A good simple non mathematical guide to game theory. Introduces all the main concepts and also recommends a beginner text if you want to study game thA good simple non mathematical guide to game theory. Introduces all the main concepts and also recommends a beginner text if you want to study game theory more seriously....more
The two main topics in this novel are set theory and geometry. The mathematics that is presented here is the usual and well known theorems. In Set theThe two main topics in this novel are set theory and geometry. The mathematics that is presented here is the usual and well known theorems. In Set theory, starting from Zeno’s paradoxes, infinite series, to the theory of sets and the continuum hypothesis. And in geometry, starting from the Pythagoras theorem, Euclid’s axioms and to the development of Non-Euclidean geometry. They are developed parallelly (and in two parallel story lines, one taking place in contemporary times and the other in 1919) showing the independence of continuum hypothesis and Euclid's fifth postulate.
The main goal of the novel seems to be the epistemological implications of the development of theory of infinite sets and Non-Euclidean geometry. It raises some very important questions about mathematical truth but the writers only give a casual overview of mathematics and they do not go deep enough to better understand their implicationson the nature of truth.
For a beginner, this could be a fascinating tour of the basis of mathematics. It does a pretty good job of introducing continuum hypothesis and Non-Euclidean geometry in elementary terms. For someone already familiar with the mathematics and philosophy dealt with in this book and its historical basis, there isn't much here as the story itself isn't very fascinating.
But i did like the last part of the book, the journal entry of the judge where he and Vijay Sahni come to terms with the lack of certainity....more
The main intent here is biographical rather than mathematical. But this isn't a very good account. He doesn't distinguish between facts and anecdotes The main intent here is biographical rather than mathematical. But this isn't a very good account. He doesn't distinguish between facts and anecdotes and the author always lets his prejudices get in the way of narrative. I guess it just reflects the times in which it was written. The parts i liked the most of this book were the mathematical parts....more
An interesting overview of the practical and theoretical limits of logic, mathematics and science. Deals with the limits of knowability, determinism, An interesting overview of the practical and theoretical limits of logic, mathematics and science. Deals with the limits of knowability, determinism, computation and predictability in science and mathematics. This is a clear and concise study of various topics from classical logic to modern physics, but lacks a quest for deeper understanding. ...more
I read this book long ago. This is probably as close as one can get to give a light overiview of the seven problems recognised by the clay institute fI read this book long ago. This is probably as close as one can get to give a light overiview of the seven problems recognised by the clay institute for a million dollar prize. The author here takes up an impossible task of explaining these problems to a lay audience. Even if he didn't entirely succeed in this, this book can be used to spark someone's interest for deeper study. Worth the read at least for the chapters on Riemann hypothesis and the P vs NP problem....more
The first half of the book is a basic overview of modern physics and i moved through it quickly. He explores the current multiverse scenario in here. The first half of the book is a basic overview of modern physics and i moved through it quickly. He explores the current multiverse scenario in here. He classifies the multiverse into four categories. Level I multiverse consists of all the objects that lie beyond our cosmological horizon. Level II multiverse apparently consists of infinite number of Level I multiverses produced by inflation with different physical constants. Level III multiverse comes from the Everett interpretation of quantum mechanics. Everett interpretation actually makes some intuitive sense to me.
The second metaphysical part of the book where he presents his thesis is what i was looking forward to. His thesis seems to be that "our universe is a mathematical structure". He isn't just suggesting that our universe is described by mathematics but that it is mathematics, including us. There is nothing out there but mathematical relations, time is an illusion and nothing in the universe actually changes. This is where Level IV multiverse comes. All the structures that exist mathematically exist in the fourth level multiverse. All the structures that exist mathematically have the same ontological status.I found Tegmark's monism, an all-encompassing mathematical multiverse to be very appealing.
He comes to his idea of mathematical universe by reducing an empirical physical model of universe to mathematics. So for example, from what i understand, there are no objects such as quarks and leptons, but there are groups and the properties of quarks are described by the group. From this and considering the explanatory power of mathematics, a mathematical universe does make some intuitive sense. Perhaps the reason why mathematics is so successful in explaining our universe is because they are one and the same. I’m not sure that he made a convincing argument if everything can be reduced to mathematics ontologically. What about an emergent property like consciousness? His suggestion of mathematical self-aware structures didn't tell me much and his conjecture that Consciousness is a state of matter didn't make much sense to me. I never really understood what he means when he talks about subjective randomness and subjective immortality either. To whom is it subjective?
A lot of criticism for this book, as it seems to me, is that his theory is not "scientific". While i agree with this, it doesn't bother me. While there is nothing new or radical about Tegmark's mathematical monism, I was actually hoping that this book would be more mathematically and philosophically enlightening. But unfortunately there isn't much discussion about mathematical structures in here and this isn't a very good metaphysical treatise either. But if you are interested in an overview of modern physics, this is a very lucid and clear account. ...more
This is a well written biography of paul erdos, a prolific hungarian mathematician who spends over 19 hours a day doing mathematics and has published This is a well written biography of paul erdos, a prolific hungarian mathematician who spends over 19 hours a day doing mathematics and has published over 1400 papers. He was a man who had no home and had travelled around the world giving lectures and staying at his friends place's. To anyone who is interested in mathematics, this book is great and very fun to read....more
Loading...
