Category: Math / Logic

Math Crankery with John Gabriel – “Cauchy’s Kludge”

(Previous post on John Gabriel: Calculus 102 (Cauchy Sequences and the Real Numbers)) Alright, now that we’ve tackled the basic definitions and theorems regarding calculus, we can start looking at Gabriel’s first video on calculus. 2. Cauchy’s Kludge Before we start, let’s play a little game. The above image is a screenshot of Gabriel’s video,…


Math Crankery with John Gabriel – Calculus 102 (Cauchy Sequences and the Real Numbers)

(Previous post on John Gabriel: Calculus 101 (Convergence and Derivatives)) Okay, now that we know what sequences are and what it means for a sequence to converge to some limit, we can finally start talking about real numbers: Irrational Numbers and Cauchy Sequences Basically the whole point of real numbers is to make the rational…


Math Crankery with John Gabriel – Calculus 101 (Convergence and Derivatives)

(Previous post on John Gabriel: The Dunning-Krüger Effect in a Nutshell) Few people can ever begin to match my intelligence and depth of insight. I am not arrogant or deluded.John Gabriel Yeah. That’s an actual quote. I’ve been made aware of Gabriel’s LinkedIn page, where he wrote hilarious posts about his new calculus and his…


Math Crankery with John Gabriel – The Dunning-Krüger Effect in a Nutshell

So, this crank John Gabriel exploded on the Mathmatical Mathematics Memes page on facebook recently, and he’s hilarious. Now, there’s cranks in every area of science of course; most notably in physics (quantum woo), biology (creationists), geology (creationists again), history (creationists again, holocaust-deniers), philosophy (theologians 😉) and of course medicine (alternative medicine, faith healing…), but…


SAT Solving: DPLL, Clause Learning and Implication Graphs

This post is primarily directed at students in the AI class at University Erlangen to explain the Davis-Putnam (Logemann-Loveland) Algorithm for SAT solving and implication graphs for clause learning. The goal in a SAT problem is to find an assignment that satisfies a set of propositional formulae , or a proof that none exist, i.e….


Basics of Abstract Logic (Also: A Pointless but Fun, Correct and Complete Calculus for Divisibility)

This post is primarily directed at students in the AI class at University Erlangen to explain the basics, and in particular the formalism we use in the lectures, of abstract logic. In its (not actually, but for our purposes) most abstract form, a logical system consists of three things: A language , i.e. a set…


Meta-Meta-Tools and Theory Graphs (What is MMT?)

I work a lot with and on a particular piece of software called MMT, which was developed by Florian, so this is my attempt to explain what it does – which is not exactly easy, as you’ll see, but one of the things you can do with MMT is make computers (on some level) understand…


An RPG magic system based on logic

http://www.aaii.com/journal/article/magic-numbers-reduce-the-math-of-annuities-to-simple-arithmetic.touch

(image source) One of our undergrad students recently finished his B.Sc. thesis on a serious game intended to teach the player to apply maths to real-world problems (this is probably going to be worth its own blog post, once the paper is publicly available somewhere), which got me thinking about other ways to teach math…


Why I tattooed Gödel on my arm

This is what the tattoo on my arm looks like (well – looked like right after I got it. You can still see the skin being noticably red/pale around it). It’s been designed by my flatmate at the time, Gwen. Without the arm it looks like this: Probably still not too legible, so let’s get…


What am I doing here? (My research topic)

Theory graph across formal libraries

In this post, I will try to explain what my Ph.D. is going to be about – of course, you can just read my proposal, but I assume that’s not really accessible to a lay-person. The broad topic is knowledge management across formal libraries, specifically libraries of formal mathematics obtained from (mostly) various computer-supported theorem…