Counting Numbers

Modern people often use real numbers to count time intervals. This is useful in many situations but it is also prone to serious errors. This article explains counting numbers and how they differ from real numbers. The reason? The Bible was written with counting numbers.

Problem of Real Numbers

The modern world is different from the ancient world in several key respects. The most noticeable is the amount of engineering used to build modern infrastructure. Engineering, as we know it today, is based on advanced mathematics called Calculus. Calculus is itself based on a system of counting and measuring called Real Numbers.

Real Numbers are an important intellectual foundation because they allow the continuous measurement of nearly all quantities. Even when the quantity is not an even multiple of an abstract base unit, the use of real numbers allow the expression of quantities to the limit of the observer’s ability to measure. Measurements like 5.3 +/- .1 are based on the real number system and include tolerance indicating to anyone using the measurement the accuracy of the value in question

Real Numbers are also used as a basis for Cartesian coordinate systems. Nearly everyone who has graduated High School understands the use of graphs to express equations described in Algebra and Calculus using mathematical functions. Conceptually coordinate systems can exist to any number of dimensions, but 1 dimensional and 2 dimensional systems are common, easy to understand, and easily drawn on graph paper.

Without hardly a moment of thought, most people drawing time lines do so using a 1 dimensional real number based measurement system. This is understandable since nearly everything else in the modern world is measurable and thus understandable using such a system.

Nearly everyone who sets out to understand the time line of the Bible makes the mistake of thinking that the Bible is supplying raw data, time measurements, using the modern Real Number system. It does not. Nor, for that matter, does the modern world consistently use Real Numbers for the measurement of calendar time.

Days, and Fractions Thereof

Think again about a measurement like 5.3 +/- .1. If the quantity in question is days this can easily be converted into hours when we know that days have 24 hours.

5.3 +/- .1 days
= 5.3 +/- .1 days * 24 hours/day
= 5.3 days * 24 hours/day +/- .1 days * 24 hours/day
= 127.2 +/- 2.4 hours

This derivation was easy, and can be understood by most readers because of high school level algebra and science classes that deal with the math and the concept of measurement and error.

The unit conversion was also easy because unit analysis allows the units of measurement to be treated like terms in the algebraic expression.

Now, take the original measurement and convert it to a calendar date. Here things get tricky.

The actual point in time is some time in day 6 not in day 5 as the Real Number expression so readily suggests. 5.3 +/- .1days is 5 days + 7.2 hours. +/- 2.4 hours. This point in time is 7.2 +/- 2.4 hours inside day 6.

If what is meant here is a time inside some week, then the day in question is day 6, Friday, by the historical convention of numbering the days in a week. Similarly, 5.3 days into some month would land on the 6th day of the month, not the 5th as some would suppose.

Why must the day number be shifted up by 1 when converting from the Real Number value into the Calendar value? Because days are still measured using a different numbering system. Days are measured using Counting Numbers.

Counting Numbers

Counting Numbers are different than real numbers in several key respects. First, they begin at "1", there is no "0" in counting numbers. The most well known historical example of counting numbers are Roman Numerals which begin with I then II and so on. There is no Roman Numeral for "zero" as there is never any need for zero in systems based on Counting Numbers. The first thing counted, whatever it may be is labeled "1". Each additional thing gets a progressively higher number.

Generally speaking Counting Numbers are 1 higher than the Real Number equivalent. Converting backwards from a time given on a 6th day will yield a Real Number statement of the time as 5.X where is represents the time within the 6th day.

Counting numbers are still used by modern people to measure months in the year. January is the first month of the modern year. January is month number 1.

Converting the month number backward into a Real Number for the same month, the value will be 0.X where X represents the time inside the month. This isn’t usually done because Month lengths are irregular. Typically the day-of-the-year is used instead when these conversions are made.

Which System is used to count Years?

Because current year numbers are so large it doesn’t make much difference, but technically speaking modern year numbers are expressed using Counting Numbers. 2010 is the counting number assigned to the specific year 2010. There was no year "0" because counting numbers have no such number. The first year in this series was the year "1".

If a date from within 2010 were converted into a Real Number, ready to be drawn on a Cartesian coordinate system graph, the time in question would be 2009.X where X represented the time inside 2010.

Avoiding Mistakes in this Area

In order to accurately draw the time lines of the Bible several analytical steps must be followed.

  • First, the number system used to write the Bible must be understood.

    Since Real Numbers are a recent, modern invention, it is likely without even reading far in the Bible that the Bible was written using Counting Numbers. The task here is simply to show that the Bible was written using Counting Numbers.

  • Second, there must be a strategy for drawing time lines stated using Counting Numbers.

    Either an extensive system of Counting Number to Real Number conversions must be undertaken, or the time line itself must be drawn using something different than a 1 dimensional Cartesian coordinate system. Ie: The Bible’s time line must be drawn using something different than what everyone learned in school.

    Though unconventional, this type of answer cleanly avoids the need for conversions between Counting Numbers and Real Numbers. It also creates a graph that can be easily compared with numbers found in the Bible.

Closing Thoughts

I’m frequently asked to edit and/or review various time lines drawn by people who have attempted to follow the Bible’s chronology. Almost without exception these time lines have been drawn using a Real Number, Cartesian system without any counting number to real number conversion. This always indicates error. Over the range of years covered by the Bible this error is often significant.

It is a major challenge to figure out how to draw the Bible’s time line and still avoid errors of this specific type.