More W. R. Myers Marching Band Pictures

I went through old pictures today and found these pictures of the marching band, or of me in the marching band uniform. These are from either 1967 or 1968, in Taber, Alberta, Canada.

The above shows the band marching south, along 50th street, with the United Church of Canada in the background.

Marching towards the east, probably on the main street.

On the front steps of our farm house, which was located about 7 and a half miles north of Taber, along Highway 36. The house is still standing, and has changed owners a few times since our family moved out.

A portrait in the living room of the farm house.

These are digital scans of color prints, which have been cropped, but not retouched.

Blast from the past

Here is an old photograph. The original was taken using a chemical color process, around 1968.

Then, a color photocopy of that photograph was made in Lethbridge, around 2000.

Finally, the color photocopy was scanned today on an HP scanner.

What you see is the tail end of the W. R. Myers marching band, probably taken on parade day, around May 24, 1968.

The reason that I scanned it was to upload it to the facebook group "I was in W.R. Myers Band!"

However, it appears that one has to be a group "admin" in order to post photos. So, here it is.

While we're at it, here is one of me, in the same uniform, but without the beret. As you can see, I used to have a full head of hair!

Tour to Nauvoo

About a month ago, Sara and I flew to St. Louis, Missouri, for a two week vacation.

We spent just over a week in the Branson area, looking at possible retirement properties.

Then, we met a bus tour to Nauvoo, led by Susan Easton Black. It was very enjoyable.

Me beside a sunstone

Gifts from China

Elizabeth worked in China for a few months last year, and brought us some gifts when she returned. Thank you, Elizabeth.

There is a small wall hanging with, presumably, the text from Mark 10:9 ("What therefore God hath joined together, let not man put asunder") in chinese characters. A wonderful daily reminder.

Many other items in silk, as well, including some ties, place mats, and slippers.

And, Sara and I enjoyed putting together the wooden model of a chinese building, shown here:

Thanks again, Elizabeth.

Mechanics' Floating Point revealed

The eight bits in the pattern are used as follows:

S EEE MMMM

S is the "sign bit": 1 means negative, 0 means positive.

EEE are the "exponent": in "excess four" notation, meaning that the usual decimal interpretation of these bits is four more than the actual power of two. When all 8 bits are 0 the entire bit pattern represents the number zero. 001 means an exponent of -3 (i.e. a multiplier of ¹/₈), 010 mean -2, and so on, up to 111 which means an exponent of 3 (i.e. a multiplier of 8).

MMMM are the "mantissa": the fractional value which is multiplied by two to the exponent value. There is assumed to be a decimal point and a "1" bit to the left of MMMM. So, the pattern 0000 represents the fraction .10000 (i.e. ¹/₂). Similarly, the pattern 0001 represents the fraction .10001 (i.e. ¹⁷/₃₂), and on up to 1111, which represents the fraction .11111 (i.e. ³¹/₃₂).

In the table below, the exponent bit patterns label each of the columns. There are only 7 patterns because the bit pattern 000 means that the entire number is zero. This wastes some of the bit patterns because the entire 8 bits represent zero whatever bit patterns are present in the S and MMMM bit positions.

The mantissa bit patterns label each of the rows.

Each cell of the table shows the real number represented by the overall 8 bit pattern. Not shown are the negative numbers, which use the same bit pattern except for the sign bit.


This table can also be found at http://sanbachs.net/mfp/mfp.html.

Mechanics' Floating Point

Several years ago (Fall 1993) I gave a presentation at Novell, as part of their informal lecture series, named "Food For Thought." Somewhere in a dusty archive there may still be a VHS video tape of the presentation, which was entitled "My Computer Can't Add." I presented part of this again during a job interview at UVSC in 2001.

The idea of a computer not being able to add may seem odd. But, a computer doesn't actually deal with numbers, but only with representations of numbers. Except for some very simple and small numbers, the representations are not completely accurate. Part of the problem is round-off errors. The rest of the problem comes from the fact that the representations are far from being a complete set, as only some of the numbers are actually represented at all.

Until recently, personal computers only represented integers between -2147483648 and 2147483647. Granted, those aren't small numbers (as in "pick a number between 1 and 100"), but they aren't big enough to handle the national debt. Newer computers are using 64 bit processors, enabling them to represent integers between -9223372036854775808 and 9223372036854775807.

However, money values and numbers used in scientific computations are generally handled by the "floating point" representation. Here one can represent approximations to real numbers in a larger range than the integer representations provide, but giving up precision. The floating point representation generally uses either 32 or 64 bits, but uses the bits differently than the way they are used when representing integers.

To make this clear, I invented "Mechanics' Floating Point" for the purpose of my presentation. This uses a floating point style representation inside of just 8 bits to represent numbers between 1 sixteenth and 8 (well, almost--the largest number representable in the scheme is actually 7 and 3 quarters). Choosing 8 bits allows one to enumerate all of the representations possible in 8 bits (there are just 256 of them (see "Powers of two")).

In a subsequent post, I will try to find a way to display the entire representation of Mechanics' Floating Point.

Falling while walking

I've had time to get over it now, but it was quite traumatic last Friday to fall down while walking.

It was early morning and I was walking to our condo from our motor home parked in a nearby lot. On one ordinary step, I twisted my left ankle. On the next step it gave way and I fell!

A perfect three point landing: left knee, right hand, and chin.

Got some road rash in all three places and tore out the left knee of my favorite jeans. So, I got a free pair of cutoffs out of the deal.

Everything is mostly healed by now, and the ankle was undamaged by it all.

Strange though, to fall while walking.