Friday May 23, 2008 7:00 am Lethbridge, Alberta

It is +7 C with a high forecast of +10 C. Sunrise 5:36 Sunset 21:20 Hours of daylight: 15:44.
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This page last updated on: Saturday, May 24, 2008 7:05 AM

A. Morning Musings

The light rain continues unabated. We had almost an inch yesterday and are expecting more of the same for the next two days. This will be very good for the land.

I have a coffee set for 8:30 this morning at the Ugly Mug. It will be good to get back into that routine.

I am feeling refreshed and perky this morning. No chores around the house that I can think of. A good day for working on a couple of the "long term activities". This might also be a good day for having a look at my model train layout. I think that one of the activities there would be to install a digital module for controlling 4 of my turnouts. I also should get back to some serious mathematics.

Long Term Activities	Planned Activities for Today	Cumulative Total
Cull professional articles	Review Psychology articles	5 hr
Prepare pdf files of my papers	Digitize 3 professional papers	4 hr
Digitize slides	Digitize slide collection	10 hr
Put away stamps		0 hr

Learning Category	Planned Activities for Today	Time
Literature	Begin morning with a Rumi reading
Puzzles & Games	New York Times crossword puzzles	1 hr
Literature	Continue reading "The Temptations of Big Bear" by Rudy Wiebe	2 hr
History	Begin reading "Indian Fall" by D'Arcy Jenish	1 hr
Mathematics	Make a few notes on symmetry	1 hr
Mathematics	Continue reading "Symmetry & the Monster	1 hr

B. Actual Learning Activities

7:00 am

Notes on Symmetry - 13

Dale Burnett

I want to make a quick note of a few principles underlying my approach to learning.

1. I build on what I already know.

2. I identify what I want to learn next.

3. I locate resources relevant to #2, based on #1.

4. I use a mix of "reading" and "doing" until I am satisfied.

That is pretty well it. But it is radically different from what occurs in most schools as I, the learner, am in control of what happens next. I set my own goals, select my own resources (which may involve discussing what I am doing with someone who is more familiar with the topic - i.e. a teacher), and follow my own schedule. And I am continually modifying all of these parameters as I proceed.

I have recently finished reading Marcus du Sautoy's book "Symmetry", but the last few chapters left me cold as I no longer felt I understood what the various people were doing as they began to identify the various symmetries that were possible in higher dimension and I had trouble imagining what they were talking about when they discussed "the monster". I have one more book that discusses this object. It is time to give that a close look. Then I need to return to more basic activities related to symmetry and group theory. I am beginning to think that the book on Fearless Symmetry as well as the online book on Algebra by Frederick Goodman are good places to focus. I also want to construct a few three-dimensional objects (the 5 platonic solids - tetrahedron, cube, octahedron, dodecahedron, icosahedron - would be a good start). I need to play with these a bit until they are firmly in my mind's eye. I should be able to close my eyes and visualize each of them, and to imagine rotating them along various axes of symmetry.

I now realize that I need to add a brief note for each entry in my Notes Index that identifies the major source of my notes for that day. At the moment I do not know which sessions contain information on my previous reading of the first 5 chapters of the Ronan book. Done. The table in the Notes Index for mathemtics now gives a much better sense of what I have been doing.

Date	Mathematics	History
500 BCE	Pythagorus
399 BCE	Thaetetus classifies the 5 regular Platonic solids in 3 dimensions: tetrahedron, cube, octahedron, dodecahedron, icosahedron.
1048 - 1131	Omar Khayyam finds geometric method for solving cubic equations.
1200	Leonardo Fibonacci wtote the first original book on mathematics published in Europe. It introduced Hindu-Arabic numerals and place-value notation.
1439		Gutenberg invents the printing press
1452 - 1519		Leonardo da Vinci
1492		Columbus discovers America
early 1500s	del Ferro, Tartaglia, Cardano, Ferrari solve cubic & quartic equations
1564 - 1642	Galileo
1642 - 1727	Isaac Newton
1775 - 1783		American War of Independence
1777 - 1855	Carl Friedrich Gauss
1789 - 1799		French Revolution
1802 - 1829	Niels Henrik Abel proves that no formula exists for equations of degree 5.
1832	Evariste Galois dies at age 20.
1842 - 1899	Sophus Lie: Norwegian group theorist

The goal today will be to reread the first 6 chapters of Ronan's book "Symmetry and the Monster" and then continue the book.

	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23
Symmetry
Fearless Symmetry
Algebra
Abstract Algebra
Creating Escher-type Drawings
Handbook of Regular Patterns
Symmetry & the Monster
The Celtic Design Book
Groups & Symmetry
Groups: A Path to Geometry
A Transition to Advanced Mathematics
Modern Abstract Algebra

Mark Ronan. (2006). Symmetry and the Monster.

I have read chapters 7 - 10 today. I will try to make a few notes tomorrow.

Tags: mathematics, symmetry

1:00 PM

There was a short break in the weather this morning. The grass was able to dry out enough to allow for a mowing. Done.

My reading of "The Temptations of Big Bear" has also triggered a memory of another book that I began a few years ago, and then other priorities entruded, called "Indian Fall". This is a history of the "last great days of the Plains Cree and the Blackfoot Confederacy" and overlaps with the story of Big Bear. What is even more embarrasing is that I have lived in that part of the province for 23 years (!) and have never read either of these books.

Now that the lawn is shorter, I can sit back and read from three books: