Palindromes

You're about to get a glimpse of the way the Mind of Kevin Bowman works. This is also an example of why people who have ADD tendencies should stay away from the internet.

For reasons I can't remember, I was talking with a work mate about strange audio processesing algorithms when I recalled seeing a farcical processing device on the internet that named all of the controls and such with palindromes. A quick search found the device in question to be the palindrometer (found here). Then I remembered hearing a satirical skit on NPR (my buddy Dave calls it National Proletariat Radio) that was an interview with a guy named Bob, who spoke entirely in palindromes. Of couse, this instigated a thourough search of the 'net for a transcript of that dialog. I did not find what I was looking for but did find several sites dedicated to palindromes and one site led me to another on which I discovered an intersting (to me) mathematical problem involving numerical palindromes (numbers like 12321).

So now I'm completely intrigued by this mathematical problem, which you can read about here. I started thinking about a related subject: what does it mean to "reverse a number"? And I discovered a couple of interesting things:
1) The absolute value of the difference of a number and it's reverse is a number evenly divisible by nine. This was really no surprise once I remembered the old accounting trick related to transposed digits (if the error is a multiple of 9, you've probably made a transposition error).
2) The result of dividing the difference mentioned above by 9 is often a palindrome! This was true for all of the numbers I first experimented with. My first experiments were with sequencial digits, like 123, 456, 987654, etc. I even tried 196 (196 - 691 / 9 = 55). However, I was able to find numbers that, when subtracted from thier reverse and divided by 9, did not result in a palindrome (72157 - 75127 / 9 = 330).
3) At least for some numbers, the process of "reverse and subtract" (and taking the absolute value) results in a palindrome. The number 196 "solves" in this case:
196 - 691 = 495
495 - 594 = 99

Subtraction is nothing more than adding with negative numbers. Perhaps this will open the door to generalizing the "reverse and add" process and help gain some understanding with the 196 problem. Or perhaps I've just found another way to waste a bunch of time.

Model Railroad Theme

I've devised a name for my model railroad empire (such as it is). The theme is urban industrial and the name of the branch is the Inter-Urban Industrial Line. Pretty generic, I know. But since this is a freelanced layout (not representing any particular "real" place), I thought I could exercise a little artistic license. The Inter-Urban Industrial color scheme is orange, black, and white. The following two pictures are the logo on black field and on orange field, respectively:

When applied to locomotives, the horizontal stripes exend the length of the cab.

The era I am modeling is the early '60s. Steam has been completely phased out so the loco' fleet is entirely diesel or diesel-electric. A future expansion will model an interchange with a Grand Trunk double-track main, so some loco's from other railroads may operate on the IUI.

Here's the complete track plan:
The 2' X 4' section in yellow is the future addition. The darker colored track near the top is hidden from view by buildings, backdrop, whatever. Structure placement and the layout of the downtown area on the right side is preliminary.

I still have to nail down the industries on the IUI. Some ideas include a pertroleum refinery, a couple of freight stations, a piano factory, a furniture factory, a brewery and/or bottling plant, a lumber yard, and distributers (in town) of fruit and bottled goods.

Miscellany

Today, I'm lamenting the fact that this blog has not been very interesting (totally boring is more like it). Creative juices have been flowing but not the kind that produce text of any sort.

I've spent quite a bit of time in the last six months thinking about and designing a modest model railroad layout. Construction will begin soon and I hope to have track laid and trains running before the New Year. My original plan occupied the entiure 19 feet of one wall in my finished basement. The final plan has been scaled back to 2' X 8' with accomodations for another 2' X 4' extention on an 'L'.

I've discovered a new addiction: Sudoku. It's a paper-and-pencil number placement game made popular by Nikoli publishing in Japan (though the game's roots are ancient). I obtained a book of 320 games, fairly evenly divided between easy, medium, hard, and extra hard puzzles. I can solve the easy puzzles in about 20 minutes. I've heard that expert solvers can complete a hard puzzle in about 10 minutes. I'll keep practicing.