Rated 5 out of 5 by MisterDarcy Three Courses in One!
If I’ve done the math correctly, there are three courses combined in this thirty-six-lecture program:
(1) mathematics with a focus on probability, statistics, and the history of geometry
(2) Western philosophy, as encapsulated in a 2,500-year survey
(3) the role that mathematics plays in our daily lives
The sum total: A Great Course called “Mathematics, Philosophy, and the ‘Real World’”!
In an all-encompassing liberal arts format, the series begins with the mathematical theories of the ancient Greeks (especially Euclid), then traces the relationship of mathematics and philosophy through the ages. The result is a humanities-based course filled with interesting sidebars and personal reflections of the instructor.
Professor Judith V. Grabiner is such a good lecturer that she could read aloud from an electronics manual and find a way to make the information both intelligible and interesting. There is also a refreshing down-to-earth quality in her lecturing. The course is packed with lively personal anecdotes, demonstrations, and the wisdom that comes from a master teacher.
As part of the inspiration for this course, Professor Grabiner cites Plato’s famous dictum that was inscribed above his Academy in Athens: “Let no one ignorant of geometry enter here.” Starting with Plato and his teacher Socrates, the lecturer demonstrates how through the ages, philosophers’ knowledge of the world has been shaped by mathematics. The discussions of two seventeenth-century French mathematician-philosophers, Pascal and Descartes, reveal how philosophy, science, and religion were intertwined. And in the section on eighteenth-century rationalism, there is a fascinating analysis of how Thomas Jefferson was thinking mathematically when he drafted the Declaration of Independence.
The lectures also touch on art history, revealing how mathematics was influential in painting and architecture. There was a detailed explanation of the uses of linear perspective in Renaissance art, wherein the painters drew upon mathematical principles to evoke three-dimensional space on the canvas. While the Renaissance painters were fundamentally Euclidean in their artistic principles, modern abstract artists like Picasso, Dali, and Duchamp were non-Euclidean in their styles of the collage, cubism, and surrealism, as apparent in a sampling of their famous works of art.
In this highly eclectic course, there were many memorable and surprising moments. Of all Professor Grabiner’s engaging stories, the most meaningful one addressed the life of the evolutionary scientist Stephen J. Gould. The lecturer described how when he was diagnosed with cancer, Gould applied his knowledge of mathematics and statistics to assess his chances of survival by charting numbers on a graph. He was ultimately successful in overcoming the cancer. As recounted by the professor in a moving and unforgettable way, this story combines all three of the course topics of mathematics, philosophy, and the real world. That story alone made this lecture series an enlightening educational experience.
COURSE GRADE: A
January 24, 2014
Rated 5 out of 5 by MariodelaParra I liked the influence of Math on modern arts
It is amazing how Professor Judith Grabiner shows the great impact of two topics of mathematics: Probability-Statistics and Geometry (Euclidean and Non-Euclidean) on the way we try to understand reality.
I liked very much the lectures on non-Euclidean geometry whit its conceptions of new spaces and its influence on architecture and modern art.
This course is very original and useful for expanding my perspectives to look at the world.
May 21, 2016
Rated 5 out of 5 by Sumar Impossible to exaggerate how good this course is
I just finished this course a few days ago, and I'm still excited and amazed by all that I've learned. When I bought this course, I thought (from the title and from other reviews) that I would be learning about the connection between math, philosophy, and their connection to the real world. Well, I got that, of course, but I got so, so much more! Indeed, what I got was a tour de force that examined the profound implications that two broad mathematics ways of thinking--the "probabilistic" and the "geometric"--have had (and continue to have) on philosophers, mathematicians, scientists, artists, corporations, policy makers, etc. I read a lot of philosophy, and have often read about how Euclid's geometry influenced certain thinkers, but never before was the extent of that influence so clearly (and powerfully) laid out than by Professor Grabiner in this course.
In the first part of the course, Professor Grabiner provides the viewer with the basic foundations of statistics and probability, discussing such things as the (somewhat surprising, for me, anyway) philosophical and religious roots of cost-benefit analysis and expected value (lecture 3), standard deviation (lecture 4), the history of the graph (lecture 5), and polling and sampling techniques (lecture 7). A lot of this information provided a nice review of my college probability and statistics classes, but was not too earth shattering ... until lecture 10. Here, Professor Grabiner connected the knowledge provided in the previous lectures to a discussion of determinism v. free will, effortlessly discussing the effect that probability theory had on leading mathematicians, scientists, and philosophers, and the effect that figures in each field had on each other. For instance, did you know that Bohr's theory of the atom was influenced by Kierkegaard's leap of faith? Or that Maxwell was influenced by Lucretius' "swerve"? Or even that the debates that were played out among religious figures centuries ago is now being mirrored, in a very specific way, in the debates between the two competing theories of the universe, quantum mechanics and relativity? It is here, in drawing connections between different fields of knowledge, where the course paid major dividends, and where Professor Grabiner is at her best.
Similarly, in the second part of the course, where Euclidean thinking is emphasized and explained, Professor Grabiner links up the philosophical story of Plato's cave to Kepler's laws of planetary motion and Newton's law of universal gravitation (lecture 15). What?!! I had no idea there was a connection here, yet now, I am convinced. I also became aware of the enormous debt to Euclid that was owed by such monumental thinkers as Descartes (lecture 22), Spinoza and Jefferson (lecture 23), and Kant (lecture 27). Simply put, without Euclidean geometry, what these thinkers said and wrote would not have been possible. But, even more than this, I now feel that, by understanding the geometric way of thinking that underlay the philosophy of these great thinkers, I now understand what they were trying to do, and the strengths and weaknesses of their approaches, in a way that I never have before. In fact, more than this, I am now convinced that I really never understood these thinkers before, and Professor Grabiner's course made me skeptical that anyone else really can either without understanding the extent to which, and in what way, these minds were directly influenced by Euclid. I now realize that I should have taken the sign that once hung above Plato's academy, which read "Let no one ignorant of geometry enter", much more seriously than I have in the past, and that it might profitably be attached as a warning label to those who would read the thinkers just mentioned. But the reverse is probably also true. We might have a sign attached above the great physics labs across the world saying something like "Let no one ignorant of philosophy enter," for, at the most fundamental level, the debate between modern physicists over their particular world views are, at their core, philosophical. "And", to quote Vonnegut, "so it goes".
Other aspects of this course that I really enjoyed learning about was geometry's impact on art (lecture 29 and 33), the tremendous philosophical, mathematical, and scientific impact of non-Euclidean forms of thinking (lectures 30-32), and the importance of Euclidean and non-Euclidean ways of thinking in the modern world (lectures 34-36). This course was a real eye-opener for me, and I can honestly say that I will not look at the world the same way again.
February 14, 2016
Rated 5 out of 5 by Juco A Tour de Force
This is a spectacular presentation of mathematics for those with a background in liberal arts. Dr. Grabiner is so plain spoken and straightforward that it takes a bit to realize what a deep understanding of classical philosophy and intellectual history she has. It is simply wonderful.
January 20, 2016