The noted Diné (Navajo) weaver Marilou Schultz recently completed an intricate weaving composed of thick white lines on a black background, punctuated with reddish-orange diamonds. Although this striking rug may appear abstract, it shows the internal circuitry of a tiny silicon chip known as the 555 timer. This chip has hundreds of applications in everything from a sound generator to a windshield wiper controller. At one point, the 555 was the world's best-selling integrated circuit with billions sold. But how did the chip get turned into a rug?

The 555 chip is constructed from a tiny flake of silicon with a layer of metallic wiring on top. In the rug, this wiring is visible as the thick white lines, while the silicon forms the black background. One conspicuous feature of the rug is the reddish-orange diamonds around the perimeter. These correspond to the connections between the silicon chip and its eight pins. Tiny golden bond wires—thinner than a human hair—are attached to the square bond pads to provide these connections. The circuitry of the 555 chip contains 25 transistors, silicon devices that can switch on and off. The rug is dominated by three large transistors, the filled squares with a 王 pattern inside, while the remaining transistors are represented by small dots.

The weaving was inspired by a photo of the 555 timer die taken by Antoine Bercovici (Siliconinsider); I suggested this photo to Schultz as a possible subject for a rug. The diagram below compares the weaving (left) with the die photo (right). As you can see, the weaving closely follows the actual chip, but there are a few artistic differences. For instance, two of the bond pads have been removed, the circuitry at the top has been simplified, and the part number at the bottom has been removed.

Antoine took the die photo with a dark field microscope, a special type of microscope that produces an image on a black background. This image emphasizes the metal layer on the top of the die. In comparison, a standard bright-field microscope produced the image below. When a chip is manufactured, regions of silicon are "doped" with impurities to create transistors and resistors. These regions are visible in the image below as subtle changes in the color of the silicon.

In the weaving, the chip's design appears almost monumental, making it easy to forget that the actual chip is microscopic. For the photo below, I obtained a version of the chip packaged in a metal can, rather than the typical rectangle of black plastic. Cutting the top off the metal can reveals the tiny chip inside, with eight gold bond wires connecting the die to the pins of the package. If you zoom in on the photo, you may recognize the three large transistors that dominate the rug.

The artist, Marilou Schultz, has been creating chip rugs since 1994, when Intel commissioned a rug based on the Pentium as a gift to AISES (American Indian Science & Engineering Society). Although Schultz learned weaving as a child, the Pentium rug was a challenge due to its complex pattern and lack of symmetry; a day's work might add just an inch to the rug. This dramatic weaving was created with wool from the long-horned Navajo-Churro sheep, colored with traditional plant dyes.

For the 555 timer weaving, Schultz experimented with different materials. Silver and gold metallic threads represent the aluminum and copper in the chip. The artist explains that "it took a lot more time to incorporate the metallic threads," but it was worth the effort because "it is spectacular to see the rug with the metallics in the dark with a little light hitting it." Aniline dyes provided the black and lavender colors. Although natural logwood dye produces a beautiful purple, it fades over time, so Schultz used an aniline dye instead. The lavender colors are dedicated to the weaver's mother, who passed away in February; purple was her favorite color.

Inside the chip

How does the 555 chip produce a particular time delay? You add external components—resistors and a capacitor—to select the time. The capacitor is filled (charged) at a speed controlled by the resistor. When the capacitor get "full", the 555 chip switches operation and starts emptying (discharging) the capacitor. It's like filling a sink: if you have a large sink (capacitor) and a trickle of water (large resistor), the sink fills slowly. But if you have a smal sink (capacitor) and a lot of water (small resistor), the sink fills quickly. By using different resistors and capacitors, the 555 timer can provide time intervals from microseconds to hours.

I've constructed an interactive chip browser that shows how the regions of the rug correspond to specific electronic components in the physical chip. Click on any part of the rug to learn the function of the corresponding component in the chip.

For instance, two of the large square transistors turn the chip's output on or off, while the third large transistor discharges the capacitor when it is full. (To be precise, the capacitor goes between 1/3 full and 2/3 full to avoid issues near "empty" and "full".) The chip has circuits called comparators that detect when the capacitor's voltage reaches 1/3 or 2/3, switching between emptying and filling at those points. If you want more technical details about the 555 chip, see my previous articles: an early 555 chip, a 555 timer similar to the rug, and a more modern CMOS version of the 555.

Conclusions

The similarities between Navajo weavings and the patterns in integrated circuits have long been recognized. Marilou Schultz's weavings of integrated circuits make these visual metaphors into concrete works of art. This connection is not just metaphorical, however; in the 1960s, the semiconductor company Fairchild employed numerous Navajo workers to assemble chips in Shiprock, New Mexico. I wrote about this complicated history in The Pentium as a Navajo Weaving.

This work is being shown at SITE Santa Fe's Once Within a Time exhibition (running until January 2026). I haven't seen the exhibition in person, so let me know if you visit it. For more about Marilou Schultz's art, see The Diné Weaver Who Turns Microchips Into Art, or A Conversation with Marilou Schultz on YouTube.

Many thanks to Marilou Schultz for discussing her art with me. Thanks to First American Art Magazine for providing the photo of her 555 rug. Follow me on Mastodon (@kenshirriff@oldbytes.space), Bluesky (@righto.com), or RSS for updates.

I heard the phrase “experience rich, theory poor” on a podcast interview between New Yorker editor David Remnick and writer Malcolm Gladwell in 2018. The phrase immediately triggered memories of my returning to graduate school in the early 1970s after serving many years as a high school history teacher and a district administrator in the Washington, D.C. schools.

That phrase captured my thoughts about the coursework I took the first year of graduate school on organizational theory, the politics of education,and the history of education. I had gained enormous and varied experiences for well over a decade in teaching history to mostly Black high school students in Cleveland (OH) and the District of Columbia. I knew chapter and verse of how classrooms operated, what happened in those schools on a daily basis, and the strengths and weaknesses of admired and trusted colleagues. I had also accumulated rich experiences in running a school-based teacher education program and then a district-wide staff development program. If my professors and peers asked me what I knew about schooling in big cities, I had stories and specific cases that I could easily draw from to illustrate point after point about the nature of teaching and administering in urban schools.

But my stories and cases were insufficient, I discovered. What became increasingly clear to me during that first year of graduate school as I digested assigned readings, listened to professors lecture, and heard seminar discussions, those stories and pithy examples I had stored up, lacked a  theoretical framework. Yes, I was an experienced practitioner but I was adrift, unable to go beyond the stories I would tell.

I lacked the language of theory, conceptual frameworks, analysis, and generalizations. Without knowing theories that helped me make sense of my experiences, I drew conclusions, advanced generalizations, and made predictions about improving schools often saying: this is what works in these schools and districts because I was there and know from first-hand experience.

Such atheoretical statements fell flat upon my professors. In two years of coursework, I learned the importance of having explicit (not tacit) conceptual frameworks to help me make sense of what I experienced. For me, then, overtly connecting theories to my work as a teacher and administrator gave me a new and richer vocabulary but also a deeper understanding of an institution in which I had worked for many years. Those theories equipped me with multiple perspectives on not only how classrooms, schools, and districts worked but also their contexts and what I could do about the mistakes I had made and failures I had experienced. The theories I learned and then later used made graduate school and the Ph.D enormously helpful when I later served as a district superintendent for seven years.

But I was also wrong.

Yes, the phrase “experience rich and theory poor” applied to me in graduate school. But in the years during my superintendency and, subsequently as a university researcher for two decades I came to see that I, like the teachers and principals I worked with, had tacit theories deeply embedded in what I and they did but I could not then articulate those hidden causal concepts rooted in my (and their) beliefs, intentions, and expriences. I lacked the vocabulary to put those tacit theories into plain English.  I was rich in theory but just didn’t know it.

Parsing the theory buried in, say a teacher’s practice, can happen when actual classroom actions are looked at closely. Consider the common  teacher practice of letting students re-take tests (see post).

Here is what middle school teacher Baptiste Delvalle does with his students:

Here’s how I explain it to my students. If you’re asked to meet a deadline in a future job, and you’re late or have poor-quality work, you might get fired. If you’re in a relationship and don’t show up to the dates, you might get dumped. If you cross the road without looking, and a car comes zooming by, you don’t get a second chance. I prefer that they get a bad grade and learn to give it their best shot on the first try, rather than to hear years from now that they’re still struggling.

Delvalle’s beliefs in how the “real” world works–you do this and that happens–led him to tell students “you don’t get a second chance” in taking a test because that is not how life is outside school walls. You do the best you can first time out.

I do not know where his theory of action about “real” life comes from, but it seems to be a mix of observations he accumulated growing up from which he learned lessons, parental teachings, reflections on real-life experiences, possible religious beliefs, and other factors. Delvalle’s practice of prohibiting re-taking tests, then, has buried within it a theory of action about how the world works. It is tacit theory embedded in the practice.

Now consider Lisa Westman’s practice of permitting re-tests for students. A veteran of 15 years in classrooms, Westman sees the same world that Delvalle sees but interprets it differently.

In addition to the daily assessments we give them now, students will take many tests over the course of their lives, such as a driver’s exam, the SAT, the LSAT, and the MCAT, to name a few. All of these examples allow retakes. The way school prepares students for real life is by ensuring they learn the content and skills necessary to live a full, productive life. Part of real life is determining next steps when life doesn’t go as planned.

Westman argues that students should be able to re-take tests as a way for students to achieve mastery of content and skills since most formal written, oral, or real-life tests in life can be re-taken until they are passed.

In Westman’s practice of students’ re-taking tests, lies her theory of action. Like Delvalle, I do not know the beliefs and values nor the experiences she had with her family, growing up, and teaching but it is clear that she sees “real” life differently than Delvalle. For her, preparing students for life means that they will make mistakes; failures will occur. Students equipped with knowledge, skills, and values will figure out what to do and how to do something better. Thus,  buried within the practice  is the tacit theory that students can correct mistakes and experience both success and failure in subsequent tasks by re-taking tests.

These teachers are both rich in experience and theory—-more tacit than explicit—-but theory no less. Dredging up the implicit theory buried in practical decisions teachers and administrators make is surely hard work but revealing to those practitioners who dig away at what they believe. Especially if they decide to write about their experiences and make explicit their theories of action.

For our weekly WeAreDevelopers Live Show I wanted to have a way to include a time progress bar into the page we show. The problem there was that these are markdown files using GitHub Pages and whilst I do use some scripting in them, I wanted to make sure that I could have this functionality in pure CSS so that it can be used on GitHub without having to create an html template. And this is it:

The bars support dark and light mode and should be pretty bullet proof. You can check out the demo page to see the effect in action with the liquid source code or play with the few lines of CSS in this codepen. Fork the repo to use it in your pages or just copy the `_includes` folder.

Using the CSS time progress bar

You can use as many bars as you want to in a single page. The syntax to include a bar in a markdown file is the following:

{​% include cssbar.html duration=”2s” id=”guesttopic” styleblock=”yes” %​}

• The `duration` variable defines how long the progress should take
• The `id` variable is necessary to and has to be unique to make the functionality work
• If the `styleblock` is set, the include will add a `style` with the necessary css rules so you don’t have to add them to the main site styles. You only need to do that in one of the includes.

Using the bar in HTML documents

You can of course also use the bar in pure HTML documents, as shown in the codepen. The syntax is:

start

	

Don’t forget to set a unique id both in the checkbox and the label and define the duration in the inline style.

Drawbacks

• This is a bit of a hack as it is not accessible to non-visual users and abuses checkboxes to keep it CSS only. It is keyboard accessible though.
• In a better world, I’d have used an HTML `progress` element and styled that one…

Humans have always invested great meaning in birds. No surprise, what with the feathers, the flight. Each week, when I look at all the stories that've been told about education and technology and try to figure out some coherence to the chaos, I think about what bird might best illustrate the thematics – the pigeon, most often and most obviously.

Today's bird is a pin-tailed whydah, a small songbird that can be found throughout southern Africa. The whydah is one of many bird types that are described as "brood parasites." Females of these species lay their eggs in the nest of other birds – in the case of the whydah, in the nests of filches, which sit on the eggs and feed the young. (Unlike that other species of brood parasite, the cuckoo, the whydah young do not kill their filch nest-mates.) This behavior – an "evolutionary strategy" – allows the whydah to offload the investment of raising their young to other creatures so they have time and energy for other activities.

Brood parasitism is not a perfect metaphor, by any means, for the offloading of ed-tech development onto teachers and students, but reading Vauhini Vara's brilliant investigation into how the tech industry is pushing "AI" in schools, published in Bloomberg this week, I couldn't help but think of the parasitism, the vampirism of Silicon Valley. Hence the whydah. Why the whydah. There's a quote in her piece from Tony Wan, a former editor from Edsurge and now a venture capitalist, that struck me:

Tony Wan, head of platform at MagicSchool investor Reach Capital, explained to me that AI education companies benefit from teachers and students flagging inappropriate content and otherwise helping guide product development. To that end, he said, “we often encourage our founders to just get this in the hands of teachers and users as quickly as possible—not necessarily as a refined product. And I don’t mean that in a bad or irresponsible way.” Wan later clarified that this “should not come at the expense of quality or pose risks.”

This offloading of responsibility, this casual but incessant leeching of money and power and data – it's all fundamental to "the business." An "evolutionary strategy," or something. Brood parasitism, except the offsprings here are products, not people.

But when it comes to venture capitalists, perhaps there isn't much of a difference? After I'd started pulling today's newsletter together – after I'd chosen that header image – I read "the big story" in the latest Wired, Emi Nietfeld's article on a venture capitalist's surrogacy – in this case literally, not figuratively: "The Baby Died. Whose Fault Is It." Only a few paragraphs into reading it, I thought, "yikes, why is the journalist telling this story" as her source – the venture capitalist in question – is so obviously unwell. But in the end, I think, the article underscores not just how fraught surrogacy can be – medically, legally, and wow my god, I had no idea – but how dangerous this specific VC might be. As Rusty Foster put it, a "case of a rich person being a titanic asshole at the expense of virtually everyone who comes into contact with her."

But there are elements to this story too that, I'd argue, extend beyond this particular case, as there is a growing interest among Silicon Valley elite not just in surrogacy, but in engineering babies – and I'm not taking with the "Mozart for Babies" soundtrack. (Also by Nietfeld in Wired in recent months: "Designer Babies Are Teenagers Now—and Some of Them Need Therapy Because of It." In The WSJ: "Inside Silicon Valley’s Growing Obsession With Having Smarter Babies." Ben Williamson on "Educational genomics and embryo selection startups.") And yes, I know some people bristle at the suggestion there's a strong link between "AI" and eugenics – "but but but I'm not racist," they splutter as they clutch their favorite chatbot to their chest – but this is all very much interconnected. Brood parasites, if you will.

If there's one thing you read this week, it really should be Vauhini Vara's article in Bloomberg: "AI and Chatbots Are Already Transforming Kids' Classrooms." If nothing else, it's a good reminder that ed-tech needs much much more investigative journalism. (Contrast Vara's article, for example, with this piece in Vox, a publication funded in part by effective altruist dollars, that wants you to believe that "AI in the classroom doesn't have to be a catastrophe.") Vara's article covers a lot of ground – various deals that various districts have made with various "AI" providers, various educators' efforts to use "AI" in their classes. But it's the inquiry into Alpha Schools that I found particularly interesting, because although there's already been a lot of reporting on Mackenzie Price and her promise of "2 hour learning," this piece finally cracks open the shady political, financial, and technological arrangements of this company.

While the school has received high-profile attention for its devotion to AI, including from the hedge-fund manager Bill Ackman, what’s gotten less notice is its ties to the administration’s businesses. State filings from as recently as December describe both Legacy of Education (that is, Alpha) and 2HR Learning as subsidiaries of a Texas software firm called Trilogy Inc. While Price is the public face of Alpha, the principal overseeing all of its campuses is Trilogy’s founder, an Austin billionaire named Joe Liemandt who said at a conference last year that he’s spent $1 billion on a mission to transform education using AI. (A Texas business filing by Trilogy in December also names Liemandt as its president and a director; his LinkedIn profile describes him as the chairman.) Price and Liemandt are longtime friends; Price’s husband, Andrew Price, is the chief financial officer of Trilogy and, according to the filings, also holds roles at Legacy of Education and 2HR Learning.

The financial arrangements among these entities is unclear, but the filings suggest that Alpha has been serving as a sort of in-house distribution channel for a corporation developing AI products for schools. Trilogy also submitted the initial trademark applications for 2HR Learning and several education products before assigning those rights to 2HR Learning itself. And positions at both Alpha and 2HR Learning were recently posted on Trilogy’s corporate LinkedIn page.

...

A publication called Colossus that profiled Liemandt in August said that he had lately been building ed tech products at a “stealth lab” staffed by about 300 people and was preparing to publicly launch a flagship product called Timeback. While the article didn’t name the lab, a Texas filing in early August recorded the formation of a company called TimeBack LLC, with Andrew Price named as a manager. A website for a product called TimeBack that fits Colossus’s description, meanwhile, calls it the system behind Alpha’s schools. And Legacy of Education has a trademark pending for the name. The article describes the product as recording a raw video stream of students, monitoring the “habits that make learning less effective, like rushing through problems, spinning in your chair, socializing,” then generating feedback for kids on how much time they’re wasting and how to do better.

Alpha’s privacy policy accounts for this sort of tracking and more, claiming far more access to student information than is typical for companies selling AI to schools, including MagicSchool. Alpha can, for example, use webcams to record students, including to observe their eye contact (partly to detect engagement and environmental distractions). And it can monitor keyboard and mouse activity (to see if students are idle) and take screenshots and video of what students are seeing on-screen (in part to catch cheating). In the future, the policy notes, the school could collect data from sleep trackers or headbands worn during meditation.

Read the whole article, all the way to the kicker, which is also superb.

Other thoughts about other things...

• "Back-to-school season means it's time to download a ton of hard-to-use apps. Were they designed by the devil himself?" asks Katie Notopoulos
• "The Mind Miners: How Silicon Valley’s AI Gold Rush is Built on African Trauma" by Uchechukwu Ajuzieogu
• Nitasha Tiku reports on the latest awfulness from character.ai: "Fake celebrity chatbots sent risqué messages to teens on top AI app"
• "They’re Stuffed Animals. They’re Also A.I. Chatbots" by Amanda Hess in The New York Times – just what you want for your kid's bedroom: a creeper
• 404 Media's Jason Koebler laments that "AI Generated 'Boring History' Videos Are Flooding YouTube and Drowning Out Real History"
• "How Are We Supposed to Talk to Our Kids About AI?" asks Kathryn Jezer-Morton in The Cut
• "Will AI avatars eventually teach our kids?" No. But TED will eventually let anyone give a talk, won't they. "Riparbelli says that humans learn better by watching videos and listening to audio, rather than by reading text." LOL. Sure dude
• "Anthropic raises $13B Series F at $183B post-money valuation." Investors include the Ontario Teachers' Pension Plan – a good reminder that venture capitalism destroys our future in a myriad of ways
• "AI Killed My Job: Translators" – I've been meaning to link to this Brian Merchant piece for a while now. Digital translation isn't good as much as it's sufficient. And culturally (this is important! and it applies far beyond translation) we've decided that mediocrity is fine as long as it's expedient
• Jon Severs asks, "Is Jonathan Haidt right about smartphones?" The article details the work of those researchers who counter Haidt's claims about social media and cellphones' detrimental effects on children. The kicker: "There’s a road here where [people say], ‘well, we don’t need science and evidence because we can see it with our own eyes’." Maybe. Maybe. I have no interest in defending Haidt – Haidt the bestselling author or Haidt the social psychologist or Haidt the conservative commentator. That said, I think it's a mistake to dismiss "common sense," to demonize parents' concerns as illegitimate, unreal, sheer fantasy. I'm reminded of Neil Postman who once observed that "social science is a vigorous ally of Technopoly," storytelling masquerading as science, in the service of totalitarian technocracy. Is one really being "anti-science" when one questions the findings of social science? Or is one simply deemed "anti-science" because one questions technology?

Thanks for reading Second Breakfast. Please consider becoming a paid subscriber. Your financial support enables me to do this work.

Happy Friday, Friends!

Today’s Journey includes two reflections: one for everyone, and a bonus one for paid subscribers.

The two reflections are:

• How Math Acceleration Enables Other Subjects

• Writing as Thinking (Book Edition) — for paid subscribers only

Let’s start with the first...

I. Math Acceleration Enables Other Subject Acceleration

We’ve talked about math acceleration before:

• It's hard to stop Math Acceleration once you start

• How fast should you accelerate your kid in math?

What surprised us, though, as our kids moved into high school-level subjects (and occasionally into early college material), was how often math becomes the bottleneck for understanding other subjects.

We, the parents, are long past our own high school years, and had forgotten how much algebra (and later, calculus) shows up everywhere.

Whether it was YouTube, Khan Academy, MIT's OCW, and others, as we introduced the kids to topics like chemistry, biology, or physics, they were immediately curious.

However, when we tried to answer their question,s we kept saying things like:

• That's actually easier to explain once you've seen algebra

• We'll come back to this after we cover a bit of calculus

• That's a good question; we need a bit more math to explain that

Basically, we’ve found that many subjects can’t fully open up until you’ve “gotten algebra out of the way” or even pre-calc or calculus.

Examples we've run into:

• Physics: Algebra-based physics is fine, but calculus opens up the why behind velocity and acceleration.

• Chemistry: Balancing equations, understanding reaction rates, and pH scaling all become easier with a feel for algebra

• Statistics: So many concepts in probability, expected value, and distributions require algebraic structure

• Biology: Pre-calc helps when modeling populations, feedback systems, or enzyme kinetics

We didn't need to accelerate everything, but math becomes a force multiplier, or maybe more accurately, a gatekeeper, especially in STEM subjects at the high school and college levels.

For example, one of our kids was watching a video on chemical reactions (read: explosions) and had some questions about how/why the chemical reactions occurred at different rates. To really answer it, we needed algebra and a taste of calculus.

Another time, one of our kids was looking at population growth models (high school biology) and wanted to know if you could predict the maximum and minimum of population sizes based on historical data. Algebra, Calculus, and statistics are needed to answer this question.

Question for your family/kid:

What subject(s) suddenly “unlocked” once math wasn’t a blocker? (Feel free to hit reply and let me know. We love hearing how this shows up in other families!)

To the free subscribers, thank you so much for being part of this journey. I hope today’s reflection was helpful. If you know someone who might enjoy this too, feel free to forward it!

For more Kids Who Love Math treats, check out our archives

Have a wonderful weekend!

All the best,

Sebastian

PS. Upgrade to read the second reflection, get a writing prompt activity to do with your kid, as well as a link to a fun video that ties in with the second reflection and is a great lesson in communication, logic, and patience.

II. Writing as Thinking (Book Edition)

The first thing we noticed when we started writing Number Theory for Kids was this: We thought we understood a concept until we had to write it down clearly for someone else.

Read more