Natural Blogarithms

Non-monotonicity of faith development

May 3rd, 2006 by SplineGuy

The spritiual journey for the Christian, although asymptotic, is not a monotone journey. Of course it is neither monotonous, but I am referring to the mathematical concept of a monotonicity as it refers to sequences of real numbers.

Def: (informal) A sequence is an ordered list of real numbers.

Def: (formal) An infinite sequence of real numbers is an function whose domain is the set of positive integers and whose range is a subset of the real numbers.

For example, consider the following sequences,

Ex: The Fibonacci Sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, . . .
       (where each number is the sum of the previous two sequences)
Ex: An Arithmetic sequence: 1, 4, 7, 10, 13, 16, . . .
       (where each number is the previous value increased by 3)
Ex: A Geometric Sequences: 3, 6, 12, 24, 48, 96, . . .
       (where each number is the previous value multiplied by 2)
For more see the Online Encyclopedia of Integer Sequences, a very interesting site that will answer the question, “What comes next?” for just about any integer sequence you can think of.

Now, back to monotonicity. A sequence is monotone if it is entirely increasing or entirely decreasing. Formally, we would say that a sequence of terms, $a_1, a_2, a_3, a_4, \ldots$ is increasing if $a_1 \leq a_2 \leq a_3 \leq a_4 \leq \cdots$ . Or it is decreasing if $a_1 \geq a_2 \geq a_3 \geq a_4 \geq \cdots$ .

Ex: All three sequences mentioned above are monotone since they are all entirely increasing. The all go up as you go further out.

Ex: 1, 3, 2, 4, 3, 5, 4, 6, . . .
This sequence is not monotone. Even though it is growing larger the farther out you go, it does not do so monotonically.

Now, consider the following spiritual application. If we think of our spiritual lives as sequences, discrete moments in our faith development, we can think about the “destination” or convergence of our sequence. We see this in Ephesians 4:11-13

It was he who gave some to be apostles, some to be prophets, some to be evangelists, and some to be pastors and teachers, to prepare God’s people for works of service, so that the body of Christ may be built up until we all reach unity in the faith and in the knowledge of the Son of God and become mature, attaining to the whole measure of the fullness of Christ

However, we certainly may stumble along the way. Even stray from the path for long periods of time, but God is faithful to complete that which he began. It seems like sometimes we are beyond reconciliation. We’ve gone too far, but what can separate us from the love of Christ?

For I am convinced that neither death nor life, neither angels nor demons, neither the present nor the future, nor any powers, neither height nor depth, nor anything else in all creation, will be able to separate us from the love of God that is in Christ Jesus our Lord.
Romans 8:38-39 (NIV)

So, the sequence of our character development is guaranteed to approach that of Christ’s character. There will be bumps in the road. But I take comfort in the guarantee of God’s faithfulness.

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