# Mathematics of Haiku

**2/15/17**

This article is about the mathematics of haiku. Wait...poetry and math? Yes, of course. They are actually *quite* compatible. Of the poems that I've written (which can be found here), of them are haiku.

A traditional haiku has a certain structure and various "rules". Of course, both of these things can be changed, altered, modified, by any degree, or strictly adhered to. One of the main things, at least for so-called "American haiku" is a syllable structure of 575, or

5

7

5

which means 5 syllables for the first line, 7 syllables for the second line, and 5 syllables for the third line.

What is interesting is that for this syllable structure alone, there are 2^{5-1}*2^{7-1}*2^{5-1} (I wrote it like that for a reason) possible syllable structures, or 2^{4}*2^{6}*2^{4} = 16*64*16 = 16,384.

This happens because 5 syllables (for example) can be expressed 16 ways like:

5

41 (ie. 4 syllables and 1 syllable, so 5 total syllables)

32

311

23

221

212

2111

14

131

122

1211

113

1121

1112

11111

This breaking down of an integer is called "integer composition". Curiously, if we didn't care about order, for example 113 is the same as 131, 311, etc., then it is called "integer partition". There is tons of research in mathematics on these topics, and they are related with number theory and binary numbers.

Similarly 7 (again, from the 575 structure) can be broken down 64 ways. In general, n can be broken down 2^{n-1} ways. Here is the breakdown for 7

7

61

52

511

43

421

412

4111

34

331

322 (ie. 3 syllable, 2 syllable, and 2 syllable, so 7 total syllables)

3211

313

3121

3112

31111

25

241

232

2311

223

2221

2212

22111

214

2131

2122

21211

2113

21121

21112

211111

16

151

142

1411

133

1321

1312

13111

124

1231

1222

12211

1213

12121

12112

121111

115

1141

1132

11311

1123

11221

11212

112111

1114

11131

11122

111211

11113

111121

111112

1111111

Of those 5 syllable possibilities, say the 23 one, there are so many 2 syllable words and so many 3 syllable words, so the 23 possibility has millions of possibilities itself. The 1112 probably has trillions.

Therefore, even using *very* small word lists for 1, 2, 3, 4, 5, 6, and 7 syllable words, I calculate total possible random haikus of over 10^{66}. What I am saying is, even *if* your vocabulary is somewhat limited, which it probably is not, you have the creative capacity inside you for making more haiku than the number of atoms in the universe.

Here is a link to download my haiku creator spreadsheet as of the writing of this article that demonstrates these ideas. Enjoy! Please do credit Statisticool.com if you use the spreadsheet however.

So don't be afraid of letting the right side of your brain mingle with your left, you never know what they might create.

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