Optimal Strategy in Dating - Part 4

(Dinning icon by Icons8)

Optimal stopping strategy came up recently in an article in Scientific American. Once, when dinning out, the physicist, Richard Feynman, asked the question if one should order a favorite dish or try something new. The same question can be asked about going to a favorite restaurant or trying a new place to dine. Richard Feynman’s “dining optimization” solution is essentially an optimal stopping rule for the explore‑exploit dilemma: how long to keep trying new dishes (or restaurants) before settling on the best one you’ve found so far.

Feynman derived a declining threshold strategy (one such declining threshold is Tn=n/(n+1), where n is the number of remaining visits; the T starts very high with the first visit and declines to 1/2 on the last visit):

- Each night you compare the best restaurant (or dish) you’ve tried so far to a quality threshold.  

- If your current best exceeds the threshold, you stop exploring and keep returning to it.  

- If not, you try a new restaurant.  

- The threshold starts high and decreases as the number of remaining nights shrinks.  

  - Early in a trip, you should be picky and explore aggressively.  

  - Near the end, you should lower your standards and exploit whatever is “good enough.”

This strategy maximizes the expected total quality of all meals over a fixed number of nights.  

Why the threshold declines

With many nights left, the value of discovering an exceptional restaurant is high, so the threshold is strict. As time runs out, the benefit of exploration drops, so the threshold relaxes. This is mathematically optimal for maximizing cumulative reward.  

In plain English, Feynman’s rule says:

Explore new restaurants until the best one you’ve found so far is “good enough” by a standard that gets easier to satisfy as your remaining time decreases. Then stick with that best one.

OEIS - Contributions

 https://www.insightest.app/apps/math/oeis/jim.html

When I create a sequence for the On-Line Encyclopedia of Integer Sequences (OEIS), I typically post it in this blog. A colleague of mine, Vincenzo Manto, created the above webpage with all my contributions.

MAGNIFICA HUMANITAS - Encyclical Letter of Pope Leo XIV

Pope Leo XIV

(Image by: Edgar Beltrán, The Pillar Deed - Attribution-ShareAlike 4.0 International - Creative Commons )

On May 25, 2026, Pope Leo XIV issued his first encyclical letter, Magnifica Humanitas. This was near the 135th anniversary of Rerum Novarum issued by Pope Leo XIII during a time of rapid technological change.

Why is this in a math blog? As many know, Pope Leo XIV, studied mathematics at Villanova University before pursuing theological studies and earning a JCD from Pontifical University of St. Thomas Aquinas in Rome. Pope Leo's recent letter is to address the rapid changes in society driven by artificial intelligence and related technologies. With his degree in mathematics, the Pope is in a good position to speak to the church about this topic.

Within the first few pages, his mathematical background comes out in the analogy: "This concept can also be illustrated by the image of a multifaceted polyhedron, in which the one truth of the Gospel is reflected from different angles."

While the encyclical is primarily theological and pastoral, his math influence seems most evident in additional sections:

1. Chapter 3: Technology and Dominance – The Grandeur of Humanity in Light of the Promises of AI (especially paragraphs on AI itself)

This is the most directly relevant section. The Pope offers a careful, almost analytical breakdown of what AI is and is not. He describes AI as systems that “imitate certain functions of human intelligence” through data, models, and optimization — language that echoes mathematical concepts like algorithms, statistical models, and pattern recognition.

• He stresses transparency regarding algorithms, independent checks, accountability, and the need to understand how systems classify people and situations. This reflects a mathematician’s insistence on verifiable processes, error analysis, and avoiding “black box” opacity.

• Discussions of bias in algorithms, data as a shared resource, and how models embed values (what they measure, ignore, or optimize) show systems-thinking typical of someone trained in applied mathematics.

2. Sections on Governance, Subsidiarity, and Ethical Regulation of AI

The encyclical repeatedly calls for transparency, accountability, independent verification, and structured participation in AI governance. These mirror mathematical and scientific habits: demanding clear assumptions, reproducible results, and checks against unintended consequences.

His emphasis on subsidiarity (handling issues at the most appropriate level) and avoiding top-down imposition of opaque systems feels informed by logical structuring of complex problems.

3. Discussions of Truth, Probability, and Decision-Making

In parts addressing truth as a common good, misinformation, and automated decision-making (e.g., credit, hiring, or risk assessment), the Pope highlights how algorithms can cloak exclusion in “a veneer of neutrality and objectivity.” This critique shows awareness of how mathematical tools can appear impartial while carrying hidden biases in their design or training data.

4. Broader Structural Approach

The encyclical’s overall organization — clear chapters, logical progression from foundations to applications, and balanced weighing of risks vs. benefits — reflects disciplined, systematic thinking. Some observers note that his math training may contribute to a more rigorous, less purely rhetorical style in addressing technical topics.

Notable Quote Reflecting Precision

One standout line (around paragraph 128) contrasts human growth with machine logic:

“For an algorithm, an error is a flaw to be corrected; for a person, however, an error can be a catalyst for profound change.”

This beautifully distinguishes deterministic systems (math/AI) from the open-ended, relational nature of human freedom and grace.

Overall Assessment: Pope Leo XIV does not engage in deep technical mathematics in the encyclical. Instead, his background seems to provide intellectual tools for dissecting AI as a complex system, insisting on clarity, ethical guardrails, and human-centered design. It helps him bridge theology and technology without being either overly fearful or naively optimistic.

His formation allows a precise critique: AI is powerful modeling, but it lacks the irreducible dignity, freedom, and relational depth of the human person created in God’s image.