La cultura también es de Ciencias
Me imagino que alguna vez, cuando habéis estado reunidos con un grupo de personas, una de ellas ha descacado por su elocuencia y por conocimiento de una determinada materia, por ejemplo de literatura, o de arte, incluso puede que os haya deslumbrado con su conocimiento en leyes, filosofía, poesía, citando incluso alguna que otra frase de algún que otro autor. Automáticamente la gente lo toma como una persona muy culta (Sin duda lo es), pero si en una misma circunstancia alguien empieza a hablar sobre partículas subatómicas, es probable que lo vean como un bicho raro.
¿Ciencias vs letras?
Si pensáis que este artículo va sobre quién es mejor o peor (los de ciencias o los de letras), estáis totalmente equivocados, ese tipo de personas merecen todo mi respeto (siempre que no sean unos fanfarrones que van soltando palabrería que dejan ensimismados a alguno que otro, pero que en ocasiones ni ellos mismos saben lo que están diciendo).
En este artículo quiero, entre otras cosas, revindicar un poco el corto papel que tiene la ciencia en la vida cultural, sobre todo en nuestro bendito país. Si señor, y es que me parece increíble que cuando se habla de desviación típica la gente pueda pensar en alguna afección de nuestra columna vertebral, y cuando alguien no sabe en que año ocurrió la revolución francesa alguno que otro se eche las manos a la cabeza ¡o la la! Pues sepan que tan grave es una cosa como la otra.
Y os puedo poner un ejemplo tonto de cual importante es la ciencia para esta sociedad, un ejemplo tan inocente como un juego de mesa. ¿Alguna vez ha jugado al trivial? Si tiene cierta edad (es decir, si es usted una persona jovencita pero sin exagerar mucho) seguro que ha echado alguna que otra partida con amigos. Pues bien, para este divertido juego, la ciencia ocuparía 1/6 de los objetivos, sin embargo la carga de «letras» 3/6. el resto es deportes y sociedad, que muy de ciencias tampoco son. Además, urgando un poco más la herida, las preguntas «de letras», que se suponen de cultura general tienen más profundidad que las de ciencias.
Seguro que os estaréis preguntando, y qué más le dará que el trivial sea más de letras, o que cuando pienses en alguien culto tu cabeza no se vaya a un científico, si además los científicos están bien vistos. Pues mi respuesta es que no me da igual, y tengo muchos motivos para ello.
Quiero recalcar de nuevo que no tengo nada en contra de las letras, es más, considero como dije que es grave no escribir bien, o no saber determinados datos básicos de la historia o de personajes importantes. Aún más, me gusta mucho la historia de la humanidad, me encanta la literatura (aunque tengo mis gustos claro está, que un libro sea una obra maestra no quita que me guste o deje de gustar), y la filosofía (que realmente está a caballo entre las ciencias y las letras).
Pero como enamorado de la ciencia y de las mates no me queda otra que defender su posición en nuestra sociedad, una sociedad que por cierto cada vez maneja más volumen de información y de datos, más tecnológica y sin embargo con mucha ignorancia científica y matemática entre la población.
Y es que una persona que sabe mucho de física o matemáticas también es una persona culta, y aquí sumo mi otra demanda, las matemáticas son básicas para el día a día, para poder mirar cara a cara a esa información de forma crítica y decirle a los ojos ¿Qué me estás contando realmente? Para revendicar ese papel igualitario voy a comentar varios casos, con los que entenderéis el porqué de mi demanda:
La información a medias es desinformación
Estamos continuamente bombardeados por datos, en las noticias, el la web, en las revistas y periódicos, datos que utilizan muchos medios para llevarnos a su terreno. Y claro, lo consiguen, ¿por qué?. Muy fácil, por el gran desconocimiento de la población de matemáticas básicas, en concreto de estadística. Antes hablaba que mucha gente no sabe, por ejemplo, lo que es la desviación típica, como mucho le suena a algo de matemáticas y poco más. ¿Por qué esto es tan grave? Fijaros el siguiente caso:
Imaginaros dos países ficticios Bienlandia, y Mallandia. Ambos países tienen poblaciones similares, de hecho ambos tienen 40 habitantes (simplificamos para que entendáis). Ambos países tienen gobiernos diferentes, de ideas diferentes, y ambos se están continuamente atacando el uno al otro.
Bueno, un día en los noticieros de Bienlandia hacen propaganda sobre lo bien que hacen las cosas el gobierno de su país, las hacen tan bien que la renta per cápita de Bienlandia es de 525, frente a los 300 de Mallandia. Eso sí, les piden un pequeño sacrificio a las clases medias para hacer mejores carreteras para ellos, ese sacrificio es de 25 menos por habitante, pero aún así, según las noticias tendrían una rpc de 500, 200 más que el otro gobierno, y todo gracias a su buen hacer.
Os voy a poner los siguientes datos, muy exagerados claro, para que os deis cuenta de la importancia de la desviación típica:
Rentas de los 40 habitantes de Bienlandia
| 100 | 120 | 110 | 105 | 90 |
| 175 | 200 | 160 | 130 | 110 |
| 105 | 100 | 100 | 100 | 100 |
| 100 | 100 | 75 | 75 | 90 |
| 120 | 120 | 120 | 120 | 100 |
| 100 | 100 | 100 | 100 | 120 |
| 105 | 105 | 130 | 75 | 75 |
| 75 | 80 | 5670 | 5670 | 5670 |
Rentas de los 40 habitantes de Mallandia
| 200 | 200 | 200 | 200 | 200 |
| 200 | 300 | 300 | 300 | 300 |
| 300 | 300 | 300 | 300 | 300 |
| 300 | 300 | 300 | 300 | 300 |
| 300 | 300 | 300 | 300 | 300 |
| 300 | 300 | 300 | 300 | 300 |
| 300 | 300 | 300 | 300 | 500 |
| 500 | 500 | 500 | 500 | 500 |
Fijaros el nivel de manipulación de los medios de comunicación de Bienlandia, y es que, aunque la media es mucho mejor en este país, los habitantes de Mallandia viven mejor, suponiendo que el nivel de vida es el mismo claro. Y ¿a qué se debe eso? a la desigualdad de salarios claro, y ¿cómo medirlo? pues con la desviación típica, por ejemplo.
La desviación típica en Bienlandia es de 1465.24€, y en Mallandia de 100€, y me dice que los sueldos de los habitantes del segundo país estan más centrados que los del primero. Realmente en la primera población estan centrados salvo tres que son desórbitados, que son los que desvirtuan esta medida.
Curanderos, homeópatas y otros espeLcímenes similares
Cuenta la leyenda, que estando enfermo, un amigo del primo de mi cuñado se tomó un remedio homeopático y se curó. Tómatelo tu también porque a mi también me funcionó, es la leche ese mejunje. Seguro que esta situación os resulta familiar, e incluso en alguna ocasión hayáis utilizado alguno de estos medicamentos para liberaros de alguna afección. Si le ha funcionado a esas personas, ¿Por qué no me va a funcionar a mí?
El problema es parecido al anterior, hay de nuevo un desconocimiento estadístico al respecto. ¿Cómo puedes asegurar que con una muestra de las personas que te lo han contado, más el número de votos positivos que hayas encontrado por internet de ese producto (que en total no creo que lleguen a un número de 20) puedes asegurar tremenda afirmación? Resulta que para que un medicamento (de los de verdad) salga a la luz, la parafernalia experimental y el estudio estadístico que conlleva es tremendo y costoso, y sin embargo 20 opiniones son suficientes (o 50, o 100) para decir que un determinado producto es puntero para sustituir al mismo medicamento. El tamaño de la muestra importa (y un estudio serio más allá del «a mi me funcionó también»).
Y es que con tan pocos datos es imposible saber si existe correlación entre la cura de una enfermedad y el método utilizado en cuestión. ¿No sabíais acaso que nos podemos curar solitos? ¿Habéis oido hablar por casualidad del efecto placebo?
«Pues yo soy dueño de mis decisiones» dicen algunos, frase que me cabrea y mucho por dos sencillas razones:
- Si el pseudomedicamento que tomas sustituye a una terapia médica. Eso es algo tremendamente peligroso. Es cierto que la medicina no es perfecta, ya que en ese caso seríamos inmortales jeje, pero avanza a pasos agigantados, a base de aciertos, y errores claro. Pero dejar de lado ese tratamiento del médico si que es un grave error, aunque con él puede que el final no sea el que se desee.
- Estos homeómatas se forran a costa de mucha gente, y lo hacen agarrándose en su desesperación, en el hartazgo de mil intentos fallidos de la medicina tradicional.
Cuando haya un estudio serio de algún remedio no tradicional que diga que éste es maravilloso, por supuesto que lo avalaría, pero me temo que muchos estudios demuestran justo lo contrario.
Fechas de cumpleaños
Es muy típico asombrarnos de las coincidencias, cuando por ejemplo en una fiesta, hablando con otra persona que conoces de poco empezáis hablar de gente y lugares y resulta que conocéis a una persona en común, «¡Vaya, si el hermano de mi amigo resulta que es el primo de tu cuñado!» Es fácil asombrarse de esas casualidades si no estás acostumbrado a las probabilidades. En este supuesto, que he sacado el libro El hombre anumérico que recomiendo encarecidamente a todos, vamos a hablar de fechas de cumpleaños.
Imaginaros una gran reunión de personas, una celebración importante, por ejemplo una boda. Como un año tiene 365 días, para que dos invitados de la boda coincidan seguro en la fecha de su cumpleaños, la boda debe de ser mínimo de 366 personas. Supongo que todos estaréis de acuerdo con esto. Decimos que la probabilidad en este caso es del 100% o 1.
Ahora supongamos que queremos averiguar el número de invitados que tiene que haber para que la probabilidad de que dos coincidan en la fecha de nacimiento sea justo la mitad, muchos habréis pensado en invitar a la mitad de personas, a saber 183, pero eso es incorrecto, solo hacen falta ¡23 personas!
Supongo que os resulta sorprendente esta cifra, pero vamos a explicarla un poco para arrojar algo de luz al asunto. Imaginaros que cogemos 5 invitados con 5 fechas de cumpleaños diferentes o no, para cada una de estas fechas tengo 365 posibilidades, por tanto para las cinco juntas, por el principio de multiplicación tengo 365x365x365x365x365 posibilidades.
Si no habéis entendido el principio de multiplicación, es muy sencillo, os lo explico en tres líneas: Supongamos que elijo solo una persona; como escribí arriba tengo 365 posibles fechas. Ahora supongamos que elijo dos personas, para la primera persona tengo 365 fechas, y una vez fijada esta fecha, para la segunda vuelvo a tener 365 posibilidades, es decir, que por cada una de las fechas de la primera persona, tengo 365 posibles fechas de la segunda. Por tanto tengo para las dos 365×365, y así sucesivamente.
Ahora elijo a 5 invitados, pero que tengan todos ellos fechas diferentes de cumpleaños ¿Cuántas posibilidades tendré? Pues bien, para el primero 365, para el segundo 364, ya que he fijado una de las fechas con la primera elección, para el tercero, cuarto y quinto 363, 362 y 361 posibilidades respectivamente. Así pues, por el principio de multiplicación, tengo un total de 365x364x363x362x361 casos en los que 5 cumpleañeros lo hacen en distintas fechas.
Pero yo estoy pidiendo justo lo contrario, es decir, que coincidan al menos 2. Como sé que sois muy listos, los casos que me faltan para llegar al total son los que tengo que contar. A eso en conjuntos se le llama el complementario. Pues bien, si la probabilidad es (Ley de Laplace) casos favorables/casos posibles, en nuestro caso será 365x364x363x362x361/3655 = 0,97286, es decir, que hay un 97,286% de posibilidades para que las fechas sean diferentes. Por tanto, para que al menos dos seal iguales será un 2,714%, ya que es lo que me falta para llegar al 100%.
Haced la cuenta para 23 personas, pequeños incrédulos, y veréis como sale aproximadamente la mitad de posibilidades 😉
¡La ciencia es cultura!
Las matemáticas, y la ciencia en sí, son fundamentales para el día a día. Nos van a hacer ver los ataques de información masiva que recibimos desde los medios de manera más crítica, y cuanto más herramientas tengamos, más difícil es que nos la introduzcan en curvatura.
Pero en este artículo no solo reivindico la necesidad de una base mínima matemática, sino de ampliar el término cultureta. Una persona que sabe muchísimo de arte es una persona muy culta, claro está, pero cuando le preguntas de matemáticas te responderá con una sonrisa diciendo que se le daban mal, pero que afortunadamente no le hicieron falta (Oye, no estoy diciendo que no haya personas de arte que sepan muchas matemáticas!!).
Pues bien, una persona que sepa mucho de matemáticas, que en su vida haya mamado muchos libros de ciencia y nada más, también es un cultureta, aunque no tenga ni pajolera de arte, así que dejemonos de rollos, que la ciencia también es cultura.
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