From Fragmentation to ψ_Integration

[David Bibby]

Dear All,

I would like to share some further reflections on the Riemann Hypothesis, this time attempting to integrate it with contemporary cultural issues by addressing a pressing concern: the fragmentation of society.

https://docs.google.com/document/d/e/2PACX-1vRdrffDUVmisTP-GxcLiP913U2ie2KhVbBqG85e_rMUjcalcH5SoF8IkJhl3tncxymKB3TX3bn32D3s/pub

"The Riemann Hypothesis stands, then, not only as a boundary of mathematical knowledge, but as a doorway to intellectual and cultural renewal. Its resolution—virtual, existential, luminous—awaits not only a mathematical proof, but a person who is willing to become."

Kind regards,

David

[Doug Mounce]

Dear David,

Interesting use of the Psi character in Lonergan's categories.  You might want to test how far the representational view of knowledge dominates philosophy of knowledge, but I would agree that philosophy of physics (which is what most people mean by "science") tends to be representational.   Also, I think presenting Lonergan's structure of method as first, second, and third operations loses some important features of interplay between the levels.  In any case, I would add ψ-gravity as an area in need of integration.  In that regard, I think that Robert A. Wilson has some intimation of structures that actually fit the data, but I can't follow his use of Lie or Clifford algebras or most of what he talks-about.  regards!  Doug

“You see, the Lorentz group is defined by the concept of inertial frame, and you cannot define an inertial frame without a background. So the Lorentz group is background dependent by definition.”

https://robwilson1.wordpress.com/2025/07/29/background-independence-2/

~/

https://staff.washington.edu/mounce/

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[David Bibby]

Dear Doug,

Thanks for your interesting remarks.

I was particularly intrigued by your notion of ψ_gravity, which seems a fruitful area for integrating mathematics and physics. The ψ-symbol indicates Lonergan’s realm of interiority, so ψ_gravity would not be an alternative theory of gravity, but an interior counterpart of gravitational theory — a shift from descriptive common-sense models (“heavy objects fall down”) toward a universal explanatory framework that situates gravitational phenomena within a coherent field of meaning.

Wilson’s observations are provocative, particularly his claim that the particle mass ratios may not be fixed constants. In Lonergan’s terms, his identification of the Lorentz group as a merely descriptive framework is significant: it suggests that the invariances we take as given may in fact be conditional on deeper structures yet to be uncovered. This points directly to the kind of shift ψ_gravity invites — from treating such structures as immutable backdrops to uncovering the deeper, relational conditions that make their apparent invariances intelligible.

Where ψ_gravity could contribute is in articulating those deeper structures not just as empirical regularities but as the conditions of intelligibility for any coherent account of space-time and matter-energy. This would involve integrating:

• the classical heuristic structures of local determinism (as in the Standard Model and QED), and

• the statistical heuristic structures of global unfolding (as in space-time and cosmology).

This marks the shift from a descriptive viewpoint — where the “background” of physics is a fixed stage and “mass” an intrinsic property — to an explanatory one, in which the background itself emerges from the relationships among the entities it contains. In this light, “mass” is not simply built in, but arises from an object’s place within a dynamically interconnected field. The same structural shift has a communal and ethical analogue: just as gravity binds matter in a shared space‑time, so a higher communal horizon binds persons through shared frameworks of understanding and purpose.

Best wishes,

David

On 4 Aug 2025, at 19:53, Doug Mounce <doug....@gmail.com> wrote:



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