Posted by: Dave Richeson | August 15, 2009

What is a howicide?

I’m a huge fan of HBO’s series The Wire. Today, while I was watching the 4th episode of season 4, I saw a curious word on the strap hanging around Sgt. Landsman’s neck: HOWICIDE.

Picture 1

At first I thought this was a mistake or an easter egg. Why would they misspell homicide? But then I quickly realized that the letters H, O, I, C, D, and E all have the same symmetry—they are unchanged if they are reflected about a horizontal axis. M, on the other hand, becomes W in that circumstance. The yellow strap was actually the back side; it says HOMICIDE on the other.

So what we have are two mirror images:

HOWICIDE
——————-(mirror)
HOMICIDE

Of course there are other letters that have this same symmetry (looking at capital letters only): B, C, D, E, H, I K, O, X.

We could use these to get all sorts of words that remain unchanged when reflected in a mirror in this way, for example:

CHECKBOOK
EXCEEDED
COOKIE
ICEBOX
BOXED
CHOKED
OXIDE
HBO

I couldn’t think of any good words that contained an M which when you reflect it it became a new word with a W. This was the best I could do.

WEEK
MEEK

There are other symmetries among the letters too. A, H, I, M, O, T, U, V, W, X, and Y are all symmetric about the vertical axis. But if we wanted to create words from these that are mirror images of themselves we’d need to find palindromes, such as:

OTTO
TOT
MOM
WOW
MA’AM

Or we could have words that were mirror images of each other like:

YAM | MAY

Finally, some letters have a rotational symmetry (rotate 180 degrees about its center): I, N, O, S, X, Z. Again, to find words that are the same when rotated, we must find palindromes using these letters, such as:

NOON

Just like our first example, M and W are paired—if we rotate one we get the other. Thus we can have other words that remain the same after rotation (I was especially proud of thinking of this one):

SWIMS

There are other possible symmetries (think O and X), but I think this exhausts the interesting possibilities (without including lower case letters).

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Responses

  1. Have you seen Weird Al Yankovic”s parody song “Bob”

    • I’ve never seen that before. It is great!

      The video reminded me of one that I noticed when I was a kid: A TOYOTA has the vertical mirror symmetry. How did I forget that one?

  2. You amaze me Dave. Seriously!

  3. Give students a transparency with these three sentences printed on it. Tell them to pick out the one that is different.

    BILLY THE KID DIED JUL 14 1881 — SHOT BY GARRET

    HICKOK DIED DEC 3 1883 — DOC BEECH DECIDED HE CHOKED.

    BROWN DIED MAR 27 1875 — HE WAS HUNG IN EL PASO

    (courtesy Harold Jacobs)

    Also consider: “dollop”

    http://scottfarrar.blogspot.com/2008/01/symmetry.html

    • Thanks. And thank for the link to your blog. That cover of the Princess Bride is great.

  4. Look up Ambigrams.


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