Computability on CS Theorems

The Lambda Calculus and the Y Combinator

Fri, 10 Sep 2027 12:00:00 +0100

Symptom

You are writing a language, or a configuration evaluator, or a template engine, and you need recursion. So you add a letrec form, and now the evaluator needs to bind a name before the value it names exists. You reach for a mutable cell, a placeholder that gets patched after construction, and something about it feels like cheating.

Kolmogorov Complexity

Fri, 09 Apr 2027 12:00:00 +0100

Symptom

You have two files, each exactly one megabyte.

The first is a megabyte of the byte 0x00. The second is a megabyte from /dev/urandom. Gzip the first and you get a few hundred bytes. Gzip the second and you get slightly more than a megabyte, because the header costs something and there is nothing to exploit.

Reductions

Fri, 05 Feb 2027 12:00:00 +0100

Symptom

You have a new problem. Your build system needs to decide whether two configuration files can ever produce conflicting outputs. Or your linter needs to decide whether a regex with backreferences can match a string of a given length. Or your scheduler needs to decide whether a set of periodic tasks is feasible.

Kleene's Recursion Theorem

Fri, 15 Jan 2027 12:00:00 +0100

Symptom

Write a program that prints its own source code. No file I/O, no reading __file__, no cheating.

The first attempt fails instantly. To print the source you must contain the source, and then the containing text is also part of the source, so you must contain that too. The regress is obviously infinite, and most people conclude after ten minutes that the task is impossible.

The Universal Machine

Fri, 01 Jan 2027 12:00:00 +0100

Symptom

You write a Python program. It runs. What ran it?

CPython — itself a program, written in C, compiled to x86 instructions, executed by a CPU whose control unit is arguably interpreting microcode, possibly inside a virtual machine, on a kernel that scheduled it, all perhaps within a container image. At no point in that stack does anyone find it strange that a program’s job is running other programs. We build emulators, JITs, WebAssembly runtimes, Docker, QEMU, and browsers that download and execute arbitrary code from strangers, and treat every layer as ordinary engineering.

The Church–Turing Thesis

Fri, 25 Dec 2026 12:00:00 +0100

Symptom

Somebody says “CSS is Turing-complete” and the room splits. Half the people treat it as a joke about a styling language, the other half as a serious claim with consequences. Both reactions are common and only one is right.

Rice's Theorem

Fri, 16 Oct 2026 12:00:00 +0200

Symptom

The security team asks for a scanner with no false positives and no false negatives. Every piece of malware caught, nothing legitimate quarantined.

The platform team asks whether the analyzer can flag every function that performs I/O, so the pure ones can be cached automatically.

The Halting Problem

Fri, 09 Oct 2026 12:00:00 +0200

Symptom

Your CI has a test that hangs. Not fails — hangs. Somebody suggests the obvious fix: before running a test, check whether it terminates, and skip it if not.

Cantor's Diagonal Argument

Fri, 02 Oct 2026 12:00:00 +0200

Symptom

Somebody proposes a tool that will find all the bugs. Not most bugs. All of them. The pitch has the shape: we enumerate the failure modes, we write a checker for each, we keep adding checkers, and the set of undetected bugs shrinks toward zero.