I struggle (gladly) with where to begin as so much of this aligns with the work or directions that I’ve come to value most in my studies. While I have the thought-energy, I’ll not save the best (to me) for last and respond first to your work on mathematical intuition, which per se, I can only observe from the bleachers, but am immediately inspired regarding the portion of your study that attends to why mathematical intuition is sometimes wrong. My enthusiasm is sparked because high up on my list of intuition-mysteries, from a depth psychological approach, and from personal experience, is that, yes, it often wrong. At first, I sought to learn something of the mechanics of why this happens (and in my opinion, this is precisely what your work is doing, and even better that it comes from a field distinct from more common depth psychology terrain ((although I have read Number and Time, and am very fond of Marie-Louise von Franz’s work—bookmark that–and I’m guessing then that your approach exemplifies the new-to-me term: complexity-science and if that misses, then of a multidisciplinary character).
Anyway, I made unsatisfactory progress in my inquiry and instead shifted the question from “why and how” to “what is the value of the wrong-intuition phenomenon.” In the end, I entertained the idea that intuition is such a powerful function–I deem it the highest value of Jung’s four functions, because it overlaps with, or brushes shoulders with, or indeed is, uh, magic, or (and pardon me for putting it so without backup, but to save time) limited omniscience—maybe prescience a better word–and “feelings” (will pick that up later). I like looking for balances (and hence counterbalances), and so inferred that intuition being so great, must come at an equally high price. Why Mickey Mantle became my go-to mascot for this phenomenon as he led the league in homeruns four times, but also led it in strikeouts five times. Not particularly good science, but enough to bring me some peace on a matter I was not making progress in. And also, as a mythologist, I appreciated Mantle’s, to some, rather mythic/legendary career/life. Bottom line: high gains, high losses, and high-stakes—After all, when “right” it utterly crushes the probability curves.
But when one acts prematurely on an intuition that later proves to be wrong, very high prices are paid. Not very scientific, Mickey Mantle, etc., but serves a value for me. Nonetheless, I may give reading your work a try if it’s not specialized beyond my means, though likely is. The struggle with multidisciplinary approaches, each approach one could camp out on for lifetimes—how much math or physics, or astronomy (my three favorites of the sciences in ascending order) to “learn” when poetry is my chosen main field. It bests, for me, the depth psychology, the alchemy studies (bookmark), and even (gasp) mythology. But they’re all so related, and I have digressed.
…but can segue via intuition into synchronicity. Primarily because acausality apparently accompanies both. And secondarily, because of my interest in synchronicity as “signs.” And I don’t mean Jung’s distinction from “symbols,” but rather the common usage, “a sign from god,” “an omen,” etc. Because just as intuitions come in the wrong variety, so do synchronicities deemed as signs. For example, I am on foot, and northward someone awaits me for something I have reluctantly committed to. To the south is the nature preserve where I really need to go walk and do “my thing” for a change—“embrace my freedom,” I think to myself. And at the moment of that last thought, torn between the two choices, a bald eagle swoops down and perches on a sign right before me that reads “ONE WAY” and the arrow obviously pointing south. And let’s add it’s my first bald eagle encounter, lifetime. And that I’m into the whole “America” thing. Point being, although I’ve not had that experience, I have had experiences that I’d say match and even surpass it in magnitude. In short, I followed the signs. And indeed they had often been, against all odds and faith, very wrong directions. In James Hillman’s view, a wrong intuition is still an intuition. Similarly can one say a wrong synchronicity (in this “sign” context) is a wrong synchronicity? Ah, but then one can look back years later and see how that “mistake” contributed to one’s deepening, individuation. Alas, strikeout. Additionally, I may have conflated sign and synchronicity too lazily. Maybe some unforeseen value in the correlation though. Anyway, to conclude the thread, my final deduction was that the deity concerned with my well-being sent a very clear message: “Stop relying on me to make your choices for you; embrace your autonomy.” Or something like that.
Back to your complexity-science/mathematical model approach (and your distinction of models from the real thing noted) of acausality of the emergence and the possibility of causality being present, but as a not-yet-identifiable presence. All of which investigating the connection between, as you say, inner and outer. And here, one might suggest that “my” inner was projected onto the eagle, but that would not be synchronicity, rather it would interpretation, or hope, even. Just felt it important to back up and distinguish that, obvious though may be. [and here I lost the thread, and was over my head anyway. So rather address the gestalt of the approach(es) you’ve shared. It feels (and by the way, I associate “feels” and even “feelings,” indeed, “emotionality,” more with intuition than I do with the feeling function, which frustrates me greatly regarding the titles Jung has applied for the four functions. Though someone may show me the err in my ways and save me, thank you in advance). (And I guess it’s obvious now, and perhaps equally frustrating, that I move ideas forward like a novice shepherd moving way too many belligerent sheep, many of whom having little to nothing to do with each other—big fan of the inductive)–point being, the gestalt of your complexity-science approach appreciates that the potential discoveries that can be, not cornered, or not initially at least, but nuanced out, or honed out, so to speak, from the traction or friction between disparate contexts when said contexts are put in the same room together (cf. alchemy/alembic). And that, if accurate, speaks very directly to the mechanics of metaphor, which is in my wheelhouse. And will resist going on about metaphor right now–sheep in all directions and as far as the eye can see.
The sleep-deprivation challenge continues, and so must etc. And can only give this a one-time read through before posting. It requires much more time than that. Anyway, I regret didn’t get to what you shared regarding imagination requiring real. In your words: “Perhaps most importantly, this model serves as an object through which one’s imagination can take flight, but flight which is not entirely free, but necessarily tied in some ways to the real world.” (similar to my thoughts on “honing out the discoveries from the traction friction of disparates” above. Only in this case it’s more “opposites”). Further, to your (intuition, maybe?) of the necessity of imagination and reality, my editor and fellow Mythblast author Bradley Olson introduced me to Wallace Stevens’s essays on imagination. Excellent stuff—especially in the first essay that addresses the necessity of the tension between imagination and “reality” as a conflict between connotative and denotative language (or one’s read of language)(attitude of the perceiver stuff), where denotation gives clear structural direction, and connotation provides the multiplicity of association, the scattered herd of belligerent sheep, if you will. Also, it brings to mind from I forget now which alchemical text, “The Emblem of Avicenna” which I think you’d appreciate: an image of a flying bird tied by a chain to a sort of toad-like/gila monsterish thing on the ground, and is also called “Fixing the Volatile.”
And that leads to the next regret, not time for diving into the alchemy. That’s one that I study pretty thoroughly, and Marie-Louise von Franz my preferred presenter–in that, and in other things.
And lastly, it should not be overlooked your: “I have found that when the individual has done the leg work, meaning when they have exhausted themselves in doing the analysis, the reflection, etc., the response by the unconscious is often stronger and of far greater clarity and relevance.” Indeed. That has been unequivocally my experience, do the inner work: meditation, dreams, poetry, science, avocation, etc.,. And fighting sleep again, but one lastly last on this: I find it very amusing that for all the hard work one does in this inner-work business, in the quest to achieve greater liberation, they are guaranteed, as a reward, to incur upon themselves not less, but ever increasing responsibility. Apparently our reward for progress is to be held accountable for the levels (or whatever one wants to call them) we achieve. Let that be a warning to all the fortunate ones who excel in the work. Ha. I sleep.