A palindromic word is a string of letters which reads the same from left-to-right or from right-to-left. For example, "POP" is a palindromic word.A palindromic sentence is a string of letters that seprate as words, left-to-right or right-to-left. Thus, "MADAM IM ADAM" is a short palyndromic sentence.
Here's one I "thunk up": GREAT SPECKLED BIRD SPECKLED GREAT.
Some one evenwrote a palindromic story which reads the same from beginning-to-end or in reverse.
Palindromes provide amusing and beautifully simple examples of symmetry, an adornment of the various arts, a feature of much of MATHEMATICS, and "behind all conservation laws of physics".
Many people know word or sentence palindromes, but are unaware of palindromes of other forms.
NUMERICAL PALINDROMESNumerical palindromes result from squares of identity strings, that is, each a string of signs all the same, such as 111, whose square is 111 x 111. In the DNA code for genes, a palindromic coding prevents certain kinds of errors. The illustration below of powers of strings of ones occurs because a 1 in a multiplier copies the multiplicand and shifts, so that the product copies the counting order of numbers -- 1, 2, 3, 4, etc. -- up to the number of ones in the multiplier, then reverses this counting order back to the starting 1. For example, 111 x 111 forms the multiplying pattern:
1 1 1 1 1 1 ---------------- 1 1 1 1 1 1 1 1 1 --------------- 1 2 3 2 1BEHOLD!
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321
Notice what happens we square an identity 2-string (all twos). In the first product, below, for 22 x 22, we have the palindrome 4 8 4, which is 4 times the corresponding case for the identity 1-string: 11 x 11 = 1 2 1. Why? The square of 1 is 1 x 1 = 1. But the square of 2 is 2 x 2 = 4 -- four times as much. Hence, the correspondent of 11 x 11 = 1 2 1 is 22 x 22 = 4 8 4, four times as much. However, something happens when we go over to 222 x 222, as in the second product below. I have written its product in two ways. The first product line ,reading "4 8 (12) 8 4", is clearly a palindrome, that is, a symmetric structure, and is four times the corresponding case for the square of the string 111 --- 111 x 111 = 1 2 3 2 1. But the second line shows the way we write this product in decimal language, "4 9 2 8 4", which is not a palindrome. that is, "the symmetry has been broken". Or, to put it another way, the symmetry has been hidden by the decimal language.SHAZZAMMM! That corresponds to something discovered only in recent years in a very advanced field of physics, called "particle theory", which has a symmetry called "gauge theory". It results in "particles without mass", like the photons of light. But it has been found that, by breaking this symmetry (or HIDING IT!) -- SHAZZAMMM! -- a massless particle can acquire mass, resulting in discovery "in the laboratory" of these particles predicted by this theory! So we have modeled in arithmetic, a pattern found in physics, and a hidden pattern found in physics, along with "increase of mass" (8 to 9)! Below are the two products.
2 2 2 2 2 2 2 2 2 2 ---------- -------------- 4 4 4 4 4 4 4 4 4 4 ---------- 4 4 4 4 8 4 ---------------------- 4 8 12 8 4