Every thinking human being tries to build his or her worldview from the store of his or her own experiences or by drawing upon one's reasoning powers or by drinking from the fount of existing wisdom and knowledge. Every human being has a personal philosophy of life and existence even if it were not as sophisticated as that of, say, Bertrand Russell.
Shakespeare has memorably stated: "There are more things in heaven and Earth,..., than are dreamt of in your philosophy." There may come a time in one's life when this worldview gets shattered and one desperately clings to some beliefs, any beliefs. As they say, Nature abhors a vacuum. Some may become devoutly religious, some may become atheists or agnostics, some may find solace in, say, Spinoza's philosophy or Nietzsche's philosophy.
I believe that even practising science and math requires a certain faith. In mathematics, we use the imaginary number to great success without any assurance that such a thing exists. In science, physicists use the Schrodinger equation and the Dirac equation for the electron which cannot be rigorously derived. Their acceptance lies in their amazing success in describing physical phenomena.
Gaurav Suri and Hartosh Singh Bal's dazzling A Certain Ambiguity: A Mathematical Novel (2007) is a work of fiction about the journey of an Indian mathematician in 1919 to small town in the US upon the invitation of a fellow mathematician. His journey, as seen through the eyes of his grandson, proves to be a transformational one.
This Indian mathematician Vijay Sahni is an atheist who refuses to believe in anything without proof beyond all doubt. He gets imprisoned in the US on a blasphemy charge and, when investigated by a judge, states that the proof should be as leak-proof as an Euclidean proposition.
Euclid was an ancient Greek mathematician known for his classic tome Elements. In this, he proposed a set of axioms that were taken a s self-evident. He showed that the entire edifice of geometry could be built on these axioms. Elements influenced several people over the centuries such as Spinoza, Descartes, Einstein and even Lincoln. It posits an order to the field of geometry and provides the hope that certainty can be found within mathematics.
It is with this notion of certainty that Sahni compares religious rituals and beliefs and finds them coming up short. Mathematics, he maintains, has no need for blind faith such as the religious have.
Unfolding events show that even Euclid's geometry may not be the unassailable monolith that it has been thought to be. This shatters Sahni's confidence in absolute certainty and in his Platonism and makes him an agnostic in everything, even mathematics.
I don't want to reveal what the transformational event was. But for scientifically literate people it may be easily guessable. The hint is: the year was 1919 and it has to do with non-Euclidean geometry.
Suri and Bal have presented the veritable history of mathematics in such a fashion that even a high school kid can understand it. This book provides the best introduction to Euclidean geometry I have ever come across. It also provides a fascinating glimpse into the mind of Georg Cantor - the genius who came up with set theory. And the discussion of Indian mathematician Bhaskara's proof of the Pythagoras theorem was an unexpected gem.
This book is as much about religion as it is about mathematics. Towards the end of the book an unexpected question popped into my head: If Euclidean geometry, which has held its sway for over 2000 years, could not be viewed with certainty, then what can one say about religions that have cropped up in the last two millenia? What can one really rest our faith upon? Can there really be scientific truth or religious truth that is present outside of human existence?
One mathematician not covered in this book but briefly mentioned is Kurt Godel. Godel is supposed to have proved that if you start with any axiom system, you will always find statements that are impossible to prove or disprove. Some statements just cannot be decided one way or the other! Maybe religious beliefs and scientific beliefs share the common uneasy feature that they need some faith to take action upon.
An extraordinary book that can change one's outlook on life.
Shakespeare has memorably stated: "There are more things in heaven and Earth,..., than are dreamt of in your philosophy." There may come a time in one's life when this worldview gets shattered and one desperately clings to some beliefs, any beliefs. As they say, Nature abhors a vacuum. Some may become devoutly religious, some may become atheists or agnostics, some may find solace in, say, Spinoza's philosophy or Nietzsche's philosophy.
I believe that even practising science and math requires a certain faith. In mathematics, we use the imaginary number to great success without any assurance that such a thing exists. In science, physicists use the Schrodinger equation and the Dirac equation for the electron which cannot be rigorously derived. Their acceptance lies in their amazing success in describing physical phenomena.
Gaurav Suri and Hartosh Singh Bal's dazzling A Certain Ambiguity: A Mathematical Novel (2007) is a work of fiction about the journey of an Indian mathematician in 1919 to small town in the US upon the invitation of a fellow mathematician. His journey, as seen through the eyes of his grandson, proves to be a transformational one.
This Indian mathematician Vijay Sahni is an atheist who refuses to believe in anything without proof beyond all doubt. He gets imprisoned in the US on a blasphemy charge and, when investigated by a judge, states that the proof should be as leak-proof as an Euclidean proposition.
Euclid was an ancient Greek mathematician known for his classic tome Elements. In this, he proposed a set of axioms that were taken a s self-evident. He showed that the entire edifice of geometry could be built on these axioms. Elements influenced several people over the centuries such as Spinoza, Descartes, Einstein and even Lincoln. It posits an order to the field of geometry and provides the hope that certainty can be found within mathematics.
It is with this notion of certainty that Sahni compares religious rituals and beliefs and finds them coming up short. Mathematics, he maintains, has no need for blind faith such as the religious have.
Unfolding events show that even Euclid's geometry may not be the unassailable monolith that it has been thought to be. This shatters Sahni's confidence in absolute certainty and in his Platonism and makes him an agnostic in everything, even mathematics.
I don't want to reveal what the transformational event was. But for scientifically literate people it may be easily guessable. The hint is: the year was 1919 and it has to do with non-Euclidean geometry.
Suri and Bal have presented the veritable history of mathematics in such a fashion that even a high school kid can understand it. This book provides the best introduction to Euclidean geometry I have ever come across. It also provides a fascinating glimpse into the mind of Georg Cantor - the genius who came up with set theory. And the discussion of Indian mathematician Bhaskara's proof of the Pythagoras theorem was an unexpected gem.
This book is as much about religion as it is about mathematics. Towards the end of the book an unexpected question popped into my head: If Euclidean geometry, which has held its sway for over 2000 years, could not be viewed with certainty, then what can one say about religions that have cropped up in the last two millenia? What can one really rest our faith upon? Can there really be scientific truth or religious truth that is present outside of human existence?
One mathematician not covered in this book but briefly mentioned is Kurt Godel. Godel is supposed to have proved that if you start with any axiom system, you will always find statements that are impossible to prove or disprove. Some statements just cannot be decided one way or the other! Maybe religious beliefs and scientific beliefs share the common uneasy feature that they need some faith to take action upon.
An extraordinary book that can change one's outlook on life.
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