Fermat's Last Theorem by Simon Singh

This is the story of the puzzle that had confounded mathematicians since the 17th century. 
‘I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain.’
It was with these words, written in the 1630s, that Pierre de Fermat intrigued and infuriated the mathematics community. 
For over 350 years, proving Fermat’s Last Theorem was the most notorious unsolved mathematical problem, a puzzle whose basics most children could grasp but whose solution eluded the greatest minds in the world. 
Many people had tried and failed, including an 18th-century philanderer who was killed in a duel. 
An 18th-century Frenchwoman made a major breakthrough in solving the riddle, but she had to attend maths lectures at the Ecole Polytechnique disguised as a man. 

In 1963, a schoolboy Andrew Wiles browsing in his local library stumbled across Fermat's Last Theorem. Aged just ten, he dreamed he would crack it.
In 1993, after years of secret toil, Andrew Wiles  announced to an astounded audience that he had cracked Fermat’s Last Theorem. 
The solution of the Theorem was one of the most important mathematical developments of the 20th century. 
In ‘Fermat’s Last Theorem’ Simon Singh has crafted a remarkable tale of intellectual endeavour spanning three centuries, and a moving testament to the obsession, sacrifice and extraordinary determination of Andrew Wiles: one man against all the odds.

[Book Description Source: www.amazon.com  and www.amazon.in] 


Ratings
Goodreads Rating - 4.21 out of 5 (17,874 Ratings; 739 Reviews - As on February 18 2017)
My Rating:  4 out of 5
My Comments:  Gripping narration about an esoteric mathematical subject. Not a single dull moment throughout the book.


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The Universe Inside You - Brian Clegg

The Extreme Science of the Human Body From Quantum Theory to the Mysteries of the Brain
Built from the debris of exploding stars that floated through space for billions of years, home to a zoo of tiny aliens, and controlled by a brain with more possible connections than there are atoms in the universe, the human body is the most incredible thing in existence.
In the sequel to his best-selling Inflight Science, Brian Clegg offers a spectacular tour through the human body.
He explores mitochondria, in-cell powerhouses once separate creatures; 
how your eyes consume million-year-old photons of light;
your many senses, which include the ability to detect warps in space and time; and why meeting an attractive person can turn you into a gibbering idiot.

Read The Universe Inside You and you'll never look at yourself the same way again.

[Book Description Source: www.amazon.com ]  

Ratings
Goodreads Rating - 3.7 out of 5 (171 Ratings, 19 Reviews)

My Rating:  3 out of 5. 


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Physics of the Impossible by Michio Kaku

A Scientific Exploration into the World of Phasers, Force Fields, Teleportation, and Time Travel

A fascinating exploration of the science of the impossible—from death rays and force fields to invisibility cloaks—revealing to what extent such technologies might be achievable decades or millennia into the future.

One hundred years ago, scientists would have said that lasers, televisions, and the atomic bomb were beyond the realm of physical possibility.
In Physics of the Impossible, the renowned physicist Michio Kaku explores to what extent the technologies and devices of science fiction that are deemed equally impossible today might well become commonplace in the future. 
From teleportation to telekinesis, Kaku uses the world of science fiction to explore the fundamentals—and the limits—of the laws of physics as we know them today.
He ranks the impossible technologies by categories—Class I, II, and III, depending on when they might be achieved, within the next century, millennia, or perhaps never.

 In a compelling and thought-provoking narrative, he explains:

• How the science of optics and electromagnetism may one day enable us to bend light around an object, like a stream flowing around a boulder, making the object invisible to observers “downstream”
• How ramjet rockets, laser sails, antimatter engines, and nanorockets may one day take us to the nearby stars
•  How telepathy and psychokinesis, once considered pseudoscience, may one day be possible using advances in MRI, computers, superconductivity, and nanotechnology.
• Why a time machine is apparently consistent with the known laws of quantum physics, although it would take an unbelievably advanced civilization to actually build one.

Kaku uses his discussion of each technology as a jumping-off point to explain the science behind it. 

An extraordinary scientific adventure, Physics of the Impossible takes readers on an unforgettable, mesmerizing journey into the world of science that both enlightens and entertains.

 [Book Description Source: Goodreads]

Goodreads Rating - 4.05 out of 5 (16,711 Ratings, 789 Reviews)

My Rating:  3 out of 5. 

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Why Life Speeds Up as You Get Older - Douwe Draaisma

How Memory Shapes Our Past
Is it true, as the novelist Cees Nooteboom once wrote, that 'Memory is like a dog that lies down where it pleases'?
Where do the long, lazy summers of our childhood go? 
Why is it that as we grow older  time seem to condense, speed up, elude us, while in old age, significant events from our distant past can seem as vivid and real as what happened yesterday?
 In this enchanting and thoughtful book, Douwe Draaisma, author of the internationally acclaimed Metaphors of Memory, explores the nature of autobiographical memory. 
Applying a unique blend of scholarship, poetic sensibility, and keen observation, he tackles such extraordinary phenomena as deja-vu, near-death experiences, the memory feats of idiot savants, and the effects of extreme trauma on memory recall. 
Raising almost as many questions as it answers, this fascinating book will not fail to affect you at the same time as it educates and entertains.
[The above book description is as per the one on the book cover]


Goodreads Rating - 3.70 out of 5 (124 Ratings; 7 Reviews)

My Comments:
Certainly this book has essays on lots of interesting topics on memory. And that's the reason I picked up this book from the library after reading the above description on the book cover.

While the content is good , the book did not meet my expectation probably because the translation from the original book in Dutch language was not up to the mark.

There may be better books than this on this subject.Need to hunt around.

Links:

• Table of contents

• Excerpts from the Chapter 1 - Memory is the dog that lies down where it pleases

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Rock, Paper, Scissors -Game Theory in Everyday Life

[Author: Len Fisher; Publisher: Hay House; Hardcover: 288 pages ]

Game theory is the study of strategic decision making. 
It has been extensively used to explain many behavioral patterns in 
economics, political science, psychology and biology.
Even in our day to day life game theory can guide us towards effective strategies to use in situations of competition and conflict.

But this book explores the other side of the game theory that concerns  cooperation rather than conflicts, collaboration rather than competition.

Len Fisher, the author discusses how game theory can help us develop 

fresh strategies for cooperation.

The book begins with a chapter that explains Nash equilibrium concepts. 
Nash equilibrium is a situation created during  interaction among two or more parties where at least one party fares worse but from which it can't escape without faring  still worse. This happens when every party acts out of self-interest leading to many serious social dilemmas and problems. 

The next chapter discusses the ways to divide resources fairly using strategies as I Cut and You Choose and shows that we can't rely on external authorities or on our own sense of fairness to produce lasting cooperation. Rather we need to explore how  our own self-interest can be used to make the cooperation self-enforcing.

The third chapter uses game theory to examine how social dilemmas actually arise. Seven social dilemmas are discussed viz;  The Prisoner's Dilemma, The Tragedy of Commons, The Free Rider, Chicken, The Volunteer's Dilemma, The Battle of the Sexes and the Stag Hunt. 

The next four chapters deal with  strategies  for cooperation that include a variant of Rock, Paper, Scissors game, new methods of cooperative bargaining, methods for eliciting trust, and the use of tit-for-tat strategies. The author discusses how such strategies emerge and how to use them to promote cooperation rather than confrontation in the society. 

Then follows a chapter that investigates the possibility of  avoiding  social dilemmas by changing the game itself, either by introducing new players or by applying quantum theory concepts. 

In the last chapter author presents his personal top ten list of tips for effective strategies in different situations which are as follows.

1. Stay if you win, shift if you loose
2. Bring an extra player in
3. Set up some form of reciprocity
4. Restrict your own future options so that you will lose out if you defect on cooperation.
5. Offer trust
6. Create a situation that neither party can independently escape from without loss
7. Use side payments to create and maintain cooperative conditions
8. Be aware of the seven deadly dilemmas, and try to reorganize the benefits and costs to different players so that the dilemma disappears
9. Divide goods, responsibilities, jobs, and penalties so that the result is envy-free
10. Divide large groups into smaller ones 

I really liked the writing style of the author which is easy to understand, humorous and autobiographical (since many game theory examples are drawn from his personal life).

 

Some  alternate titles for this book could be "Game Theory for Dummies" or "Game Theory Without Tears"

 

I highly recommend this book to anyone who wants to know the basics of game theory in a quick and interesting manner.

 

 Links 

• Author's Website
• Goodreads Ratings and Reviews -  Average Rating 3.33 / 5;  437 ratings; 73 reviews

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The Code Book

Author:      Simon Singh
Published:  1999
Publisher:   Fourth Estate Limited
Hardcover: 416 pages

The need for information security which is  widely recognized in this Internet Age is not a new need at all. It,though not as pervasive as today,  has existed for thousands of years and has a fascinating history of its own.


The high risk of secret and confidential messages sent by kings, queens and army generals falling into the  hand's of the enemies led  to the development of codes and ciphers. This heralded the birth of  Cryptography which is a method of disguising a message in a manner that only the intended recipient can read it. To counter Cryptography the unauthorized message interceptors worked on breaking the code. Thus evolved the science and art of codebreaking i.e. Cryptanalysis.


So the entire history of cryptography is the story of ongoing battle between Cryptographers (code makers) and Cryptanalysts (code breakers). And this story - right from the origin of ciphers in ancient Greece till the recent advances (till 1999) in Quantum Cryptography- is brilliantly narrated by Simon Singh in this book.


Singh mentions in the introduction to the book the two main objectives of his writing this book.
The first one is to chart the evolution of  codes. He describes how the battle between codemakers and code breakers involved diverse range of disciplines like mathematics, linguistics, information theory, quantum theory etc. and their associated technologies and inspired a series of remarkable scientific breakthroughs. He also enthralls us with " stories of political intrigue and tales of life and death to illustrate the key turning points in the evolution of codes", just to mention a few - the Babington Plot, the unbroken Beale Cipher, cracking of the Enigma code by  Alan Turing (of the well known Turing Test fame), decipherment of Egyptian hieroglyphics through Rosetta Stone.
The second objective of the author is to demonstrate how the subject of cryptography is as relevant today as it was before. Apart from providing one of  the best explanation I have ever come across of the prevalent encryption algorithms , standards and techniques  like DES, RSA, PGP, he explores the promising Quantum cryptography which can lead to unbreakable ciphers. He also discusses the debate between two schools of thought - one which lobbies for  restricting   the use of cryptography to ensure law enforcement and national security and the one which presses for its widespread use to protect the privacy of the individual.


This book also introduces us to the tireless cryptographers and cryptanalysts who had to remain anonymous  and never gained public recognition during their lifetimes. This was due to the politically or militarily sensitive nature of their contributions and inventions which could not be disclosed to public.
For example, by 1975, James Ellis, Clifford Cocks and Malcolm Williamson working for Britain's Government Communications Headquarters (GCHQ) had discovered all the fundamental aspects of public-key cryptography. Yet they all had to remain silent since their work was a classified information. They had to sit back and watch as Rivest, Shamir and Adleman the researchers in MIT rediscovered their discoveries over the next three years and became famous in cryptographic circles for their RSA algorithm.
Similarily during Second World War, the work of Max Newman and Tommy Flowers resulted in development of Colossus machine in Britain. Colossus was a precursor to the modern digital computer. Yet it was destroyed after the war and those who worked on it were forbidden to talk about it. This secrecy on the part of British Government meant that Eckert and Mauchly of the University of Pennsylvania got the credit for the invention of the first digital computer- ENIAC.


The technical concepts in this book are very lucidly explained and should no pose problems for a lay reader. Also an extensive list of further readings has been provided for the readers who seek more details. 


One of the most interesting books I have read this year. It has sparked an interest for Cryptography in me. Hence strongly recommend it as an introductory book on history and concepts of Cryptography and Cryptanalysis !


Useful Links:
Cryptography section of the author's website which has :

• information about the TV series based on this book (The Science of Secrecy)
• some cryptograms(coded messages) for you to try and crack
•  a free downloadable CD-ROM version of The Code Book.

An Interesting Trivia from the Book:
Alan Turing (of the well known Turing Test fame) was conceived in the autumn of 1911 in India, where his father was a member of Indian civil service. His parents were determined that their child should be born in Britain, and returned to London, where Alan Turing was born on 23 June 1912 !

25 Big Ideas - the Science that's Changing our World

Author:         Robert Matthews

Published:   2007

Publisher:    Oneworld Publications

Paperback: 200 Pages

The 25 Big Ideas described in this book are based on the discoveries which make a point that the universe in which we live in is magical, bizarre, strange and defies common sense. These ideas have challenged many eminent scientists and mathematicians. These ideas prove that in reality science is not as objective as it is made out to be but it has its own uncertainties and subjectivity since it is a human endeavor. There is still a long way to go before we understand completely our universe.

The book consists of 25 chapters (one for each idea) categorized under the following heads as follows:

• Ourselves - and Others: Consciousness, Small World Theory, Game Theory
• Doing the Impossible: Artificial Intelligence, Information Theory, GM Crops
• Life: Out of Africa, Nature versus Nurture, The Selfish Gene
• The Earth: Catastrophism, Plate Tectonics
• Mathematics that Counts: Bayes's Theorem, Chaos, Cellular Automata, Extreme Value Theory
• In Sickness and in Health: Evidence-based Medicine, Epidemiology
• The Physics of Reality: Special Relativity, Quantum Entanglement, The Standard Model, The Theory of Everything
• The Universe- and Our Place In It: The Big Bang, Dark Energy, Parallel Universe, The Anthropic Principle

Each chapter is brief (6-8 pages) and self-contained. It begins with a very succinct summary which introduces the idea in a nutshell and explains it relevance in our day to day life. This serves as an appetizer for the the reader to proceed with the chapter. The chapter then takes us through the story of how the idea evolved, its current state of understanding. It also explains the associated technical terms  and provides suggestions for further reading.

A very well-written book which attempts to explain the abstruse ideas in a very interesting manner . But it requires the reader to have at least a high-school level knowledge of science and mathematics to fully appreciate and enjoy it.

Useful Links:

• Summary of all the Ideas and Further Readings
• Sample Chapter  :  Consciousness.

Profiles of the Future - An Inquiry into the Limits of the Possible

Author:      Arthur C. Clarke

Published:  1965

Publisher:   Bantam

Paperback: 240 pages

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Readers in India

 

The author Arthur C. Clarke a renowned science fiction author who was also a distinguished scientist and inventor wrote the first edition of this book  way back in 1962 . Subsequently he updated it a few times to sync up with the latest developments in science and technology. The 1965 edition which I just finished reading, was purchased by my dad in mid-sixties. And having  just glanced at the cover of this book off and on over the last 40 years, it is only recently I chose to read it.

It was a cumbersome read in the sense that the book being almost as old as me , the binding had become weak and  its pages were falling apart every time I  turned them ! But what a  fascinating forecast of  what future has in store for us !

The predictions made by the author of the future are very imaginative and yet have a firm grounding on the laws of science and technology. He talks about - the fourth dimension, conquering  the laws of gravity, the exploration and colonization of  outer spaces,  mining the seas for energy and minerals, pulling asteroids to Earth to supply needed materials, breeding smaller size and more efficient men who consume

less food etc.

 When you read  this book , you will be astounded by author's vision. Some of his predictions have already come true, some are closer to becoming true and some are still  in the realm of fantasy.

 Here I would just quote a few extracts from Chapter 16 of this book - The Voices from the Sky. Just bear in mind that he wrote this in early 1960s

1. "In a few years every large nation will be able to establish  (or rent) its own space-borne radio and TV transmitters, able to broadcast really high-quality programs to the entire planet."

2. "The advent of global TV and radio coverage will end, for better or worse, the cultural or political isolation which still exists over the whole world, outside the great cities."

3. "... the time will come when we will be able to call a person anywhere on Earth, merely by dialing a number. He will be located automatically, whether he is in mid-ocean, in the heart of a great city, or crossing the Sahara."

4. "The business of the future may be run by executives who are scarcely ever in each other's physical presence. It will not even have an address or a central office - only the equivalent of a telephone number. For its files and records will be space rented in the memory units of computers that could be located anywhere on Earth:"

5."And so the captains of industry of the twenty-first century may live where they please, running their affairs through computer keyboards and information handling machines in their homes"

6. "The time will certainly come when surgeons will be able to operate a world away from their patients,..."

7. "Modern facsimile systems can automatically transmit and reproduce an equivalent of an entire book in less than a minute."

Wow ! Clarke  had  predicted - sattelite TVs, globalization, mobile phones, internet, telecommuting, telesurgery, e-books at least 20 years before they became a world-wide reality.

And I am glad that he lived to see these predictions come true in his lifetime. He passed away just two years back in 2008 at the ripe old age of 90.

However I could not say the same for my dad . He passed away in 1981. He was just 53.  I am sure he would have enjoyed the realization of the predictions he read in this book which he bought in mid-1960s.

I highly recommend this book to all the science and technology enthusiasts  and lay readers who have a flair for imagination.