Monday, June 14, 2010

Car Talk Goes Linguistic (kinda)

If you listened to this week's Car Talk, you heard the answer to last week's puzzler, which contained a semi-linguistic related brain tease. Unbeknownst  to the Tappet Brothers was the fact that there were a few extra puzzles hidden within their main one. First, the puzzler as it was presented on the show:

This was a puzzler that I'm stealing from the late Martin Gardner. I'm going to give you a number and you're going to tell me what's unique about the following number: 8,549,176,320. Now if you want a hint, I'll point out that there are 10 digits in that number. The question is, what's unique about this number? 

The answer requires some linguistic gymnastics. The extra puzzles are somewhat hidden until the first puzzle is solved:

The number 8,549,176,320 is the result of taking the written form of each numeral and alphabetizing them from A-Z.

So this list

Zero 
One
Two
Three
Four
Five
Six
Seven
Eight
Nine

Becomes this number
Eight
Five
Four
Nine
One
Seven
Six
Three
Two
Zero

or 8,549,176,320 (note that one could argue that 236,719,458 is every bit as "unique" in this same sense).

While gnawing on this otherwise trivial puzzle, I noticed a couple of more interesting facts.

  • There are three letters that start two numbers: T (two, threeF ( four, five), S (six, seven).  In all three cases, the numbers are consecutive, hence the letters "pattern together" in a certain sense (also notice that in the alphabetized version, each pair's order is reversed). Is there any historical reason for this, or just coincidence? Care to write a FOPC statement that correctly captures this fact?
  • It became quite clear to me that accessing numbers and lexical items interfere with each other while trying to write the number down. Since I was driving in a car when I first heard the puzzler, I didn't write the number down, but I figured I could reconstruct it easily, but then I jumped on the DC metro with no writing tool, so I couldn't write down the letters then alphabetize them in front of my eyes, so I had to "figure it out" in my head. No worries, I thought, I'm a smart guy and a little Saturday morning brain tease is better than coffee. So I flipped out my archaic, obsolete cell phone and wrote the number into a text message. What I discovered was something akin to a numerical Stroop effect where the numbers interfered with my ability to choose the correct button to push. So I wanted to type the letter "T" for "two" (which is the number 8 on my keypad), but instead I typed the letter "A" because that's on the number 2 button. I had a similar problem just now when typing on a full keyboard. When I tried typing the number names above, I regularly typed the number from the topmost key row instead. Somebody must have studied this kind of interference already, right?

2 comments:

glossographia said...

The numeral-pairing has been mentioned and I know there has been some literature on it (maybe something cited in Hurford's _Language and Number_?). It's pretty widespread in the Indo-European languages of Europe (e.g. duo/tres, quattuor/quinque, sex/septem) but sporadic elsewhere. On the other hand, it appears in other languages - e.g. Japanese, but not in successive numerals: http://paleoglot.blogspot.com/2008/02/hidden-binary-behind-japanese-numeral.html .

There are many different numerical Stroop effects, some of which are talked about by Stanislas Dehaene in his _The Number Sense_, others known mostly in the specialist literature on numerical cognition. I can't recall where I first heard of the one you mention but I've certainly experienced it. I'm doing some work on phone numbers right now so this is a particular interest of mine.

- Steve Chrisomalis

Chris said...

Steve, thanks for the excellent link and suggestions! I knew there had to be something out there.

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