1995

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For the individual and the family, there are a number of well-recognized reasons to seek to build up a family. Personal security in later years and the need for labour on the family land are not the least of them for subsistence farmers the world over.

More questionable is the tendency of the major religions to encourage
large families. The cynical would argue that this is an easy policy whereby
the numbers of the faithful can be increased with little investment in
missionary activity. But the faithful are reassured by holy scripture and
notably, for the people of the Book, by the key phrase "be fruitful and
multiply" (*Genesis 1:28*) .

In this case everything hangs on the understanding of "multiply". This understanding was of little importance when population levels were far from being critical. This is no longer the case. There is therefore merit in exploring possible misinterpretations of what was originally intended.

At present, with widespread education and teaching of arithmetic, there is little ambiguity to any understanding of "multiply". Is that so true of the period when the text was written?

For a start it is important to put current understanding of arithmetic in perspective. It was not until the 14th century (??) that the current numerals became commonly used. The zero in the pattern of numbers was a relatively late arrival. Without the zero, division becomes a very challenging arithmetical operation. In Roman times, there were no operations for multiplying or dividing as they are now known. The only procedure necessitated adding or subtraction.

Ironically it is Islam, as a historical torchbearer of mathematics, which through
its architectural motifs, is most sensitive to complex tiling patterns over
three-dimensional surfaces. There is a traditional antipathy of Christianity
to mathematics, dating back to St Augustine: "The good Christian should
beware of mathematicians, and all those who make empty prophecies. The danger
already exists that the mathematicians have made a covenant with the devil to
darken the spirit and to confine man in the bonds of Hell." [St. Augustine
(354-430), *DeGenesi ad Litteram*, Book II, xviii, 37]. But, ironically
again, the much quoted Biblical injunction to "go forth and multiply"
or "Be fruitful and multiply" (*Genesis* 1:28) -- on which policies
with disastrous and far reaching implications for the planet are based -- is
not subjected to dialogue between theologians and mathematicians.

What then could be the sense of "being fruitful" to "multiply" when the phrase was first used?

At the time this injunction was written, multiplication was not understood as a mathematical operation. Only addition and subtraction were possible. It might therefore be better translated as "increase", as featured in some Papal writings that also deal with the remainder of that same injunction, namely to "fill the earth and subdue it". From a mathematical perspective, "increase" may occur in many ways, some of which might be better associated in a theological perspective with "increase in comprehension", some "expansion" of the person, "growth in wisdom". It makes all the difference whether such increase is based on concentric circles radiating "out" from the person (to greater understanding of external reality), moving "within" the person (as progressively increasing understanding of internal reality), or rather as some form of serial replication. Similarly "subdue", and associated notions of "domination", would be well understood by mathematicians as achieving some form of cognitive control or comprehension of a complex phenomenon.

Consider the case of an amoeba. It is common to perceive an amoeba as "dividing" in order to reproduce. In this sense it "multiplies" by dividing. Can a woman also be said to divide when giving birth to a child? Some would argue that this is how they feel about the process, whether physically or emotionally. The same ambiguity prevails when a community grows beyond a certain critical size and then divides -- through a process whereby there is an effective multiplication.

This ambiguity is inherent to understanding of many growth processes. A growth in understanding is readily associated with the greater subdivision of a domain of knowledge. Progressive specialization is the continuing division of areas of expertise. This multiplies the number of things that are known.

If "multiply" in the original phrase is to be understood to mean "growth", it may be important to recognize the necessary division which accompanies that growth. In the case of the individual, it is clearly ridiculous to interpret such growth as an unrestricted increase in size, which might then result in some form of giantism if successful. Rather there is the expectationthat after reaching a certain physical size, growth will take other forms, expressed by such phrases as a growth in skills or a growth in maturity. Again a form of division somehow counteracts the simplistic understanding of additive growth.

In the case of a community, growth beyond a certain point evokes a need for some form of order. This order is usually closely associated with some form of functional division, and a division of responsibility. Even the largest of countries, or the United Nations system itself, evokes a need for organization into a comprehensible number of parts. Growth can be tolerated provided ways can be found to divide the whole into parts.

Is it wise to assume that "being fruitful to multiply" implied no need for appropriate"division"? Would it not be more appropriate to explore the implications for sustainable communities of the ambiguity in multiply-divide? No multiplication without division, no division without multiplication? The tao of mathematics?

Resistance to any such exploration comes in part from a sense in which "adding" (as the foundation of "multiplying") is seen as inherently more positive than "subtracting" (as the foundation of "dividing"). Taken further it is easy to understand how dividing can be seen as "evil". The process is obviously "divisive" and thus a favoured instrument of the devil. Religions can easily play on this.

The questionable status of subtraction in the collective psyche is also highlighted by an analysis of GNP, understood to be a measure of the health of a country. Unfortunately GNP increases when forests are cut down, with every oil spill, and with every cancer patient or accident. The greens argue that if the planet is to be saved then economists must learn to subtract as well as to add.

The challenge to understanding increases if the multiply-divide polarity is framed in terms of the integrate-differentiate polarity. The latter might almost be orthogonal to the former, with differentiation carrying some of the sense of both multiply and divide. Here it is clearer that without adequate differentiation, integration is of lesser import.

How should the phrase "being fruitful and differentiate" then be understood? How far is it useful to go in differentiation before some degree of integration is necessary to maintain any sense of significance? Is it purely a coincidence that there is so much concern with integration in modern societies? But note the ambiguity around "discrimination", readily condemned as an attitude but yet who would want to associate with someone completely lacking in discrimination?

What is the process of coherence that a simplistic approach to "multiply" ignores? Is the desperate search for a new social order a symptom of the failure to discover the secret of dividing? Whether at the individual, community, national or global level, sustainable identity may be associated with the ambiguity of the multiply-divide, integrate-differentiate polarities. The vain attempt to associate it with a polar understanding is a recipe for dissatisfaction and disaster.

Perhaps stretching this exploration too far, there is a need to recognize that the desperate search for unity at every level of society cannot be achieved through multiplication and differentiation alone. Simplistically, unity is achieved by dividing by the number to which multiplication has brought us.

Other mathematical challenges of the Bible |

(1 Kings 7:23 NIV) The value of pi (or Could such an argument then be extended to the interpretation of "multiply"? --- It has been alleged that the US State of Lousiana (at
the time of the Scopes
Monkey Trial in 1926) endeavoured
to introduce legislation to enshrine the value of pi in law as being
equal to exactly 3 (John
L. Farrands, 1993, p. 50). However
on 18 January 1897, a bill was indeed introduced to the House of Representatives
of the US State of Indiana (House Bill 246, |