A few days ago I started the yearly routine of reviewing The Playlist. Which, due to generational reasons, I will, below, refer to as The Mix Tape (tMT). I formally started making the yearly tMT in 2010, meaning I have 16 now that 2025 is coming to an end.

The criteria for a song to appear on tMT is that it must have connected with me emotionally in a personal way at some point during the year. These are akin to musical Cupid arrows. I never see it coming until it hits me square in the heart. And then I can never unsee it.

Some songs were released this year. Some are incredibly specific live tracks. Others are callbacks or connections to other art that evokes the music. Some remind me of relationships, or the state of the world as I’ve experienced it, for this most recent trip around the sun.

Starting the yearly tMT routine requires listening to the tracks as I’ve added them over the course of the year. In this sense, it’s an audio chronology of the year. When December lands it’s a matter of arranging the pieces to create a story that makes sense of my experience. It’s not something any other person could possibly be connected to the way I am, because the nuance is deep. But general themes often emerge, providing consistency across the year. Not always, or even often, themes that feel good. Sometimes because the themes are connected to recent wounds, or others because they point the way to learning and becoming more of myself, which is a place I’ve always most easily associated with fear. That is to say, the present is a weird place.

If you’ve made it this far, congratulations! You’ve made it to the point I’d like to make. Which is, for me, tMTs are functionally tattoos. I have zero physical tattoos. I’ve toyed with the idea for years and played over options but never quite landed on something that felt right. And I’ve wondered, as I do, why that is the case.

I think it’s because these yearly playlists are my tattoos.

They each tell a story tied to a past moment. They evoke emotions connected with many different phases of life. They remind me of who I was, and who I wanted to be. Sometimes I’m not proud, after the fact, of a song that landed on a particular tMT years ago. But it reminds me of who I was and how I’ve grown. It’s a way that I’ve stitched together a relationship with my past self, and it’s my belief that whatever helps us do that is beneficial.

Reordering the tracks this year was particularly satisfying. I see the songs as the idea of the tattoo, but the track ordering to be the design. Great idea with a poor design lands you on Reddit. Bad idea with great design is a crap shoot. Good idea with great design and you have something worth showing off.

Here’s my attempt to show off my newest tattoo.

Happy New Year

2025 tMT Notes:

It’s possible, in Apple Music, to modify the start and stop times for a given track, which I find to be incredibly helpful. But these changes are local per account, so the modifications I’ve made don’t automatically transfer to you. Spotify doesn’t have this feature at all. The following stop times have been set for these three tracks:

• Ahead By a Century - 5:10
• Black Sheep - 7:31:5
• Chonkyfire - 5:12

Apple Music

Spotify

Evidently there’s a newish biography out about Grigori Perelman, the man primarily responsible for solving the Poincaré Conjecture. Masha Gessen, a Russian journalist and author, has released “Perfect Rigor: A Genius + the Mathematical Breakthrough of the Century”, a work about the life of the curious mathematician who has vanished from the professional math community. She explains her work in an interview with failuremag.com, in which she describes the rationale behind the work, and gives some insights into both the Poincaré Conjecture and the life of Perelman.

There’s no doubt that Perelman’s response to solving one of math’s longest standing problems is part of what is so intriguing to the lay reader. He turned down a Field’s medal and withdrew from professional mathematics. Pieces on him tend to accentuate his eccentricities. Part of what makes the story so very interesting is Perelman’s response, as well as the other cast of characters involved in the solving of the problem. Though it came out in mid-2006, the New Yorker has a fantastic article about the solving of the Poincaré Conjecture and the controversy surrounding it. If you’d like to understand to a greater extent Perelman’s response to his solution, read this article. It’s long, but extremely informative and complete.

Matt Gaffney, a 15 year veteran of professional crossword puzzle writing, wrote an article in late November for Slate about the likeliness of two crossword puzzle creators replicating the same, or approximately the same, puzzle. Crosswords exhibit 180-degree rotational symmetry, meaning that “if you turn the grid upside down, the pattern of black squares will look the same as it does right-side up.” Couple that with a specifically themed puzzle (e.g. Halloween and Edgar Allen Poe), a certain number of long word entries, and general crossword rules (e.g. no two letter words are allowed), the probability may be higher than you think.

In a nutshell, Gaffney found that he had inadvertently used many similar aspects of a puzzle that had been released earlier in the year, and thus traces several reasons why this may have been the case. One interesting twist to the story is what happens when Gaffney asks a third crossword creator to write a similarly themed puzzle. Do you think that this third puzzle turned out to have similar entries to the first two? Read to find out!

As I look through articles that I’ve bookmarked over the last many months, I realized that I had saved two that concerned machines that were built to interact with themselves in novel ways. I find this self-interaction quite entertaining for a reason I can’t quite pinpoint. Perhaps it’s because I generally think of a machine as a black box that takes an input and produces an output. I tend to segregate the input and the output entirely from the black box. But these machines are built only with the purpose of performing an action on themselves. They are input, output, and black box. And I find that extremely entertaining.

First, take this iteration of Claude Shannon’s “Ultimate Machine”, whose sole purpose when turned on is to immediately turn itself back off again:

As the video explains, you can find plans for building your own machine of the same type at Instructables. It should be said that I was introduced to this machine via Boing Boing much earlier when they directed me here. These folks call the machine the “Leave Me Alone Box”, and there are several videos on the site devoted to showing different fan-made machines in action. It looks like this site will also eventually sell a kit which allows you to build your own box. Kevin Kelly also has an article that gives some history about this “Ultimate Machine”.

Secondly, take Michael Kontopoulos’ machines that are built only with the task of nearly knocking themselves over:

Machines that Almost Fall Over from Michael Kontopoulos on Vimeo.

The artist explains his intentions on his website as trying “to capture and sustain the exact moment of impending catastrophe and endlessly repeat it.” I love it! So close to falling, and yet so far away! There are lots of other interesting projects to find on Michael’s website as well.

Having just completed both of Lewis Carol’s books concerning Alice and her adventures in Wonderland, the recent Boing Boing post about Melanie Bayley and her research into the idea that scenes were added into the narrative after the initial draft in order to mock new math of the day, namely symbolic algebra. As one example, Bayley likens the Mad Hatter tea party scene to the concept of the quaternion introduced by William Rowan Hamilton. Without giving away the punchline, Bayley paints an interesting picture of why the three guests at the tea party are stuck at their table, constantly swapping seats. Read the full article at New Scientist here, which gives many more examples of how Carol lampooned the so-called “new math”. Who likes imaginary numbers, anyway?

My mother-in-law made me privy to a story that aired on NPR about a group of people who built a copy of Charles Babbage’s Difference Engine using only materials available from the Victorian age, which is a feat which alluded the mathematician during his lifetime. This machine is the second of two that has been built, and is on display at the Computer History Museum in Mountain View, Calif. through the end of 2010. Concerning the physical dimensions of the machine:

“The Difference Engine fills half a gallery and stands taller than most men. It’s 5 tons of cast iron, steel and bronze woven together from 8,000 distinct parts. Though it looks like it could be a sculpture, the machine is essentially a giant calculator.”

In other words, it’s gigantic. And it works. It was the best computer that money could buy in 1840, which is probably why it was never actually built. Way too complex and way too much money. It’s worth checking out the NPR story just to see the photos of this monstrous machine. There’s also a video of the machine in action on the Computer History Museum webpage for the Babbage Engine exhibit here.

Ever since I heard about Logicomix, a graphic novel about the 20th century search for the foundations of mathematics, I was extremely excited to read it. And I’m happy to say that now I’ve finished it, it most certainly met, and exceeded, my rather high expectations.

First, I think it’s appropriate to explain what Logicomix is, and what it is not. First, it is a work of fiction. The authors are clear on this point, and explicitly spell it out in the epilogue. This graphic novel is meant to be a piece of art, not a pristine account of history. But its account of history will definitely give the reader an accurate outline of what happened in mathematics in the 20th century, even if the details aren’t entirely accurate, and even if certain liberties are taken in order to present a story which engages the reader in its narrative format.

Logicomix tells the story of 20th century mathematics by using Bertrand Russell as a narrator. The story is framed as a talk which Russell is giving to an audience directly before Britain’s entrance into World War II. He traces his life’s story from childhood through his work as an activist, and along the way we meet the familiar set of characters from that day, including Frege, Whitehead, Gödel, Wittgenstein, Cantor, etc.

The story is compelling. The authors, Apostolos Doxiadis and Christos Papadimitriou, do an amazing job of following Russell’s career, and of showing the personality and human struggle behind a quest centered around the abstract notion of truth. While most of the characters are obsessed with matters of the brain, the story also focuses on the heart as well. For instance, Logicomix does a good job explaining Russell’s obsession with madness, and his fear associated with it. There is also an aspect of meta-story in Logicomix, whereby the authors themselves appear throughout to drive home points and debate various tidbits of the story. This is an interesting aspect that mirrors to some extent Gödel’s meta-logical statements. I thought this was a good touch.

The art, done by Alecos Papadatos and Annie Di Donna, is stunning. As a material object, this graphic novel is beautiful. I’m a huge proponent of quality, and everything about the novel breathes quality. From the art to the color to the fonts to even the dimensions of the page and panels, Logicomix is extremely well engineered. Kudos to them both!

As a work of historical fiction, this story should appeal both to lovers of logic and mathematics as well as those who enjoy a fantastic story. The authors are using history to drive home what I believe to be an accurate and well-stated point, which I will not divulge here. If there are any flaws, I would point out two. First, Gödel is treated somewhat like a deus ex machina. Rather than providing more exposition into his life, the authors are content to have him come and go quite quickly, though I must admit that I LOVED the first panel in which he appears. It’s probably my favorite panel in the entire work. Secondly, there’s nothing about Turing, other than to mention him in the meta-story toward the end. One cannot truly understand logic without knowing something about computability. Granted, it seems that a sequel may be a possibility which begins with Turing and ends in the 21st century, but only time will tell. Until then, Logicomix comes as highly suggested.

There have been a few posts I’ve seen recently about math related comics. First, Boing Boing clued me into The Thrilling Adventures of Lovelace and Babbage, which is pretty much exactly what is sounds like. This webcomic gives some great info (both truth and pseudo-truth) about both Charles and Ada. Sydney Padua, the author of the comic, explains:

It’s a punchline. As in “Wouldn’t it be hee-larious if there was a comic about Ada Lovelace and Charles Babbage fighting crime? Thanks, I’ll be here all week!” The imaginary comic was the punchline to Lovelace: The Origin, drawn because my good buddy Suw Charman got me drunk started a Noble Enterprise called Ada Lovelace Day.

Secondly, Jim Holt wrote a book review last Sunday that introduced me to Logicomix, which the official website describes as follows:

Covering a span of sixty years, the graphic novel Logicomix was inspired by the epic story of the quest for the Foundations of Mathematics.

This was a heroic intellectual adventure most of whose protagonists paid the price of knowledge with extreme personal suffering and even insanity. The book tells its tale in an engaging way, at the same time complex and accessible. It grounds the philosophical struggles on the undercurrent of personal emotional turmoil, as well as the momentous historical events and ideological battles which gave rise to them.

The role of narrator is given to the most eloquent and spirited of the story’s protagonists, the great logician, philosopher and pacifist Bertrand Russell. It is through his eyes that the plights of such great thinkers as Frege, Hilbert, Poincaré, Wittgenstein and Gödel come to life, and through his own passionate involvement in the quest that the various narrative strands come together.

VERY cool. I’ll definitely be picking this up before too long. The art looks fantastic, and I’m sure the story matches up! Check out the review linked to above for a fuller introduction to the story.

I’m rather late on the draw in regard to this note, but I just wanted to say that I was profoundly glad to hear that the Prime Minister of England released a letter of apology on September 10 recognizing Alan Turing for his monumental “contribution to humankind”, including work in computation, mathematics, and code-breaking.

Despite his contributions, Turing was convicted under English homophobic laws and sentenced to chemical castration. As PM Brown writes, “In 1952, he was convicted of ‘gross indecency’ - in effect, tried for being gay.” Given the choice between going to prison and undergoing hormone treatments, he chose the latter. Less than three years later Turing was found dead, apparently the result of a cyanide overdose. His death was judged to be a suicide.

While the note obviously cannot change the past, I’m glad to see the British government deliver the note. And I’m extremely proud of those individuals who lobbied the government to acknowledge this terrible mistake. Again, as PM Brown wrote, “So on behalf of the British government, and all those who live freely thanks to Alan’s work I am very proud to say: we’re sorry, you deserved so much better.” So very true.

I’m trying to fill this autumn with plenty of seasonal activities, and so I’ve decided to try to read the complete works of Edgar Allan Poe during the month of October. I’ve also been reading some biographical information about the writer, and must admit that I had never heard about the cryptographic challenge that Poe issued to readers in the Alexander’s Weekly Messenger in December 1839. R. Morelli has a fantastic overview of this cipher challenge here. In sum, Poe proposed that “he could solve any simple substitution cipher that readers of the magazine cared to submit. A simple substitution cipher is one in which the same symbol stands for the same letter of the alphabet in the concealed message.”

It appears that Poe did very well with the challenge.

Also, fans of Poe’s writing will know about the short story The Gold Bug, and how this story of a treasure hunt relies on the solving of a cryptogram. Poe’s works are in the public domain, so it’s possible to read this story online through Google Books here, or to download the story (amongst others) from Project Gutenberg here.