Ever since I created Calibrated Gematria, I've been wanting to expand it to accommodate Roman numerals. This page is where you can watch me stumbling toward that goal. "Under construction" would be an extreme understatement.

Clearly, Roman Numeral Calibrated Gematria (RNCG) means more than just another set of letter-number mappings. If **IV** and **VI** are to return two different values, the gematria mechanism itself must be modified. It can't be as simple as just adding up all the letters in a word.

So here's my first attempt at a rule:

If a letter's value is lower than that of the letter which follows it, then it is subtracted from the word total; otherwise, it is added.

This works for Roman numerals. For example, **IV** is <1, 5>, which becomes -1 + 5 = 4; whereas **VI** is <5, 1>, which becomes 5 + 1 = 6. When I try to apply it to number words, though, I find it less than satisfactory.

**Six** is the natural number to begin with, since **i** and **x** are Roman numerals, leaving **s** as the only unknown quantity. **Six** = <**s**, 1, 10>, which must equal 6, so I need the letter **s** to represent subtracting 3. This, it turns out, is impossible. If I define **s** as -3, we get <-3, 1, 10>. Because -3 is less than 1, it must be subtracted from the total, giving us 3 - 1 + 10 = 12. If we instead define **s** as 3, the result is the same; 3 is now greater than 1 and must be added, which is the same thing as subtracting -3. No matter what value we assign to **s**, it's impossible to make **six** equal 6.

So here's my modified rule:

If a letter's

absolutevalue is lower than that of the letter which follows it, then it is subtracted from the word total; otherwise, it is added.

This makes **six** doable. If **s** = -3, then **six** = <-3, 1, 10> = -3 - 1 + 10 = 6.

Here are the letters we have defined so far — the Roman numerals, plus **s**:

**c**= 100**d**= 500**i**= 1**l**= 50**m**= 1000**s**= -3**v**= 5**x**= 10- Undefined: {
**a**,**b**,**e**,**f**,**g**,**h**,**j**,**k**,**n**,**o**,**p**,**q**,**r**,**t**,**u**,**w**,**y**,**z**}

And here are some basic number words to be used for calibration:

**one**= <**o**,**n**,**e**> = 1**two**= <**t**,**w**,**o**> = 2**three**= <**t**,**h**,**r**,**e**,**e**> = 3**four**= <**f**,**o**,**u**,**r**> = 4**five**= <**f**, 1, 5,**e**> = 5**six**= <-3, 1, 10> = 6**seven**= <-3,**e**, 5,**e**,**n**> = 7**eight**= <**e**, 1,**g**,**h**,**t**> = 8**nine**= <**n**, 1,**n**,**e**> = 9**ten**= <**t**,**e**,**n**> = 10**eleven**= <**e**, 50,**e**, 5,**e**,**n**> = 11**twelve**= <**t**,**w**,**e**, 50, 5,**e**> = 12**thirteen**= <**t**,**h**, 1,**r**,**t**,**e**,**e**,**n**> = 13**fourteen**= <**f**,**o**,**u**,**r**,**t**,**e**,**e**,**n**> = 14**fifteen**= <**f**, 1,**f**,**t**,**e**,**e**,**n**> = 15**sixteen**= <-3, 1, 10,**t**,**e**,**e**,**n**> = 16**seventeen**= <-3,**e**, 5,**e**,**n**,**t**,**e**,**e**,**n**> = 17**eighteen**= <**e**, 1,**g**,**h**,**t**,**e**,**e**,**n**> = 18**nineteen**= <**n**, 1,**n**,**e**,**t**,**e**,**e**,**n**> = 19**twenty**= <**t**,**w**,**e**,**n**,**t**,**y**>

The two letters to tackle next are **e** and **n**, the only unknown quantities in **seven**, **nine**, and **eleven**.

Barring some error of mathematical reasoning, the following table includes all possible solutions for **seven** = 7.

e |
n |
seven |
nine |
eleven |
---|---|---|---|---|

-8 | 9 | 7 | 9 | 62 |

-7 | 9 | 7 | 10 | 61 |

-6 | 9 | 7 | 11 | 60 |

-5 | 9 | 7 | 12 | 69 |

-4 | -9 | 7 | -23 | 58 |

-4 | -1 | 7 | -3 | 58 |

-1 | 3 | 7 | 4 | 61 |

0 | 5 | 7 | 9 | 60 |

1 | 7 | 7 | 14 | 59 |

2 | 9 | 7 | 19 | 58 |

3 | 11 | 7 | 24 | 57 |

4 | -1 | 7 | 5 | 50 |

4 | 7 | 7 | 17 | 50 |

6 | -3 | 7 | 5 | 58 |

6 | 9 | 7 | 23 | 58 |

7 | -5 | 7 | 6 | 47 |

7 | 9 | 7 | 24 | 47 |

8 | -7 | 7 | 7 | 46 |

8 | 9 | 7 | 25 | 46 |

9 | -9 | 7 | -10 | 45 |

**Eleven** appears to be a lost cause, but we have two different solutions that work for both **seven** and **nine**. I opt for the latter of the two, because it has the useful feature of a zero value for **e**, making it possible for **ten** to equal **-teen**. Once **e** and **n** have been assigned, the values of a few other letters can be derived trivially. Here, then, are the updated code and calibration set:

**c**= 100**d**= 500**e**= 0**f**= 1**i**= 1**l**= 50**m**= 1000**n**= 5**o**= 4**s**= -3**t**= 5**v**= 5**x**= 10- Undefined: {
**a**,**b**,**g**,**h**,**j**,**k**,**p**,**q**,**r**,**u**,**w**,**y**,**z**}

- Hits:
**one**= 1,**five**= 5,**six**= 6,**seven**= 7,**nine**= 9,**ten**= 10,**sixteen**= 16,**seventeen**= 17,**nineteen**= 19 - Misses:
**eleven**= 60,**fifteen**= 11

**two**= <5,**w**, 4> = 2**three**= <5,**h**,**r**, 0, 0> = 3**four**= <1, 4,**u**,**r**> = 4**eight**= <0, 1,**g**,**h**, 5> = 8**twelve**= <5,**w**, 0, 50, 5, 0> = 12**thirteen**= <5,**h**, 1,**r**, 5, 0, 0, 5> = 13**fourteen**= <1, 4,**u**,**r**, 5, 0, 0, 5> = 14**eighteen**= <0, 1,**g**,**h**, 5, 0, 0, 5> = 18**twenty**= <5,**w**, 0, 5, 5,**y**>

**Two** is now impossible to solve, since every possible value for **w** will yield a number either greater than 3 or less than -6. We therefore use **twelve** to calibrate **w** and then **twenty** to calibrate **y**. There are infinitely many solutions for the set {**three**, **four**, **eight**}, none of which can deal with **thirteen** or **eighteen**, so of them I choose the one that happens also to yield the correct value for **forty**.

**c**= 100**d**= 500**e**= 0**f**= 1**g**= 17**h**= 21**i**= 1**l**= 50**m**= 1000**n**= 5**o**= 4**r**= -13**s**= -3**t**= 5**u**= 22**v**= 5**w**= -38**x**= 10**y**= 63- Undefined: {
**a**,**b**,**j**,**k**,**p**,**q**,**z**}

- Hits:
**one**= 1,**three**= 3,**four**= 4,**five**= 5,**six**= 6,**seven**= 7,**eight**= 8,**nine**= 9,**ten**= 10,**twelve**= 12,**fourteen**= 14,**sixteen**= 16,**seventeen**= 17,**nineteen**= 19,**twenty**= 20,**twenty**= 20,**twenty-one**= 21,**twenty-three**= 23,**twenty-four**= 24,**twenty-five**= 25,**twenty-six**= 26,**twenty-seven**= 27,**twenty-eight**= 28,**twenty-nine**= 29,**forty**= 40,**forty-one**= 41,**forty-three**= 43,**forty-four**= 44,**forty-five**= 45,**forty-six**= 46,**forty-seven**= 47,**forty-eight**= 48,**forty-nine**= 49

- Misses:
**two**= -39,**eleven**= 60,**thirteen**= 12,**fifteen**= 11,**eighteen**= 13

This leaves only seven letters unassigned. **Zero** seems the most natural choice for calibrating **z**.

**z**= 9**zero**= 0