Deriving a Quine in a Lisp

As with my previous post, this post is another excerpt that will be included in my final Master’s thesis, but I decided it is interesting enough to post it on its own.

We start with a definition of diagonalization (or quotation), as discussed in The Gödelian Puzzle Book:

Definition 1: For an expression $P$ in which a variable $x$ occurs, we say that its diagonalization $D(P(x))$ is the substitution of the variable $x$ with the quoted expression $P(x)$.

This definition allows us to represent self-referential expressions.

Equational reasoning in Racket

This post is an excerpt that will be included in my final Master’s thesis, but I decided it is interesting enough to post it on its own.

We will define a few of Peano’s axioms together with a procedure for substitution in equations so that we can prove some theorems using this system.

Encoding probability and random variables in Racket

This blog post will serve as a quick tutorial to basic probability and random variables, and encoding them in Racket. It assumes basic knowledge with sets and programming.

Stay Home

I would like to mathematically demonstrate how important it is to stay home in times like these. My article will be a very short version of the cite below. Let’s start with a simple task:

Begin by asking how a rumor might spread among a population. Suppose on Day 1 a single person tells someone else a rumor, and suppose that on every subsequent day, each person who knows the rumor tells exactly one other person the rumor. Have students ponder, discuss and answer questions like: “How many days until 50 people have heard the rumor? 100 people? The whole school? The whole country?Exponential Outbreaks: The Mathematics of Epidemics

Formalization of Boolean algebra pt. 2

In my previous post I’ve said that to prove that from $x * (\neg x + y)$ it follows $x * y$ will be slightly more complicated. That’s what we will do in this post.