Re: [lonergan_l] Ψ -transformations explained simply

[David Bibby]

Dear John,

Here is a "simple" explanation of ψ_transformation, courtesy of ChatGPT.

Best wishes,

David

A ψ_transformation is a way of talking about what happens when our understanding shifts into a new pattern of intelligibility. It names the movement of consciousness when we are no longer satisfied with a partial or fragmented grasp of things, and we integrate those fragments into a new, higher viewpoint.

Lonergan often describes how insights don’t just accumulate; they can reorganise our whole horizon. A ψ_transformation is that reorganising shift: the point where our questioning, insights, and judgements come together in a fresh unity of meaning.

One analogy is a “phase change.” Just as water doesn’t gradually turn into ice molecule by molecule, but shifts state at a threshold, so too our understanding sometimes reorganises itself all at once. Another analogy is moving from a local puzzle-piece to seeing how the whole puzzle fits together.

So, ψ_transformation is not a technical algorithm, but a name for the inner dynamic of consciousness: the leap from the local to the global, from fragments to a whole. It’s part of how insight grows into understanding, and how understanding develops into wisdom.

On Monday 1 September 2025 at 21:49:28 BST, 'David Bibby' via Lonergan_L <loner...@googlegroups.com> wrote:

Dear John,

Thanks for your question and the reference to Sizikov’s article.

The first thing to say is that the ψ_transformations discussed on this site are entirely distinct in origin and purpose from the Ψ-transformations employed by Sizikov and Chichinadze. The latter arise in computational optimisation, where the aim is to locate the global maximum of a continuous function. Their constructed Ψ-function is a heuristic device, obtained statistically, that serves as a guide for where the global optimum might lie.

By contrast, the ψ_terminology I am employing comes from Lonerganian philosophy and mathematics, where the focus is on modelling insight, personhood, and proof. Here the goal is to illuminate the structure of consciousness itself, with ψ representing the dynamism of consciousness, sublation, and the integration of intelligibility.

In this context, ψ_transformation is a movement in “insight space.” A helpful analogy might be a unitary transformation in quantum mechanics: such a transformation changes the form of the wave function (also using the symbol Ψ) while preserving the probability density. This has no physical, measurable impact, but it does alter the mathematical expression, which is its meaning or intelligibility.

That said, there are some resonances between the computational and philosophical contexts. In each case, the Ψ symbol concerns moving from local traps toward a higher integration. In optimisation, Ψ-transformation avoids being stuck in local minima; in ψ_proof, ψ_transformation avoids being confined to partial or lower-level intelligibility. Both point to a structural need to move from the local to the global through an auxiliary operation that cannot be reduced to stepwise deduction.

I am still exploring how ψ_transformations could contribute to an overall solution, but I hope this helps to clarify the distinction and remove any misconceptions.

Best wishes,

David

On 1 Sep 2025, at 07:34, 'John Raymaker' via Lonergan_L <loner...@googlegroups.com> wrote:



Journal of Physics: Conference Series

Journal of Physics: Conference Series

DAvid, your comments on Ψ -transformations are quite technical and interesting. I am trying to understand what you wrote. Could you elaborate a bit more as to how Ψ -transformations can be part of an overal solution, John

DPaper • The following article isOpen access

Application of Ψ -transformation to the search for continuous function’s global extremum on simplex

A Sizikov

Published under licence by IOP Publishing Ltd
Journal of Physics: Conference Series, Volume 1203, International Conference "Applied Mathematics, Computational Science and Mechanics: Current Problems" 17–19 December 2018, Voronezh State University, Voronezh, Russian FederationCitation A Sizikov 2019 J. Phys.: Conf. Ser. 1203 012073DOI 10.1088/1742-6596/1203/1/012073

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Abstract

A nonconvex problem of mathematical programming, the acceptance region of which is simplex. A two-stage algorthm is suggested to solve the problem. At the first stage, the global optimum region is determined; at the second stage, local clean-up of the solution is carried out. The first stage is realized by the Ψ -transformation method, which is an alternative to direct random search techniques. The method is to build and use Ψ -function. Ψ -function is built emperically based on statistic tests. To perform the tests, the generator of random points evenly distributed in simplex is used. Even distribution in simplex is achieved through affine and linear transformations of points evenly distributed in a unit hypercube. For refinement of the approximate solution obtained at the first stage, the method of regular simplex reflection is used. Examples are discussed. The example of algorthm usage to optimize the hydrocarbon mixture make-up is presented.

 • The following article isOpen access

Application of

Journal of Physics: Conference Series

Paper • The following article isOpen access

Application of Ψ -transformation to the search for continuous function’s global extremum on simplex

A Sizikov

Published under licence by IOP Publishing Ltd
Journal of Physics: Conference Series, Volume 1203, International Conference "Applied Mathematics, Computational Science and Mechanics: Current Problems" 17–19 December 2018, Voronezh State University, Voronezh, Russian FederationCitation A Sizikov 2019 J. Phys.: Conf. Ser. 1203 012073DOI 10.1088/1742-6596/1203/1/012073

DownloadArticle PDF

Authors

References

Article metrics

97 Total downloads

Share this article

Article information

Abstract

A nonconvex problem of mathematical programming, the acceptance region of which is simplex. A two-stage algorthm is suggested to solve the problem. At the first stage, the global optimum region is determined; at the second stage, local clean-up of the solution is carried out. The first stage is realized by the Ψ -transformation method, which is an alternative to direct random search techniques. The method is to build and use Ψ -function. Ψ -function is built emperically based on statistic tests. To perform the tests, the generator of random points evenly distributed in simplex is used. Even distribution in simplex is achieved through affine and linear transformations of points evenly distributed in a unit hypercube. For refinement of the approximate solution obtained at the first stage, the method of regular simplex reflection is used. Examples are discussed. The example of algorthm usage to optimize the hydrocarbon mixture make-up is presented.

  to the search for continuous function’s global extremum on simplex

A Sizikov

Published under licence by IOP Publishing Ltd
Journal of Physics: Conference Series, Volume 1203, International Conference "Applied Mathematics, Computational Science and Mechanics: Current Problems" 17–19 December 2018, Voronezh State University, Voronezh, Russian FederationCitation A Sizikov 2019 J. Phys.: Conf. Ser. 1203 012073DOI 10.1088/1742-6596/1203/1/012073

DownloadArticle PDF

Authors

References

Article metrics

97 Total downloads

Share this article

Article information

Abstract

A nonconvex problem of mathematical programming, the acceptance region of which is simplex. A two-stage algorthm is suggested to solve the problem. At the first stage, the global optimum region is determined; at the second stage, local clean-up of the solution is carried out. The first stage is realized by the Ψ -transformation method, which is an alternative to direct random search techniques. The method is to build and use Ψ -function. Ψ -function is built emperically based on statistic tests. To perform the tests, the generator of random points evenly distributed in simplex is used. Even distribution in simplex is achieved through affine and linear transformations of points evenly distributed in a unit hypercube. For refinement of the approximate solution obtained at the first stage, the method of regular simplex reflection is used. Examples are discussed. The example of algorthm usage to optimize the hydrocarbon mixture make-up is presented.

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[PIERRE WHALON]

Or a rose by any other name… how about vertical shift in horizon, à la MiT?

Pierre

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[David Bibby]

Dear Pierre,

That’s a sharp observation. It’s natural to equate ψ_transformation with what Lonergan calls a vertical shift in horizon. You’re right to ask whether introducing new terminology is really doing more than renaming the familiar.

I see a few possible benefits:

1. Contextual Precision

• Vertical shift in horizon is already a Lonerganian term, but it lives in a primarily philosophical and theological vocabulary.

• ψ_transformation anchors the same phenomenon in a transdisciplinary context. It lets us draw bridges to mathematics, physics, and even computing without overburdening Lonergan’s own terms.

• The ψ-symbol signals: “this is the same interior movement, but now expressed in a formal-symbolic register that allows for analogy with quantum transformations, phase transitions, or algorithmic shifts.”

2. Symbolic Power

• The ψ-symbol already carries connotations from quantum mechanics (wave functions), optimization (Ψ-functions), and psychology (as shorthand for “psyche”).

• Using ψ as a unifying symbol subtly reminds readers that we are talking about something that oscillates between subjectivity and formal structure.

• It makes explicit that insight and horizon-shifts can be treated not just descriptively but also formally, as transformations in a space of intelligibility.

3. Pedagogical Distinction

• For Lonerganians, “vertical shift in horizon” is already well-understood.

• For readers from outside Lonergan (mathematicians, physicists, computer scientists), ψ_transformation may be more immediately graspable, since it resonates with their own technical idioms.

• The terminology thus helps mediate across audiences without diluting Lonergan’s original meaning.

4. Creative Freedom

• “Vertical shift in horizon” is tied to Lonergan’s own context and carries theological resonances.

• ψ_transformation, while rooted in the same reality, frees us to explore new analogies (e.g. sublation, phase transitions, inverse orders) without constantly having to qualify how close or far we are from Lonergan’s wording.

So in a sense: yes, it’s “a rose by another name.” But sometimes renaming is not about difference in essence, but about opening up new fields of relation and conversation. ψ_transformation lets us preserve Lonergan’s depth while speaking in a register that mathematicians and scientists can engage with as their own.

Kind regards,

David 

On 3 Sep 2025, at 15:03, 'PIERRE WHALON' via Lonergan_L <loner...@googlegroups.com> wrote:

Or a rose by any other name… how about vertical shift in horizon, à la MiT?

To view this discussion visit https://groups.google.com/d/msgid/lonergan_l/EBD2010D-B511-4D40-897A-E87E76C16BD8%40aol.com.