• My trip through the Starmaze: a world in the 9th dimension

    There are times when I get tired of all of the major sites and apps that make up a lot of the seen Internet. Sadly, I was born too late to experience the wonder of Geocities and intricate handmade websites run by just a single person. But, on some evenings, I still search for those smaller websites that no one else normally sees. I find the wonder of coming across hidden blogs and pages really fun.

    It was a night like this when I stumbled across John Cartan's writing about the Starmaze last year, and I quickly became fascinated. Unlike every other corner of the web, Cartan's website wasn't trying to sell me a useless product or tell me about news I've already heard a dozen times. It was instead a series of journal-like recordings about some strange discovery that he called the Starmaze. 

    It started with a game he had come across on a computer years ago that involved a square divided into nine sections where each section could be turned on or off. The game began with the middle section of the grid turned on, and the outer eight sections turned off. Clicking one of the sections would turn on/off other parts of the grid in a predictable way, but you could only click the sections that were already turned on. The goal was to click the sections in a way to end up with the outer eight squares turned on, and the innermost square turned off.

    Being interested in games myself, this sounded familiar to me immediately. I've seen, in several video games before, puzzles just like this — the player starts with a blank grid and has to fill in all the sections by pressing them in a specific pattern. The difference this time, though, was that in Cartan's puzzle, only the "on" sections could be pressed. This small change made the puzzle far more difficult than the ones I'd encountered in the past. You can try it yourself, if you want.

    I couldn't figure out the solution to the puzzle, so I continued reading, expecting an explanation of the rules and methods of solving it. Maybe, I thought, the webpage would end with some interesting insight, and I would be done. In the end, I was correct that Cartan would offer up an explanation of the rules and methods, but I never expected how far it would go. It wasn't a simple explanation, and it wasn't even one that he knew immediately. It wasn't a puzzle that could be understood in one night. 

    Cartan saw the puzzle as a maze, with the "on" sections being doors that lead to new rooms with new doors. This approach made the puzzle — once seen as just 9 sections — seem instead like a new, vast world. So, he started trying to map out how the rooms connected to each other, but it didn't seem to function like a normal 2D — or 3D — world. I recommend that you read his own documentation about him discovering this, but he eventually came to the incredible insight that the maze wasn't easily translating to a 2D map because it wasn't a 2D maze. It was, as he calls it, the Starmaze — a maze that exists on a ninth-dimensional hypercube.

    Once math became involved, my interest, which was already quite high, managed to double. I won't spoil everything here, as that defeats the purpose of Cartan's wonderfully crafted pages, but I can tell you that he writes about every step of his discovery in a greatly intriguing way. There's lots of material to get through, and, like the Starmaze, I didn't go through it in a linear way. The site's pages are connected through hyperlinks spread across Cartan's writing, so the viewer can directly read more about whichever parts of the story interest them. Because of this, I spent hours reading the parts that fascinated me most, and still hadn't covered everything. I covered enough at this point, though, to grow a fascination for higher dimensions. I was especially inspired by his 3D rendition of the 9D puzzle, as it made it feel like a tangible world. Of course, I had to learn as much as I could.

    A portion of John Cartan's 3D map of the Starmaze

    As a person who loves games and math, the Starmaze was a perfect challenge for me. I wanted to be able to understand and visualize it, so I got started learning about the next dimension up — the fourth dimension. Now, everyone who I talk to about this tells me to read Flatland, and I know, and I should, and I will. Instead though, at this time, my father gave me the book The Fourth Dimension by the great writer and professor Rudy Rucker. I also got a copy of Fantasia Mathematica for Christmas since I asked for it after reading about a story in it on Cartan's website. Much later, Cartan would eventually tell me that "There is a long history of mystics who have gotten hooked on higher dimensions and maybe spent a little more time on it than they should have. To an actual mathematician, a 9-dimensional hypercube is ordinary to the point of being trivial or mundane. But if they are honest, and remember why they became mathematicians in the first place, they will admit to experiencing the same wonder that you and I have felt contemplating things just beyond our reach." 

    He would be correct — at this point in time, I was most definitely experiencing great amounts of wonder towards the Starmaze and towards higher dimensions in general.

    School — before the pandemic — always took up several hours of my weekdays. Of course, I appreciate my education, and I work as hard as I can, but there will always be times where I've finished my work or my exam and can't use my phone or leave until everyone else has finished. This happened weekly, if not daily. After reading about the Starmaze, that was all I could ever think about during these times of sitting in a soundless classroom in the middle of the day. So, I decided to use these times productively. On his website, Cartan describes a mathematical triangle that allows you to figure out how many lower-dimensional cubes are in a higher-dimensional cube. For example, a 3D cube has 6 square (2D cube) faces and 12 line segments (1D cubes). The triangle could tell you that. It could also tell you things you don't know, like that a 14th-dimensional hypercube contains 1,025,024 5th-dimensional hypercubes. Cartan calls this "Cartan's triangle," and has one available on his website to see, but I know from my own experience that I only absorb so much information through visuals. So, I decided to handwrite my own in my math notebook at school, which I think was a good way to spend my time. I enjoyed making it much more than I'd enjoy anything else I had access to in that environment. And by making it, I was actually able to find patterns and surprise myself. It also gave me an excuse to ramble on to any poor kid walking by who happened to ask, "What's that?" Some of those kids have come back later to talk more, though, after they too got interested and started researching higher dimensions, so I regret nothing.

    My Cartan's Triangle

    Even after I finished my Cartan's triangle, I wasn't satisfied. I was really happy, of course, but I wanted to create more and I wanted to learn more. Then, I thought of something that made me surprise myself. If you'll recall, I mentioned before that Cartan found that it wasn't exactly easy to map the Starmaze onto a 2D space. Again, I recommend that you read his own documentation of this, but he eventually did figure out a way to do it. He created a couple of rules and a great system to translate the 9D maze into the second-dimension, and it was really beautiful looking. Using simple red and blue lines, you can traverse this hypercube several dimensions higher than we could ever really imagine. So in 1987, Cartan printed out the map on a scale that took up 16 pieces of paper put together, and he spent days meticulously coloring in each and every line. Now that my triangle was done, I could think of one other thing I could do — I could make my own starmap.

    John Cartan's starmap

    Although an image of the starmap like the one that Cartan had himself wasn't available on his site, he did still have a different image of the starmap available that was used to show the solution. I was happy with it, so I printed it out. I didn't have the courage to construct it on the scale of 16 pieces of paper like Cartan did, so I settled with the scale of four pieces of paper. Next, the red and blue lines were essential, so it was my job now to color in those lines. Unlike the original starmap, though, the map I printed out was black with white edges, meaning normal markers or pencils wouldn't show up on it. So, I decided to use red and blue gel pens to color in the lines over the darkness. It was a Friday night and my parents had just left town for the weekend, and I didn't have plans myself, so I figured that I could finish it by Sunday evening. 

    This was very, very incorrect.

    Using a guide on Cartan's site, I spent hours coloring in the map that weekend, and by the end, I was not halfway done. I had to go back to school again on Monday, but I would devote a couple of hours the next weekend to coloring in the map, and then again the next weekend. In the end, as I had worked, I'd managed to listen to 9 hour-long episodes of my favorite podcast, the entire audiobook of The Great Gatsby, lots of music, and more before I was finished. The months it took me to finish my 4-page map gave me great new respect for Cartan coloring in his 16-page map. At one point, I had to order new pens to finish, as mine had run out of ink from the coloring. But in the end, this tracing activity taught me more about the maze than I ever could have gotten from just staring at the map. There were many patterns and rules and symmetries, and I understood how the map worked in the second-dimension now. I would be slightly surprised when Cartan would later tell me that besides me and him, there was no one else who had printed and colored the starmap, to his knowledge.

    My starmap

    I don't think I'll ever be able to fully wrap my head around the Starmaze, but I am always grateful that I stumbled across it one night as I clicked through links and pages. It's inspired my thoughts and given me a whole new interest (and new reading material). It's brought me closer to ones who know more about higher dimensions than I do, and it's given me a really cool poster to hang next to my desk. And maybe, one day, if the universe collapses and we get swallowed into a ninth-dimensional hypercube, I can put my geographical knowledge into the new society we create. Thanks for everything, John Cartan.

  • Four great SoundCloud songs you've probably never heard

    I use Apple Music for the majority of my music listening. It works well and lets me add most of my favorite songs, but there's a lot missing from it. From what I've heard, it takes a little bit of work to get your songs up on iTunes/Apple Music. Unless an artist is well known and doing well in their music career, oftentimes, it's simply not worth it to publish to Apple Music.

    SoundCloud, on the other hand, provides extreme simplicity when it comes to publishing music, and makes it easy for listeners to find your songs. So, lots of artists get their start on SoundCloud, which entices me to use it alongside Apple Music. Yeah, there's a popular and pretty true idea floating around that SoundCloud is full of mumble rappers, but this isn't about that part of the site. If you look, it's easy enough to find a lot of gems on SoundCloud.

    Here are four good songs I've found on SoundCloud that have less than 10,000 listens at the time of posting this.

    1. "Decadence" by Gr._.ff

    The lack of attention to this song has astounded me since I found it. It starts off with a pretty sweet melody but completely switches mood halfway through, and I love that about this song. I've had a few friends who judged this song before it was even a few seconds in, but I think that you have to listen to the entire song to fully appreciate this one.
    Age of song: 3 years old
    Listens: 7,332
    Likes: 174

    2. "Going Up?" By capt beard

    I love capt beard's music, and this is the song that let me discover him. I found it on a SoundCloud station while I was on a bullet train in Japan, and the aura of the song fit the scene so well that I instantly fell in love. Also, my dad really likes this song. Also also, you can download the album that this song is from here.
    Age of song: 1 year old
    Listens: 6,516
    Likes: 205

    3. "The Road of Gold" by Jonas & Warren

    This song is like no other song on this list. It seems to combine lots of different genres and eras in its sound. Like the others, though, it's a great song, and it has only a very few listens. Give this song a go; it's really pretty great.
    Age of song: 1 year old
    Listens: 129
    Likes: 4

    4. "Flying Cars" by Larry Goldings

    This one is a short one at just 57 seconds. But, it's unique and makes me happy in a melancholy way. I found it in the early summer when I was coding a lot and had non-intense electronic/chiptune music accompanying me while I worked. This tune came on, and I liked it a lot.
    Age of song: 1 year old
    Listens: 1,856
    Likes: 61

  • Making a Rock Paper Scissors game with an Arduino compatible device

    This summer, I have been working as an intern at a company called Switch Science in Tokyo, Japan. I am writing about my experience here in the form of blog posts, and you can find my first post here.

    On Thursday last week, I was given a thermal camera to work with along with my M5Stack. My goal was to connect them together and display the thermal data in the form of a picture on the M5Stack's screen. The thermal camera was called the MLX90640 by Melexis. After briefly reading about it, I was confident that I knew where to connect the wires and which I2C address to use, but I quickly realized that the size of the pins on the thermal camera were too small to connect to the wires' pins. Although I could plug them into each other, the connection would only work properly half of the time. So my coworker Kazunori helped me by cutting the end of the wires and soldering them straight to the camera's pins. It seemed to connect well, and I continued trying to figure out how to display the data from it.

    Then, Monday morning, the camera suddenly stopped connecting. I spent a few hours trying to figure this out on my own before I asked Kazu for help. He suggested we try to connect a different camera, but no cigar. We also tried a different Arduino sketch made by a different person, but it also didn't work. Eventually, we tried using a different, brand new M5Stack, and it connected!

    But then a few minutes later it stopped connecting again.

    Due to this issue having already taken a full work day and being pretty inconsistent, I decided to quit the project and start something new.

    On Tuesday, I got to the office wondering what to work on. I opened my backpack to grab my stuff, and saw both my old M5Stack and my new one from Monday. This gave me the idea to make a game involving both M5Stacks. I decided to create a simple Rock Paper Scissors game where players would each select their option on their M5Stack and then the screen would display who won. Truth be told, I was a bit cocky and thought I could finish this project in just one work day, but this was not the case.

    I worked with my M5Stack and my computer's serial port in order to simulate the other player's M5Stack because it was easier than continuously uploading new code, unplugging the M5Stack, uploading it to the second M5Stack, unplugging that one, and then plugging them to each other. I'd rather just run it while it was still connected to my computer and then simulate the other M5Stack manually on Arduino's serial port. Therefore, at the end of the day, when I thought my game was working great, I was a bit surprised to see that when I uploaded the code to both devices and played them against each other, it was an absolute mess.

    I honestly cannot describe what the error was that prevented my game from working, as I think there were many. I was overwhelmed to say the least, and the next day I was not very motivated to figure this out. I got a bit of work done, but I was tired and it went slowly. At least I got it from looking like a meme of sorts to being coherent, although still not what I wanted. Some values would persist even after the round ended and all variables were supposed to be reset, but nothing was consistent. For example, sometimes you could choose rock, paper, or scissors, and it would tell you if you won or lost without the opponent even picking their choice yet. Other times, the opponent's status would read as "READY" from the beginning of the round (it should only turn to "READY" after the opponent makes their choice), and then when you picked your choice it would just continue saying "READY" instead of revealing the opponent's choice.

    Then, this morning, I decided I was going to finish making this game before lunchtime. I did quite a bit of stuff, but by the end, the trick was to make a "value monitor" and add it to my reset function that ran before / after each round.

    I was finally able to see that the "oppChoice" integer (if the other player chose rock, paper, or scissors) would continue switching values between your choice and the other players choice after the first round, even when the reset function played. This was because the serial input ("mailbox[0]") kept on reading these values off when it should not have. I was finally able to acknowledge and fix this issue (it would take another few paragraphs to explain, and I'll save you that catastrophe) and the game finally WORKED! (See photo at top of this post.)

    I am not saying it is perfect, as the player must hold down their choice for a second for it to register and the results are not well centered, but I will continue to fix these issues and get my project to the best state that it can be in, even if it is just Rock Paper Scissors.

    I will continue to post about my internship in the near future! Thanks for sticking around.

  • HAPPY WORLD and its dark underside is a game you'll want to play more than once

    Earlier this month, a game called HAPPY WORLD by Jimi Masuraki was released on itch.io. When I first downloaded it, I honestly thought I might play it for 15 minutes during my free-block at school, at then uninstall it and be done. But after five or ten minutes of completing simple quests and making the digital people happy, I realized that this wasn't another free lackluster game.

    Not only did the adorably simplistic art style and funny nonchalant conversations between the player and the entities in the game cause me (and a few of my classmates) to laugh out loud, but once I got home and got further into the story, I found that there was intentional – and dark – lore in the game that was left for the player to discover on their own. I immediately knew that I was going to have to finish the game to unravel all the secrets — and in just less than an hour I did — but it wasn't the ending that I was looking for. I restarted the game and started my attempt to figure out how to trigger the game's true ending, and I was not at all disappointed.

    I do not plan to spoil anything here, but if you are looking for a quick, free, and overall fantastic game to play, I recommend HAPPY WORLD. It's an incredible mix of a happy-go-lucky simple world, and a darker, more depressing one hidden underneath. I truly doubt you'll be disappointed. You can download it for free here.

    Also, you can go to Jimi Masuraki's Patreon page here, because he makes pretty great, fun games that you really can't find anywhere else.

  • Interview with Prince Ea

    I like Prince Ea's videos because he talks about important issues in the world: the health of our planet, racism, and being kind to each other. He made a video about a DNA test he took to learn about his heritage and I interviewed him about it.

    What events in your early years shaped who you are today?

    Good question, two events. Number one, I had the opportunity to get a decent education. Secondly I received the love of both of my parents. These very important factors that made me the person that I am today.

    How did you come up with the concept for this video?

    Well I had the opportunity to work with an amazing creative agency Berlin Cameron and director JJ Augustavo from Skunk, who really put the awesome video together. When I wrote the piece, I just wanted it to come from my heart. Through the MyHeritageDNA test, discovering that I had a connection to a number of ethnicities not only amazed me but visualized what I had been thinking for a long time. Namely, that we can't be restricted to one box. It was this realization and my BA in Anthropology that really helped me come up with the words for the piece.

    How did you feel after discovering your diverse heritage?
    That is pretty cool. Despite what society told me, I'm not just "one thing." I, along with every other human, am a mix of many beautiful ethnicities.

    What can young people do to improve the world?

    To improve the world they can improve themselves. Good action will arise spontaneously from being a good person. Cultivate the qualities of compassion, patience, love and watch the world change.

    How do you feel these labels of heritage affect young people today?

    These labels of heritage may give the young people a sense of pride. This is dangerous because if you pledge allegiance to a particular label, then some people become "other." This inevitably turns into "us" vs "them." When you analyze your own genes, you will find that these labels are not so "solid," after all. There is no "us" vs "them," only "we". I think everyone should take a MyHeritage DNA test, find out the answers and discover more about themselves. Once we have informed ourselves can we then have a better conversation about the labels applied to us.

    What makes you hopeful for humanity in the future?

    For every act of unkindness, there are a thousand kind acts. The media shows the world in a particular way but I believe that love and compassion are the higher nature of the human being. As we continue to evolve, we will become a more peaceful, mindful and loving species.

  • Prince Ea puts the school system on trial

    Richard Williams, aka Prince Ea, is an amazing spoken word artist who helps make people aware of their lives and surroundings. With his videos, he reminds us that we can make a difference. He has a new video about the modern school system and how, in his opinion, it needs to be improved. It shows that the school curriculum may not be as perfect as we thought. Does it need to change? Well, we'll let you watch and decide for yourself.

  • Undertale offers a new spin on retro RPG video games

    Undertale is a new 8bit RPG that's much different from the rest. In most games, you have to kill bosses and monsters to survive. In this game, it's up to you whether you want to kill anyone, and depending on your choices, you can make friends that you would have lost, engage in secret fights, and much more. You have so many choices in the game that you can replay it over and over to achieve all the endings. But be careful, because even if you reset the game, some characters might have a vague memory of you.

    The fighting style of Undertale is also unique. When an enemy attacks you, instead of automatically losing your health, you can dodge their attack by moving your "soul" across the screen to avoid being hit. Because of this, you don't have to lose any damage throughout the battle.


    Undertale starts by your character falling down a giant hole at the top of a mountain and waking up in a world full of monsters. They were all banished to live apart from society for the rest of their lives by humans who sealed them underground with a magic spell. The monsters have figured out that the only way to undo the spell is to have the power of seven souls, but since monsters' souls disappear after they die, they've spent years killing the humans who fall into the underground to gain their souls. Because of this, most of them want to kill you so they can leave, but it's up to you if you want to hurt them back, or show them that you both can find peace.


    I highly recommend going to Steam and buying Undertale. I'm 12 and it's my favorite game, while I also know adults who love it as much as I do.