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#george polya
garadinervi · 11 months
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George Polya [Pólya György], (1945), How To Solve It. A New Aspect of Mathematical Method, Doubleday Anchor Books, Garden City, NY, 1957, Second Edition
(on the way of André Azevedo)
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elegantzombielite · 2 years
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"Pedantry and mastery are opposite attitudes toward rules. To apply a rule to the letter, rigidly, unquestioningly, in cases where it fits and in cases where it does not fit, is pedantry ... To apply a rule with natural ease, with judgment, noticing the cases where it fits, and without ever letting the words of the rule obscure the purpose of the action or the opportunities of the situation, is mastery."
George Polya, mathematician (13 December 1887-1985)
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regexkind · 9 months
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My JOI videos were made without reference to any prior art besides "How to Solve It" by George Polya. Hence I'm always saying shit like "look at the unknown!" and "is this masturbation session similar to any you've done before?" and "can we generalize the lessons from this orgasm?"
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mathspathere · 1 year
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"Las matemáticas son un lugar donde puedes hacer cosas que no puedes hacer en el mundo real" George Polya.
¿Qué os parece esto? Yo creo que los matemáticos somos poderosos.
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influencia123 · 1 year
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Primero que nada, Heurísticos. El caso de Benedictino para una aproximación a los procesos heurísticos.
La marca de agua embotelladas Benedictino es una de las más posicionadas y populares entre el público general chileno, la compañía Aguas del Sur, matriz de Benedictino, es fundada en el año 2005 con tres socios iniciales: Rodrigo Gonzalez, Rodriguez y Marcelo Guital (Echeverría, 2007), lo que comenzó como un emprendimiento arriesgado no fue fácil en un inicio. Pero con cierta sagacidad y picardía, la naciente marca logró posicionarse entre el colectivo, tanto fue así su éxito que incluso fue vendida a Coca Cola por US$5 millones.
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En una entrevista a Marcelo Guitar del programa Mentiras Verdaderas de La Red, Ignacio Franzani le pregunta sobre cuáles fueron las estrategias de marketing no convencionales, con lo cual Guitar se explaya:  “Ah bueno poner botellas en los basureros de la gente con mayor poder adquisitivo, llenar el basurero entonces cuando la persona iba llegando a la Dehesa entonces veía que había una botella que alguien había consumido…” (Mentiras Verdaderas La Red, 2016), con lo cual luego prosigue: 
“Colocamos en los baños de los aeropuertos en el urinario, del hombre una botella arriba, el baño lo hacen dos veces aseo, entonces lo pongo a las ocho, lo sacan a las dos, a las dos y media (hace como que posiciona una botella) y luego lo sacan a las diez y ahí está, mientras tú estás orinando hay una botella”. (Mentiras Verdaderas La Red, 2016) 
Lejos de querer hacer este escrito como uno de los varios que existen sobre Guitar y su ejemplo de emprendimiento y superación, he querido citar este caso ya que considero es un muy buen punto de partida para ejemplificar el tema del cual se ha querido escribir hoy: los procesos heurísticos. 
Proveniente del griego, heurística tiene como definición hallar o inventar y no es casualidad que cuyo pretérito perfecto sea eureka. En otros tiempos fue llamada herética  o “ars inveniendi” la cual fue catalogada como una ciencia bastante mal definida que se relacionaba tanto a la lógica, la filosofía o la psicología (Polya, 1989) . Se solía exponer en líneas muy generales pero rara vez de manera detallada, actualmente está olvidada. Su objeto de estudio fueron las reglas, métodos del descubrimiento y la invención (Polya, 1989), de este estudio se han encontrado trabajos entre los comentaristas de Euclides y entre los ensayos más populares en relación a la construcción  de sistemas heurísticos de Descartes y Leibniz, ambos filósofos y matemáticos célebres. La heurística moderna trata de comprender el método que conduce a la solución de problemas, particularmente las operaciones mentales útiles en el proceso. 
En general se considera a la heurística un rasgo característico de lo humano desde cuyo punto de vista puede describirse como el arte y la ciencia del descubrimiento y de la invención o de resolver problemas mediante la creatividad y el pensamiento lateral o pensamiento divergente (Heurística, 2022). 
La popularización del concepto se debe a George Pólya, con su libro Cómo resolverlo (How to solve it). Habiendo estudiado tantas demostraciones matemáticas desde su juventud, quería saber cómo los matemáticos llegan a ellas. El libro contiene la clase de recetas heurísticas que trataba de enseñar a sus alumnos de matemáticas (Heurística, 2022). 
Si bien encontramos la heurística en materias como la matemática, la ingeniería e incluso como metodología científica, es en el campo de la psicología y en su  búsqueda de la explicación a ciertos procesos mentales en que la heurística toma un protagonismo mayor. Para Daniel Kahneman la definición de técnica heurística “se trata de un procedimiento sencillo que nos ayuda a encontrar respuestas adecuadas, aunque a menudo imperfectas, a preguntas difíciles” (Kahneman, p. 133, 2017) en donde a rasgos generales existe una pregunta original que nos pide una evaluación que intentamos hacer y que al no encontrar una respuesta satisfactoria a esta, encontramos una pregunta relacionada más fácil y la respondemos. La pregunta heurística es la pregunta más simple que respondemos en lugar de la más difícil, esto es lo que Kahneman cataloga como sustitución. Cabe mencionar que las heurísticas que se le adjudican a los procesos de cognición, al menos en gran parte del estudio por parte de la psicología social, no son elegidas, sino más bien son una consecuencia de un control impreciso que tenemos sobre la “puntería” de nuestras respuesta hacia ciertas preguntas (Kahneman, 2017). 
Tabla 1
Ejemplos de alternativas heurísticas al razonamiento cuidadoso que algunas veces dan resultado y otras veces conduce a serios errores. 
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Nota. Kahneman  (2017, p. 134).
Para Daniel Kahneman existen dos formas en que la mente opera y llega a respuestas, el sistema 1 o también conocido como pensamiento rápido caracterizado por una forma intuitiva y automática de pensar va construyendo interpretaciones coherentes de lo que va sucediendo alrededor, las cuales muchas veces caen en inconsistencias producto de estos procesos automáticos que explican la heurísticas de los juicios (como los ejemplos citados en el cuadro anterior). El Sistema 2 o pensamiento lento centra su atención en las actividades mentales esforzadas que lo demandan, como por ejemplo los cálculos complejos.  Las operaciones del Sistema 2 están a menudo asociadas a la experiencia subjetiva de actuar, elegir y concentrarse. 
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La mente (o más bien el Sistema 1) al no tener una respuesta determinada o automática, como lo es la resolución de una multiplicación con cierto grado de complejidad, implica que el proceso se convierta en un trabajo mental: deliberado, esforzado y ordenado, un tipo de pensamiento lento. 
¿Eres un experto en aguas embotelladas? Muy probablemente no, pero algo que hacemos a menudo y muy bien es llegar a conclusiones por medio de poca información o relaciones carentes de lógica. Es probable que el efecto positivo que tuvo la estrategia de marketing (que para algunos es poca convencional, pero personalmente encuentro que no lo es y está más presente de lo que se puede llegar a pensar) del agua embotellada haya sido el resultado de un proceso heurístico: 
Quiero comprar una botella, ¿Cuál es la de mejor calidad? (no soy experto en aguas embotelladas, por ende respondo esto con una pregunta más fácil) ¿Qué hace a un producto de calidad? (usualmente los productos de mayor calidad suelen tener un precio elevado, las personas con mayor poder adquisitivo suelen adquirirlas) Recuerdo haber visto botellas vacías en basureros de La Dehesa/baños del aeropuerto. Las personas que viven o frecuentan estos lugares suelen tener cierto poder adquisitivo, y el hecho de tener poder adquisitivo lleva a las personas a escoger teniendo en consideración más opciones  - Esta botella de agua debe ser mejor que las demás. 
[Este puede ser un ejemplo de la trayectoria heurística en relación a la campaña de agua embotellada anteriormente citada, aunque apelando a la subjetividad del individuo se debe dejar en claro que es solo un ejemplo de los variados estímulos o situaciones que pueden llevar a alguien a la toma de una decisión en relación a la compra de un producto]. 
Si bien estos proceso heurísticos tienden a acertar en cuanto a sus predicciones y la toma de decisiones frente a situaciones en las que no sabemos del todo cómo actuar (no somos expertos en aguas embotelladas) o en contextos que implican una sobrecarga de información, hay ocasiones en las que estas reglas heurísticas caen en fallos, y es que estos proceso heurísticos no solo se aplican en la compra de productos y la evaluación hacia ellos, sino que también se aplican y están muy presentes en las formas de interacción social, lo que pensamos, cómo lo hacemos y cómo actuamos en lo que significa vivir en sociedad. 
Uno de los heurísticos más generalizados es el heurístico de representatividad, el cual consiste en “una estrategia para hacer juicios basada en el parecido que tienen los estímulos o eventos que se evalúan, con otros estímulos o categorías” (Baron & Byrne, p. 90, 2005). Mientras más similar sea un individuo a los miembros típicos de un grupo, es más probable que pertenezca a dicho grupo, lo cual puede ser la razón por la cual al ver al estereotipo de flyte muy marcado en su actuar (forma de hablar, caminar y vestir) crucemos la calle para evitar ser asaltados o “cogoteados”. Es probable que con el hecho de cruzar evitemos un robo, y en el caso de que hayamos errado en nuestra predicción, es mucho más valioso lo que se evita que la culpa por haber juzgado a un libro por su portada, cosa que en general hacemos y suele funcionar. 
Otro de los heurísticos más generalizados es el heurístico de disponibilidad que consiste en “una estrategia para hacer juicios basada en la facilidad con que determinados tipos de información son traídos a la mente” (Baron & Byrne, p. 90, 2005) lo que puede explicar el porqué cuando se nos pregunta: 
¿Qué es más común en el idioma inglés: las palabras que comienzan con la letra k (por ejemplo king) o las que tienen k  en su tercera letra (por ejemplo awkward)? 
escogimos la opción primera, cuando en el idioma inglés existe el doble de palabras con la letra k ocupando la tercera posición que ocupando la primera. El heurístico de disponibilidad sugiere que mientras más fácil sea traer información a la mente, mayor será su impacto en los juicios o decisiones subconscientes (Baron & Byrne, 2005). El hecho de que podamos traer fácilmente una información a la mente, sugiere que debe ser importante  y deberá influir en nuestros juicios y decisiones, esto puede incurrir en errores. Uno de estos errores y también uno de los más generalizados, es el que la gente tiende a expresar mayor miedo a  morir o ser herido en un accidente aéreo que a un accidente de tránsito, incluso cuando los accidentes de tránsito son mucho más frecuentes. Esto puede deberse a que los accidentes de avión son mucho más dramáticos y reciben más atención de los medios de comunicación que los que reciben los accidentes de tránsito, dando como resultado que el accidente de avión sea más recordado y por lo tanto tengan un impacto mayor en el juicio y pensamiento de los individuos (Baron & Byrne, 2005). 
En el caso de la estrategia marketera del agua embotellada anteriormente citada se pueden apreciar ambos procesos heurísticos, primero el heurístico de representatividad y el adjudicar a ciertas personas con determinado poder adquisitivo un mayor gusto o apreciación por el agua embotellada (quizás porque al tener mayor poder adquisitivo poseen mayor número de posibilidades) y en el caso del heurístico de disponibilidad, el hecho de que se vuelva familiar cierta imagen en cierto contexto producto de una prolongada exposición ayuda a que esté mucho más disponible para la mente cuando por ejemplo, nos toca comprar agua.
Referencias bibliográficas  
Baron, R. y Byrne, D. (2005). Psicología Social. S. A., Madrid: PEARSON EDUCACIÓN.  
Canal Mentiras Verdaderas La Red. (21 de septiembre de 2016). Dueño de empresa de agua reveló la mejor técnica de marketing.  [Archivo de Vídeo]. Youtube. https://www.youtube.com/watch?v=8quNyEaE69o 
Heurística. (2022, 8 de agosto). Wikipedia, La enciclopedia libre. Fecha de consulta: 16:41, febrero 2, 2023 desde 
Kahneman, D. (2017). Pensar rápido, pensar despacio. Barcelona, España: Penguin Random House Grupo Editorial. 
Polya, G. (1989). Cómo plantear y resolver problemas. D. F., México: Editorial Trillas. 
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etextbooky · 1 year
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College Algebra (7th edition) – James Stewart – eBook
College Algebra (7th edition) – James Stewart – eBook
College Algebra (7th edition) By James Stewart – eBook PDF: Author(s) James Stewart Dr. James Stewart��(late) received his M.S. from Stanford University and his Ph.D. from the University of Toronto. James did research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Dr. Stewart was most recently Professor of Mathematics at McMaster…
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nosazena · 1 year
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Nosazena 30
The NFT journey continues with the latest from the Nosazenas series. “Geometry is the science of correct reasoning on incorrect figures.” ~ George Polya
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gioithieusachaz · 2 years
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SÁNG TẠO MỚI TRONG HÌNH HỌC
SÁNG TẠO MỚI TRONG HÌNH HỌC
CUỐN SÁCH ĐỤNG ĐẾN HAI VẤN ĐỀ HAY VÀ KHÓ NHẤT TRONG TƯ DUY ĐÓ LÀ SÁNG TẠO VÀ TÍNH MỚI!   Sáng tạo là lĩnh vực nghiên cứu đã được đề cập từ rất lâu trước đây chứ không phải bây giờ mới có. Nhiều nhà văn, nhà tâm lí học, nhà giáo dục học, … cũng như nhà toán học đã dày công tìm tòi nghiên cứu trong đó có thể kể đến các cái tên nổi bật như Leibnitz, Lécne, George Polya, Goncurt, Albert Einstein,…
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persephones-fruit · 5 years
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If you want to climb the Matterhorn you might first wish to go to Zermatt where those who have died are buried.
George Polya
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Request Rules
"Are your requests open?" Yes usually! If not I will specifically state in my bio that they are closed. This will only happen if I am too busy with life, losing interest or away from proper internet connection.
I can write Polyamorous ships! As someone who is Polya, I'd be happy to!
This blog will be primarily composed of x readers, headcanons, maybe a few series and quick one-shot fics.
As of right now, I currently write for MCYT, RWBY and Seven Deadly Sins (Bit rusty tho so some things may be off).
I HEAVILY PREFER TO WRITE FEMALE READERS AND GN READERS. I have gotten told many times that my male reader fics are way too feminine so. This being said, there is a high chance that my GN stories may have some female pronouns sprinkled in by accident. I write many stories at once, so that's why. Please just send me an ask and be nice about it.
For future reference, I will not write anything that the mcyt creators are uncomfortable with. Such as shipping Ranboo, Tubbo or Tommy with anyone. MAJORITY OF MY FICS WILL BE IN THE DREAMSMP AU UNLESS STATED.
Please do not ask me to write for your OC or ask me to give the reader a specific description. That makes it no longer a reader and instead an OC. Although, if you give me a certain trait to write the story around, that is allowed. (i.e: reader with heterochromia/ two different colour eyes, certain hybrids, etc.)
I often forget TWs, which if I do for something severe please remind me, but I will NOT label everything. Such as saying "TW: Swears" in a Tommyinnit fic. We all know it's gonna happen. If you need a TW for that, watch a different streamer m8.
I love my angst.
Please. When giving requests, to make my life much easier, BE SPECIFIC. Headcanons or fic? Platonic or romantic? Content creator or Character? Dream SMP Au or another Au?
If I learn that one of my fics involves something that makes a creator uncomfortable, I will remove the fic.
MY PREFERENCE ON WRITING EACH CHARACTER
Tommyinnit, Ranboo and Tubbo - 7/10 not my favourite characters but I have gotten used to writing them. Strictly Platonic CC and VERY EXTREMELY light romance in character. (i.e: No kissing or saying ily, but cuddling/hugging/holding hands is okay.)
Dream, Bad, Schlatt, Eret - 7/10 I believe I can write them decently. This being said I don't have much experience. Schlatt is platonic out of character I believe? But because I'm not sure, I'm not taking risks.
George - 1/10 I don't really like George, in character and the streamer... He's too plain for me and I don't think I would be able to write a good story for him.
Technoblade, Ghostbur - 9/10 I love these men, lmao. Techno's hella fun to write and Ghostbur is literally an angst-loaded bullet pointed at someone's head. Out of character Techno is strictly platonic and will rarely be written.
Sapnap, Karl, Sam/Warden Sam, Fundy, Niki, Puffy - 4/10 I don't know them that well to be honest..??? But I do like their characters, so I will write them if requested to. Just give me a bit of time.
Philza - 10/10 LET ME WRITE THIS MAN I LOVE HIM. Out of character is also strictly platonic.
Wilbur - 5/10 I haven't really focused on Wilbur? I joined the fandom shortly after he lost his last canon life so. This being said, I do enjoy what I've read about him.
Quackity, Ponk, Purpled - 1/10 I don't know them and don't really watch their streams. Sorry.
I will not write: Non-con, incest, underage relationship, etc. Basic knowledge here.
Things I can write but need to be specified. Will be updated.
Depression is a common plot, and I can write it, but see the suicidal tendencies are iffy here. Some things I will write are "how would ___ react after their death" but won't specify it as suicide. Another very very iffy topic is self-harm. I won't write it actually being done. I can write "___ seeing scars/marks" but that's pretty much it.
I will not romanticize mental illness.
Some things I would be glad to write
Lover Scenarios
Yandere Characters
Soulmate AUs (Please be specific on which one)
Parental AU (Where Reader is a child found by ___)
Zombie apocalypse AU
Etc!
Please don't be shy to request!
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garadinervi · 7 years
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George (György) Polya (Pólya), (1962, 1967), La scoperta matematica. Capire, imparare e insegnare a risolvere i problemi, Volume I and II, Feltrinelli, Milano, 1971
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jochmus · 3 years
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A Discussion of One Approach to a Universal Characteristic
I have felt inspired yesterday to make this attempt as a text post on Tumblr. By the subject’s weighty history and definition, it should by no means be an easy endeavor. However, there are two individuals from my readings that have inspired me, named John Locke and George Polya. Although I own both of the texts that interest me by these men, I have not read those specific texts unfortunately. Another influence was the eloquence of Euclid’s axioms, indeed I have not read the Elements either except for like the first page. I tend to become distracted very easily, and this is not something that I am very proud of. 
Now I must reveal my passion for the works of Ramon Llull. He was the guy behind the most complete version of Characteristica Universalis, but that is only because he managed to inspire Leibniz to come up with his Characteristica, which was never really worked on or implemented, and the system that Llull created is called Ars Magna, in four distinct stages. The term Ars Magna itself with regards to Llull refers to the Ternary Art, which refers to the wheels or volvelles that he used have elements or principles being divisible by 3. Furthermore this also by coincidence is the third phase of the art, but the phase and divisibility of the wheels are distinct things. 
Enough of Llull. Leibniz is really the only person to be regarded here, as it can be assumed that he wished to update Ars Magna to the science of the time and his own distinguished opinion. That being said, he never managed to create such a thing, but merely wrote to his collaborators and associates about what a proper implementation of this Universal Characteristic would look like. His letters are somewhere in the order of magnitude of 10^5, which is a complicated way of saying 10,000. Indeed I do not remember the estimated number from the Wiki, but I do believe it was something like 30,000. 
By the way, the Wiki does list 21 different attempts at Characterica Universalis, which is the number if I recall correctly, that this scholarly text on Llull mentioned that the man had written this many different version of his system. Quite interesting, but I cannot lower myself into base numerology. That has been superseded. To return to Ramon Llull for a moment, the man allegedly got his system from the Sufis. This precursor system is called Zairja, and there are a couple of texts available on that subject, one written by modern scholars and another written by a Tunisian historian who wrote the Muqaddimah. A hint for those of you curious about the latter text: The chapter about Zairja is in the third volume of that text, and is available on the Internet Archive. 
Back to Leibniz; for some reason essay writing is quite tiring. From what we can discern about what he stated that this system would look like, well I have some bad news. Leibniz simply took the diagram that Empedocles created in antiquity and said “There.” What I mean by this is that Leibniz just took the four elements and their supposed connections, in doing so adding another four nodes to the diagram, and being content with drawing lines between said nodes in order to ratiocinate (think) on paper. Anyone can tell that this is follysome since we now know for a fact that the Classical Elements theory is rubbish. In fact, I have a hot take that it was not only responsible for the idea of “race,” but also the idea of depression. I have created an acronym for the various iterations of Classical Element theory, that is “EHTR” (pronounced ‘ether’) or Element-Humor-Temperament-”Race.” Indeed this may come as quite a shock everyone, but Kant the philosopher was really racist and decided to rank the “races.” I am not going to get into this, but I will say that it may have become esoteric or something through the likes of Manly P. Hall, who mentioned the same scheme Kant used, albeit reordering some things, after the latter mapped it to an analogy about the caste system mentioned in the Bhagavad Gita. I can feel the cancelation brewing already. 
There are probably many different ways to attain this Universal Characteristic. I find that I have provided enough introductory information on this subject, so let us move on to the main part of this essay. Unfortunately, this whole thing was spurred on by a feeling of grandiosity, so I really don’t know how valid my intuition is. Furthermore I forgot what it was that I could use to implement Charicterica Universalis. That being said, I think it was along the lines of a study of analogy, using mathematics, so that we could potentially describe the various processes that underlie reality. The other part was a return to metaphysics proper, or the three general distinguishing features of it according to some textbook, those features being categorization (which is what I consider to be important in particular with regards to this endeavor), thinking and a sense of supremacy regarding the method. Personally I really don’t think that the last one means much, and is in fact a detriment to updating philosophy as should be periodically done in my opinion. Science will always push the boundaries. 
I am going to split the remainder of this essay into three parts: The first part will be about analogy; the second, categorization; and thirdly an obscure paradox that I came up with last night, as a bonus for making it to the end of the essay. You could just skip to the paradox, if you would like, in fact I will bold the title for you, in case I have wasted too much of your time and am boring you. 
On Analogy
I envision analogy as not something fundamental, as the man who wrote Zen and the the Art of Motorcycle Maintenance stated that analogy is irreducible to sub-elements; and I argue against that position taken by the author of that text. I am honestly getting tired of writing and I have written the later parts of this essay before I wrote this part, so here goes nothing. 
In the next part I briefly mention knot and graph theory. I envision analogies as graphs, as I was inspired by Schrödinger’s book What is Life that the genetic material was a crystal. Not true, but why could this crystal represent mimesis, as opposed to “genesis?” (Genesis as in genes, an improper way to say that mind you.) Yes, I really think that this is the case, but it does sound kind of crazy now that I have it on paper after having it in my mind for a few years. I don’t know. I dislike the designation that Dawkins created for such things, the “meme” which he literally took from some German scientist with the same first name, and removed the ‘n’ in mneme to create this Internet garbage we see today. 
Then there are the developments with the idea of metaphor. I don’t really feel like getting into these because I am too tired and I keep making typing mistakes. Just know that it is possible to limit portions of the structure of the analogy to make it more congruent with other analogies or structures. Lastly, it really feels like the literary criticism movement is starting to claim all of the universe as its “text.” That is a portion of Structuralism, at least, according to PhilosophyTube. She stated that Structuralism started as literary criticism, and what do we as human beings do? Why we map the text to the whole of the universe. Some could argue that is a kind of metaphysics were it to be loosely understood. ...
On Categorization
The general gist of what I am thinking of here is that Ars Magna’s major issue is that it is not chaotic enough, if that makes any sense. What I am attempting to get at here is the thing about the questions generated in that system solely referring to the statements created. There is no architecture or complexity there to be studied and afterwards engineered, as it is just base multiplication to generate the questions. What I would like, is for the creation of the questions to be irreversible and chaotic, indeed those are separate things, much like the weather. Knot theory, or graph theory would come into play here, I am not sure which but that is what my intuition is telling me. Also, many statements could be superimposed to generate a set of questions, or a single question. Hopefully my mathematical studies will enable me to investigate this further in the future. 
It must be stated now that the whole category term does apply in my opinion to Ars Manga. This is because the system abstracts the categories into a table of about 54 “elements” which are then combined a second time to produce very short strings of text, for instance “BCD.” Of course, the strings could very well be longer, and could incorporate more intricacy in this manner, but it is really the interaction between all of these strings which constitutes the architecture of the system, although this is done in a manner contrary to the mainstream Lullists, which is an anachronism, really. 
Case in point the categories must translate into natural phenomena and vice versa. At the same time, if the categories were generative, then they must be irreversible in order to be as intricate as possible. The sky is the limit with this, “New Lullism.” I don’t feel like explaining any more, but if someone wants me to tell them about why the standard categories must be reversible, and the generative categories the reverse, then I will explain this another day. Indeed, it may be a false distinction; there may very well be four types of category system, that is:
Standard reversible;
Generative reversible (Ars Magna);
Standard irreversible;
Generative irreversible.
That is all for this part.
The Paradox
There is a possibility for a Universal Library, but the one available on the Internet is not feasible for conducting research on, because it is an art website and is not powerful enough to locate texts and be practical. I am talking about an implementation for the Universal Library called the Library of Babel. You can visit the website at libraryofbabel.info. I do not have the energy to disclose the theory behind this whole thing right now, but on request I will write about it another day. 
The mathematical constant “pi” supposedly does not repeat. Yet there is a trichotomy to be established here, when the constant is juxtaposed with the Universal Library, either; 
1). The Universal Library is effected by Gödel’s Incompleteness Theorem (was stated by two separate mathematics professors to likely be the case);
2). Pi does indeed repeat minute portions of itself after a significantly large computation of it is conducted, with an upper bound order of magnitude of around 10^5000. Note that this is a back-of-hand calculation;
3). Pi cannot be mapped to the Universal Library.
This trichotomy may indeed be defective as I am not trained in logic, and also I had to make up the last one as I forgot what it was. Oh well.
Thank you very much for reading all of this. Have a swell day. 
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diyscholar · 7 years
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Domain 3 : The Sciences
The DIY Scholar came into to being to expand my ideas and opinions and skills. There are 17 subjects that constitute the Program. 15 of them are domain centric and 2 of them are variable focused.
Domain centric - the subjects fall under the umbrellas of the Arts, the Sciences and the Humanities.
Variable focused - reading the assigned texts and taking MOOCs.
This post’s aim is to share with you the syllabus I have designed for myself in the domain of the Sciences. In here you will find the subjects I have decided to study and the learning materials I have assigned for them.
1. Python 
 Before we can think about making a computer bend to our wishes we need to know what does it mean to compute. Among the plethora of programming languages out there Python, as far as my research and survey went, seemed a nice place to start. 
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To accompany John Guttag’s book is John Guttag’s series of lectures titled ‘Introduction to Computer Science and Programming’ at MIT.
‘Introduction to Computer Science and Programming’ by John Guttag
2. Mathematics
A little bit of Math never hurt nobody. I want my interest in Science to pay off to an extent where I may be able to understand ideas in a mathematical context. And for that tutoring and practice is the best option. To bolster my understand and my interest I have assigned myself the following texts.
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Tom Leighton, the cofounder of Akamai, the legendary tech company takes a class at MIT conveniently (in my case) titled ‘Mathematics for Computer Science’. These texts are to be accompanied by the rigour of Leighton’s lectures.
‘Mathematics for Computer Science’ by Tom Leighton
For a better understanding of a rich history of Mathematics in India I have also prescribed a series of lectures given at IIT Bombay titled, ‘Mathematics in India - From Vedic Period to Modern Times’, delivered by M.D. Srinivas, M.S. Sriram and K. Ramasubramanian.
‘Mathematics in India - From Vedic Period to Modern Times’ by M.D. Srinivas, M.S. Sriram and K. Ramasubramanian.
3. Biology
Biology is a science whose time has come. To understand the impact and the mechanics of Biology I have assigned myself these texts. 
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In parallel, I plan to pay close attention to the video lectures of Robert Sapolsky’s course at Stanford titled, ‘Human Behavioural Biology’. Along with that I also intend to brush up and update my Biology basics with Robert Weinberg’s ‘Introduction to Biology’ course at MIT. 
‘Human Behavioural Biology’ by Robert Sapolsky
‘Introduction to Biology’ by Robert Weinberg
The text, ‘The Emerging Mind’, is based on a series of talks under the auspices of the ‘BBC Reith Lectures Series’ by V.S. Ramachandran in 2003. 
‘The Emerging Mind’ by V.S. Ramachandran
4. Psychology
I want to make sense of myself in relation to my mind and no science can more clearly provide me answers for this search than Psychology. The reason for the addition of Psychology is for me to intuitively grasp and concatenate ideas with respect to Biology as well. Here are the assigned texts.
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Coupled with these assigned texts are two lecture series. The first is titled ‘Introduction to Psychology’ and its given by Paul Bloom at Yale. The second is titled ‘Philosophy and Science of Human Nature’ and its given by Tamar Gendler at (once again) Yale. 
‘Introduction to Psychology’ by Paul Bloom
‘Philosophy and Science of Human Nature’ by Tamar Gendler
5. Artificial Intelligence
Probably the most important innovations in the coming few decades will be in the field of Artificial Intelligence. Its invention and reasoning techniques will disrupt industries and change the way we live. I think its very important to have a decent understanding of the mechanics of the ideas in Artificial Intelligence as it can aide in our betterment.
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Deepak Khemani’s lectures on Artificial Intelligence at IIT Madras have been prescribed along with his book, ‘A First Course in Artificial Intelligence’. Also assigned are the series of lectures given by Patrick Winston at MIT titled ‘Artificial Intelligence’. In addition, for the sheer joy of what boundless imagination and creativity looks like, I have assigned myself a series a lectures delivered by Marvin Minsky at MIT titled ‘The Society of Mind’ which has Marvin’s book, ‘The Emotion Machine’ as its primary text.
‘Artificial Intelligence’ by Deepak Khemani
‘Artificial Intelligence’ by Patrick Winston
‘The Society of Mind’ by Marvin Minsky
This effectively brings me to the end of my syllabus/ curriculum design in the Sciences domain with respect to my DIY Scholar Program.
Thanks for reading.
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itssergiooo · 3 years
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"In order to solve this differential equation you look at it until a solution occurs to you" -George Polya
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ahmedkhfagy · 4 years
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A great discovery solves a great problem but there is a grain of discovery in the solution of any problem. Your problem may be modest; but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery.
George Polya
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linusjf · 5 years
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George Polya: Pedantry and mastery
“Pedantry and mastery are opposite attitudes toward rules. To apply a rule to the letter, rigidly, unquestioningly, in cases where it fits and in cases where it does not fit, is pedantry … To apply a rule with natural ease, with judgment, noticing the cases where it fits, and without ever letting the words of the rule obscure the purpose of the action or the opportunities of the situation, is…
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