The Trinity and Mathematics
November 9, 2001
The Christian doctrine of the Trinity is a stumbling block for some individuals, especially those who adhere to other religions. Atheists may claim that this doctrine is irrational. Many Jews and Moslems have the impression that the Christian religion is polytheistic, which is abhorrent to them. The doctrine is nowhere explicitly enunciated in the Bible, but is the result of Christian theologians trying to reconcile seemingly contradictory scriptures. This seeming contradiction consists of two basic biblical truths: 1) that there is one God (clearly stated in Deut. 6:4 "Hear, O Israel: The LORD our God is one LORD") and 2) the many scriptures which indicate that the Father, the Son (Jesus Christ), and the Holy Spirit each has the attributes of God yet are distinct Beings. Any Christian text on Theology can provide many supporting scriptures for this second point, so it is not believed to be necessary to expand upon it here. So, is there one God or are there three Gods? The doctrine of the Trinity states that there is one God, yet each member of the Godhead mentioned above is God and is distinct from the other members. This, indeed, sounds like a contradiction. It is usually explained by referring to it as a mystery, something which is incomprehensible to humans, and yet is still true. Our natural way of thinking tells us that there is no way that 1 + 1 + 1 = 1. Yet this is what the doctrine of the Trinity tells us is the case about God. Throughout history there have been many attempts to use analogies in order to illustrate the Trinity. For instance, one such analogy is the egg, consisting of the yolk, the white, and the shell. There is one egg, with three parts. However the egg fails as an adequate analogy since there is no way that a yolk can be considered an egg. Nor may either of the other parts be considered an egg. The egg analogy is simply three parts of a whole which is not analogous to the Trinity. Nor is even the triune nature of man (spirit, soul, and body) an adequate analogy. Again, these are simply three parts of a whole, similar to the egg analogy. There have been many other such attempts and they all, likewise, fail to adequately illustrate this doctrine. A mathematical attempt to explain the Trinity has been to replace 1 + 1 + 1 in the above equation with 1 x 1 x 1. 1 x 1 x 1 does equal 1; but this is not analogous to the Trinity. In reading this equation, we would say "one times one times one equals one". If I said two times four, we would understand that to mean that we have two groups of four, which is equal to eight, objects. Therefore one times one means one group of one which is just one and in no way may be considered to be two. In the same way, one group of one group of one is just one, and in no way may be said to be three.
However, there is a mathematical way to illustrate
how 1 + 1 + 1 can equal 1.
This is by using the concept of infinity: one infinity plus
one infinity plus one infinity equals three infinities, and,
as any student of mathematics knows, three times infinity equals one infinity.
So one infinity plus one infinity plus one infinity equals one infinity.
One infinite Father plus one infinite Son plus one infinite Holy Spirit equals one infinite Godhead.
Since God is infinite, this is a suitable mathematical description of the doctrine of the Trinity.
This in no way detracts from the mystery of the doctrine since infinity, like the Trinity, is beyond our ability to comprehend.
It is simply hoped that this mathematical description will satisfy those who accuse Christians of having a conception of God which is irrational or polytheistic.
© 2001 Arthur Manning
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