An Example of a "Learning Process" Journal (using the 2 colored box format)

"The Road to Reality " by Roger Penrose (Preface. pp. xv - xxi)

• "I have not shied away from presenting mathematical formulae. ... I have thought seriously about this question and have come to the conclusion that what I have to say cannot reasonably be conveyed without a certain amount of mathematical notation and the exploration of genuine mathematical concepts." [p. xv]
• "I am an optimist in matters of conveying understanding." [p. xvi]
• "... can see only the stern face of a parent or teaher who tried to force into them a non-comprehending parrot-like apparent competence - a duty, and a duty alone - and no hint of the magic or beauty of the subject might be allowed to come through." [p. xvi]
• "We cannot get any deep understanding of the laws that govern the physical world without entering the world of mathematics. ... It is for this reason that I have spent the first 16 chapters of this work directly on the description of mathematical ideas." [p. xix]
• "Do not be afraid to skip equations (I do this frequently myself) and, if you wish, whole chapters or parts of chapters, when they begin to get a mite too turgid!" [p. xix]
• "It is always the case, with mathematics, that a little direct experience of thinking over things on your own can provide a much deeper understanding than merely reading about them.
• http://www.roadsolutions.ox.ac.uk

This appears to be an amazing book! I first noticed it on a shelf in Chapters on Monday of this week. On Wednesday we were in Chapters in Calgary and I decided to buy it, together with another book that looked interesting: Group Theory and Chemistry. On Thursday I read the first two chapters of The Road to Reality and today (Friday) it is time to make a few notes.

The link provided has an apology for some of the misprints and errors with the References. Penrose hopes to begin adding the solutions section shortly.

Before making notes on the individual chapters, I want to try mapping out the overall structure of the content using Inspiration. Fascinating. There is no apparent structure in the Table of Contents, but there are a total of 34 chapters. I have created two columns, one for mathematics and one for physics, but I am not sure if I will be able to rearrange some of the nodes (or create additional links - more likely) as I read the chapters.

"The Road to Reality " by Roger Penrose (Chap. 1 The roots of science. p. 7 - 24)

• Key idea of chapter: "the remarkable relationship between mathematics and the actual behavior of the physical world" [p. 21]
• Map of the structure and ideas of chapter 1: The roots of science.

The diagram for this chapter is all I need for notes.

For each chapter I want to be sure to address the following points:

• Key idea in 1-2 sentences
• Concept map
• Important quotations
• Questions that occur to me
• References worth noting
• Web sites that might serve as supplements

In making the notes for chapter 1, I began with the important quotations (a selection of the better yellow-highlighted sections in the book). Then I tried to summarize the chapter in a sentence. I followed this with a concept map.

The following web site gives further information on the claim that R. Brooks & J. P. Matelski were the first to think of the Mandelbrot set:

http://www.nature.com/news/2004/041115/pf/432266a_pf.html#B4

Here is the actual reference:

Brooks, R. & Matelski, J. P. in Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference (eds Kra, I. & Maskit, B.) 65-71 (Princeton Univ. Press, Princeton, 1981).

I then bumped into these URLs while looking at other google hits:

http://www.fortunecity.com/emachines/e11/86/enm3.html

http://www.fortunecity.com/emachines/e11/86/newmath.html

http://fractals.iut.u-bordeaux1.fr/jpl/history.html

I located the first URL by using the two words Brooks Matelski in a google search. What a wonderful way to spend an hour!

Science Index