Category: Mathematics

Formal systems meet psychological stuckness

As I was rewatching Interstellar a few days ago, a question popped into my mind:

Is there a relationship between black holes (spacetime disturbances) and psychological stuckness (and similar phenomena)?

But since I don’t know much about physics, I re-framed it as:

Is there a relationship between formal systems (paradoxes) and psychological stuckness (and similar phenomena)?

Sure, if we construct the analogy 🙂 In this post, I’ll give that a try.

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Gestalt Therapy Meets Set Theory

If you’ve been following my blog, you’ve probably noticed my shift towards psychology in the past period. And before that, I spent a lot of time tackling mathematics and proofs, especially set theory.

Gestalt therapy focuses on how awareness organizes figure and ground in contact with the world. Set theory, with its emphasis on partitions and transitions, gives us a playful but precise language to represent these processes.

This blog post will be a conjuction of both ideas.

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Writing your third program with Budge-TP

In a previous blog post, we showed an implementation of a subset formal system of Peano’s axioms that could represent numbers and the addition operator. In a blog post before that, we showed and implemented a formal system that could represent numbers and the addition operator at a more basic level.

This blog post will show yet another way to represent numbers and arithmetic operations such as addition, subtraction, multiplication, and division. Finally, we’ll extend this system to also support complex arithmetic operations (combining the previous basic operations).

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Write a mathematical proof generator for AoC 1-1 2022

For last year’s AoC, I decided to use 20 different programming languages. For the year before that, I used Haskell. This year I decided to not participate as I’m already busy with other stuff, but I thought I could try something different.

So the first task of AoC day 1 is essentially giving you a list of lists, and you need to sum each element and find the max. Here’s a one-liner in Python:

max([ sum(x) for x in L ])

But I thought to myself, why write code in a “normal” programming language to solve an easy problem? Why not complicate things a little bit and write a code that generates mathematical proof in Budge-TP? In this post, we will write a Python script that will solve AoC 1-1 by generating Budge-TP code.

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