Use of mathematics in the works of Jorge Luis Borges
Introduction
This essay is based on the enigmatic use of mathematics in the works and stories of the famous Argentine writer Jorge Luis Borges. While we know that he is an emblematic writer of literature, his writings were not only simple stories or poetry, but that everything has a background that makes you foil with what he writes, however, many of these writings have math and mathematical backgrounds, given To this, this essay is based on the life of Jorge Luis Borges, his literature, his mathematical learning and how he reflected him in his works.
Developing
Jorge Luis Borges was an emblematic Argentine writer, icon of Hispanic literature, who achieved not only a scope in Spanish -speaking literature, but also throughout the world, given to his great writings that convey wisdom, emotions, feelings, as well as Also reflections. He is a writer I have always admired, since I consider myself a recurring reading of his literature, with whom I grew up. However, when reading several essays of known authors of the time, as well as curious data, I realize that several works have mathematical references, as well as many complex issues of mathematics.
Like I will ask yourself what is related to mathematics with the works of Jorge Luis Borges? Because in reality if they have much relationship, although at first glance it does not seem, only a true connoisseur or expert in mathematics could identify it with the naked eye, since some of Borges’s works are not only letters, but combines the numbers and They have a certain link between mathematics and the emblematic Argentine writer. Borges was not passionate only to literature and letters, he also was on the subject of mathematics. He was for many years a constant reader of mathematical books, it should be clarified that there were many mathematical books that he did not understand in its entirety. Only a connoisseur of mathematical themes can notice that in the most notable works of Jorge Luis Borges, such as "El Aleph", "Death and compass", "The Babel Library", among others, have many mathematical references, Because I am not an expert or knowledgeable of mathematics, but rather a reader of another type of content, such as romantic novels, stories, poetry, etc., I cannot easily identify in his works that relationship between Borges and mathematics, However, thanks to the content of Guillermo Martínez’s book in his book "Borges and Mathematics", now I can capture and assimilate this similarity, the most notorious example is the use of finite and infinite numbers, paradoxes, etc. I really do not have a great mathematical understanding to know that other issues he has included or embodied in a hidden or secret way in his works, since he never officially pronounced that in his works he had included this type of mathematical content. I must assume that for a fervent reader of mathematical themes, he could become a captivated and attracted reader of Borges’ works, simply by the wonderful way in which the Argentine author turned mathematics into something narrative.
Guillermo Martínez’s initial approach (author of "Borges and Mathematics") to Borges’s works was something sporadic, since he did not read everything throughout, but was reading in parts and by stories that he knew that they already possessed These references, to complete all the works, all this with a mathematical look, to find out what could find of them in their writings. He is still a writer and mathematic.
Concentrating more thoroughly on the work of the author Guillermo Martínez, in which he writes about Borges and mathematics, I realize the different perspectives or frames in which you can focus on any work you read, I mean this, to what If you read a romantic novel, you can focus on a lyrical theme, a critical theme, or in the same way, although not very common, in a mathematical theme, that is why many times when reading a work, we see below it , since we do not give a certain specific approach and maybe you can understand the plot, but not the background, it is what happens to Borges’s works, since the reader can exist that only reads the works without giving them a meaning, and He manages to capture below the work, or if not, an introverted reader who analyzes and one the parts of the work, which will do this last type of reader, is to give meaning to the work, so he will understand that in certain works of Borges are used mathematical references, with this he may capture ar above the work.
I do not know exactly how much study time Borges dedicated to mathematical, metaphysical books, etc., but what is clear to me, is that without any difficulty he could capture this knowledge secretly in his works, which I consider that he puts it by Above other authors since it makes other types of readers, mathematical experts or public are interested in their literary works.
As I mentioned earlier, everything is about looking at a specific angle the works of Borges, since there is a lot of relationship of different topics in his works, and you will wonder what kind of topics I mean? Well, even if you do not believe it, not only includes mathematical references or issues, but also issues related to physics, science, among other issues that when you focus on them, you can discover great similarity between them and their literature. It is the great example of renowned Borges stories, such as "El Disco", "The Pascal Sphere", "The Babel Library" (very good for mathematical references), etc., but the one that does contain these three themes that I approached as I approached how Focus example, is the work "El Aleph".
Jorge Luis Borges refers to the finite and infinite numbers in some works, he mentions the MenGenlehre directly, what is the MenGenlehre? It is the theory of sets, that is, the relationship between certain elements or properties, branch of mathematical logic, which for example, this issue is taught in "Mathematics to think". The Aleph, literary work of Jorge Luis Borges, is in reference to “Aleph” that in mathematics is a Hebrew lyrics that mathematicians use to refer to the set of sets, which its graphic symbol represents one arm pointing to the sky and another arm pointing to the earth, this means what are finite things and infinite things, the finite context represents or refers to having the same amount of elements, while in reference to the infinity, there could be various varieties of infinity. This and other mathematical concepts fascinated Borges totally, because in reference to the infinite mathematical, not necessarily the whole is greater than anywhere, but there are parts that may be bigger than the whole, or some that are equivalent to the whole. Personally, I think they are very complex issues, that really, not everyone might be deeply interested in issues such as these, because they have a certain level of understanding and logic, that for me, it is not something that is easily, however, Borges can create A connection between those who are not interested in mathematical purposes and mathematics, because at the end of everything you make you understand mathematical issues in the form of narrative, which are immersed in the literature in a very striking way that manages to capture the care of the reader and makes the same reader believe some interest in these concepts and why of the purpose of combining mathematics in his works, or at least that was my case.
On the other hand, to purely understand these elements, it is enough to start something basic as the example of telling, so it begins when you are a boy, counting the amounts and logically relate that if there are 5 batters in a room and in the Another room 5 doctors, for mere logic you know that those 5 doctors will have a robe, this could be an example of finite numbers, because you loved rooms had the same closed number of elements, but if they talk about infinites, The human being has been into practice since the operation was taken and when the unknown of how many quantities exist, because what no one has reached that because it is somewhat infinite, the numbers are infinite. So complex is the infinite since Borges used it in many works, how "The Book of Arena", "The Babel Library"; Among another, (works that I already mentioned above).
Another mathematical concept that Borges used, was that of languages, theme that is evident in the "Babel Library", staging in reference of artificial languages, that is, the possibility that every intelligible book exists, that every word that It can be formed by X or y y lista will have a meaning, in this work first it is presented to a librarian who seeks the catalog of catalogs, this is also guided by the infinity, since in the library that is presented, he can contain countless books, since first they would have to classify, for example, separate by shelves books that are only in Spanish, another in English, German, French …, as well as classify books by number of words used in it, by the number of pages, the book size, the types of prologues, the different topics, etc., and this is how in this book it is presented as something infinite, since the amount of books that could be in the library is not enumerable from Babel. On the other hand, the infinity in the “sand book”, which shows that of a finite segment can be subdivided infinite segments, as was the example that in the pages of a book, everything is fractional, but there are always Other intermediate numbers to these and in the same way he cannot find the page he is looking for because there are always other pages that sprout in the middle, Borges tries to show that if there are many fractional numbers such as natural numbers, what do I mean by this? In a nutshell, fractions are rations of natural numbers, and for every numerator, there must be infinite denominative numbers, that is, many rational combinations.
Another idea of Borges in his works, where he shows his great knowledge about the "Paradox of Russell", or as Guillermo Martínez "paradox of the imagination" calls it this was a theory that discredited and contradicted the original theory of sets of George Cantor , because for example, the set of all palm trees, is not a palm tree, although the set of all concepts, if it is a concept itself. This is an issue which, if you ever heard from the set theory or taught you at school, you must know it, and if not, to understand it better, an example, if there is a person who is a cook and only cook for people They don’t know how to cook, and if she cooked, do you enter the group of people who don’t know how to cook? No, since as I mentioned earlier, it is that by having a set of several elements, they mean that this person enters the classification of people who do not know how to cook.
Although not only were these concepts that Borges used in his works, nor only in these writings, that is, there are a number of ideas that he took from mathematics, for example recursion, since at some point he mentions that the first Approach that had with infinity was for a can of cakes that brought to some Asian warriors in a corner and repeated the can with the same scene and thus indefinitely, and this takes it with the map of England that is repeated in a corner The same map because it is very precise and that creates an infinity. On the other hand, I used it in stories not so well known and in poems such as "chess", where when reading it it costs to understand it and give it a meaning or meaning, since it speaks about where the plot of a God behind God begins, to What refers that the player is moved by a God, behind that God there is another God, and thus indefinitely, so the idea of infinity appears, all are elements that come from mathematics.
Guillermo Martínez to finish his book, closes with the question “Why does Borges interest mathematicians?"Ask the one that if you answer, since these previous elements (I refer to El Infinito, Russell’s paradox and languages) are themes that Borges is involving in his stories, either in the entire context or only by fragments. There are many mathematical or lawyer experts of science, which are truly attracted to their writings, and these at the end of reading them are amazed by the amount of references either mathematics, physical, etc., of their stories, that is why many authors of these branches write about it showing their admiration towards the author, why? Of course because of the outstanding ability of Jorge Luis Borges to involve these sciences in his writings and in a very attractive way, in the same way many more merits are attributed by the great content in his works and for having a perfect essay, and for everything This was a very recognized author in his time, but without a doubt, although he is no longer in this world, he will continue to admire and distinguish for such an artistic ability embodied in literature.
Borges understood an indefatigable intellectual capacity, Borges was a very curious person, so much curiosity was to discover new schemes that came out of his own standards, he was a consumer of Russell’s books that served him to be able to possess the knowledge he had, not only Of mathematics, but also physical, metaphysics, among other branches, all these were intellectual interests. It did not include small references, but also lessons, fragments and examples of these issues.
His great intellectual interests were discovered because in the National Library there is a list of the books that Borges chose when he was mentioned place, but this may not assure us that all were really read (speaking in another context), because If it is clear that many have mathematics or physical books in our homes, but that does not ensure that we have already read them, more because it is not easy to read that kind of content, many times you start it and you never know how to finish it, they are personally difficult To grab me, but returning to the main comment about Borges’s readings in the library, all this is a clear example that he really read them, for the richness of knowledge he possessed, apart because by capturing these mathematical concepts in His works, gives the tone as far as he came to read them.
The most interesting thing is the mystery that if Borges I take mathematics as inspiration for his fictions, or he only used them as references.
There is a very important issue within all this essay, and they are mathematics, these are not only numbers, but it is a science that takes care of the entire structure, throughout the course I could understand the importance of mathematics in different Areas of study, this is, in any profession they are immersed and have great value, it is involved from dance, music, law, architecture, poetry, literature, etc. It should never be questioned to be used, since since the beginning of humanity they have been indispensable, they are a construction that the society itself has been building, the power of mathematics is to sip, because of this, without them there would be no there would be no technology, because they are the basis of these technological advances. Also, on the other side of the currency of the trial, there is the importance of literature, it allows us Allows readers to know new themes and discover new doors of wisdom. Thus, through literature, such as Guillermo Martínez’s essays and stories, but especially “Borges and Mathematics”, I could discover this incredible union and combination of the writings of Jorge Luis Borges with mathematics, and That we can connect with the thoughts and ideas that he left on earth embodied on paper, so we must also enhance and recognize the work of this author since in my opinion, the two authors allowed me to better understand these mathematical issues, than in A principle did not understand in its entire Poetry, but it had never occurred to me to look at the writings with an angle based on scientific or mathematical approaches.
conclusion
In conclusion, these mathematical issues and some others that are immersed and somewhat secret in the works of Borges, are of great help for a better understanding of their stories, so when reading them you can relate them to these elements of mathematics, and will create a better Reading satisfaction, as well as strengthening interest in certain mathematical aspects.
I recommend that reading any book, poetry, story, etc., try to look for a thematic angle, so that you can discover if you have references with other topics and be more satisfactory.
Bibliographic reference
Martínez, Guillermo (February 19, 2003). «Borges and Mathematics». Retrieved on May 9, 2020.
Free Use Of Mathematics In The Works Of Jorge Luis Borges Essay Sample
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Use Of Mathematics In The Works Of Jorge Luis Borges
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Use of mathematics in the works of Jorge Luis Borges
Introduction
This essay is based on the enigmatic use of mathematics in the works and stories of the famous Argentine writer Jorge Luis Borges. While we know that he is an emblematic writer of literature, his writings were not only simple stories or poetry, but that everything has a background that makes you foil with what he writes, however, many of these writings have math and mathematical backgrounds, given To this, this essay is based on the life of Jorge Luis Borges, his literature, his mathematical learning and how he reflected him in his works.
Developing
Jorge Luis Borges was an emblematic Argentine writer, icon of Hispanic literature, who achieved not only a scope in Spanish -speaking literature, but also throughout the world, given to his great writings that convey wisdom, emotions, feelings, as well as Also reflections. He is a writer I have always admired, since I consider myself a recurring reading of his literature, with whom I grew up. However, when reading several essays of known authors of the time, as well as curious data, I realize that several works have mathematical references, as well as many complex issues of mathematics.
Like I will ask yourself what is related to mathematics with the works of Jorge Luis Borges? Because in reality if they have much relationship, although at first glance it does not seem, only a true connoisseur or expert in mathematics could identify it with the naked eye, since some of Borges’s works are not only letters, but combines the numbers and They have a certain link between mathematics and the emblematic Argentine writer. Borges was not passionate only to literature and letters, he also was on the subject of mathematics. He was for many years a constant reader of mathematical books, it should be clarified that there were many mathematical books that he did not understand in its entirety. Only a connoisseur of mathematical themes can notice that in the most notable works of Jorge Luis Borges, such as "El Aleph", "Death and compass", "The Babel Library", among others, have many mathematical references, Because I am not an expert or knowledgeable of mathematics, but rather a reader of another type of content, such as romantic novels, stories, poetry, etc., I cannot easily identify in his works that relationship between Borges and mathematics, However, thanks to the content of Guillermo Martínez’s book in his book "Borges and Mathematics", now I can capture and assimilate this similarity, the most notorious example is the use of finite and infinite numbers, paradoxes, etc. I really do not have a great mathematical understanding to know that other issues he has included or embodied in a hidden or secret way in his works, since he never officially pronounced that in his works he had included this type of mathematical content. I must assume that for a fervent reader of mathematical themes, he could become a captivated and attracted reader of Borges’ works, simply by the wonderful way in which the Argentine author turned mathematics into something narrative.
Guillermo Martínez’s initial approach (author of "Borges and Mathematics") to Borges’s works was something sporadic, since he did not read everything throughout, but was reading in parts and by stories that he knew that they already possessed These references, to complete all the works, all this with a mathematical look, to find out what could find of them in their writings. He is still a writer and mathematic.
Concentrating more thoroughly on the work of the author Guillermo Martínez, in which he writes about Borges and mathematics, I realize the different perspectives or frames in which you can focus on any work you read, I mean this, to what If you read a romantic novel, you can focus on a lyrical theme, a critical theme, or in the same way, although not very common, in a mathematical theme, that is why many times when reading a work, we see below it , since we do not give a certain specific approach and maybe you can understand the plot, but not the background, it is what happens to Borges’s works, since the reader can exist that only reads the works without giving them a meaning, and He manages to capture below the work, or if not, an introverted reader who analyzes and one the parts of the work, which will do this last type of reader, is to give meaning to the work, so he will understand that in certain works of Borges are used mathematical references, with this he may capture ar above the work.
I do not know exactly how much study time Borges dedicated to mathematical, metaphysical books, etc., but what is clear to me, is that without any difficulty he could capture this knowledge secretly in his works, which I consider that he puts it by Above other authors since it makes other types of readers, mathematical experts or public are interested in their literary works.
As I mentioned earlier, everything is about looking at a specific angle the works of Borges, since there is a lot of relationship of different topics in his works, and you will wonder what kind of topics I mean? Well, even if you do not believe it, not only includes mathematical references or issues, but also issues related to physics, science, among other issues that when you focus on them, you can discover great similarity between them and their literature. It is the great example of renowned Borges stories, such as "El Disco", "The Pascal Sphere", "The Babel Library" (very good for mathematical references), etc., but the one that does contain these three themes that I approached as I approached how Focus example, is the work "El Aleph".
Jorge Luis Borges refers to the finite and infinite numbers in some works, he mentions the MenGenlehre directly, what is the MenGenlehre? It is the theory of sets, that is, the relationship between certain elements or properties, branch of mathematical logic, which for example, this issue is taught in "Mathematics to think". The Aleph, literary work of Jorge Luis Borges, is in reference to “Aleph” that in mathematics is a Hebrew lyrics that mathematicians use to refer to the set of sets, which its graphic symbol represents one arm pointing to the sky and another arm pointing to the earth, this means what are finite things and infinite things, the finite context represents or refers to having the same amount of elements, while in reference to the infinity, there could be various varieties of infinity. This and other mathematical concepts fascinated Borges totally, because in reference to the infinite mathematical, not necessarily the whole is greater than anywhere, but there are parts that may be bigger than the whole, or some that are equivalent to the whole. Personally, I think they are very complex issues, that really, not everyone might be deeply interested in issues such as these, because they have a certain level of understanding and logic, that for me, it is not something that is easily, however, Borges can create A connection between those who are not interested in mathematical purposes and mathematics, because at the end of everything you make you understand mathematical issues in the form of narrative, which are immersed in the literature in a very striking way that manages to capture the care of the reader and makes the same reader believe some interest in these concepts and why of the purpose of combining mathematics in his works, or at least that was my case.
On the other hand, to purely understand these elements, it is enough to start something basic as the example of telling, so it begins when you are a boy, counting the amounts and logically relate that if there are 5 batters in a room and in the Another room 5 doctors, for mere logic you know that those 5 doctors will have a robe, this could be an example of finite numbers, because you loved rooms had the same closed number of elements, but if they talk about infinites, The human being has been into practice since the operation was taken and when the unknown of how many quantities exist, because what no one has reached that because it is somewhat infinite, the numbers are infinite. So complex is the infinite since Borges used it in many works, how "The Book of Arena", "The Babel Library"; Among another, (works that I already mentioned above).
Another mathematical concept that Borges used, was that of languages, theme that is evident in the "Babel Library", staging in reference of artificial languages, that is, the possibility that every intelligible book exists, that every word that It can be formed by X or y y lista will have a meaning, in this work first it is presented to a librarian who seeks the catalog of catalogs, this is also guided by the infinity, since in the library that is presented, he can contain countless books, since first they would have to classify, for example, separate by shelves books that are only in Spanish, another in English, German, French …, as well as classify books by number of words used in it, by the number of pages, the book size, the types of prologues, the different topics, etc., and this is how in this book it is presented as something infinite, since the amount of books that could be in the library is not enumerable from Babel. On the other hand, the infinity in the “sand book”, which shows that of a finite segment can be subdivided infinite segments, as was the example that in the pages of a book, everything is fractional, but there are always Other intermediate numbers to these and in the same way he cannot find the page he is looking for because there are always other pages that sprout in the middle, Borges tries to show that if there are many fractional numbers such as natural numbers, what do I mean by this? In a nutshell, fractions are rations of natural numbers, and for every numerator, there must be infinite denominative numbers, that is, many rational combinations.
Another idea of Borges in his works, where he shows his great knowledge about the "Paradox of Russell", or as Guillermo Martínez "paradox of the imagination" calls it this was a theory that discredited and contradicted the original theory of sets of George Cantor , because for example, the set of all palm trees, is not a palm tree, although the set of all concepts, if it is a concept itself. This is an issue which, if you ever heard from the set theory or taught you at school, you must know it, and if not, to understand it better, an example, if there is a person who is a cook and only cook for people They don’t know how to cook, and if she cooked, do you enter the group of people who don’t know how to cook? No, since as I mentioned earlier, it is that by having a set of several elements, they mean that this person enters the classification of people who do not know how to cook.
Although not only were these concepts that Borges used in his works, nor only in these writings, that is, there are a number of ideas that he took from mathematics, for example recursion, since at some point he mentions that the first Approach that had with infinity was for a can of cakes that brought to some Asian warriors in a corner and repeated the can with the same scene and thus indefinitely, and this takes it with the map of England that is repeated in a corner The same map because it is very precise and that creates an infinity. On the other hand, I used it in stories not so well known and in poems such as "chess", where when reading it it costs to understand it and give it a meaning or meaning, since it speaks about where the plot of a God behind God begins, to What refers that the player is moved by a God, behind that God there is another God, and thus indefinitely, so the idea of infinity appears, all are elements that come from mathematics.
Guillermo Martínez to finish his book, closes with the question “Why does Borges interest mathematicians?"Ask the one that if you answer, since these previous elements (I refer to El Infinito, Russell’s paradox and languages) are themes that Borges is involving in his stories, either in the entire context or only by fragments. There are many mathematical or lawyer experts of science, which are truly attracted to their writings, and these at the end of reading them are amazed by the amount of references either mathematics, physical, etc., of their stories, that is why many authors of these branches write about it showing their admiration towards the author, why? Of course because of the outstanding ability of Jorge Luis Borges to involve these sciences in his writings and in a very attractive way, in the same way many more merits are attributed by the great content in his works and for having a perfect essay, and for everything This was a very recognized author in his time, but without a doubt, although he is no longer in this world, he will continue to admire and distinguish for such an artistic ability embodied in literature.
Borges understood an indefatigable intellectual capacity, Borges was a very curious person, so much curiosity was to discover new schemes that came out of his own standards, he was a consumer of Russell’s books that served him to be able to possess the knowledge he had, not only Of mathematics, but also physical, metaphysics, among other branches, all these were intellectual interests. It did not include small references, but also lessons, fragments and examples of these issues.
His great intellectual interests were discovered because in the National Library there is a list of the books that Borges chose when he was mentioned place, but this may not assure us that all were really read (speaking in another context), because If it is clear that many have mathematics or physical books in our homes, but that does not ensure that we have already read them, more because it is not easy to read that kind of content, many times you start it and you never know how to finish it, they are personally difficult To grab me, but returning to the main comment about Borges’s readings in the library, all this is a clear example that he really read them, for the richness of knowledge he possessed, apart because by capturing these mathematical concepts in His works, gives the tone as far as he came to read them.
The most interesting thing is the mystery that if Borges I take mathematics as inspiration for his fictions, or he only used them as references.
There is a very important issue within all this essay, and they are mathematics, these are not only numbers, but it is a science that takes care of the entire structure, throughout the course I could understand the importance of mathematics in different Areas of study, this is, in any profession they are immersed and have great value, it is involved from dance, music, law, architecture, poetry, literature, etc. It should never be questioned to be used, since since the beginning of humanity they have been indispensable, they are a construction that the society itself has been building, the power of mathematics is to sip, because of this, without them there would be no there would be no technology, because they are the basis of these technological advances. Also, on the other side of the currency of the trial, there is the importance of literature, it allows us Allows readers to know new themes and discover new doors of wisdom. Thus, through literature, such as Guillermo Martínez’s essays and stories, but especially “Borges and Mathematics”, I could discover this incredible union and combination of the writings of Jorge Luis Borges with mathematics, and That we can connect with the thoughts and ideas that he left on earth embodied on paper, so we must also enhance and recognize the work of this author since in my opinion, the two authors allowed me to better understand these mathematical issues, than in A principle did not understand in its entire Poetry, but it had never occurred to me to look at the writings with an angle based on scientific or mathematical approaches.
conclusion
In conclusion, these mathematical issues and some others that are immersed and somewhat secret in the works of Borges, are of great help for a better understanding of their stories, so when reading them you can relate them to these elements of mathematics, and will create a better Reading satisfaction, as well as strengthening interest in certain mathematical aspects.
I recommend that reading any book, poetry, story, etc., try to look for a thematic angle, so that you can discover if you have references with other topics and be more satisfactory.
Bibliographic reference
Free Use Of Mathematics In The Works Of Jorge Luis Borges Essay Sample
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