Wednesday, February 19, 2025

First they came for the Copy Editors. . .


Apologies for abusing the famous Holocaust poem in the title, I noticed today that the genAI bubble is making enormous progress at replacing developers.  I, personally, enjoy chatting with AI chatbots to accomplish many tasks and I am collecting my own personal sets of prompts and meta-prompts.  However, I cannot imagine what it would be like for a non-coder to use a genAI to write code because I already can code.  I suppose it would be akin to my using a genAI to compose and sell Hindi poetry and Hindi songs.  I speak no Hindi, have no sensibility for Hindi audiences' taste in music or how to earn money in a Hindi-speaking music market, etc.  The phenomenon is also like the Chinese Room thought experiment.

Side note on the title of this post

Niemöller famously and poetically articulated the wave of the Nationalsozialistische Deutsche Arbeiterpartei (Nazi) popular Zeitgeist ideology that swept across the population of Germany and led to death camps, extermination of people, etc.. Although there are many variations of the poem, the most common written version in Holocaust museums is:

First they came for the Socialists, and I did not speak out--
Because I was not a Socialist.
Then they came for the Trade Unionists, and I did not speak out--
Because I was not a Trade Unionist.
Then they came for the Jews, and I did not speak out--
Because I was not a Jew.
Then they came for me--and there was no one left to speak for me.

However, Niemöller likely used the word "Communists" in the original oration.

Monday, February 17, 2025

Travel


I enjoy leisure travel.  As I mentioned previously here

I want not only to see the sites when I travel, but also smell the diesel fumes, taste authentic street food, and hear the "flavor" of local dialects.  But more than that I want to feel and viscerally experience the attitudes, values, opinions, and sensibilities of the locals, to "get into their heads."  I love to experience the culture, not just observe it.

So when I came across this (long) gem of travel tips from the founder of Wired magazine, I read it with much interest.  Kevin Kelly breaks travel down into "rest and relaxation" (R&R), engagement and experience (E&E), and business travel.  He gives many small bits of advice for each type of travel with wisdom gained from his own hard-won "quantity time" traveling and thoughtful introspections.  If you enjoy traveling, check out the article.

Sunday, February 16, 2025

Poor Charlie's Almanac by Charles Munger & Peter Kaufman (2008)


Fantastic!  I don't care about stock picking or investing, but the wit and wisdom of Charles Munger in these engaging dialogs and speeches are fantastic. Highly recommended! 5/5 Stars.

Saturday, February 15, 2025

Trusted Execution Environments and Byzantine Fault Algorithms


After Reading Martin Kleppman's famous book I became fascinated by Byzantine Faults and algorithms. These concepts and applications are used mostly for space probes and other hostile environments. This new paper on trusted execution environments (TEE) therefore caught my attention. We are finally looking at more and better hardware to provide security guarantees.  It's a great survey paper.

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.

Thursday, February 13, 2025

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.

Tuesday, February 11, 2025

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.

Saturday, February 8, 2025

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:

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

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

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

    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.