## Friday, July 27, 2012

### Absolute and Relative Roman Numerals

 Mini-Series On Classical Mathematics: (10-2)*(10-2)=64 As History of Mathematics ... Sigh ... Absolute and Relative Roman Numerals Two is Still Not a Number With any Square Root Now, for the essay:

 I=1 II=2 III=3 IIII=4 VI=(5+1) VII=(5+2) VIII=(5+3) VIIII=(5+4) IV=(5-1) IIV=(5-2) IIIV=(5-3) IIIIV=(5-4)

If you cannot have absolute numerals meaning "as many as fewer than none", you can have relative numerals not only adding but also detracting "as different as fewer than other number by itself". And the Romans had that.

IIIIIIIIIIV*
IIIIIIIIIIVI
IIIIIIVIVIIIXII
IIIVIVIIIIXIIXVIII
IIIIVIIIXIIXVIXXIIII
VXXVXXXXVV

They also had a smaller multiplication table "than we do" (though a longer one than computers have). Not that we have not got their multiplication table too if we want to, but the one we learn in school is longer.

And here are the examples of how the work out together, with a V modified by relative numerals I - IIII on the right or the left:

VI*
XXVVV
VII

XXV V V I
XXXVI
IV*
IVI
VXXVV

I | V V ||XXV
V V || XXVI

Let's skip intermediates and go directly to the last two multiplications of these simple Roman Binomials, shall we:

VIIII*
XXVXXV
XXXVIIIII

XXV XX XX XVI
L XXV VI
LXXXI
IIIIV*
XVIXXIIII
XXXXVV

XVI | XX XX || XXV
XX XX || XXV XVI
X || V V I

Which means that in Roman Subtraction, to simplify the algorithm, something subtracted from the subtrahent is instead added to the total from which one subtracts:

IV || V
V || V I.

Which in turn works out as the "multiplication table of signs" which in turn has after Wallis and others been misunderstood as if absolutely negative numbers (there is no such thing) could by themselves make positive products.

As simple as "Romani ite domum!" (Which does not always necessarily come across as a blasphemy against Our Lord, as said in previous, unless you would say that Écône is rather telling the Vatican - in very correct Latin usually - "Romani venite domum", but that subtlety may securely have been lost on Anglican and Atheist critics of Latin Mass Society).

Hans-Georg Lundahl
BpI, G. Pompidou Library
Day of Sts Aurelius and Natalia,
Martyrs of Cordoba

27-VII-2012

For this and previous two posts, many thanks extended to the Latin and Greek Studies Seminar of Copenhagen in ... was it 1992 or something?

Now, in case anyone wonders what I think about e or π or φ or the Mandelbrot formulas, those simply are not numbers.

π is a proportion between the diameter and the perimeter (περιµετρoc=π) of a circle.

These are not numbers and do not belong to Arithmetic, they are proportions and belong to Geometry.