Above the Law

Some people must think that they are above the law.


Here is the closeup:



(In reality, this is at the beginning of a walking bridge over a busy street and the city probably does not want signs to distract drivers. However, the plan reading is so much funnier.)

The Trinity is Antitransitive

I grew up going to St. James United Methodist Church in Sioux City, Iowa. Every time I return home and attend church there, I rethink many of the thoughts that I have had in that building over the years.

One of those thoughts is that I have always liked one of the stained glass windows next to the pew in which my family regularly sits.

In particular, I have always liked the visual representation of the relationships in the trinity.

However, I have never known why I liked it...until now!

The Trinity is an antitransitive relation.

Now, to explain what that means.

A relation is the formal mathematical notion most closely related to the word I used before, "relationship". In the case of the Trinity relation, each pair of (distinct) words (i.e. God, Father, Jesus, Holy Spirit) is ascribed either "is" or "is not" (so the Trinity relation is a binary relation). (For each pair of identical words, the window does not state the relationship but it is implied that each word is related to itself, thus ascribed an "is" and making it a symmetric relation.)

To understand an antitransitive relation, it helps to know what a transitive relation is. A (binary) relation is transitive if

for all words x, y, and z, if x is related to y and y is related to z, then x is related to z.

The most commonly known transitive relation is the equivalence relation. As everyone knows, if x is equal to y and y is equal to z, then x is equal to z.

An antitransitive relation has the exact opposite conclusion about every triple of words. A (binary) relation is antitransitive if

for all words x, y, and z, if x is related to y and y is related to z, then x is NOT related to z.

Although somewhat counterintuitive, I believe it is the mathematical beauty of the Trinity that drew me to this window all those years ago.

(Or maybe it is because it also looks like a planar embedding of K₄...nah.)

My Favorite Christmas Songs

Now that Thanksgiving is over, many people (including my wife) new permit Christmas music to be played. For the last two Christmases, I have saved my favorite Christmas songs and favorite version. Here is my current list:

1. Angels We Have Heard On High - Chris Tomlin - WOW Christmas: Green
2. Away in a Manger - Casting Crowns - WOW Christmas: Green
3. Breath of Heaven (Mary's Song) - Amy Grant - Home For Christmas
4. Do You Hear What I Hear? - FFH - WOW Christmas: Green
5. It Came Upon a Midnight Clear - Kutlass - WOW Christmas: Green
6. Light of the Stable - Selah - Rose of Bethlehem
7. Little Town - Amy Grant - A Christmas Album
8. Mary Did You Know? - Clay Aiken - WOW Christmas: Green
9. O Come All Ye Faithful
10. O Come, O Come, Emmanuel - Rebecca St. James - Christmas
11. O Holy Night - Josh Groban - Josh Groban In Concert
12. O Little Town of Bethlehem
13. Silent Night
14. The First Noel - Mark Schultz - WOW Christmas: Green
15. We Three Kings - DC Talk - Joyful Christmas
16. Welcome To Our World - Michael W. Smith - WOW Christmas: Green
17. What Child is This? - Rebecca St. James - Christmas

Of these, my favorite is We Three Kings by DC Talk because it is the most unique of all these songs.

You should notice that I have three songs listed without a version. This is because I don't know what my favorite version of these songs is. Do you have a favorite version of one of these songs? If so, please share it with me. Maybe it will become my favorite as well.

Do you have a favorite Christmas song that I don't have listed? Please share it with me. Maybe I will it will become my favorite as well.

UPDATE:

Here are some new additions.

1. 2000 Decembers Ago - Joy Williams - A Christmas Reunion
2. Christmas This Year - tobyMac - (No album)
3. Emmanuel - Michael W Smith - WOW Christmas (Red)
4. The Night Before Christmas - Brandon Heath - WOW Christmas 2011
5. When Love was Born - Mark Schultz - WOW Christmas 2011

Now, I really prefer to have one favorite version of each song, but Wee Three Kings by Go Fish from Christmas With A Capital 'C': Snow Deluxe Edition is too good to pass by.

Corn Maze

Yesterday, I went to my first corn maze at Treinen Farm with my bible study group. I have heard other people describe their corn maze experiences and combined with my low expectations of corn mazes, I was mostly excited to hang out with my bible study group.

However, I am happy to say that this corn maze was amazingly fun. They give you a partial map and indicate where to go to find the next piece of the map. Here is the maze:

The start (and end) is in the middle on the right side.

Two people in our group tracked our progress using the GPS in their phone. Here is what one of them recorded us walking, which was about a mile long:

There were seven checkpoints in the maze. Checkpoints 8 - 10 were after we left the exit of the maze. The yellow in the bottom left is my addition. The GPS tracking doesn't match up well with the maze in that corner. The yellow is what I think we did over there.

I was leading the group to the first checkpoint when I got lost. I took the second left instead of the third just before the checkpoint. However, I redeemed myself later by finding the way to checkpoint 5 after someone else got us lost.

In addition to the seven checkpoints that gave us more of the map, there were eight secrete locations, unmarked on the map. I wanted to find these locations as well, but most in the group didn't seem interested.

I am already excited for next year's maze...and maybe I can find the secret locations as well!

How to Save Embedded Videos and Other Files

Many sites with videos use embedded flash players to show videos. I often want to download the whole video to avoid pauses for buffering and watch when offline.

To accomplish this in Firefox, add the Live HTTP Headers add-on. Then when obtaining the video (or other file), this add-on will give you the direct address to the file. Using Linux, I download the file using the command wget.

ItsHidden Points to Me

In the summer of 2009, a new VPN service ItsHidden was announced. At the time, there were no instructions to help me get this to work on Ubuntu.

After a while (several days as I remember), I figured out how to make it work. The steps were easy to do but hard to figure out in the first place. Both by design and some chance, I had started an Ubuntu blog about a month earlier to both share helpful information I learned about Ubuntu and (a bit more selfishly) give myself a place to post information that I may want to again in the future. The steps to get ItsHidden working on Ubuntu was exactly the what belonged on the site.

Fast forward over two years (to today). I was just looking at ItsHidden's website and noticed that they link to my blog post!

The last bullet point is my URL (without a hyperlink though).

Old graphicx Bug

I just ran into a bug using the LaTeX package graphicx. I tried to include a graphic with a file name of the form "name.txt.png" and the file really is a PNG file. However, graphicx said ".txt.png" is an unknown graphics extension. *Sigh*...thanks for the hot tip.

A quick Google and I find that this has been a bug since 2004! This is such a simple fix. Why hasn't this been done???