Backyard Starship by J.N. Chaney and Terry Maggert (2021)

One of the genAI chatterbots recommended this series based on my reading history and ratings so I read the first book in the series.  The series is better-suited to an 11- or 12-year-old. 2/5 Stars.

The Lessons of History by Will & Arielle Durant (1997)

This extremely dense collection of aphorisms and pearls of wisdom is a very thin shell of the 11 volume The Story of Civilization that won the Durants so many accolades and awards.  My buddy Senthil recommended it so I picked it up.  It is so dense and profound, the reader must constantly pause and ponder.  Now I am curious about Will Durant's magnum opus. 4/5 Stars.

Attack Surface by Corey Doctorow (2020)

Fun thriller with odd twists and turns but I found the characters and events contrived and unrealistic. I do not recommend this one.  Doctorow has written better books in the same genre. 2/5 Stars.

Lawvere's Fixed-point Theorem blows my mind

Lawvere's fixed-point theorem explains why self-reference is unavoidable in any system that allows for functions to be applied to themselves. It provides a mathematical way to understand the idea of "I" in self-reference.

Think of it like this:

• A statement that refers to itself.
• A program that reads and modifies its own code.
• A formula that says, "If proving me means I'm true, then I'm proved."

These kinds of self-referential structures often seem paradoxical or nonsensical. Lawvere's theorem helps us understand why these paradoxes arise.

The Core Idea: Russell's Paradox and Self-Reference

Imagine a set that contains descriptions of everything. Now, try to define the set of all things that don't describe themselves. Here's the problem:

• If the description includes itself, then it shouldn't be in the set.
• If it doesn't include itself, then it should be in the set.

This is Russell's paradox. The same kind of paradox appears in many areas of logic, mathematics, and even computer science.

Cartesian Closed Categories: The Setting for Lawvere's Theorem

Lawvere's theorem applies in a structure called a Cartesian closed category (CCC). Here's what that means:

1. Multiplication of objects (taking products).
2. A special object (terminal object) that acts like a "unit."
3. Exponentials: For any objects X and Y, you can form an object Y^X, which represents all possible maps from X to Y.

In standard set theory, Y^X represents all functions X → Y. In category theory, exponentials serve the same purpose, but in a more general setting.

There is also an evaluation map:

ev:(YX)×X→Y

which takes a function from X to Y and applies it to an input X. This evaluation behaves in a universal way, meaning it can describe every function application in the category.

Category theorists use this abstract approach because they prefer not to "look inside" objects. It's like how a strict vegan insists on keeping their lifestyle separate from certain foods—they avoid breaking the rules even when it might be convenient.

How Lawvere's Theorem Works

Lawvere's theorem uses exponentials to model self-reference. Here's how:

• Suppose we have an object X in a CCC and a function

  f:X→XX

  This means each element of X is assigned a function from X to X.

• Now, combine f with the evaluation map to define:

  δ:X→X

  This δ is called the diagonal map or self-application map.

• Lawvere's theorem states that if δ acts like a fixed-point operator (meaning there exists an x such that δ(x) = x), then there must be an element x such that f(x) maps x to itself.

In simpler terms:

• The object X contains a self-referential element.
• This element must describe itself in the way f defines.
• Self-reference is forced by the structure of the system.

Why This Matters: Gödel, Tarski, and Halting Problems

In set theory, this theorem explains diagonal arguments, like those used in:

• Gödel's incompleteness theorem: "This statement is unprovable."
• Tarski's undefinability theorem: "Truth cannot be defined within the same system."

The key idea is that once functions themselves become objects (via exponentials), self-reference becomes inevitable.

For example:

• Gödel's theorem builds a function from X to X^X that represents "provability" inside the system.
• Tarski's theorem does the same for "truth" inside the system.
• The Halting problem constructs a function that tries to analyze its own ability to decide halting.

Each case involves embedding a system inside itself, forcing it to evaluate its own rules. This always leads to contradictions or limitations.

The Big Picture

Lawvere's theorem tells us that any system capable of defining functions from objects to themselves will eventually run into paradoxes. You cannot build a system that fully captures its own behavior without creating a self-referential feedback loop.

If you try to define something like "this program decides if another program halts," you're inherently creating an arrow X → X^X, which lets the system analyze itself. That's exactly how Gödel's and Tarski's results work.

In the end, Lawvere's theorem formalizes why self-reference is inescapable. It proves that if you have a system rich enough to describe itself, paradoxes aren't just possible—they're guaranteed.

Fwd: Miss Moriarity, I presume? by Sherry Thomas (2022)

I am enjoying this series. This book is another fun adventure that includes the mysterious super-villain (Moriarity). 5/5 Stars.  

Revenge of the Tipping Point by Malcolm Gladwell (2024)

I almost always enjoy Gladwell's stories and books.  This one is fantastic and highly recommended. 5/5 Stars.

Needle by Hal Clement (1949)

I liked this story. There are many contrivances and holes in the plot but the magic system is great and the characters are all compelling. I also enjoyed the dated science of 1949 including our lack of understanding of viruses back then. 4/5 Stars.

If I betray these words by Wendy Dean and Simon Talbot (2023)

This book presents a fascinating and in-depth collection of vignettes that highlight the dedication and idealism of medical professionals. It vividly illustrates the struggles these devoted doctors face against the encroachment of private equity firms and other large corporate entities that destroy the integrity of patient care.

Through these narratives, we witness firsthand the detrimental impact of prioritizing shareholder value over patient well-being. The most valuable aspect of the book lies in the authors' insightful recommendations for how physicians can effectively navigate these challenging circumstances to ensure high-quality care for their patients.

Overall, this book is a thought-provoking examination of the intersection between medicine and corporate interests, offering both inspiration and practical guidance for healthcare professionals. 4/5 Stars.

Hellconia Spring by Brian Aldiss (1952)

I did not like this book. There is no plot. None of the characters is likeable.  There is gratuitous and needless violence. 2/5 Stars.

Die Kinder der Finsternis von Wolf von Niebelschütz (1959)

Normalerweise genieße ich Geschichten, die den Leser in einen Schnappschuss aus dem Leben eintauchen lassen. Und ich bin neugierig auf das 12. Jahrhundert in der europäischen Geschichte, insbesondere auf Friedrich I. (Barbarossa) und das Heilige Römische Reich. Der Schreibstil ist sehr gut. Die Charaktere sind interessant. Mir gefiel die interessante Formalität, mit der die Leute miteinander sprachen. Der Grund, warum mir dieses Buch nicht gefallen hat, ist, dass das Eintauchen zu tief war. Es gibt eine ständige, böse, brutale, beiläufige Gewalt und Machtmissbrauch, die sehr deprimierend ist. Jeder hatte ein bizarres Glaubenssystem und eine grundlegende Wahrnehmung der Realität. Die Heiden, Christen und Muslime lebten in einer Fantasiewelt und leugneten die offensichtliche objektive Realität. Ich glaube, diese Beschreibung ist wahr, aber ich wollte mehr über das Gesamtbild erfahren, nicht nur über die kleine Provinz. 2/5 Sterne.