On Cardinals, Ordinals, and Millennia

Saturday, August 12, 2000

With the end of the year 2000 fast approaching we earth-bound folks will soon be preparing for yet another end-of-the-millennium celebration. With that in mind we need to discuss Roman numerals, counting, and measuring.

This is not about known errors in timekeeping which result in the new Christian year beginning in the wintertime rather than the spring when Jesus the Christ was probably born. Nor is it about some astronomical error which places the birth in the year 3 BC. The subject is how we measure and count and how the difference seems to have been obscured in modern education.

The baby Jesus was born while the sun was moving northward in its yearly passage through the heavens. (It was the sun doing the moving in those geocentric days.) The Romans who ruled the world didn't pay a lot of attention until the sun found its way back to the south and returned to the same place where it was at the birth. At that time the Child celebrated His first birthday and some individual scratched a short vertical line on the wall to indicate the end of the first year. That scratch we now call a Roman numeral which represents the interval of time from birth until one year later.

Note that roman numerals have no zero. They are ordinals or counting numbers which usually are represented in spoken English as “first”, “second”, “tenth” and the like. In use they always refer to objects that can be counted.

Now as the Child reached the end of His second year of life a second line was marked next to the first and it became II. When a full decade was reached the IIIIIIIIII stretched around the corner and a bright Roman decided to represent all those Iʼs with a single X. When the Child celebrated His eleventh birthday he was one decade and one year old represented by XI.

Fast forward through the middle ages to the age of scientific enlightenment. The Arabic number system with decimal fractions is well established and we have taken to measuring things with rulers and comparing to international standards. There is in Paris a standard meter stick which is graduated in centimeters and millimeters and which can be compared with the kingʼs arms to measure out a yard. By placing the meter stick with the end marked zero at the kingʼs nose we read 0.9144 meters at the kingʼs outstretched thumb. 0.9144 is a cardinal number (note 5) which represents a measurement of something which cannot be counted. The number is not exact for there is always some error associated with its determination. In spoken English we say a yard is nine hundred fourteen point four millimeters. It doesnʼt help to talk about the 914th mark on the meter stick.

There is also a meter stick of time (note 1). We can't pick it up but we can imagine it placed so that the zero falls on the instant of birth of that Child above. The stick is also logically extended to the "left" of zero into negative time which is another concept foreign to Roman numerals. To record the time of occurrence of an event we compare a clock to the meter stick of time and write down a cardinal such as 1935.31347 which happens to be the instant of my birth expressed in years.

Now should I choose to copyright this document (I donʼt) I might write down something like “Copyright, The MacNauchtan Laboratory, MM” because weʼre in the year designated by the cardinal numbers between 2000.00 and 2000.99999 and the Roman numeral MM represents 2000 right?


The Romans didnʼt have the concept of cardinals (note 2). The first year of our Lord is designated in our modern way by cardinals in the range 0000.0000 to 0000.9999. What is the proper Roman numeral for that year? Remember that there is no zero. We saw in my third paragraph that the Romans called that period the first year and designated it with the numeral I. The year 0001.0 to 0001.9 they would call II and so on. My copyright ought to read MMI for this year.

The incorrect assignment of Roman numerals to modern dates probably resulted from lack of attention to detail when the first printed books appeared. Perhaps we can blame it all on Mr. Gutenberg but it would be interesting to see how the letters of St. Paul were dated.

Now there are some folks who believe that the millennium ends at the end of the 2000th year and they argue that we are in the year MM so we need to celebrate at the end of the coming December 31. By all means letʼs have a party. Bring on the beer and wine (legal and taxed), the cigarettes and hemp (illegal or sued to death), the rockets and gunpowder (illegal or politically incorrect) and letʼs listen to Shakespeare and kill all the lawyers (note 3). But Jesus the Christ still celebrated His 2000th birthday at the end of 1999 designated MM by the Romans. He lives (note 4).

If thou wisheth to figure the length of the fence count not the poles but the spaces between poles lest thou be in error by the length of one stringer.

note 1: As far as modern science knows there is no fundamental quantum of time which can be counted. Time flows continuously at least down to femtosecond levels.

note 2: There were, and still are, ordained cardinals in the Roman Catholic church but thatʼs different.

note 3: King Henry the Sixth.

note 4: Some, especially in Colorado, think He has been living for 3/4 of a year more starting at the immaculate conception.

note 5: I'm using the term cardinal in the dictionary sense here. There is also the concept of cardinality of infinite sets which is for another place.

Douglas P. McNutt, PhD
The MacNauchtan Laboratory
7255 Suntide Place
Colorado Springs, CO 80919-1060
voice 719 593 8192