Literate Scientist

Because I plan my own engineering autobiography I now started reading various biographies and autobiographies to see what people write there. This month I started reading the biography of P. A. M. Dirac. I usually read a chapter or two during my lunch time and so far progressed to the page 184. The book is very interesting and I’m looking forward for the next lunch to read next chapter every day.

The Strangest Man: The Hidden Life of Paul Dirac, Quantum Genius

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I was always intrigued by String Theory since 90s when my boss at Interactive Products, Inc., the physicist in the past, mentioned that in that theory mathematical apparatus changes every 6 months. While waiting for a flight in London Heathrow airport in 2002 I bought a popular book “The Elegant Universe” by Brian Greene. Later I read two books about String Theory Not Even Wrong and the Trouble With Physics that criticise the theory. Last year I also read The Road to Reality that has a few critical chapters about String Theory. However I always wanted to understand the mathematics behind the theory and see derivations. And I was delighted when the first edition of Barton Zwiebach’s book appeared in print and I immediately bought it. Although I read only a few chapters of it and never finished it, when the second edition came out I bought it too and started reading the book again. I hope to finish it this year.

A First Course in String Theory

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These two volumes I bought a few years ago, started reading the first chapter and then other books got reading priority, for example, Rosen’s “Life Itself”. A few weeks ago I picked up the first volume again and started reading from the beginning. I’m was really amazed how I understand it better after reading Rosen’s books. These volumes are highly recommended to learn about models of reality and mathematical modeling itself. The first chapter that discusses the relationship of models to observation is awesome. The book requires an undergraduate engineering level of mathematics: linear algebra, calculus and a bit of mathematical analysis. You will also learn about catastrophe-theoretic models, chaos, cellular automata, geometry of human affairs, patterns, fractals, and many other things. There is even a discussion about controversies in catastrophe theory involving Rene Thom. I think the first volume of this book set is a prerequisite reading before starting with classic Structural Stability And Morphogenesis.

Reality Rules, 2 Volume Set

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OpenTask plans to publish the extended and edited version of this blog as a book:

Literate Scientists and Their Books: An Independent Guide to Understanding Reality (ISBN: 978-1906717520)

- Dmitry Vostokov @ LiterateScientist.com -

Robert Rosen mentioned this book in his Essays on Life Itself which I’m reading now (Chapter 9, Genericity as Information) and I immediately ordered it. It arrived today and a brief glance at it convinced me that I shall start reading it now as it might give some additional insight into Rosennean Complexity. I hope to write more about this book and ideas it will have brought to me when I finish reading it.

Structural Stability And Morphogenesis (Advanced Books Classics)

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This is my second Rosen’s book and I started reading on 1st of September, 2008, a year after I read “Life Itself”. Essays were written after the latter book and were intended to clarify it. Therefore if you are about to start reading Rosen’s works it is probably better to read essays first. I’m almost halfway through it and particularly like the discussion about mimesis, its roots and history. This is highly recommended book to read and if you were trained in chemistry, physics and computer science like myself you would find revelations on every page and would never look at modern science with the same eyes again.

Essays on Life Itself

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If you ask me now what book I recommend for a broad overview of mathematics I would not hesitate to point to this latest book that I just started reading:

The Princeton Companion to Mathematics (Hardcover)

Although it is 1000 page book with two columns of text it is actually intended to be read from cover to cover! This book is now on top of my math overview recommendations which previously included these books:

• The Road to Reality
• Comprehensive Mathematics for Computer Scientists
• Mathematics: Form and Function
• All the Mathematics You Missed
• The Nature and Growth of Modern Mathematics

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This is out-of-print book that is hard to find now. I was very keen and fortunate to buy it from a 3rd-party seller a few years ago and immediately read it then. It gives great overview of modern mathematics from the perspective of the founder of category theory. The similar overview of modern mathematics can be found in The Road to Reality, 2 volumes of Comprehensive Mathematics for Computer Scientists and the recent 1000 page “The Princeton Companion to Mathematics”. One note that I didn’t like is the following passage from page 439:

“Not all outside influences are really fruitful. For example, one engineer came up with the notion of a fuzzy set…”

Mathematics: Form and Function

Here is the table of contents showing the breadth of material:

CHAPTER I
Origins of Formal Structure
The Natural Numbers
Infinite Sets
Permutations
Time and Order
Space and Motion
Symmetry
Transformation Groups
Boolean Algebra
Calculus, Continuity and Topology
Human Activity and Ideas
Mathematical Activities
Axiomatic Structure

Chapter II From Whole Numbers to Rational Numbers
Properties of Natural Numbers
The Peano Postulates
Natural Numbers Described by Recursion
Number Theory
Integers
Rational Numbers
Congruence
Cardinal Numbers
Ordinal Numbers
What Are Numbers?

Chapter III Geometry
Spatial Activities
Proofs without Figures
The Parallel Axiom
Hyperbolic Geometry
Elliptic Geometry
Geometric Magnitude
Geometry by Motion
Orientation
Groups in Geometry
Geometry by Groups
Solid Geometry
Is geometry a Science?

Chapter IV Real Numbers
Measures of Magnitude
Magnitude as a Geometric Measure
Manipulations of Magnitudes
Comparison of Magnitudes
Axioms for the Reals
Vector Geometry
Analytic Geometry
Trigonometry
Complex Numbers
Stereographic Projection and Infinity
Are Imaginary Numbers Real?
Abstract Algebra Revealed
The Quaternions - and Beyond
Summary

Chapter V Functions, Transformations, and Groups
Types of Functions
Maps
Whats is a Function?
Functions as Sets of Pairs
Transformation Groups
Groups
Galois Theory
Construction of Groups
Simple Groups
Summary: Ideas of Image and Composition

Chapter VI Concepts of Calculus
Origins
Integration
Derivatives
The Fundamental Theorem of the Integral Calculus
Kepler’s Laws and Newton’s Laws
Differential Equations
Foundations of Calculus
Approximations and Taylor’s Series
Partial Derivatives
Differential Forms
Calculus Becomes Analysis
Interconnections of the Concepts

Chapter VII Linear Algebra
Sources of Linearity
Transformations versus Matrices
Eigenvalues
Dual Spaces
Inner Product Spaces
Orthogonal Matrices
Adjoints
The Principal Axis Theorem
Bilinearity and Tenso Products
Collapse by Quotients
Exterior Algebra and Differential Forms
Similarity and Sums
Summary

Chapter VIII Forms of Space
Curvature
Gaussian Curvature for Surfaces
Arc Length and Intrinsic geometry
Many-Valued Functions and Riemann Surfaces
Examples of Manifolds
Intrinsic Surfaces and Topological Spaces
Manifolds
Smooth Manifolds
Paths and Quantities
Riemann Metrics
Sheaves
What Is Geometry?

Chapter IX Mechanics
Kepler’s Laws
Momentum, Work, and Energy
Lagrange’s Equations
Velocities and Tangent Bundles
Mechanics in Mathematics
Hamilton’s Principle
Hamilton’s Equations
Tricks versus Ideas
The Principal Function
The Hamilton-Jacobi Equation
The Spinning Top
The Form of Mechanics
Quantum Mechanics

Chapter X Complex Analysis and Topology
Functions of a Complex Variable
Pathological Functions
Complex Derivatives
Complex Integration
Paths in the Plane
The Cauchy Theorem
Uniform Convergence
Power Series
The Cauchy Integral Formula
Singularities
Riemann Surfaces
Germs and Sheaves
Analysis, Geometry, and Topology

Chapter XI Sets, Logic, and Categories
The Hierarchy of Sets
Axiomatic Set Theory
The Propositional Calculus
First Order Language
The Predicate Calculus
Precision and Understanding
Godel Incompleteness Theorems
Independence Results
Categories and Functions
Natural Transformations
Universals
Axioms on Functions
Intuitionistic Logic
Independence by Means of Sheaves
Foundation or Organization?

Chapter XII The Mathematical Network
The Formal
Ideas
The Network
Subjects, Specialties, and Subdivisions
Problems
Understanding Mathematics
Generalization and Abstraction
Novelty
Is Mathematics True?
Platonism
Preferred Directions for Research
Summary

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If you ask me to recommend the only one semi-popular book about modern physics that has everything in it and explaining all necessary mathematics too I would not hesitate to point to Roger Penrose’s book:

The Road to Reality: A Complete Guide to the Laws of the Universe

It is not a light read and requires some mathematical maturity. It has more than 1,100 pages and my first attempt to read it in 2005 when I bought a hardcover edition lasted until the page 160. Since then I read many other popular and semi-popular physics and math books and now feel more confident. I started reading it again last week from the first page before tackling with The Anthropic Cosmological Principle book which is heavy on general relativity and it reads very well now. Therefore I would recommend not to give up reading this book and even read it couple of times to thoroughly understand various mathematical ideas and their connection with physics. It is well worth it if you are keen to understand modern science. There is no other science book with the same breadth and depth covering both physics and mathematics. It looks like it springed various smaller books like The Comprehensible Cosmos I read earlier.

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If you want to learn about standard model of particle physics and understand associated concepts including QED and QCD, Lie groups and gauge theory this popular book is down to the facts and non-speculative: it even barely mentions string theory.

Deep Down Things: The Breathtaking Beauty of Particle Physics

I read it in succession to another similar great popular book that uses a bit more math but in addition lucidly explains special relativity that was only briefly touched in Deep Down Things book:

The Great Design: Particles, Fields, and Creation

I read both books last year and now I’m reading Roger Penrose’s book The Road to Reality and review it as soon as I finish.

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