As a math teacher, I find that visual portrayals facilitate understanding of mathematical concepts. Sometimes, my attempts to think visually bleed into my more theological thoughts. Among other loosely related mathematical concepts I've heard or considered that have afforded some cause for reflection:
#1 - Upon the consummation of the present world, one wonders if our knowledge (or, perhaps, certain other capacities indicating spiritual growth) in this present life will become statically determined by our course in this life or able to further increase. If the latter - which is my intuition and suggested in eschatological passages such as Isaiah 65 and Revelation 21-22 - we might consider our relationship to God as asymptotic. Often times, we hear or talk about God as "infinite." In this analogy, God would rather be like the definitive line towards whom we would ever become closer over the unending progression of time - but without intersection or mergence. This analogy would preserve the Creator-creature distinction but allow us to entertain hypothetical futures as fully sanctified and glorified people yet with the potential for greater conformity to Christ-likeness.
#2 - Some biblical scholars (example) have found what appear to be intricate patterns in Scripture. Chiasms and parallelisms are more well-known examples, but so-called "deltaforms" remind me of the concept periodicity or reverberations. In fact, one day, I envision the possibility of something like a huge screen (extrapolate an IMAX theatre) in which it might be possible to display the entire Bible. To fit our field of vision, perhaps the display would have be coded. In any case, given this scenario, I imagine it would also be possible to highlight or "colorate" verses in this display in which certain symbols, words, numbers, letters, phrases, sentences, themes, and so forth appear. Upon doing so, it would not at all surprise me if patterns were to emerge in some cases - even intertextually, depending on one's canonical organization (e.g. Hebraic Tanakh vs. Protestant Old Testament). This could make for compelling apologetic argumentation regarding textual issues.
#3 - Factor trees are akin to Porphyrian trees. These are useful in various contexts in which one wants an understanding of the scope of subject matter. One might take inspiration from these paradigm models. A massive project I've imagined would be to classify how different traditions interpret various verses. I don't have in mind an atomistic structure in which literally every interpretation provided by every person who has ever lived is displayed within the "tree." Selectivity would be needed regarding which traditions to include and who would function as representatives within each tradition. Even so, an interactive layout along these lines would be quite helpful for catechesis, systematics, comparative religion, etc.
#4 - Finally, what prompted this post is a recent mathematical metaphor has come to mind: in our postlapsarian context, I think we can picture ourselves as zero-dimensional figures, "points" on a one-dimensional, bisected line that represents our lifetime. Even from conception - our "origin" and the "origin" or middle of the bisected line - we have a continuous orientation, attraction, and/or "face" towards negative "values" (which is typically leftwards on a number line).
There are layers here: without divine intervention, our negative moral "values" from conception become intensified the longer we live, i.e. the further that we walk "leftwards" over time. In fact, in a sense, the timeline of our lives started at zero from birth. This is interesting in that typical countdowns end with zero; otherwise, we tend to count upwards from zero. In this picture, however, we are at allowed to continue to exist on the number line of life with an orientation and intensification towards negative values. This exhibits the extent to which our lives are on borrowed credit and the extent to which we presume upon God's goodness and patience.
Now, it takes a transcendent God immanently applies higher dimensional, redemptive grace to our zero-dimensional selves through His incarnate Son. Mathematically speaking, we literally experience a "transformation" as we are reflected across the axis of the number line and turned "about face" to become soldiers for Christ, oriented on a path towards positive "values," i.e. the "right[ward]," heavenly city.
I've thought about whether this illustration could be depicted in different terms. For example, can we consider ourselves as two-dimensional figures who must live and move - whether we travel up, down, left, or right - on a sinful plane of existence? If this is intelligible, it would seem to similarly require a transcendent God to immanently apply higher dimensional grace to our two-dimensional selves through His incarnate Son. In this case, it would seem our selves would be transformed into three-dimensional figures with the orientation towards moving forward towards Christ-likeness (albeit the potential to slide "backwards").
There are both limitations to these metaphors and potential for further development. For example, a limitation of these metaphors is that they are best understood within the setting of a postlapsarian context. In particular, the illustration in which we become "three-dimensional" objects might provoke the misconception that our ontology changes when God applies redemptive grace to our lives, whereas our sinfulness is accidental to our human nature. What is essential to humanity is to have an ethical orientation. The fall of mankind in the first Adam and redemption of those in the last Adam connote changes to our ethical orientation, not to our ontology. Therefore, perhaps the metaphor in which we begin and end as zero-dimensional "points" is more apt (although having a so-called negative orientation again suggests it is better thought of given a postlapsarian context).
Or consider that while the timeline which we have been considering may be conceived of as strictly one-dimensional - a straight line in either direction - it is also possible to conceive of it as, say, two-dimensional. For instance, humans are three-dimensional: it is easy enough for us to conceive of a situation in which we view something that initially appears to be a simple, straight line is actually a two-dimensional figure once we pivot our perspective. Say we have a overhead, helicopter view of what appears to be a straight line. When our helicopter lands, we actually see that the object is actually a two-dimensional polynomial (like a rollercoaster that never turns sideways but does go up and down).
Applying this new setting to the metaphor, we would still be zero-dimensional points on this polynomials, and references to end behaviors, timelines, etc. would still apply. Now, however, we are afforded more freedom of imagination. Consider relative maximums and minimums: these might depict temporal goods or trials that people experience. Or think about the fact that different polynomials have different y-intercepts: from an "overhead" perspective, this would be the "origin" of man, the point on the "line" in which the x-coordinate is zero. From a perspective in which we can view the two-dimensional polynomial, however, we can speak of different y-intercepts as depicting natural or circumstantial advantages or disadvantages that exist from conception. God gives some more "talents" than others, after all.
Surely, more could be said. I wish I had artistic or technological proficiency to show these or other ideas I've had (example). But those are certainly not talents with which I have been endowed!
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