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Mathematics
- GenresMathematics
348 pages, Hardcover
First published January 1, 1963
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58 people want to read
About the author
Robert Maynard Hutchins
661 books42 followersRobert Maynard Hutchins (LL.B., Yale Law School, 1925; B.A., Yale University, 1921) was an educational philosopher, dean of Yale Law School (1927-1929), and president (1929–1945) and chancellor (1945–1951) of the University of Chicago.
While he was president of the University of Chicago, Hutchins implemented wide-ranging and controversial reforms of the University, including the elimination of varsity football. The most far-reaching reforms involved the undergraduate College of the University of Chicago, which was retooled into a novel pedagogical system built on Great Books, Socratic dialogue, comprehensive examinations and early entrance to college. Although the substance of this Hutchins Plan was abandoned by the University shortly after Hutchins resigned in 1951, an adapted version of the program survives at Shimer College in Chicago.
Editor-in-Chief of Great Books of the Western World and Gateway to the Great Books; co-editor of The Great Ideas Today; Chairman of the Board of Editors of Encyclopædia Britannica (1943-1974).
He was the husband of novelist Maude Hutchins.
While he was president of the University of Chicago, Hutchins implemented wide-ranging and controversial reforms of the University, including the elimination of varsity football. The most far-reaching reforms involved the undergraduate College of the University of Chicago, which was retooled into a novel pedagogical system built on Great Books, Socratic dialogue, comprehensive examinations and early entrance to college. Although the substance of this Hutchins Plan was abandoned by the University shortly after Hutchins resigned in 1951, an adapted version of the program survives at Shimer College in Chicago.
Editor-in-Chief of Great Books of the Western World and Gateway to the Great Books; co-editor of The Great Ideas Today; Chairman of the Board of Editors of Encyclopædia Britannica (1943-1974).
He was the husband of novelist Maude Hutchins.
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Displaying 1 - 2 of 2 reviews
March 20, 2022
This volume made for incredibly fun and fascinating reading that is guaranteed to scratch that part of the mind that makes us all want to live life forever and a day at least for as long as we continue to learn about the universe, or perhaps, even make our own being a cause of itself thus getting us out of the trap of existence since infinite regresses can exist.
It never ceases to amaze me that if you removed all the rational numbers between zero and one, you made no difference whatsoever in the overall measure of the numbers remaining. Thomas Pynchon and Gravity’s Rainbow gets that fact, and my personnel hero, Georg Cantor does too. Interesting sidenote about Cantor, he spent his most creative part of his life in an insane asylum.
The editor allowed for redundancy in his story telling. Bertrand Russell and Edward Kasner stories mirrored each other. I don’t blame Kasner because Russell told the stories so well that they bear repeating after 30 years, but the editor could have given less similar stories priority.
One of the redundancies is so important that I can’t help but want to share it. One of the most fundamental theorems ever is wrong when applied to infinities: the sum of the parts is less than or equal to the whole. Cantor shows that is not correct when dealing with infinities. Russel tells us, and Kasner repeats it.
Whether one is checking into Hilbert’s infinite hotel, or racing a hare against a tortoise, this fact has ramifications beyond the ordinary.
I noticed, as I was reading Thomas Aquinas today, he made use of the fact the sum of the parts must be less than or equal to the whole thus proving his main point, but since he was dealing with an infinite God his proof won’t work, while using his Aristotelian certainty that an infinite regress is not possible thus insisting on an uncreated Creator (a necessary first mover) for which we must be beholden to.
It should be obvious that Cantor shows an infinite regress is allowed. I’m not saying that something can be the cause of itself, but I can’t state unequivocally that it is not allowed as scholastics did and most modern-day apologist do.
For those readers of Gravity’s Rainbow, they will realize why I cited Pynchon above since Pynchon gives the world an infinite regress from its beginning with Wernher van Braun's ironically un-self-aware epigram and its opening sentences on page one and through out including an infinite machine gun used in WW I which becomes the best car that was ever made.
I miss Martin Gardner when he wrote for Scientific American and The Skeptical Inquirer, but these articles in this volume whetted my appetite for seeing beyond the ordinary as Martin Gardner would make his readers do and they brought back fond memories for what still can be when one comes across mathematically inspired well written articles.
There is no royal road to Geometry and as these articles in this volume will clearly make the reader ask: which Geometry do you even mean since there are at least three viable, coherent, consistent geometries we know about?
Einstein describes the universe as a whole and it’s not Euclidian (it’s Reimann, of course). Einstein needs continuity and gives us a continuous universe(s), while quantum theory gives us a discrete world(s), each world view breaks down in two places, the universe’s beginning and black holes. They’ll be a couple of articles on what continuity means. This volume really never stops giving.
For those, who find this kind of stuff as cool as I do, I heartedly recommend this volume. Obviously, in 1963 they did not know where this stuff would lead for understanding the universe at large, but it shows how we got here today.
It never ceases to amaze me that if you removed all the rational numbers between zero and one, you made no difference whatsoever in the overall measure of the numbers remaining. Thomas Pynchon and Gravity’s Rainbow gets that fact, and my personnel hero, Georg Cantor does too. Interesting sidenote about Cantor, he spent his most creative part of his life in an insane asylum.
The editor allowed for redundancy in his story telling. Bertrand Russell and Edward Kasner stories mirrored each other. I don’t blame Kasner because Russell told the stories so well that they bear repeating after 30 years, but the editor could have given less similar stories priority.
One of the redundancies is so important that I can’t help but want to share it. One of the most fundamental theorems ever is wrong when applied to infinities: the sum of the parts is less than or equal to the whole. Cantor shows that is not correct when dealing with infinities. Russel tells us, and Kasner repeats it.
Whether one is checking into Hilbert’s infinite hotel, or racing a hare against a tortoise, this fact has ramifications beyond the ordinary.
I noticed, as I was reading Thomas Aquinas today, he made use of the fact the sum of the parts must be less than or equal to the whole thus proving his main point, but since he was dealing with an infinite God his proof won’t work, while using his Aristotelian certainty that an infinite regress is not possible thus insisting on an uncreated Creator (a necessary first mover) for which we must be beholden to.
It should be obvious that Cantor shows an infinite regress is allowed. I’m not saying that something can be the cause of itself, but I can’t state unequivocally that it is not allowed as scholastics did and most modern-day apologist do.
For those readers of Gravity’s Rainbow, they will realize why I cited Pynchon above since Pynchon gives the world an infinite regress from its beginning with Wernher van Braun's ironically un-self-aware epigram and its opening sentences on page one and through out including an infinite machine gun used in WW I which becomes the best car that was ever made.
I miss Martin Gardner when he wrote for Scientific American and The Skeptical Inquirer, but these articles in this volume whetted my appetite for seeing beyond the ordinary as Martin Gardner would make his readers do and they brought back fond memories for what still can be when one comes across mathematically inspired well written articles.
There is no royal road to Geometry and as these articles in this volume will clearly make the reader ask: which Geometry do you even mean since there are at least three viable, coherent, consistent geometries we know about?
Einstein describes the universe as a whole and it’s not Euclidian (it’s Reimann, of course). Einstein needs continuity and gives us a continuous universe(s), while quantum theory gives us a discrete world(s), each world view breaks down in two places, the universe’s beginning and black holes. They’ll be a couple of articles on what continuity means. This volume really never stops giving.
For those, who find this kind of stuff as cool as I do, I heartedly recommend this volume. Obviously, in 1963 they did not know where this stuff would lead for understanding the universe at large, but it shows how we got here today.
October 2, 2017
The book I read is #9 from the series “Gateway to the great books”
My favorite part was mathematics,in life
The types of people that would like this book are those that are creative and like complicated problems and are interested in space and time
My favorite part was mathematics,in life
The types of people that would like this book are those that are creative and like complicated problems and are interested in space and time
Displaying 1 - 2 of 2 reviews