We bring you a brand new Mensa Cats cartoon by J.B. (that’s Jason Berry of Vacuum Tree Head). This one expresses not one but two of Zeno’s famous paradoxes in a single frame.
The first is the better-known Dichotomy Paradox, from which the punchline derives. In order to walk into the bar, Zeno (or any of the other patrons) must first walk halfway; and to travel from the halfway point, he must travel half of that distance, and then half of that distance, and so on. It seems that this process of walking halfway would continue forever and one would not arrive and one’s destination, yet we know in reality that we do.
The second paradox is the Arrow Paradox. Consider the frame frozen in time, as indicated by the liquid in mid spill behind the young lady cat, or the multiple instances of Zeno along his path. At any given moment, there is no motion. Zeno’s position does change between moment, but there is an infinite number of other frames, each with a fixed position. As copies/frames of Zeno get closer and closer together, the change in time between them gets infinitesimally small. Yet the process 0f adding up these infinite frames with zero motion in each results in Zeno walking halfway into the bar.
The two paradoxes (and the third, commonly referred to as “Achilles and the tortoise”) are closely related. The first deals with infinitesimal subdivisions of space, while the second deals with infinitesimal subdivisions of time. The key is that while any infinitesimal quantity is smaller than any quantity we can express, it is always still greater than zero. And adding up an infinite number of infinitesimal quantities can sometimes yield a finite number.
Take the halving process in the Dichotomy paradox. Zeno moves half this distance, then half of that, and so on. This can be expressed as an infinite sum.
As one gets closer to infinity, the sum gets closer and closer to one. More formally, we can say that as we approach infinity, the sum goes to 1. So an infinite number of subdivisions still reaches our goal of the full distance.
This process of applying operations to an infinite number of infinitesimal subdivisions is the principal behind calculus, and a marvelous thing to behold once one gets used to it. The mathematics does not necessarily answer the metaphysical questions raised by these ancient paradoxes, but it is what most interests us at CatSynth. It’s been a while since we last shared the joy and beauty of mathematics on these pages, but it is high time we resume the practice.
Cat playing the organ [Walters, W. 438, 15th c.]. Posted by Damien Kempf on Twitter and spotted by astute reader @endlessscribe.
The image comes from a 15th century prayer book in the collection of the Walters Museum based in Baltimore. From the museum’s digital library:
This late fifteenth-century Prayer Book was made for the Use of Rome and illuminated by followers of Willem Vrelant of Bruges. The manuscript was probably created for the couple depicted in two full-page miniatures (fols. 13v and 103r). The representation of the bride in the full-page miniatures, as well as references to her in suppliant prayers, indicates that the manuscript was commissioned primarily for the bride’s use. Further evidence of this is the prominence of women throughout the illuminations and drolleries, from one who was caught in adultery being brought before Christ, to Veronica extending her veil to Christ as he carries the cross. The decorative aspects of the manuscript stray from the typical border designs of this time period, focusing more on illusionistic Ghent-Bruges’ illumination (post-1475) and less on the Vrelant acanthus-floral borders. Among the number of full-page miniatures, fol. 229v stands out as an exceptional example of an imitation of a late fifteenth-century panel painting.
Interestingly, I did not see the cat among the includes samples.
A few years ago, I traveled California’s Highway 41 on my 41st birthday. I had hoped to make this a regular tradition, but various circumstances have kept me from following through, until this year, when I drove the southern half of CaliforniaHighway 45. It wasn’t exactly on my birthday, and I didn’t complete the route, but was still a fun and eccentric way to celebrate the conclusion of my 45th year of life. It was also a good excuse to try out the new travel-mapping feature in our Highway☆ mobile app.
Highway 45 begins in the small town of Knight’s Landing in Yolo County, so I first had to schlep up there via Interstate 80 and then turn north on Highway 113 near U.C. Davis. 113 is a major freeway at this point, but a bit further north it narrows to a two-lane country road before reaching the junction with 45.
Knight’s Landing was actually a very small but cute town along the Sacramento River. Before embarking on the formal part of the trip, I stopped along the levee at Front Street to view the continuation of Highway 113 across the river. Front Street was rather beaten up compared to the rest of the town center, perhaps due to the nature of the levee or to discourage unnecessary driving, but it made for a nice little walk.
I then returned to the car and finally turned onto Highway 45, heading northwest out of town.
The highway zig-zagged on a grid between fields on the western side of the Sacramento River, but far enough for the river to mostly remain out of sight. But there were some lovely wide-open farmland vistas, made more dramatic by the bands of clouds in the sky marking what was a lovely day after a week of dreary weather.
It is when the landscape opened up that I was able to fully relax into the trip. There is always a point along the journey during which stresses, mundane or otherwise, start to melt away and the road, landscape, and solitude take over the mind. As Highway 45 is remarkably well signed, there was no ambiguity or uncertainty. The result is a sense of flow and well being that allows one to both think about other ideas, like music, while remaining fully engaged in the moment. It is something I have experienced many walking the streets of San Francisco, but not lately. I certainly hope it isn’t gone – as much as I enjoy these long excursions to other regions, I would love to return to the sense of external flow in my own community as well. Perhaps it is the familiarity or the many stresses and dramas, but I hope to regain it.
The highway turned due north in Colusa County, providing great views of the Sutter Buttes, considered to be one of the worlds smallest mountain rangers.
The Buttes are a small circle of volcanic lava domes that rise suddenly from the rather flat Sacramento Valley. The contrast is fascinating, and I would love to come back and explore the geology at a warmer time of year. Unfortunately, public access to the Buttes remains limited as far I can tell. (If any readers have any advice or new information about public access to the Sutter Buttes, please share in the comments.)
At this point, Highway 45 comes closer to the river, and between Grand Island and Grimes, comes right up against levees, before turning north again. It is not surprising to see such high levees, as the entire region seems like a giant flood waiting to happen.
Further north, we join with California Highway 20, a major east-west highway in this rural part of the state connecting to Yuba City to the east and to Lake County far to the west. The road became wider, smoother, and significantly busier as we continued on the duplex into the town of Colusa.
Colusa is a picturesque town on the river, with a small but nice town center and a quiet park along the levee and riverbank. It had warmed up considerably since I last got out in Knight’s Landing, so stopped for a bit to enjoy the sight and sound of the river. You can see a bit in this Instagram video.
Nearby I found The Tap Room, a small pub that had a large selection of beers including some local brews. I don’t think they had Sutter Butte Brewing, but they did have some selections from Berryessa brewing including this IPA.
In the enjoyment of the trip, I had completely forgotten that it was St. Patrick’s Day. But I was quickly reminded by the bartender who was decked in bright green regalia and informed me of the holiday pub crawl that would be happening that evening. This was the talk of the local patrons who started trickling in as the afternoon wore on. Everyone was friendly and welcoming, but a night of drinking was not going to be compatible with my plan to get back to the city safely at a reasonable hour. So I bid farewell and headed out on Highway 20 back to I-5 and I-505 to return to the Bay Area.
Tired but accomplished, I crossed the Bay Bridge back into San Francisco and home later that evening. That would usually be the end of the story, but after resting, we made the last-minute decision to go out again that night. So I found myself getting dressed up and heading back over the bridge for the third time to Oakland to see Chrome withHelios Creed. We met up with quite a few friends at the show and had a great time. You can see a bit of Chrome’s performance in this CatSynth TV.
It was a great day of diverse geography and experiences, albeit a long one. Not every day can or should be like this, but hope there are more to come this year…
See more Northern California in our Highway☆ app, available on the Apple App Store and Google Play Store.
I have been spending a lot of time at the main software-development and video workstation of late. As we have seen before, Sam Sam loves to drop by and say hi.
She seems to really like the open shelves as much as I do.
As one can see, cat decor abounds in the studio. But we also have some other items on display in these shelves.
On the left (of course) is a Bernie Sanders action figure, made by Brooklyn-based FCTRY, as well as a signed card from the 1990s when we still just Vermont’s representative. And to the right of Bernie is our Lego recording studio.
The studio is from a series of Lego kits specifically aimed at young women, and I loved the idea of having a “studio in the studio.” It’s great the engineer is a woman, but we thought it needed one more addition.
Yes, that’s a little Lego black cat! A tribute to Luna, whom we still miss dearly. 💜
Apparently, even Lego cats shed. But our life-size studio tends to be entropy-prone as well, especially before and after live shows. It definitely needs another clean-up…but first we have a lot of creative projects ahead this weekend. We hope you all have a happy and productive weekend as well.
It’s time for another round of catch-up on recent musical adventures around the Bay Area. And so today we look back at last month’s performance by Rent Romus’ Life’s Blood Ensemble at the Ivy Room in Albany, California, where the celebrated the release of their new album Rogue Star. It was the subject of a recent episode of CatSynth TV.
As Romus explained on stage (and in our video), Rogue Star is a deliberate reference and homage to David Bowie’s final masterpiece Black Star. In particular, it is inspired by the work of saxophonist Donnie McCaslin (Romus’ brother-in-law) on Black Star. Indeed, the title track of the new album as performed that night did reference the style and material of McCaslin’s work. But this was a point of departure, and the ensemble moved in different directions as they performed other tracks from the new album.
Several of the band members contributed compositions to the album and to the performance that evening, including “Think!” by Heikki Koskinen (e-trumpet) and “Space is Expanding” by Safa Shokrai. Shokrai’s piece picked up on the theme of space and cosmos that winds through many of Life’s Blood Ensemble pieces as well as through Romus’ other projects. Koskinen’s composition offered frenetic ensemble runs punctuated by silences and small staccato hits from his e-trumpet as well as other instruments.
Rounding out the ensemble were Mark Clifford on vibraphone, Timothy Orr on drums, and Joshua Marshall on tenor saxophone. As always, I was impressed at the way the ensemble functioned as a unit, whether in the middle of a swinging “cool jazz” idiom or more seemingly free and chaotic sections. In some ways, it is in the silences between phrases where this is most apparent.
Before closing, I should also say something about the Ivy Room. This venerable institution has gone through multiple incarnations in the ten years since I moved to San Francisco and started playing and attending shows there. Of course, I had a lot of fun performing at “Hootenannies” back in 2008, 2009 and 2010, and enjoyed the kitschy decor. But from a musical point of view – and especially a jazz-ensemble point of view – this current incarnation is the best, with a sizable stage, lighting and sound reinforcement. I hope to bring my current band there sometime soon.
This is such heartbreaking news. Bento, the Keyboard Cat has passed away 😿
His humans made this wonderful tribute to Bento and his legacy, including many classic clips; and a sweet story about how he was a source of inspiration for his human companion, Charlie Schmidt.
Bento was actually the second Keyboard Cat. The original, Fatso, also lived with Schmidt but passed away in 1987, long before the age of internet memes. You can read more about the story of Fatso, Bento, and Schmidt at the Keyboard Cat Wikipedia page. Like my cats, Bento was a shelter cat and became a public face for the Shelter Pet Project. We saw him featured in billboards and bus stops here in San Francisco.
Keyboard Cat has always been a favorite of mine – how could it not, given the combination of interests. We always had fun with the early “play him/her off” videos, and it became a frequent tag-line of mine to say “You have been played off by the Keyboard Cat”, especially when someone loses a political election. I wish we had been able to cross paths in person.
We at CatSynth extend our sympathies to Charlie Schmidt and the rest of Bento’s family. Rest in peace, Keyboard Cat, you have been played off. 💕
Sometimes Sam Sam ends up in CatSynth pics of her own, as when she recently got up to explore the redesigned studio space. She is fascinated by the new decorative shelves as well as the narrow band between the video/office corner and the modular synth.
Perhaps she is picking up some scents on the modular case from our recent live performances.
I have been having a lot of fun in the studio lately, especially making videos and exploring our synthesizer collection in greater depth. I really should be working on some more formal compositions, but it seems I am in more of experimenting and exploratory mood at the moment. I have also, unfortunately, been battling insomnia. It ebbs and flows, and on the worst night (about a week ago), I decided to sit up for a while and play with the Roland JP-08 boutique synth.
The size is actually ideal for playing in bed late at night. I spent some time exploring the architecture (it’s basically a Jupiter 8 with a few extensions) and came up with some new and unusual patches. We hope to share them with you in an upcoming CatSynth TV.
