For years I struggled to clarify exactly what a Turing machine needs to do, and more importantly, how Turing conceived of it. Even after I finished a CS degree I wasn’t able to “build one from scratch” because I hadn’t yet independently realized what he had…

Recently I had a moment of insight and hit on an improved analogy for the “program” of a Turing machine, which Turing describes as “a book”. I took this one step further and clarified that each page in this book can be thought of as a unique state. A page contains a single instruction to follow (which takes the form of a conditional statement). This subtle step is something Turing didn’t include in his paper (instead he skipped ahead and simply refers to it as a ‘big table’, which can be tough to digest at first)

I feel this is the key to make the mechanism behind Turing machines more concrete and intuitive for the new learner. I hope Turing would approve of my modification to his analogy…and after reading his paper some 20 times, I can say with certainty that he would.

Here is the video on how it all works (this is also the 2nd last video in the CS series)

This video was on the tip of my tongue for years, it feels wonderful to finally move on. It features Aristotle, Leibniz, Adam Smith and Charles Babbage. It’s the main “case study” for this series, after which we’ll move into more modern views on computers and computability.

Posted a new video this week I’m really happy with. It covers abstraction, deduction & syllogisms through the lens of Aristotle’s work on Logic. Now that this video is complete I can finally get to the real meat of this series…. the dream of a “Universal Computer”. This video also features my son Booker, his second appearance in an Art of the Problem video.

I’ve seen so many botched, overcomplicated, misconstrued and boring attempts at explaining algorithms to new minds that it was a huge relief to finally finish this video. My goal here is to explain procedural knowledge (know-how) via a thought experiment involving actors. I cover what I consider the two core ideas behind algorithms and where they came from. I also extend the explanation to setup a future video on time/space complexity. You’ll see no mention of while loops, for loops, or bubble sort…horse before cart. This is part 2 in the series on Computer Science.

This first video explores declarative vs. procedural knowledge through the lens of the Turing Test & Oracle machines. It’s intended to hook + ground the viewer in some basics before building towards Logic & Turing Machines. After this video we will dive deeper into procedural knowledge via. Algorithms. Then we’ll explore more history (arithmetic vs. formal logic) before building towards 20th Century ideas.

After a long period of research I’m happy to report Art of the Problem’s third episode is in production. This episode will act as the final piece of a CS trilogy. Here is the first video which gives an overview of the series: (or watch on YouTube)

I’ve also published an essay version of this video with extra links below (or read on Medium).

Around 100 years ago something really exciting was happening.

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