What if the same mathematical structures that govern quantum phase transitions in superconductors also govern thermodynamic systems at completely different scales?
What if the cosmic microwave background radiation—which we've assumed comes from the Big Bang—might actually contain significant contributions from early galaxy formation processes that happened billions of years later?
What if the universe's missing matter—40% of all the protons and neutrons that should exist—has been hiding in plain sight within the fractal filamentary structure of the cosmic web?
And what if all three of these discoveries point to the same underlying truth: that the universe operates through recursive mathematical processes at every scale, from quantum mechanics to cosmic structure formation?
Dear Joseph Trukovich , For a substantive discussion, it is necessary to define recursion, a recursive process and a recursive structure at least at a philosophical level. After all, any deterministic system exists as a recursive process - the next state of such a system depends on the previous one.
Boris, you're absolutely right that substantive discussion requires clear definitions. Here is a start:
Recursion: A relation where an entity is defined in terms of itself through finite intermediate steps, with a base case preventing infinite regress.
Recursive Process: A temporal sequence where the same operation repeatedly applies to its own outputs, maintaining operational invariance across iterations.
Recursive Structure: Organizational patterns where identical relational structures appear at multiple hierarchical levels.
Your on point about deterministic evolution. Genuine recursion requires self-reference - the process operates on conditions/structures it previously created - not just state dependency.
Gjergo & Kroupa's galaxy formation framework. If ancient stellar processes contribute to CMB radiation, and if this modified background then influences future star formation conditions with the same physical processes, this could represent recursion. However, demonstrating that the feedback loop actually closes with operational invariance requires further evidence.
Sun & Maciejko's topological correspondences. This shows mathematical universality (same equations in different domains) but no self-reference. This mathematical universality across scales may indicate scale-invariant physical principles that could enable genuine recursion elsewhere.
Cosmic web structure. Connor, L. et al. (2025) in Nature Astronomy Article A gas-rich cosmic web revealed by the partitioning of the mi...
(needs to be cited in paper) demonstrate that galactic feedback processes enrich the intergalactic medium, which forms cosmic web structure. If this connects to recursive galaxy formation, it might suggest a mechanism:Galaxy formation → stellar feedback → IGM enrichment → cosmic web structure → future galaxy formation sites
I don't have my own definition of recursion, but yours is not perfect. It seems to me that it is necessary to highlight how recursive processes differ from deterministic ones. Or to declare deterministic processes recursive. After all, even a series of natural numbers can be represented as a recursion: each subsequent number is one more than the previous one.
the topic of recursion is very close to me. on my page in researchgate.net you can see my articles on recursive mathematics and dynamic recursive model of phyllotaxis
video from my latest article https://youtu.be/qBZrIjCBfc0?si=qxd1vjwhhUuwbnB-
No mine is not perfect or I would probably have some sort of "major award"...it is a work in progress!
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