Reflective Palindromes
Nichael Cramer
[[This sounds like it should be an oldie, but I've not seen it discussed
here before, so...]]
CASE 1:
Are there any non-trivial reflective palindromes?
By a reflective palindromes, I mean a phrase (etc) that would still be
readable if it were reflected horizontally through its center letter (e.g.
as if it were being viewed in a mirror).
[NOTE: I'm following normal palindrome convention and ignoring spaces,
punctuation, etc.]
A simple example would be "MAXAM" (the name of a timber company).
Obviously, such a palindrome would be necessarily restricted to using the
letters:
A H I M O T U V W X Y X Y Z
and the numbers:
8 and 0
[Interesting that all of the last *9* letters of the alphabet work.]
Now, if we define as "strong" those reflective palindromes that are
restricted to the characters above, we could define a class of "weak"
reflective palindromes that allowed typographically "shakier" cases like
the following:
p <==> q
b <==> d
And some more questionable cases:
[E <==> 3 (?)]
[P <==> 9,4 (?)]
[Z,2 <==> 5,S (?)]
[0 <==> O (?)]
[How closely some of these pairs match is necessarily dependent on the
typeface used, of course.]
CASE 2:
So long as we're being perverse, how about "rotational palindromes";
i.e. a phrase, etc. that survives being rotated through 180dg about
its center letter.
An example is the sentence "NO SIX IS ON." (It is left as an exercise for
the reader to contrive a situation in which this sentence is meaningful ;).
Here the set of usable characters for the strong case is rather small:
H I N O S X Z 8 0
However, the weak case gives rise to some interesting pairs:
q <==> b
P,p <==> d
6 <==> 9 [Shades of Jimi ;) ]
W <==> M
And the "more questionable" pairs:
[E <==> 3 (?)]
[q <==> 6 (?)]
[Z <==> 2 (?)]
[5 <==> S,5 (?)]
[0 <==> O (?)]
Enjoy
NICHAEL
Stanier A
?An example is the sentence "NO SIX IS ON." (It is left as an exercise for
?the reader to contrive a situation in which this sentence is meaningful ;).
Anyone who knows the game of cricket could think of many situations in which
this would be a perfectly reasonable thing to say.
Dan Tilque
>Are there any non-trivial reflective palindromes?
>
>By a reflective palindromes, I mean a phrase (etc) that would still be
>readable if it were reflected horizontally through its center letter (e.g.
>as if it were being viewed in a mirror).
>
>letters:
> A H I M O T U V W X Y X Y Z
>and the numbers:
> 8 and 0
>
>[Interesting that all of the last *9* letters of the alphabet work.]
Try 8 of the last 9 letters; Z is not allowed in this type of palindrome.
The best single word I can think of is MAXAXAM which is a company which
makes a non-conventional type auto transmission. It may not be in
existence anymore. The founder of this company deliberately came up
with a palindrome composed solely of the letters M A and X.
For a phrase, how about TOO HOT TO HOOT.
---
Dan Tilque -- da...@mrloog.WR.TEK.COM
"The Mars mission won't be cheap -- the cost is currently estimated at
$400 billion, not including reality -- but the potential benefits are
enormous. For openers, we will earn as a nation, more than 500 million
Frequent Flyer miles."
-- Dave Barry
Badger BA 64810
>In article <50...@bbn.COM> ncr...@BBN.COM (Nichael Cramer) writes:
>>
>>CASE 1:
>>Are there any non-trivial reflective palindromes?
>>
>>By a reflective palindromes, I mean a phrase (etc) that would still be
>>readable if it were reflected horizontally through its center letter (e.g.
>>as if it were being viewed in a mirror).
viewed upside-down. I coined the word ``pomwod'' as a self-defining instance.
Also, it is amusing to construct ``letters'' from combinations of
other standard ASCII characters. This allows some creativity in
composing the letter forms. For example, here's some interpretations
of "HAWK" which are pomwods:
>| /|\ \|/ |<
>[ /o\ \o/ ]<
>|/|\|/|< reads >| /| \|/ |<
>< /*\ \*/ ><
Obviously I'm taking great liberties with the letter shapes (particularly H = >|)
but it's fun. The transformation of A into W is also quite shocking.
By the way, see Scott Kim's book ``Inversions'' for many artistic examples
of letter changing. Also, Douglas Hofstadter's ``Metamagical Themas'' and
Omni magazine's Game column have had ``Ambigrams'' which can be read
various ways.
----- - - - - - - - ----
Bernard A. Badger Jr. 407/984-6385 |``Get a LIFE!'' -- J.H. Conway
Harris GISD, Melbourne, FL 32902 |Buddy, can you paradigm?
Internet: bbadger%x1...@trantor.harris-atd.com|'s/./&&/g' Tom sed expansively.
Nichael Cramer
>Nichael Cramer errs & errs:
>>Obviously, such a palindrome would be necessarily restricted to using the
>>letters: A H I M O T U V W X Y X Y Z
>>Try 8 of the last 9 letters; Z is not allowed in this type of palindrome.
>Observe that "X" and "Y" occur twice in Nichael's original...
Quite right, a triple typo on my part.
By way of apology I'll tell you about a neat --related-- hack that my boss,
Bill, showed me back in my undergrad days when I used to work setting up
the freshman physics labs at IU.
One day he calls me over and says "Have you ever heard of Aluminum
Dioxide?" I said I hadn't and he explained that it had this amazing
property. Namely, the way in which it transmitted light was *radically*
different, depending on whether the incoming light was red or blue.
This stuck me as a little strange until he showed me this contraption he
had built. Basically it consisted of a dowel rod (about 3/4in in diameter)
made of a transparent material, which was held about two inches off of a
piece if cardboard be two small metal brackets. In cross-section it looked
like this:
--------------------------------------------
| |
+= Cylinder of Aluminum Dioxide =+
|| ||
| -------------------------------------------- |
| |<--Bracket
| |
-------------------------------------------------- <--Cardboard
On the cardboard were written the words:
ALUMINUM DIOXIDE
With the "ALUMINUM" written in large, bright red letters and the "DIXOIDE"
written in large, bright blue letters.
And sure enough, when I looked through the tube at the printing underneath,
the red "ALUMINUM" was inverted, but the blue "DIOXIDE" was unaffected!
NICHAEL
Hint follows:
--> ;-)
