This is a description of an emblem, a vivid and possibly surreal image, with associated meanings. I think that deliberately crafting emblems for oneself is possibly useful (I have written about the project in a post called "Deliberately creating mental-entities; chunks"), but certainly fun.
You may be able to assemble a novel concept by putting two familiar concepts beside or in sequence to one another. This is often how conceptual blending is described. However, in the opposite direction, you may also be able to "parse" a familiar concept into subconcepts. These subconcepts are not necessarily smaller or simpler concepts in any way - they're only "sub" concepts in that that you could recombine them, via conceptual blending, into the "super" concept. These subconcepts might be novel, or one or both of these subconcepts may be familiar.
Let me tell you about one time that this occurred to me. I was sitting in the window of the student center at the Portland campus of the University of Southern Maine (the window is about a foot deep, and the bus stop for the shuttle bus to the Gorham campus is right outside, so it is a good spot to wait for the bus, which I did a lot when I was a teenager taking classes at USM and living in Gorham). I was taking a linguistics class, and I learned the word "monopthong", meaning "a vowel phoneme that has a single perceived auditory quality". I was already familar with the meaning of the word "dipthong" and the "mono-" and "di-" greek prefixes meaning "one" and "two" in other contexts such as "a diatomic molecule". However, learning the word "monopthong" caused my understanding of "dipthong" to split. Due to my unfamiliarity with the greek "pth" consonant cluster, I had not previously understood it as containing an occurrence of the "di-" prefix.
To be explicit, I realized that "dipthong" = ("di-" / "pthong"), where "dipthong" and "di-" were familiar to me, and "pthong" was novel to me. (The slash between "di-" and "pthong" is intended to be a non-commutative binary conceptual blending operator, borrowed from Margaret Masterman's interlingua NUDE.)
Let me tell you another occurrence, also from linguistics and/or phonetics. The letter j or g in English spelling often indicates a sound that occurs at both the beginning and end of "judge", at the end of "nudge", and the beginning of "genius". In learning IPA, I discovered that there is no symbol for this consonant. Rather, IPA renders this as a cluster of two consonants - first a symbol /d/ for a voiced alveolar plosive sound familiar as the initial consonant of the word "duck" (and which Kingsley Read calls "day"), and then another symbol, /ʒ/, for a voiced palato-alveolar fricative, familiar as the middle consonant of "vision", which IPA names "ezh" (and which Kingsley Read calls "j'ai")
This was an example of my discovering, realizing, or learning that "jay" = ("day" / "j'ai"), even though all three of those were familiar concepts to me.
I associate to this phenomenon of parsing a familiar concept into parts an image from China Mieville's "Embassytown": "the enormous rock that marked [Embassytown's] edge, which had been split and set again with mortar". Embassytown cannot quickly be summarized, but "the rock which had been split and put back together again" is an important symbol, in a book about symbols.
There is the resonance between, on the one hand, the word "monolith" with an etymology of "one rock" and my memory of encountering the word "monopthong" - they share the same greek prefix - and, on the other hand, the meaning of the "-lith" greek suffix - rock - and the literal rock at the edge of Embassytown.
I associate to this an argument from Galileo, that argues against a default (established by Aristotle) theory that heavier objects fall faster. Galileo imagines dropping and timing a barbell-shaped rock, and gradually shifting the barbell's proportions, making the connecting part thinner and thinner, until the "barbell" can be viewed as two spheres falling adjacent to one another, either lightly touching at a single point, or connected by a tiny strand of gossamer. If and when we eventually break the strand of gossamer, Aristotle's theory would predict that the rocks suddenly start falling half as fast. This seems unreasonable. We have (unstated in the original) expectations of some sort of continuity or symmetry or relevance that constrain what forms the law of gravity might potentially have - it must treat effectively identical situations identically, regardless of whether we "parse" the situation as one barbell-shaped object, or two lightly connected objects.
Galileo's argument has some relevance to Bond Graphs. Bond graphs are a system of modeling that is particularly appropriate for modeling power trains, that emphasizes the possibility of "lumping" subparts of the system. The theory of bond graphs is again too large to quickly summarize, but to gesture at the relevance: given a power train with stages A, B, C, and D, you could view it as (A / BCD), or (AB / CD) or (ABC / D), and each of these ways of viewing the whole need to be compatible, which yields some useful constraints.
Overall, I will call this emblem "The Dilith", and visualize it as a boulder with a diagonal "/" of mortar through it.