Author Archives: vihart

How We Reopen

A month ago I became involved in a bipartisan effort to really understand what it would take to get through the COVID-19 crisis in the US.

My first contribution was helping write a white paper on digital contact tracing. It was inspiring and humbling to work with so many incredible folks jumping in to help and being willing to evolve their thinking as they shared their concerns with each other and as the situation evolved.

And so I’ve thrown everything into continuing to work with this group. Today we have released a Roadmap to Pandemic Resilience that puts together all our previous research into a comprehensive and actionable plan with bipartisan support:

It’s a good plan. The basic idea is to massively scale up testing, tracing, and supported isolation (TTSI). We propose a national Pandemic Testing Board to immediately get the supply chain working on this.

We can then reopen in 4 phases, starting by supporting those most vulnerable and prioritizing the essential workers who are already out there.
Our group already has some connections in politics, but as the situation is changing quickly I hope any of you who feel inspired to reach out to your local and elected leaders will do so. We think this has a real shot of happening, because everyone wants a way out of this that minimizes loss of life as well as economic losses, and we don’t have to choose one or the other.

Supporting materials like in-depth papers on different aspects:

Some recent press:

I am genuinely excited and hopeful. The folks working on this are amazing! I know most of what people hear about on the news is extreme disagreements about two bad plans and which is worse, shutdown until a vaccine or reopen and surrender to the virus, but I have faith that we all want a better alternative. That’s how we’ve already gotten bipartisan momentum. We CAN do this.

I know many of you are probably having a rough time of it right now, and I hope you’re taking care of yourselves. I’ve focused my life around working from home for long enough that stay-at-home orders have impacted me a lot less than many other people. I’m grateful to have a full time job with benefits, and extraordinarily lucky that my organization is supportive of employees spending time on outside efforts during this crisis, so I can contribute to things like this.

On a more personal note, as some of you know, John Conway died of COVID-19 earlier this month. I met him many times, and his comments that Pi should be 2Pi were the inspiration for my first annual Pi Day video 10 years ago. In the blog post for this year’s Pi Day video, which was a PSA on coronavirus, I worried I would be seen as overreacting. I was willing to be seen as overreacting.

I almost didn’t include this sentence, for fear of looking dramatic:

“I have a lot of older friends, relatives, and colleagues, and from what I understand it is likely that many of them will get this new virus in the coming months and years, and unlikely that all of them will live through it.”

I don’t like it. I don’t like it.

There’s a lot about this I don’t like.

There’s a lot about this situation I can’t control.

But there’s things I can control, and those things include how much energy I spend focusing on the things I don’t like and how much energy I spend promoting the things I do. I think it’s healthy and necessary to take time to recognize and have feelings about the sad and frustrating things we can’t control. I have every sympathy for those who don’t have time or energy to spare for anything except anger and blame. I’m in a position to have time and energy to be sad sometimes AND work towards solutions most of the time, so that is exactly what I am going to keep doing.

Please give the video and report a look if you can, I have hope and faith in amounts I haven’t had in years. This will not be easy, but we really can do this.

My best to you,


Full video script:

So you might see something I’ve been working on in the news this week, a “Roadmap to Pandemic Resilience”. And this is a for-real thing that represents a consensus of people with every political belief and expertise, like, republicans and democrats and libertarians, economists and health officials and ethics and civil liberties folks (and at least one mathematician), all agreeing.

So there’s a few ways we could respond to this pandemic. In the US we already closed down a lot of stuff for a while and it’s hard, but now it looks like the curve is starting to flatten and we know it’s going to keep falling in the near term and all of us want to get back to our lives. We don’t know exactly what this side of the curve will look like, you’ve probably seen versions that are… optimistically symmetric but unrealistic, it’ll probably look less like this and more like this which I modeled off of Spain, ok so say we reopen soon, and… whoops that’s not ideal, ok say less-affected areas can reopen, NY is still closed, then some of us at least get a month of freedom and economic activity before we have to re-shut down and do it all again and again. 

It would be a reopening rollercoaster, and it would at least spread out the cases, but this plan has a lot of unknowns. It wouldn’t be back to business as usual when things are open, because businesses won’t be able to rely on each other to stay open, or on their workers to not all fall sick at once. Anywhere could be the next hotspot. It makes it hard to plan, and hard to feel safe.

So here’s another way to respond, the plan all these folks agree on is to reopen the economy this summer in 4 phases, so that the curve keeps falling and we can stay open, while protecting your health and civil liberties.

There’s three things we need to do this:

Number 1 is testing. We simply need more tests, a lot more, like millions a day. And these tests will be fast, no one wants to wait days for their results.

Number 2 is tracing. Contact tracing is how we let you know if there’s a chance you’ve been exposed, so you can get a test and find out fast whether you should isolate to stop it from spreading further.

And number 3 is supported isolation. Anyone who tests positive, or is waiting for their results, needs support to isolate at home, with health care, supplies, and job protections.

Testing, tracing, supported isolation.

It’s possible, but it takes resources, so we made our plan as epic as we need it to be to get this done responsibly this summer.

Ok so first is Phase 1.

Here’s where we see the curve flatten and fall by giving our essential workers the support and care they need. 40% of the economy is already open, thanks to essential workers like nurses, grocery store workers, utilities maintenance workers, police and firefighters, restaurant and delivery workers. They didn’t ask to be put on the front lines of this crisis, but they have stepped up to the challenges.

So in phase 1 we grow our resources to support our essential workers and turn our current limited-economy into a pandemic-resilient foundation.

We’ll hear from our neighbors and friends who work in delivery and law enforcement that thanks to testing and tracing they don’t have to wonder anymore if they might be spreading this disease without even knowing it, and don’t have to worry about coworkers having it without knowing it. When someone tests positive they get sick leave, they have other worker protections, so no one is worried about getting fired for being sick if they take a test.

We’ll hear from our elders in care facilities that now there’s testing in place to be sure that there’s no chance for this disease to spread out of control. That goes for anyone in frequent contact with essential workers, including folks in jails and prisons.

Some folks will be going through online training to fill in for essential workers. Maybe a teacher you know trains to do in-home childcare to sub in for someone who has gotten ill. And maybe a neighbor who has experience caring for an elderly relative decides to take the course and is ready to fill in.

How and where testing gets done might also depend on the community. We know that the best way to prevent spread is to find out who was in contact with someone who tested positive, so that those people can be tested quickly and have results within 24 hours. Some communities already have networks of contact tracers that people trust to do this work in a way that protects their rights, while in some communities we might hear about people working together to build these networks, maybe some will use technology to help. The better we are at contact tracing, the faster we can move on to phase 2, but worst case we just have to make a lot more tests, ‘cause in phase 1 most of us are still isolating at home so we only need to produce enough tests to keep those essential workers safe.

Meanwhile we’ll hear about all the innovative ways communities and companies are expanding contact tracing and making it work to bring down the number of cases to where we can move to phase 2.

In Phase 2

Now we’ve got our stable foundation of 40%, now we expand essential workers to 70%. Communities will be empowered to put programs in place to train and hire more people in essential jobs, lightening the burden on the current essential workforce. We’ll be able to address supply chain problems, you can find toilet paper in stores and order pasta online again.

We might see one city get more busses on the street and hire more folks to drive those busses, so that expanded essential workers can get to their jobs safely without being in a crowded environment. Another city without busses to spare might invest in hiring a set of workers to build out more public transit infrastructure.

More people will get hired to serve in roles in unemployment and retraining so more people can access support. A doctor who has tested positive and has to isolate might teach courses on how to do a swab test. A contact tracer with 20 yrs experience might partner with their county to start an online training program for contact tracers.

Maybe the Bay Area leans heavily on app assisted contact tracing. Maybe LA partners with an organization like the National Council of La Raza UnidosUS to work with immigrants on community run contact tracing they trust. In a rural county like mine maybe we do most of our contact tracing the old fashioned way over the phone with one of our local figures that everyone already knows anyway, and we can take a test at the old elementary school if we need to. Maybe we apply for funding to expand our tiny hospital, and there’s a demand for construction workers to build it out.

During this phase, which will probably be most of June, we can allow a relaxation of certain social distancing measures for those essential workers on the front lines. We’ll still have to cancel large gatherings, but the group of expanded essential workers can safely visit and support each other. We’ll see restaurants that are currently doing takeout for the general population can be open to serve essential workers on-site. If there’s any question of exposure, there’s enough tests to find out and the health resources to respond as necessary. We’ll see our friends and relatives in essential sectors go from stressed and scared to secure and supported.

Before long, 70% of the population is part of a smoothly working pandemic resilient economy, and so we move on to phase 3.

Phase 3

Phase 3 is short and sweet. It gets our workforce back to 100%, though some of us will still be working from home. It lasts just a week or two, and by the end there will be no corona-induced unemployment.

Phase 3 is where non-essential businesses like hair and nail salons, work that can not be done remotely, will restart with safety precautions like public mask wearing. Maybe a friend reopens his hair salon giving priority to essential workers in his community like doctors and bus drivers. He knows they are able to get testing if there’s a chance they’ve been exposed, so that if any of his clients do test positive he will be informed by a contact tracer that he should get tested too in case. He makes sure to only have one client in his shop at a time and takes special precautions to clean down surfaces between clients. 

Office workers and mathematicians like me will still be working from home in phase 3, and asked not to go out for just this next week or two, but now I can get a home visit from a hair colorist or a massage therapist. I’ll leave the on-location visits for the workers who don’t have the at-home job security I have, just until we’ve ramped up our supplies to where we can move to phase 4.

Phase 3 also increases support for the unemployed, homeless, and under-housed. This phase is probably early July, so I’ll be looking to my county for guidance on whether it’s safe to have a small 4th of July gathering, maybe keeping our distance outside on the porch or following other recommendations.

And then, at the end of July, we enter:

 Phase 4.

The last 20% of workers, still working from home, can start going to the office again. You might start going in just a few days a week after taking a test, covered by insurance, and then working from home for the rest of the week while a different group of workers has in-office days. Some industries might phase things differently, and different offices will make different decisions based on guidance and resources.

We can plan for summer barbecues with our family and friends because we’ll have clear guidance about safety and access to tests. We can go to parks and go shopping wearing a mask without fear that coronavirus is lying in wait on every surface.

A restaurant owner in NY, where tables are usually spaced close together, might have to reduce capacity, but they are happy to have office workers able to dine out again. In my town maybe most restaurants have enough space that folks can keep a safe distance at about the usual capacity. Maybe our local club replaces the dance floor with safely spaced bar tables, and they hire local performers to give live shows so that they can charge a cover to make up for reduced capacity.

In phase 4, Students can go back to school. Well, it’s probably summer vacation for most, but some school districts might have summer classes where students can get out of the house and catch up on what they missed in spring. Summer sports teams might have to get creative. Football, hockey, and basketball coaches will be inventing and sharing drills that have reduced contact. Parents might take turns attending games so that they can fill every other bleacher seat to maintain distance. There’s enough tests that professional sports organizations can pay to have players tested every day to identify cases before they can spread, meaning we can expect to see televised sports again.

We’ll have enough tests for educational institutions to be able to get additional testing support, like maybe my cousins’ college dorms are pretty crowded so they can expect to test more frequently if they want to stay there.

In phase 4, life enters a comfortable new normal for the year before a vaccine, with communities receiving up to date information on what’s safe and the economy coming back into full swing. Things won’t be quite the same. We’ll be wearing masks in public, moving large events online, and keeping a bit more distance than usual. But some of our investments will benefit us in the long term, like expanding our public transportation and health infrastructure. Our economy will be pandemic resilient not just for this pandemic, but ready to hold strong against future attacks.

Throughout these four phases, we’re going to see communities being empowered to find creative ways to reopen in ways that are safe, legal, and supported with the healthcare infrastructure they need to do testing, trace those who have been exposed, care for the sick, and support those who must isolate at home.

So you might be wondering, how do we get these resources available for states and local governments to use? Basically we need a national Pandemic Testing Board with strong but narrow powers to get the supply chain moving, with $50-500 billion in funding over two years, depending on how effectively we do contact tracing, plus an expanded Health Reserves. It’s a war-time-level investment that we are more than capable of, and it costs a lot less than repeatedly shutting down the economy, in both lives and money. We’ve done our homework on this so check it out along with the body of supporting work if you’re interested.

And people across disciplines and ideologies agree on this plan. We can do this. You can do this. Connect with your communities, look for ways to be involved or create them where you are, this is for real and I’ve never felt so encouraged and hopeful. Everyone I’ve worked with on this project has jumped in to say what can I do, how can I help. People who disagree on everything else and who would ordinarily refuse to be in a room together are working together on this in ways I would never ever have expected possible, it’s kind of miraculous, and I wanted you to know. I wanted you to know it’s real, that if you see it on the news with some big institutional names attached claiming all this good stuff about partnership and cooperation, I’ve been in the room with these folks, (I mean, virtually in the room but y’know), and it’s true. People are working together, they are deciding together that we can do this. And we can.

If you’re the hashtagging profile picturing type, lemme tell you, hashtag, HowWeReopen. We’ve got icons too, see links below like Let people know, including your local leaders and elected officials, that they should take a look at this report sooner rather than later. I mean we’ve already got a lot of momentum but things are moving so fast with this pandemic, we could use all the momentum we can get, and I’m pretty sure time isn’t obeying the laws of physics right now so yeah, your help would be appreciated.

Ok, that’s all for today, I send my best to you and I’m looking forward to seeing the future you help create.

Outpacing the Virus: New Whitepaper Published

Three weeks ago, the US seemed to have trouble taking COVID-19 seriously. I wrote about how I focused my annual Pi Day video around sneakily getting information to people who were resistant to seeking it out. I was skeptical that the US would pull together the political will to take the measures necessary to slow the spread of this virus.

 In the week that followed everything changed, with lockdowns and stay-at-home policies going into place, and the two weeks between then and now feel like a year.

At first, I tried to resist digging in on what I thought might be solutions and focus on understanding a bigger picture of the situation and the impact on the future. I ended up focusing on trying to understand one area where I was seeing a lot of misinformation and miscommunication, particularly technological responses to the virus.

And so, in a massive collaboration involving a dozen experts in different fields, we wrote an extremely comprehensive and up-to-date whitepaper on contact tracing for COVID-19 and mitigating privacy concerns, and it is very good!

Here is the link to the paper:

Here is a Washington Post op-ed that references us: 

I’m extremely proud of this paper, and of my collaborators. It’s been a pleasure to work with such amazing folks jumping in with passion and enthusiasm together on this common goal. I learned so much in the past week.

I hope all of you are staying safe and finding ways to be you in this new world.


Pi Day Rant 2020

The annual Pi Day video is here!

I was going to do a simple video this year, just check in and say hi rather than produce a full-on vihart-brand video. But like many folks, I am extremely concerned about the novel coronavirus. I have a lot of older friends, relatives, and colleagues, and from what I understand it is likely that many of them will get this new virus in the coming months and years, and unlikely that all of them will live through it. I know this is true for many other folks as well, but it might not feel real until it’s too late. I’m not panicking about the end of the world, and I don’t think the economy is necessarily doomed, but I’m guessing by the end of this many of us will be impacted on a deep emotional level through the losses that matter.

I’m also very aware of how individuals doing the simple things can make a huge difference to how fast it spreads and the overall impact over time, and as I had a Pi Day video to produce I took the opportunity to do a bit of an undercover PSA.

I started with a list of communication goals, including the major symptoms, what to do if you have it, what to do in general, and to explain the reasoning behind why doing these things matters. The goal was to sneak these things into a fun video that might reach people who wouldn’t ordinarily click on a coronavirus PSA, the same way I sneak mathematics into videos for people who might not click on a math explainer. It was a bit rushed as I only had a few days to write and produce it, but I like how it came out.

Forgive me if this video comes across as a bit irreverent toward a problem that, in the worst case, might become a major tragedy that can’t be spoken of lightly. But for now I’d rather have a chance of reaching those who don’t take it seriously now, at the risk of it not aging well if things go really south. Here’s hoping we all do our part, take it seriously, and in the end are left looking like we overreacted and there was nothing to worry about in the first place!


Video script:

It’s March 14th which means it’s time to celebrate the worst number in the universe. Now, I know that usually on Pi day 3.1 million people flood the streets to celebrate or protest, but this year due to the new coronavirus we are having a purely online event so I will have to ask you to please restrain yourself somehow from gathering into a large pi-enthused or pi-furious crowd.

Now I know you’re thinking, well, if everyone’s gonna get this virus anyway why not get out there with your pro or anti-pi signs, get in a fight, express yourself with vigor and spittle? I mean, new coronavirus cases are growing exponentially, before too long there will be 3.14 million cases worldwide and if the exponential trend continues then after that there will be 3.14 trillion people who have it and there’s not even that many people on the planet which I guess means we gave it to aliens, or maybe time travel or zombies are involved? I don’t know exactly how it’s gonna happen but the math checks out. Probably aliens. And you know what? Pi is the real problem here, because Pi is buddies with e and e is so fundamentally intertwined with exponential growth that if the coronavirus has exponential growth then e definitely has also caught it by now and so Pi…

Is that a cough, Pi? Do you have a fever?

Ok so maybe there’s other curves in mathematics besides the pure exponential, like the sigmoid, which, I dunno, sigmoid kinda sounds like an alien to me, and sure the sigmoid tapers off eventually, maybe at like some percentage of the human population, maybe more, including aliens, or ghosts, but the beginning is still exponentially increasing so e is still involved and probably Pi and e weren’t very careful about not spreading it between them because they figured if e gets it Pi is getting it no matter what so why bother, I guess Pi didn’t realize you get less sick if you just get coughed on once than if you’re makin out with each other all day and if you think Pi and e aren’t that close in this equation well maybe Pi got it while commuting, long story short I’m not saying you can’t use Pi in your calculations, but don’t you think the right thing for Pi to do is take a sick day this Pi Day? I mean if you’re Pi’s boss and you’re saying Pi, I need you to come help me with this circumference, then you’re partly responsible when Pi shows up despite being sick and then ALL the other numbers you need start getting sick too.

Or maybe you can’t get a virus from a mathematical abstraction, but you still have to worry about the physical pi-day pies. May I suggest that for safety reasons you eat all 2-pi radians by yourself. Also don’t share your pi glass of water (which is like a half glass of water but half the long way), and definitely don’t share your 3.1fork.

Now you may be thinking, well, Tau is 2*Pi so if Pi gets the new virus then Tau will too, and realistically Tau is probably going to get sick, if not from Pi then from 2 or I dunno,  planck’s constant or something. But there’s a big difference to the world between the scenario where numbers get sick just a few at a time, and the scenario where a lot of numbers get sick at the same time. Especially for e, pi, and tau, which are pretty old numbers. If they get the new coronavirus they’ll probably have to go to Hilbert Hospital to help them get better, but Hilbert Hospital doesn’t have enough room to fit all the numbers. So if Pi goes to school or work even though it has a cough or a fever, and then it spreads the virus even just to a small area of neighboring numbers it could mean there’s no room left in the hospital and all those numbers die and no one can do calculations involving circles anymore and that’s it for technology, no more internet, no more games, wheels just stop working, it’s like dividing by zero.

But, say Pi washes their hands frequently with soap and water, stays home, and calls their healthcare provider. Maybe a friend volunteers to  drop off some supplies so Pi doesn’t have to go to the store. It might not save the world, but it does save lives. If Tau gets coronavirus even just a day or two later than it would’ve otherwise, by then maybe e is feeling better so there’s room in the hospital and both Pi and Tau live and we can have round things again, happy Pi Day!

Which by the way coronaviruses  are called coronavirus because the virus itself has a mathy roundyshape with sticky-outy-bits like a corona, a crown, and it’s made out of stuff that soap smooshes apart which is why soap is antiviral as long as you smoosh it around real good, take that coronavirus, get ‘em, yeah, smoosh those shapes, smoosh those shapes, smoosh those…

Artificial Intelligence, Universal Basic Income, and the Value of Data

I wrote a quite long and substantial piece on AI, basic income, and labor rights regarding data creation. If you worry about AI-related job loss and AI’s impact on the economy, or if you often think about social media systems or the influence of tech companies, you’ll probably find a lot of references and ideas in here:

CDG office with dome under construction

Introducing: The Art of Research

After a year and a half of being heartbroken over the loss of my old research group eleVR, I’m excited to announce that I’m doing research again! Check it out over at The Art of Research.

This is the latest in a series of unconventional research groups I’ve been a part of, following the Human Advancement Research Community at Y Combinator Research and the Communications Design Group at SAP, inspired by Xerox PARC. I just posted a history of our groups, their influences and the thinking that went into them, and how our current approach draws from our history:


Pi Day 2019: 6 Digits of Pi!!! 🍰

This is our 9th annual Pi Day video!


It’s March 14th, 2019. That’s 3 14 19, which as we all know are the first six digits of pi.

Now this is our 9th annual Pi Day video, I understand by now there’s some of y’all who know a few digits of pi, or maybe you’re the one who gets tasked with checking against a printed copy while that kid in math class tries to break the school record during the annual pi day competition, do all schools have that or is it just me?

Anyway you have the printed copy and they’re like 31415926535979… and you’ll be like wait, did they get that 8? but you don’t have time to think about it because they’re all like 323846264338… and you’re like well that all sounded right, unless they did miss that 8 earlier in which case all of that was wrong because once you skip a digit everything’s shifted, the 9 should be the 8 and the 7 should be the 9 and the 9 should be the 7 and there’s cascading failure, oh except when there’s two 3s in a row one of them is right just by chance, i mean the shifted version will be right whenever there’s two in a row or it’s right twice in a row when you come across three numbers in a row, and at the Feynman point which is 6 9s in a row then 5 of them will be right in a row, but point is once you skip a digit then what you’re reciting might sound like pi but it might as well be random digits.

Then again, the word mispelling is still the word misspelling even if we misspell it and miss the second s, it’s not like “oh no, you missed the s, now the p is wrong and the e and you got one L correct by chance but on the whole it’s a loss. We know what word it is, it still means what it means and we understand it even when it’s technically wrong, and maybe Pi is still Pi no matter what mistakes a Pi reciter might make.

So that’s why Pi Day 2019 has the first six digits of Pi and is thus even more pi-like than 3/14/15 a few years back which only has the first 5 digits. So there’s a typo, so what, let’s not nitpick. We can all empathize with skipping a digit of pi here or there, we’ve all done it, right? And if you don’t know many digits of pi may I suggest that you use digit skipping to your advantage and skip right to the Feynman point like this: 3141 999 999, and there you go, you know ten whole digits of pi, just not all in a row.

In fact, if you want to learn to recite a thousand digits of pi real quick, you can just skip everything that’s not 9s. Check the rules of your local pi day competition, as long as you’re reciting actual real digits of pi maybe it doesn’t matter what order they’re in or if you get them all.

Now you might think you could use this trick to recite infinite selected digits of pi, 9s forever, but no one has found a proof that that’s true. After a certain point you might run out of 9s, or maybe not, no one knows. Yet.

Anyway 31419, pi of the year, skips the 5, so if you do know a lot of digits of pi this year’s pi day challenge is to recite pi but skip all the 5s. It’s a little harder than it sounds, but it’ll help you get to the end faster because now Pi is 10% shorter. Or so we conjecture. And if you don’t know a lot of digits then your challenge is to recite pi but skipping to all the 9s and keep repeating 9 until the word loses all meaning and you have an epiphany that words are just sounds made out of our vibrating meat flaps and it is utterly impossible magic that they ever manage to mean anything. Good times.

Ok happy Pi Day, go eat half a pie, good luck with your life and stuff!

The Mathematics of Monkeybread

New video about Monkeybread! Secretly part of the Scutoid series, but mostly about Voronoi diagrams, and a little bit about the mathematical features of the Bundt pan. Hopefully you’ll never see baked goods in the same way again.

I wrote a little bit about the process here:


So say you’re ruining yet another batch of cookies because, who knows, too much butter? Not enough flour? Didn’t chill the dough long enough? Could be anything, there’s too many variables and this is why baking from scratch is hard and I’ll stick with mathematics thank you very much.

But I do know one delicious recipe that’s hard to get wrong. And by the way this video is in VR180 so use a headset or look around by moving your phone or dragging the video because today we’re making Monkeybread.

Monkeybread, aka puzzle bread or pull-apart bread, is a classic american food invented in the 1970s to take advantage of pre-prepared refrigerated biscuit dough for an easy-to-make snack suitable for groups of children and/or adults with no plates or utensils necessary.

I’ll be making the dough bits round to better simulate properties of Voronoi diagrams, but the basic idea is that each ball of dough is like a little cell coated in cinnamon sugar, and large amounts of brown sugar butter. Lots and lots of butter.

In the oven all these spheres of dough will expand and develop facets as they smoosh into each other, so they’re more polygonal and no longer spheres. What kind of shapes would you expect the cells to form? 

Let’s go back to my batch of cookie, and I’ll use icing to draw the lines where the cookieblobs hit each other. It looks a lot like a Voronoi diagram, which is a kind of diagram where you start with a bunch of points, or, cookiedough blobs, and then it’s as if each point spreads out until it gets all the area that’s close to it, or at least, closer to it than to any other point.

If you started with points organized into a very efficient cookie packing like this, then the Voronoi diagram would look like a bunch of hexagons, except on the edges where technically the cell includes the slice of space going infinitely off the cookie sheet, not that I have enough dough for infinitely large cookies, which just marks another place where mathematical theory is better than the realities of baking.

But for our more randomly placed cookie blob sheet, the Voronoi cells are irregular polygons, and these look pretty typical for 2D Voronoi cells.

But what about 3D Voronoi cells?

There’s many theoretically perfect way to pack spheres together where they’d expand into perfectly fitting cubes or rhombic dodecahedra or other fun shapes, but when you toss all the dough balls randomly into a bundt pan we’ll get more typical random Voronoi cells. I mean it’s not quite mathematically Voronoi-y because of how dough works and physics but it’s similar enough that our Monkeybread bits will have that distinctive Voronoi flavor.

The Bundt pan, by the way, not only makes genus 0 baked goods into genus 1 baked goods, but the hole in the middle adds surface area, which is not only great for having lots of glaze or crust but essential for Monkeybread in particular so that more cells are on the surface. You eat it by just grabbing a cell and pulling it apart from the bread, and the toroidal shape means you can pick at it from all sides, including inside.

Bundt pans also provide areas of both negative and positive curvature to observe, which helps better simulate a comparison to the formation of epithelial cells, hence the Scutoid connection (more about scutoids next time).

Altogether, Monkeybread is quite the mathematical snack.

Vi Hart

Some More Great Authors


I was wondering whether to work, not work, or trick-myself-into-working-through-pretending-it’s-not-real-work today, and remembered that last year on MLK day I had the same conundrum and decided to fake-work by writing a post about a few of my very favourite authors: Helen Oyeyemi, Octavia Butler, and Toni Morrison, who whether through statistical improbability or otherwise all happen to be black women.

One year later, they are still a few of my very favourite authors, though none of them have published anything in the past year to talk about. Oyeyemi at least, who is the living author of the bunch, has Gingerbread coming out this March and I am eagerly awaiting it!

But then I realized that through statistical improbability or otherwise, I have three more great black women authors to talk about this year.

4. Nnedi Okorafor

Here’s another author where I am baffled that no one introduced me to her work before last year, especially because in addition to being a great writer of weird scifi/fantasy she has math bits in her work! I love all these things, why did no one tell me???

Binti is her scifi series with mathy main character. Akata Witch and Akata Warrior are a fantasy duology that is lighter and more accessible, very fun and has some memorable world building. Lagoon is more strange and literary with odd perspectives and oh do I love anyone who can write an alien or nonhuman mind.

I first heard her name connected to Who Fears Death, a book that I’ve heard is great and has lots of critical acclaim and stuff, but I’ve heard is an emotionally tough read, so for both those reasons I’m saving that for later. In the mean time, I’ve read six of her other books and plan to keep nomming up her catalog and whatever she writes next.

5. N.K. Jemisin

Jemisin is known for her Broken Earth trilogy, a wildly popular gritty post-apocalyptic fantasy series, and I’ll admit I have some conflicting feeling about it.

I stopped reading part-way through The Fifth Season despite the excellent writing because, well, it is very cruel and graphic not just in cliche “Look at me I’m a gritty fantasy book!” way, but in creative inventive new ways, and I don’t need creative new cruelties in my head. But people kept recommending it to me so I pushed through, and I’m glad I did because it smoothed out with less of the cruelty and more of the superb writing and worldbuilding.

I will definitely be looking out for whatever Jemisin writes next, and can heartily recommend the Broken Earth trilogy to anyone who can stomach, say, watching game of thrones.

6. Tomi Adeyemi

Woooo! Debut author on scene!

It’s not hard to read through Adeyemi’s entire catalogue because she just published her debut book, Children of Blood and Bone, in 2018. It won a lot of well-deserved awards. Definitely YA fiction, doesn’t have the strangeness or literary quality that would make it a favourite for me, but Adeyemi is an author I’ll be watching, and Children of Blood and Bone is a book I’d recommend to all fans of YA fantasy.

This book follows the standard formula fairly closely, but not stiflingly closely, and is overall well done and light and fun to read. The kind of book capable of winning popularity contests among books (which it did), but it’s not as shallow as most popular YA fantasy, and it has that magical feeling that I love reading.

I’m looking forward to Adeyemi’s next book, and even more so to her next series or single!


Oh my goodness, there are so many great books to read in the universe! And so many great authors! But Helen Oyeyemi is still my fav! Uggghh I am so excited to read all the books!!!!!!


New video, and also a new page about scutoids that is still a work in progress. The video is in VR180 and super fun to watch in a headset, if you have a google cardboard or something!

Script and description:

So you may have heard of… bees. Yes, bees are pretty great at making hexagons, as seen in this honeycomb that I regret picking up because now I can’t touch anything with my stickyfingers but anyway bees make not just hexagons but 3d hexagon pockets with depth, full of bee candy, so maybe they’re like hexagonal prisms, although not exactly cuz the bottoms of the candypockets aren’t flat but kind of faceted, you can see the facets real well in this beeswax candle that just has the bottoms of the cells,

But that’s not the point, the point is that hexagonal cells fit together really good to make a flat sheet, and it’s not just bees that use hexagons see here’s a wasp nest and besides the hexagon thing wasp nests are totally different, they’re made out of paper not wax, they don’t store wasp candy, they don’t even store food in here they’re just wasp pockets for more wasps, anyway, you might start to wonder what other things are made out of hexagons, like what about our cells? What shape are the cells in your own hand?

Usually when people talk about cells they draw this flat diagram that’s all roundy, but of course in real life cells are 3d, wait are eggs a cell? Well let’s just use it as the nucleus of a bigger cell, and then there’s other kinds of cell bits in there so let’s stuff those in, and while some cells might be roundy and floating around in your blood stream or whatever some kinds of cells are snuggled up next to each other with no space inbetween so they get all squished into really shapey shapes, even if they began life wanting to be round.

It’s kind of like monkey bread. You can start with these round cells floating in butterstuff, lots and lots of butterstuff to properly simulate the mathematics of course, and once the cells puff up and all connect to each other then they get less roundy and more faceted like a cell with shapes. Hmm… now that I think of it there’s a lot of mathematics in monkey bread, more on that another time.

Or maybe cells are like a bubble foam. Individual bubbles are all roundy like a free floating cell, but once you stick a bunch together they get all this shape stuff going on.

Anyway if you’ve ever played with beeswax you might notice that a sheet of hexagons is pretty good at rolling up, or bending one way or another, but it doesn’t like to be roundy. And animals have lots of roundy bits, and anti-roundy bits, and most animals aren’t made by bees, and roundy shapes just don’t like to be all hexagons all the time, like a soccerball has 20 hexagons but 12 pentagons too. 

so long story short some scientists and mathematicians were wondering what different shapes a sheet of cells might be made out of and they did math to it and discovered that cells can sometimes be like a hexagonal prism, and they can sometimes be pentagonal prisms or other kinds of prisms, or pyramid-like prisms called frustums, but another kind of shape came up, one that didn’t have a name.

This shape has one polygon on one end, in this case a hexagon, and a different one on the other end, such as a pentagon, and to get from one to the other it has this little triangle. And you know how I feel about triangles.

And they named it the Scutoid. And yes, they scoot. scoot scoot scoot.

This shape is so new to the world of human language that I had to get in touch with one of the authors of the paper, Clara Grima, to ask whether scutoids had to be hexagons to pentagons, and it turns out scutoids come in many forms, but point is that scutoids are alive not just in your body but as a new subject of research being done by living mathematicians and computational biologists right now.

Scutoids are a brand new 2018 shape and winner of the 2018 Shape Awards, yaay scutoid, you won a new award we just made up right now, but anyway next time I’ll show you how to make your own scutoids, well, technically you’re making scutoids all over your body all the time but you know what I mean ok bye!


Scutoids are the Best Shape of 2018! This video is VR so if you have a cardboard or other headset you can see the shapes be even shapier in stereo, or looking around in magic window on a phone is pretty cool too. Or you can mouse around the video on a desktop.

Scutoids are officially named for the first time in this paper: “Scutoids are a geometrical solution to three-dimensional packing of epithelia”

Special thanks to Clara Grima for answering my scutoid questions, and to Laura Taalman and Tom Ruen who contributed to the creation of paper scutoid nets based off of 3D scutoid models by Laura Taalman, who invented the packable pair of identical scutoids (see ) , and John Peplinski, who created the space-filling cairo tile scutoid design (see ). More on that next time!

Also thank you Caleb Wright, Albert Wenger, Pat Devlin, David Perryman, Jade Bilkey, Chris Pierik, Donald “Chronos” King, Andew Romaner, Jodi Vezzetti, Carol Ghiorsi Hart, Andrea Di Biagio, Charley Sheets, Yana Chernobilsky, David A Smith, Michael Tiemann, and all of my patrons on Patreon!

You too can support my work here:

Fifty Fizzbuzzes

One of the many things I learned from Evelyn Eastmond in my time working with her is this technique for deeply exploring, releasing yourself from preconceptions, thinking in new ways.

This technique is called “Make 50 of Something”, and to do it, you make 50 of something. In one big marathon. Maybe over a few days, but it’s important to do them one after another, exhausting your possibilities to break and illuminate habits. This is in contrast with thing-a-day or thing-a-week marathons, where you’re making habits and have time to think between things.

50 is a LOT, and it takes you on this weird journey of ups and downs and complexifying and simplifying and combining and taking apart. It can be oddly emotional and intense. It gets at something and teaches us something that is hard to find if we space things out or wait for inspiration.

This technique was meant for artists, but my research group has used it for VR stuff and programming language design too. So now to learn python, over the weekend I made 50 implementations of fizzbuzz.

Fizzbuzz is a classic kids game where you take turns counting, but if the number is divisible by 3 you say “fizz”, and if it’s divisible for 5 you say “buzz”, and if it’s divisible by both you say “fizzbuzz”. Now it has become a common programming exercise and interview question.

Fifty is a lot of programs, even if many are just 1 to 5 lines. It was an intense exercise. The first 20 or so are fairly normal programming exercises. But 50 is a lot, and things start to get weird.

Some of my fizzbuzzes output the solution. Some of them are flagrantly wrong. Some write you poetry, some play you songs.

Some favourites you might check out:

#22, which uses a linear regression and proves AI is smarter than humans.

#32, which plays a quite musical auralization of the algorithm.

#40, a chatbot that will listen to you and write you a poem.

#48, a complete text adventure with sound effects and monsters to fight.

Twitter user @quasiben was kind enough to figure out how to host an interactive version with all the dependencies.

To play with it, go here and click Fifty Fizzbuzzes.ipynb (it might take a minute to load).

It’s also on my github here, where it’s read-only, unless you download the file and run it, for which you’ll need jupyter python stuff. I use Anaconda.


This project made possible by my supporters on Patreon. Thank you, good humans!