Literate Scientist

I admit Semiotics is the big gap in my education which mostly lies in natural and computer sciences. I know less about social sciences and try to fill various gaps. The reason why I came upon this discipline is that I’m interested in signs and their interpretations, especially their relation to various structures. I started reading this book in September and almost read 1/3rd of it during my flight to Russia via Zurich.

Semiotics: The Basics

As a by-product of reading I was able to provide a kind of theoretical explanation for the phenomenon of bugtations:

Bugtations: a semiotic approach

- 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)

- Dmitry Vostokov @ LiterateScientist.com -

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

- Dmitry Vostokov @ LiterateScientist.com -

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

- Dmitry Vostokov @ LiterateScientist.com -

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

- Dmitry Vostokov @ LiterateScientist.com -

This is encyclopedic work I bought a few months ago in a local book shop and just started reading. Highly recommended for education and another view on human history.

Ideas: A History of Thought and Invention, from Fire to Freud

The second encyclopedic book seems was written before the previous one but looks like the logical sequel to it. I start reading it as soon as I finish “Ideas”.

The Modern Mind: An Intellectual History of the 20th Century

- Dmitry Vostokov @ LiterateScientist.com -

I remember from my school days during Soviet Union times about pollution in dying capitalist societies. I came upon this book a few years ago while preparing for my environmental study assignment in University. Being curious about diverse reviews I bought this book. I started reading it a few months ago during my lunch time and I would recommend it to everyone to learn how to do statistics right.

The Skeptical Environmentalist: Measuring the Real State of the World

- Dmitry Vostokov @ LiterateScientist.com -

Thorough understanding of evolutionary theory and its applications to other disciplines was one of omissions in my education besides vague recollection of what I learnt at school 20-25 years ago. I actually remember pictures from Darwin’s books I looked at when I was a child I bought this book and started reading after seeing many references to it in Breaking the Spell from the same author. Currently I’m halfway through it. As far as I understand Dennett’s view of evolution is the computational one. Anyway there is much to learn from this book.

Darwin’s Dangerous Idea: Evolution and the Meanings of Life

- Dmitry Vostokov @ LiterateScientist.com -

I’ve never read anything about religion since earlier school probably 25 years ago and my education was almost materialist-marxist-leninist. However I recently became interested in various religions mostly because of the diverse workplace and my ongoing philosophical education. I stumbled upon this book in a local shop, bought and started reading while commuting to work. Halfway through I became interested in evolutionary theory and learnt about meme. Because of so many references to Dennett’s earlier book I put it aside after I finished the first two parts and I think I come back to the last third one called “Religion Today” after I finish “Darwin’s Dangerous Idea” book.

Breaking the Spell: Religion as a Natural Phenomenon

- Dmitry Vostokov @ LiterateScientist.com -

I’m the father of two and very interested in understanding what kind of parenting my children need. What amount of pressure do they need? What is the difference between the Soviet-type school I attended in 1977 - 1987 and the modern school? This is why I bought this book in a local bookshop a few months ago, started reading this month and already halfway through. Very interesting read. Even applicable to work as well. More pressure - less creativity. I really liked debunking the myth of multitasking.

Under Pressure: Rescuing Our Children from the Culture of Hyper-Parenting

- Dmitry Vostokov @ LiterateScientist.com -