The Trinity: A Numerically Consistent God

Back in 2011 during a math class, one of the lectures caused me to start thinking about the properties of the number one. That led to some thought about the Trinitarian nature of God which is assumed in the Bible, and this is an attempt to organize those thoughts. Here I will demonstrate how our theological understanding of the Trinity is inherent in the numerical idea of “one”. If we try to define the number 1 using basic arithmetic we find a mathematical expression that models a Triune relationship. I will then compare the model to various teachings about the Trinity, both to the traditional Church teachings that are laid out in the Athanasian Creed, as well as to teachings that are commonly viewed as heresy.

It is important to acknowledge from the beginning the fact that every other illustration previously tried fails in one way or another to accurately represent what is taught in Scripture. It is because of these attempts that heresies and division are introduced into the Church, so such illustrations should not be held on to very firmly and rejected as soon as a conflict with Scripture is found. Even so, curiosity has prompted me to examine the initial idea as far as such study will take me. This is not a "proof" of what Christianity teaches about God but an illustration based on the assumption that those teachings are true.

If we're going to try to illustrate a non-physical reality, we're going to have to depart from physical illustrations. The second Commandment teaches us that God is not like any created thing, so we ought not to use created things to try to represent him. However, the concept of “one” is uncreated. Even though it is found within Creation, the idea of “one” exists as an eternal truth. Because numbers are a conceptual reality rather than a physical one, a numerical model may not be prone to the same errors that are introduced by physical models. Throughout the Bible God describes himself as one (Deuteronomy 6:4), so it may help to examine the numerical idea of "one" to understand its properties.

Think for a moment about the concept of "1." If we try to define the number 1 numerically, we would start by writing a vertical line as follows:

1

We see that and associate meaning with it because we've been taught to do that ever since we learned to count.  But suppose we didn't know what that symbol meant. It needs a precise definition to describe its value. Mathematicians use the equal sign, which is a statement both that something has value and that this something is completely described by whatever comes next. In plain English, the equal sign is a form of the verb "to be."

1=

But an expression of one with only one operand is incomplete and meaningless:

1=?

If God is one being, then his being cannot be only one person because the statement of being would be incomplete. A statement of being must contain a definition. Religions that teach that God is one being and only one person would be correct to say that God is unknowable. Such a god could not be self-aware nor would it exist; it would be unknowable even to itself. Suppose we try an expression with two operands:

a.         1=1

b.         1/1=

c.         1x1=

These are the only possible expressions of one with a single value; addition and subtraction involve more than one value. The first is logically useless because it is defined as itself. Everything that exists is equal to itself, but that is circular reasoning, and is not meaningful. Such a god would be knowable only to itself; it could not express itself outside of its own being. The second and third lack a result; they are incomplete statements of being. If God is a being who is self-aware and can make himself known, then he must have more than two persons within his being. Now consider an expression that is personified by three operands:

1/1=1

This is the simplest meaningful expression of the value of 1. It is defined by an interaction between the numerator and denominator and summarized by the result. This expression of “one” is meaningful and precisely defines the concept of one, because there is no other number that can achieve the same relationship. For example,

0/0 = Undefined

Infinity/Infinity = Undefined

-1/-1 = 1

2/2 = 1

With the exceptions of zero and infinity, every number divided by itself reduces to one, so one is the only number that keeps its proper value when denominated by itself. Only numbers denominated by one retain their own distinct value. As a side note, this demonstrates a few things from Scripture. Firstly, no one other than God can be self-existent (denominated by oneself). Secondly, anything that tries to define itself apart from God dies, meaning that it reduces to something other than itself.

The key to this definition is the equal sign, because it is a statement of being: that meaning or value exists. As a form of the verb “to be”, the equal sign is the “I Am”, or the statement of existence that unifies the expression. The Hebrew name for God is Yahweh, which means I Am. The name implies his eternal, self-existent nature.

Now for the sake of argument, suppose we were to try an expression with more than three operands. Since the definition of one is already complete using three operands, a fourth operand would contribute nothing. The expression would always simplify into one using the original three operands, leaving the basic form unchanged. For this reason, the definition of one using itself cannot contain more than three operands. (It can be rearranged using multiplication instead of division, but we will consider that variation later)

Summary of Doctrinal Teachings

The initial three points are a short summary drawn from the book Systematic Theology, by Wayne Grudem, and the rest are derived from the Athanasian Creed, which detailed the orthodox understanding of the Trinity as early as the fifth or sixth century A.D. (the precise date is uncertain):

1. God is three persons.

2. Each person is fully God.

3. There is one God.
4. The three persons remain distinct and unique though they form one being, and the one being remains indivisible though it is three persons.

5. The Father is neither created nor begotten (generated).

6. The Son is of the Father alone; not made, nor created; but begotten.

7. The Holy Spirit is of the Father and of the Son; neither made, nor created, nor begotten; but proceeding.

8. The three persons of God are co-eternal; none come into existence before or after the others.

9. The three persons of God are co-equal; they are equal in substance and equal in importance.

Doctrinal Analysis

Here I will examine the illustration and compare it to the orthodox teachings of the Trinity outlined above.

1/1=1

1. There are three distinct operands, (or roles or persons) which carry unique functions: Numerator, Denominator, and Result.

2. Each operand is equal to the whole of the expression.

3. By definition, there is only one value of 1 expressed.

4. The Numerator is not the Denominator or the Result, the Denominator is not the Numerator or the Result, and the Result is not the Numerator or the Denominator. The three operands remain distinct from each other while also being inseparable.

5. The Numerator is not “made” by either of the other two operands or by anything else; it “just is.”

6. The Result is the exact representation of the Numerator, and is generated or “begotten” by it.

7. This point is tricky to argue, since it appears that the Result must flow from the Numerator and Denominator together. However, if we review how the illustration is built, we see that the concept of the denominator naturally follows once the other two operands have been considered. So it is not the second but the third operand necessary for a complete definition of the being. This is more clearly evident in the transition between the two-operand and three-operand examples above. The numerator and result could, in theory, know each other apart from the denominator, but this knowledge would be circular and internal only; nothing external to the relationship could have knowledge of it at this point. To be knowable externally as well, the denominator must also exist, completing the meaning of the other two operands. In the same way, the Spirit is the one who reveals the knowledge of God.

8a. The concept of 1/1=1 is an eternal truth having neither beginning nor end. There can never be a moment when 1/1≠1.

8b. Each operand is necessary for the existence of the other two; therefore none of the three can come before or after the others:

0/1≠1

1/0≠1

1/1≠0

9. The three operands are equal in value and their respective functions are equally important to the definition.

Also,

10. The quantity 1 must exist prior to the existence of any other number, because no other number precedes it in value, but it also can exist without any other number, being fully self-sufficient.

11. No number other than one can search out the value of one without expressing a value less than 1 (e.g. 1/2, 1/3, 1/4, 1/5, ...).

The following variation of the three operands may also be examined:

1=1x1

This arrangement of the equation occurs in the baptism of Jesus, because the Father sent the Spirit to equip the Son for ministry. The Result of that ministry was to glorify the Father, during which time the focus of the equation was reversed. There are still three operands that are distinct: Multiplicand, Multiplier and Result. Each operand remains distinct from the other two, functionally different, and inseparably unified. The Son would be the multiplicand, the Spirit would be the multiplier, and the Father would be the result.

Somewhere I have seen an illustration similar to this which at first glance appears helpful, but which fails in specific ways:

1x1x1=1

Although there is one value and one statement of being, there are four operands, or persons, two of which are identical in function.

There is one final numerical arrangement possible in the illustration, when the Son returned to the Father and together they sent the Spirit to empower the Church:

Father/Son = Spirit

This is equivalent to the original equation (1/1=1), so it carries all the same qualities.

Comparison to Scripture

Deuteronomy 6:4, “Hear, O Israel: The Lord our God, the Lord is one.”

There is only one statement of being: one equal sign.

1 Corinthians 8:6, “yet for us there is but one God, the Father, from whom all things came”

This allows us to suggest that the numerator is the Father, because the numerator is the operand from which value is derived, and which begets or generates the value of the result.

1 Corinthians 2:10b, “The Spirit searches all things, even the deep things of God.”

Luke 1:35, “The angel answered, “The Holy Spirit will come upon you, and the power of the Most High will overshadow you. So the holy one to be born will be called the Son of God.”

Isaiah 61:1a, “The Spirit of the Sovereign Lord is on me, because the Lord has anointed me to proclaim good news to the poor.”

These three verses make it plausible to think of the denominator or the multiplier as the Holy Spirit. The denominator is the operand that defines the value of the numerator and reveals that value in the result. Without the denominator, we cannot know the value of the result. The multiplier is the operand that gives power to accomplish something.

Genesis 1:2, “Now the earth was formless and empty, darkness was over the surface of the deep, and the Spirit of God was hovering over the waters.”

Romans 8:11, “And if the Spirit of him who raised Jesus from the dead is living in you, he who raised Christ from the dead will also give life to your mortal bodies because of his Spirit who lives in you.”

1 Corinthians 2:9-10a, “However, as it is written: “No eye has seen, no ear has heard, no mind has conceived what God has prepared for those who love him” — but God has revealed it to us by his Spirit.”

1 Corinthians 2:14, “The man without the Spirit does not accept the things that come from the Spirit of God, for they are foolishness to him, and he cannot understand them, because they are spiritually discerned.”

These verses teach that we cannot know or receive Christ unless the Spirit makes him known to us, and that we are dead unless the Spirit gives us life. This is the same, both in the first creation and in the second creation which is Christ. This function parallels that of the denominator which gives substance to the numerator and reveals the result.

Hebrews 1:3 “The Son is the radiance of God’s glory and the exact representation of his being,”

This verse suggests that the Result is the Son, Jesus. The result is the exact representation of the numerator.

John 5:19, “the Son can do nothing by himself; he can do only what he sees his Father doing, because whatever the Father does the Son also does.”

As is the numerator, so is the result. They are identical in value and attributes, but different in role: the value of the result is fully dependent on the value of the numerator, and the function of the result is to fully display the value of the numerator.

Comparison to Known Heresies

Modalism (Sabellianism) is the belief that God is one person taking on different modes. This illustration avoids Modalism because there must always be three different operands in unison, not one operand. The numerical illustration differentiates between the concept of a "being" and the concept of a "person."

Arianism is the belief that the Son was "created" and thus not coeternal with the Father. It confuses the meaning of the word "begotten" in John 3:16, and tries to make sense of the Father-Son relationship in a temporal sense rather than an eternal sense. This illustration avoids Arianism, because the Result must be co-eternal with the Numerator and the Denominator, even while it proceeds from them.

Subordinationism is the belief that the Son and the Spirit are not equal to the Father in nature and substance. It mistakes submission to the Father as a matter of value rather than role. This illustration avoids Subordinationism, because the Denominator and Result (Spirit and Son) are of one substance with the Numerator, and therefore share the same attributes.

Adoptionism is the belief that the man Jesus was adopted by the Father as his son, thus denying the eternal nature of the Son. This illustration avoids Adoptionism, because the Result exists from the same moment that the Numerator and Denominator exist, and vice versa.

Tritheism is the belief that the three persons of God are three beings rather than one being. This illustration avoids Tritheism, because there is only one value of one involved in the definition.

Objections

1. Doesn’t the equal sign add something to the doctrine of the Trinity? What about the use of the division and multiplication signs?

As a part of the expression, the equal sign does not itself exist but declares the existence of the three operands. If we were to take out the equal sign, it would be like God saying “I” without following it with “Am.” Similarly, the division and multiplication signs are not themselves parts of the expressions but are operations carried out between the parts. These specific operations may be seen in 1 Corinthians 2:9-14 and Isaiah 61:1.

Final Thoughts

Thank you for staying with me for all of that! In the traditional sense this is not an illustration, but an essay on the concept of "one." This is not to say that the number 1 is God, but that God describes himself using the properties of the number 1. Because of this, it seems reasonable to suggest that any qualities reflected in the nature of "oneness" should also to be consistent with the nature of God. I've examined this illustration as far as I can, considering established Church teachings, relevant parts of Scripture and known heresies each without finding fault. If in any way it should seem to differ from Scripture, then I look forward to discussion on it.

On the other hand, if it does prove accurate then it should still be handled carefully; only God can change a person's heart and demonstrate his own existence, and he does this personally through his own words, written down in the Bible, and not by logical arguments made by man. With that in mind, Scripture mentions four areas in which we are to worship God, and the mind is one of them (Mark 12:30). I hope this is useful toward that end. 

For anyone reading this who has not repented and turned to Jesus for safety from God's wrath, I hope and pray that my God will save you from the power of sin and death as he has saved me. Because of what Jesus did, I have an eternal guarantee that my God will show mercy to me on the day when all men are brought to justice, because my God cannot change his mind.

"Men swear by someone greater than themselves, and the oath confirms what is said and puts an end to all argument. Because God wanted to make the unchanging nature of his purpose very clear to the heirs of what was promised, he confirmed it with an oath. God did this, so that by two unchangeable things in which it is impossible for God to lie, we who have fled to take hold of the hope offered to us may be greatly encouraged. We have this hope as an anchor for the soul, firm and secure. It enters the inner sanctuary behind the curtain, where Jesus, who went before us, has entered on our behalf." -Hebrews 6:16-19