Why Don't They . . .

Expand the organizing capability of my Nokia phone to have more memory and more options.  I'd like multiple lists in place of the single to-do list, and I'd like sublists of list items.  I'd like for priority classes to be expanded from three to any number.  I'd like ranking by both importance and urgency.  I'd like for an alarm to be attachable to any item.

Attach GPS capability to a camera so that location as well as time is automatically recorded.  Also make easy provision for adding tags or descriptions on the spot.  If this is too hard, have a separate hand-held gadget into which to insert the SD card for that purpose.  Have a photo printer which will print the picture on the front and the data on the back.

Have a wireless remote for the camera allowing for complete control including LCD viewing.  Likewise for the tripod.

Have a label printer attachable to multiple devices by cord or preferably wireless.  Make it portable.

Build an interface to multiple devices smaller than a netbook (much smaller).  Make keyboards and displays separate devices.  Make all devices handheld.

Make a wireless phone that is just a phone (with connections) - no camera and no games or gadgets.

How about a phone that will serve as a remote control for multiple devices.

A flexible time recorder that will automatically record a variety of preset items.  Add a USB port, a bar-code reader, an SD card slot, and a credit-card reader.

Have a calendar in some hand-held device with enough storage to also serve as a journal.

In other words, divide and combine in new ways for the most functional set.  Make some or all of them programmable.

And, finally, why aren't gutters made to rotate for easy dumping?

Oh, I'd also like a robot that would keep my driveway clear of snow.

What to Get The Man Who Has Everything

A bag to keep it in
Something to eat or drink
The address of your favorite charity
Praise
A hand (help)
A hand (clapping)
A kiss
A piece of your mind
Pictures of yourself or his grandchildren
The time of day
A willing ear
What for
A poem you have written
Five
Undying love

What's wrong with this picture?

The small blue square on the left is what I bought from Staples.  The rest is all packaging.

What is a Lie group?

The most general definition of a Lie group is a group that is also a smooth manifold.  Do you suppose that will satisfy my girl friend who asked what my new book was about?

Quaternions

Quaternions are an extension if the concept of complex numbers into four dimensions.  The algebra of quaternions was discovered by Hamilton in 1843, a hundred years before I graduated from High School, so why hadn't I heard of them when I got my Masters in Mathematics.  Better late than never.

The Two-Square Identity

I just learned that

(a sum of two squares) x (a sum of two squares) = (a sum of two squares)

More specifically

(a squared + b squared) x (c squared  + d squared) = (ac - bd) squared + (ad + bc) squared

I thought that was cool.

cos(alpha + beta)

I remember quite a bit of trig including some of the derivates and the Taylor expansions, but not the formulas for the sums of angles or their derivations.  Simple ones exist based upon rotations of the complex plane, but I wanted a straight geometric one.  I found one described by M. Bourne based on the unit circle abbreviated as follows:

We draw a circle with radius 1 unit, with point P on the circumference at (1,0).
We draw an angle alpha from the centre [sic] with terminal point Q  at (cos alpha, sin alpha).
We extend this idea by drawing:
   The angle beta with terminal points at Q (cos alpha, sin alpha) and R (cos(alpha + beta), sin(alpha + beta))
   The angle -beta with terminal point at S (cos -beta, sin -beta)
   The lines PR and QS which are equivalent in length.

Now we have
   PR squared = cos(alpha + beta) squared + sin(alpha + beta) squared
         = 2 - 2cos(alpha + beta)
    QS squared = (cos(alpha) - cos(-beta)) squared + (sin(alpha) - sin(-beta)) squared
         = 2 - 2 cos alpha cos beta + 2sin alpha sin beta

So cos(alpha + beta) = cos alpha cos beta - sin alpha sin beta.

If you remember some trig and draw your own diagram you will see that it works.

Society of Actuaries

I am a former member (an FSA) who dropped out when I was no longer working in the field.  Today I visited their on-line site and barely recognized the place.  I had hoped to find reference material for the underwriting part of an exam, but apparently there is no equivalent in the current syllabus.  Also they have added a new designation in addition to ASA and FSA.  I'm just as happy that I left when I did.  Of course I am retired now.

Hobbling Along

About three weeks ago I stumbled over a box in the basement and hit my left knee on a wooden stool.  Just as I was about recoved, about a week and a half ago, as I was climbing a carpeted stairway my right foot slipped and I fell on the left knee again I think bending it back further than it wanted to go.  This time there was swelling which has now gone down.  Oddly, there were no purple bruises either time.  I'm doing fairly well again although when I go up a step the right leg has to do the lifting.  Although I got to the mailbox a couple of times avoiding the icy spots and ran an errand for which I didn't have to leave the car, today is the first day I drove to McDonalds for coffee.  It was a test of what you can do while housebound and living alone.  A friend did grocery shop for me once and has offered to do more.  A phone and being able to go on line both help.  Also the attached garage.

The Red Guitar

This is a picture my late wife obtained from her friend, Carol Hedges, mother of Peter Hedges who wrote What's Eating Gilbert Grape and An Ocean in Iowa.  I remember an event at our house at which Carol "supervised" us and a group of our friends in painting murals on the walls of a room that was about to be paneled.  If the people who own the house now (or later) ever decide to remove the paneling, they are in for a surprise.

Naive Lie Theory

I just bought a book with that title.  It is one ot the Springer Undergraduate Texts in Mathematics and is by John Stillwell, Professor of Mathamatics at the University of San Francisco.  It is just what I needed.  It has, in the first two chapters, clarified ideas that I knew something about, especially quaternions and simple groups.  I find his end-of-chapter discussions interesting.  When I finish I should be in a position to understand a book I already had called Symnetry and The Monster by Mark Ronan.

In the Preface he mentions another book called Naive Set Theory by Paul Halmos.  Maybe I'll get it to.