfuerzo y ademas si eres mujer nacida en esa epoca.Gracias a todo esto hizo varias investigaciones matematicas como geometria de descarte , matematicas egipcias ,paradoja de zenon…
QUE GRAN MUJER
La actuacion dew esta mujer en su epoca me parece muy importante ya que le pillo la querra ella siguio estudiando asta que pudo sin que se lo impediera nadie.
la paradoja de la tortuga y aquiles me parece muy interesantecuando la leí,aunque no la entendi y sigo sin entenderla.saludos para “to” 3ºa
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