Vaccine challenge trials NOW!

Update (May 5): Here’s a Quillette article making the case for human challenge trials. I think there’s an actual non-negligible chance that this cause will win—but every wasted day means thousands more dead.

I’ve asked myself again and again over the last few months: why are human challenge trials for covid vaccines not an ethical no-brainer? What am I missing that all the serious medical experts see? And what are we waiting for: for 10 million more to die? 20 million? So it made me feel a little less crazy that the world’s most famous living ethicist agrees.

I loved the way James Miller put it on my Facebook:

This is the trolley problem where the fat man wants to jump knowing his chance of death is below 1% and our decision is whether to stop him.

Like, suppose someone willingly sacrificed themselves so that doctors could use their body parts to save 10 million people. We might say: we would’ve lacked the strength to do the same in their place. We might say: we hope they weren’t pressured or coerced into it. But after the deed is done, is there anything to call this person but a hero, or even a martyr? Whatever we feel about the fireman who sacrifices his life in the course of saving 10 kids from a burning building, shouldn’t we feel it about this person a million times over? And of course, I deliberately made this vastly more extreme than the actual situation faced by young, healthy volunteers in a covid challenge trial, who in all likelihood would recover and be fine.

Regarding the obvious question: so would I volunteer to take an unproved vaccine, followed by a deliberate covid injection? Sure! Unfortunately, I might no longer be a candidate: I’m now nearing middle age and pre-diabetic, I help watch two young kids, and I live with two immunocompromised parents. But on the principle of walking the walk: if it were a vaccine candidate that I considered promising (and there are now several), and if it were practical to isolate me away from home for the requisite time, and if I could actually be of use, then absolutely, jab me.

On a somewhat related note: Last night I watched the Ender’s Game movie with my 7-year-old daughter Lily (neither of us had seen it; I’d read the book but only as a kid). Not surprisingly, the movie was a huge hit with Lily; she’s already begging to see it again. As for me, my first thought was: what a hackneyed sci-fi premise, that the entire human race is under attack from some alien species, and that all human children grow up in the shadow of that knowledge. Nothing whatsoever like the real world of 2020! My second thought was: what a quaint concept, that faced with a threat to humanity, the earth-authorities would immediately respond “quick, we need to find and train and cultivate super-geniuses willing to break the rules, and put them in command!” Only in the movies, never in real life! Except in, y’know, WWII, where that mindset was pretty crucial to the Allied victory? But 75 years later, yes, it reads to us as science fiction.

To inject a tiny note of optimism, I’m hopeful that we will eventually see some fruits of genius commensurate with the threat, whether in the realm of treatments or vaccines or contact-tracing apps or PPE or something else that no one’s thought of yet. Right now, though, the sad fact is this: as far as I know, the only indisputable work of genius to have arisen in response to the covid crisis has been the Twitter account for steak-umms.

120 Responses to “Vaccine challenge trials NOW!”

  1. John Figueroa Says:

    Thanks for posting this; I’ve signed up. I’m young and healthy enough that I imagine I’d be accepted. I hope this successfully gets off the ground

  2. gbd_628 Says:

    Anyone know if having a previous mental health history would disqualify one from getting selected?

  3. Aleksei Besogonov Says:

    > What am I missing that all the serious medical experts see?

    A bad vaccine can be _worse_ than simply useless, by making people MORE susceptible to CoV or to other diseases. This is especially problematic, because millions of people will get this vaccine.

    As for trials themselves, Derek Lowe has a nice description of problems:

  4. Domotor Palvolgyi Says:

    We watched E.T. with my kids, a bit less violent.

  5. Paul Beame Says:

    There is a big safety concern here: There is a reason that there currently isn’t a vaccine for the original SARS. As quoted in regarding these challenge trials for SARS-Cov2,

    “researchers’ main safety concern is to avoid a phenomenon called disease enhancement, in which vaccinated people who do get infected develop a more severe form of the disease than people who have never been vaccinated. In studies of an experimental SARS vaccine reported in 2004, vaccinated ferrets developed damaging inflammation in their livers after being infected with the virus.”

    Now one would hope that they would know about these risks from animal models ahead of time, but it should give one a bit of pause on this.

  6. Anonymous Says:

    “First of all, one must suppose that the doctor, as a private person, cannot take any measure or try any intervention without the consent of the patient. The doctor has only that power over the patient which the latter gives him, be it explicitly, or implicitly and tacitly. The patient, for his part, cannot confer rights which he does not possess. The decisive point, in this problem, is the moral legitimacy of the right which the patient has at his own disposal. This is where is marked out the moral frontier for the doctor who acts with the consent of the patient.

    As far as the patient is concerned, he is not absolute master of himself, of his body, or of his soul. He cannot, therefore, freely dispose of himself as he pleases. Even the motive for which he acts is not by itself either sufficient or determining. The patient is bound by the immanent purposes fixed by nature. He possesses the right to use, limited by natural finality, the faculties and powers of his human nature. Because he is the beneficiary, and not the proprietor, he does not possess unlimited power to allow acts of destruction or of mutilation of anatomic or functional character…

    The patient has not the right to involve his physical and psychic integrity in medical experiments or researches, when these interventions entail, either immediately or subsequently, acts of destruction, or of mutilation and wounds, or grave dangers.” –Pope Pius XII

    (So, what would Pius XII have said about human challenge trials for COVID-19 vaccines? I’m not totally sure)

  7. The enemy gate is in lockdown Says:

    as far as I know, the only indisputable work of genius to have arisen in response to the covid crisis has been the Twitter account for steak-umms.

    Has anyone considered the possibility that heavily processed food is the real reason America can’t get things done anymore ?
    If Ender had to grow up eating this stuff the Dragon army would just be bouncing of walls in random directions.

  8. Jo Says:

    As already explained by Aleksei Besogonov and Paul Beame here, there is a not insignificant chance that the “cure” would be worse than the ailment.
    I would see another real danger: vaccine trial goes awry, people die -> anti-vaxxers all over the world get their rethorical ammunition for the next 30 years, vaccination rates decline further, people start dying again “en masse” from tetanus, measles and whatnot.

  9. Gerard Says:

    @ Anonymous #6

    “As far as the patient is concerned, he is not absolute master of himself, of his body, or of his soul. He cannot, therefore, freely dispose of himself as he pleases. Even the motive for which he acts is not by itself either sufficient or determining. The patient is bound by the immanent purposes fixed by nature…”

    I absolutely reject these statements to the extent that they are used as an excuse to impose the moral beliefs of a subset of humans on the individual in matters that affect only his own interests. Nature may be my master by fact but I will never accept it as my master by right.

    The source of these statements is further evidence of how much of the moral and legal basis of western society is still based on a logically absurd belief in a perfectly good and all powerful being which nonetheless created the profoundly flawed human species, whose only purpose seems to be to inflict suffering upon its members.

    That said I do not agree with Scott that the type of trials he proposes are an “ethical no-brainer”. I think there’s a big difference between an individual choosing to take actions which entail certain risks and a researcher accepting to be an agent in the accomplishment of such actions, let alone in actively soliciting volunteers for the process. It’s a little like the difference between the following three cases:
    – a person terminating their own life
    – a person asking a doctor to perform euthanasia on them
    – a doctor asking patients to volunteer for euthanasia to free up resources for others.

    In the first case the individual should have that right. In the second he should still have the right to ask and I would argue that the doctor should have the right to agree (though that is not legally the case in the US at present) but I certainly don’t think the doctor should be obligated to agree. The third case strikes me as being ethically quite dubious because it is likely to involve a certain amount of subtle but real pressure for the patient to accept.

  10. Scott Says:

    Jo #8:

      I would see another real danger: vaccine trial goes awry, people die -> anti-vaxxers all over the world get their rethorical ammunition for the next 30 years, vaccination rates decline further, people start dying again “en masse” from tetanus, measles and whatnot.

    That’s what this is really about, isn’t it? Because of the anti-vaxxers, vaccine researchers feel themselves on the defensive, not like the heroic conquerors of death that they are. So they won’t distribute vaccines, like the Oxford one, that already exist and look to be extremely effective against covid, without years of testing that would’ve been considered redundant in a saner world. So the world’s economies will remain shut down for several more years while millions needlessly die. In other words, yes, the anti-vaxxers are going to kill us, just by a slightly more complicated route than the one we’d previously thought. 🙁

  11. Nick Nolan Says:

    WHO paper about human challenge trials: EXPERT COMMITTEE ON BIOLOGICAL STANDARDIZATION Human Challenge Trials for Vaccine Development: regulatory considerations

    “in appropriate situations, it maybe considered ethical to ask healthy and informed adults to consent to volunteer and participate in a human challenge trial whether they will receive an investigational vaccine that may or may not protect them from the challenge organism, a placebo that will not protect them, or only the challenge organism itself. However, accepting such risks requires absolutely that the elements of voluntary consent are based on truly being informed.”

  12. Oli Says:

    John, I live in the UK and am young. How do I sign up?

  13. Scott Says:

    Nick Nolan #11: I’m glad that the WHO agrees with me (and with Peter Singer)! So then, why don’t they start challenge trials for the Oxford vaccine today? What’s the holdup?

  14. Douglas Knight Says:

    But what is the factual analysis?
    How much time would challenge trials save?
    The alternative, which is has started for some vaccines, is vaccinating medical workers because they are likely to get infected.

  15. Corbin Says:

    When I read this post, I was reminded of a famous short story, “The Ones Who Walk Away from Omelas,” concerning humanism and sacrifice.

  16. Nick Nolan Says:

    Scott #11 Oxford started Phase I trial for ChAdOx1 vaccine. In Phase I focus is on vaccine safety. Phase I lasts 6 months. It starts with 2 patients that are observed few days (only one gets ChAdOx1). Then six and then more.

    Human challenge becomes more relevant in Phase II when effectiveness and dosage of the drug is tested together with continuing safety assessments.

    You might be able to combine safety and effectiveness trials earlier, but you can’t hurry up the safety testing. Follow ups months or even year later is needed to rule out side effects. Imagine what would happen if you rush the vaccine testing, vaccinate 10 million people before finding out that 1% of them get crippling autoimmune disease where symptoms start to show up 12 months after vaccination.

  17. Shmi Says:


    The movie, by the virtue of being a movie, glosses over a few details, especially those that Orson Card is very explicit about in the books: it took decades and two extremely bloody wars won by a fluke (and by a deus ex machina) before a few souls in the military came to accept that they need an unorthodox solution. It also took decades to get the Earth unified, due to this external threat.

    Moreover, OSC (an early victim of the cancel culture, due to his conservative social views) has an extremely low opinion of the government and of the military in general, and the two people in the series who led to the emergence of Ender, Hyrum Graff and Mazer Rakham, fight the inept establishment every step of the way, and set up trolley problems for breakfast.

    Basically, OSC has held a more cynical and sobering view of the government structures than most people at least since the Reagan times.

    Oh, and he wrote one blog post touching on the pandemics (, with at least a couple of points worth quoting:

    7. People find reasons to blame the people they already hate for anything that goes wrong. The more unbigoted they pretend to be, the more amusing their bigotry actually is. Until they start calling for pogroms.

    8. Good people show their goodness by doing good things while being patient with others. People who aren’t doing good things or at least being patient with others are showing us something, too.

  18. Phil Says:

    Challenge trials aren’t an ethical no brainer because it’s not clear how beneficial they will be. With an active pandemic, it’s not exactly difficult to find vulnerable populations that will yield results equally well (imagine vaccinating 1000 NYC doctors or grocery store workers, for example). Additionally, a challenge trial requires developing and testing a challenge protocol. You can’t just vaccinate people and then have a covid positive person randomly spit on them. The challenge protocol has to be controlled and have known results. That means infecting people and not giving them the vaccine! Obvious risks aside, this also takes a lot of time. I think there’s a case for challenge trials happening alongside ordinary trials, but the issues involved are not trivial.

  19. James Gallagher Says:

    It’s a little puzzling to me how, during the (very comparable) 1957-58 Influenza Pandemic a vaccine was developed within months – was this just due to less stringent regulations? And if so, did we get very lucky that it seemed to work without side-effects?

    (The historical record of that pandemic in the UK has similarities with what is happening now, with school closures and loss of earnings.)

  20. JimV Says:

    As a wish-fulfillment fantasy for kids, maybe “Ender’s Game” is enjoyable. It (the book) left a metaphorical bad taste in my mouth after I read it when it first showed up in the paperback section of a news store many years ago. It made me consider Card a bad person. If I recall correctly it starts with a survival-of-the-fittest duel between Ender and an older brother (I hope they left that out of the movie), and Ender finally solves a video game by randomly bashing something.

    And it is totally unrealistic. Children of that age do not have fully formed brains! In an email debate about it I was told, of course young children are better at video games than adults. No, the data I then looked up in Wikipedia said that the then world-champions of various popular video games ranged from 28 to 32 in age. Of course if a child spends six hours a day playing video games in the basement while the mother and father are working, they will seem better because of that biased sample.

    There are so many great science-fiction novels which have never been used for movies, but instead Hollywood goes for unrealistic, mleodramatic, wish-fulfilment trash.

    But I loved “Searching for Bobby Fischer” and when I proudly screened the VHS tape for a young nephew, he was bored by it, so probably your Lilly would be too. But it is a better movie!

    Sorry for the rant, thanks for the post.

  21. Radford Neal Says:

    I haven’t seen the Enders Game movie. I did read the book, and the short story that came before the book, both many years ago. I liked the original short story better than the book. By my recollection, the short story had a somewhat different theme, which was more interesting than that of the book.

    As I recall (perhaps inaccurately after all these years), in the short story, one ultimately realizes that the reason for having the children fight the war was not that they were more capable than adults would be, but rather that by having the children fight, the adults could commit genocide without guilt.

    Train the kids to win at all costs. Tell them not to destroy the planet. They don’t obey. Not our fault! And the kids are just kids, so of course, not their fault either!

    I’m not sure that either the book or the short story is suitable for 7-year-olds. Maybe the movie has yet another theme…

  22. John Michael Figueroa Says:

    Oli #12:

    I juts filled out the form on 1DaySooner.

  23. Raoul Ohio Says:

    Actual information from Ars:

  24. Anonymous Says:

    I also remember being quite put off after learning of Card’s various notions, but they’re his notions to have and he’s using them to write science fiction books, not to run for office. Fwiw it did make for a rather original treatment of sexuality and relations in the sequels.

    Also I don’t know if this part made it to the movie but he deserves a lot of credit for the subplot of geopolitics made malleable by puppeteered online discussion forums.

  25. Scott Says:

    Everyone: I have multiple strong disagreements with Card’s politics, and I also thought that Ender’s Game was a great story (admittedly, I didn’t read the sequels, which might have colored things differently for me). And it’s not just that I see no contradiction here; rather, I thought the story is great precisely because of how effectively it transcends the time and place and beliefs of its author, channeling emotions (a child’s anger at injustice, his fears of failure, his dreams of saving humanity…) that could be given countless mutually-contradictory political flavorings. And I worry that when critics take the stance (as many all but did), “Card opposes gay marriage, ergo Ender’s Game must be a terrible book” … then when people see that the book is plainly not terrible, they’ll think the critics must have lied to them about everything and Card must be right about gay marriage after all! But that’s just nuts: in the deepest analysis just like in the most superficial, the one thing really has nothing to do with the other.

  26. Liron Says:

    We should also be doing challenge trials with prophylactic Hydroxychloroquine and variolation protocols, right?

    There’s a significant chance that having a COVID patient spit in your butt might lead on average to getting an only flu-level-dangerous case followed by immunity. A few bits of knowledge on this subject are worth trillions.

  27. Edan Maor Says:

    Card is one of my favorite authors, and I learned a lot about morality from his books (Ender’s Game being one obvious example).

    I also disagree with most of his political stances, to put it lightly.

    FWIW, I also really liked most of the sequels to Ender’s Game, especially the immediate sequel, Speaker for the Dead.

  28. JeanTate Says:

    I too found the book a lot darker than the movie, but of course one can enjoy either without enjoying the other. When do you think Lily might show an interest in reading the book? When might you read it?

    I’ve learned enough about trials to have formed the view that the ethics can be very complicated indeed (that’s “can”, not “must”). Certainly “no brainer’s” do not exist. And I doubt that comments here are a effective and efficient way to discuss covid-19 challenge ones.

  29. John D. Says:

    I agree Dr. Lowe and others that no actual medical trial can be rushed. There may be a medicine out there among the myriad possibliities, but the odds are extremely low that the one randomly assigned to *you* would be it.

    On the subject of expertise, it may be that the 1940s Manhattan-Project-style approach of gathering the relevant experts is just a continuation of the 1930s New Deal thinking: gather the experts to try to fix this overwhelming problem. It was considered radical at the time, but became standard after. And now I find it sad that there are many who don’t *want* this to be standard anymore, and in fact are actively against the idea of expertise in general. Expertise has become “political” and attacked for it.

    What do I mean? I mean the old “politically-correct” bugaboo that right kept railing about has now metastasized into their own political filter for everything. If you point out an *objective* fact that contradicts the leader, you are being “political.” A weblog demonstrates a fact. “Why are you being political?” comes the refrain, with “politically incorrect” the silent implication. But surely science, and medical science, is objective? So the CDC makes recommendations–and then the CDC is “political” and told it should not be. “Why should we even have this massive organization, when it tells us what we don’t believe? We don’t need them!”, they seem to say. It seems reality itself has become political.

    Expertise can predict that certain things will happen, and then they do in fact happen! But the people in charge will not listen. Perhaps all we can do is keep demonstrating our expertise over and over until others finally notice that Cassandra was right. I keep thinking of the protest sign: “In every disaster movie there’s a scientist being ignored in the beginning.”

    If not, there’s the more recent, cynical, and chilling sign: “Hello, my name is Science. You killed my funding. Prepare to die.”

  30. asdf Says:

    Sounds like a lopsided proposition: sign up for 1% chance of dying or somewhat higher chance of having permanent lung/liver/brain/whatever damage, in exchange for helping pharma companies make billions on monopoly rents from the vaccine.

    If the formula is to be made available royalty-free to anyone who wants to manufacture it, and the vaccine itself will be free to everyone (like smallpox vaccine was), then I guess sign me up. Otherwise, if 50% of the vaccine revenues will be split among the volunteers/victims, either equally or weighted by some prior estimate of vulnerability, then the vanishing sliver of libertarianism in me might be interested. But a direct handout to pharma crooks? I’m reminded of HPMOR:

    Professor Quirrell’s lips curled, “a hero out of stories, relentlessly self-effacing and too humble for vengeance. Tell me, child, have you ever seen a drama where the hero, before he consents to save his country, demands so much gold as a barrister might receive for a court case?”

    (Harry Potter responds mentioning Han Solo, but he takes Quirrell’s point. Quirrell:

    “Well, in magical drama it is not so. It is all humble heroes like Dumbledore. It is the fantasy of the powerful slave who will never truly rise above you, never demand your respect, never even ask you for pay. Do you understand now?”

    Anyway there don’t seem have been many primate trials of these vaccines yet. Usually they’d do those before humans. Given how incompetently the pandemic is being managed at the political level, there is an awful lot of low-hanging fruit to pick up before taking serious risks to accelerate vaccines by a few days or weeks.

  31. Scott Says:

    asdf #30: I’m also not interested in gaining days or weeks. I’m interested in gaining months or years—by taking the vaccines that already exist right now, and testing and mass-producing and distributing them as if the survival of civilization depended on it. Yes, I agree that this should be done in a non-profiteering way, but my even greater interest is in preventing tens of millions of people from needlessly dying.

  32. Steve E Says:

    It’s worth noting that over the past six weeks, the FDA’s stance has shifted from “We won’t approve anything” to “We’ll approve anything.” I do urgently want human trials for vaccine candidates to begin now, but it’s also difficult to imagine that harmful vaccine-candidates and treatments *won’t* be approved in the current regulatory climate, simply because almost everything is being approved.

    All of which is to say that while the risk of not rushing vaccines to market is much greater, there is also a larger-than-normal risk of rushing vaccines to market. I want vaccines in spite of the risk, not because the risk doesn’t exist.

  33. Yovel Says:

    On a lighter note, how do your studies with your children going?
    I’m looking forward to your post on this, since I can’t wait to try your methods on my unsuspecting siblings 🙂

  34. Bunsen Burner Says:

    Getting a vaccine is certainly important, but people are talking like it’s a silver bullet. The immunity is unlikely to be permanent, and probably far from full proof. In the meantime we’re bound to get strains of the virus turning up that are immune to the vaccine. Not only is COVID not going away but there is definitely more pandemics in our future. I’d like to hear how to make our word more resilient to these outbreaks.

  35. Scott Says:

    Domotor Palvolgyi #4:

      We watched E.T. with my kids, a bit less violent.

    Lily also enjoyed E.T.; maybe we’ll watch it together again. And she enjoyed Jurassic Park until the t-rex scene. (Admittedly, my dad humor didn’t help: “OK Lily, no more t-rex! It’s safe to open your eyes again!” T-rex: immediately roars into the camera. Lily: runs away.) Then again, given that she was able to watch Ender’s Game all the way through—she averted her eyes only for the scene where they operate on Ender—you’ve made me realize that it’s probably time to revisit Jurassic Park! While we’re on Spielberg, I could also try Raiders of the Lost Ark on her.

  36. Scott Says:

    Yovel #33:

      On a lighter note, how do your studies with your children going?
      I’m looking forward to your post on this, since I can’t wait to try your methods on my unsuspecting siblings

    I’ve now given Lily 44 days of consecutive daily math lessons. Topics have included:

    The Collatz conjecture
    The powers of 2 (and how exponential growth relates to coronavirus)
    Bits and bytes
    Conway’s Game of Life
    Handwavy discussion of the butterfly effect, determinism, predictability, reversible vs. irreversible laws, entropy, free will and the strong AI debate
    Letter substitution ciphers
    The one-time pad
    Hilbert’s Hotel
    Cantor’s diagonal proof
    Solving simple equations
    Commutative, associative, and distributive
    Pascal’s triangle and its applications (including an hour spent flipping coins)
    Prime vs. composite numbers; why there are infinitely many primes
    Famous open problems about primes (Goldbach, twin primes, Mersenne primes)
    Zeno’s paradox and simple infinite series
    Adding and multiplying fractions
    Rational vs. irrational numbers
    Proving the Pythagorean theorem
    √2 and its irrationality
    π: why the same constant arises for both circumference and area of circles
    Buffon’s needle
    e and some situations where it shows up—including the secretary problem
    The golden ratio
    The Fibonacci sequence
    The birthday paradox
    Hex (and why the first player has a forced win)
    Making math games in MS-DOS QBASIC
    Ruler-compass geometry
    Logic puzzles (the wolf, goat, and cabbage, the troll who always lies or always tells the truth, the surprise quiz paradox)
    Eulerian tours
    Planar and non-planar graphs; embeddability on a torus

    One thing that’s become obvious is that I have no special gift for teaching 7-year-olds. I’d say Lily’s understanding and interest in the material have been dramatically uneven. When it’s a game that she and I can play, or a secret code she can design, etc., her understanding and interest have generally been superb; she often wants to continue even after the lesson. On the other hand, when it’s a theorem to prove, or a pattern to explain, her understanding and interest have generally been poor (or maybe it’s my teaching that’s been poor). The challenge, from my standpoint, is that the whole point of the lessons is to get her to focus, not on this or that particular situation, but on what has to be true for general reasons!

    As often as not, I can’t predict whether a topic will be a smash hit or a bomb with her until I try it out. (For example, the secretary problem was a smash hit. Ruler-compass geometry, and trolls who always lie or always tell the truth, were both bombs. Who knew?)

    Anyway, I plan to keep going with this for as long as the quarantine lasts! Some likely future topics:

    The four-color map theorem (of course, not its proof 🙂 )
    Stable marriages
    Bipartite perfect matchings
    Sorting algorithms
    Minimum spanning tree
    The game of Nim (and variants)
    Evaluating game trees
    Adding and multiplying negative numbers
    The Cartesian plane
    Complex numbers
    Monty Hall problem
    Ackermann numbers
    Boolean logic gates
    Turing machines
    The halting problem
    Busy Beaver numbers
    NP-complete problems
    P vs. NP
    Speed, distance, and time
    Mass, density, and volume
    Motion of thrown objects; Galilian physics
    Basics of special relativity

    And then we can start on qubits and quantum information … wish me luck! 🙂

  37. Filip Says:

    Scott #36: Given how much children rebel against parents, why spend time on open problems :)) Use your time slot on the core concepts & learning to learn and she will be able to find and understand the open problems that are fun to her — maybe proving Gil Kalai’s conjectures on quantum computing? “Taking Children Seriously”, after all.

  38. Raoul Ohio Says:

    Just to lighten up the mood, check out this parody of a Quantum Computing Roadmap:

  39. Phil80 Says:

    Are we willing to accept a Thalidomide in order to salvage an economy? I wonder.

  40. Chan Bae Says:

    Scott #36: What did you talk about in the lesson on Buffon’s needle and how did it go?

  41. Nick Says:

    How about arithmetic in different bases? As a mediocre working programmer, that’s something I wish I had learned as a kid. And I don’t mean discussing the general concepts, I mean drilling and memorizing, just like traditional times-tables. Addition and multiplication both for octal, dozenal, and hexadecimal. Along the same lines, maybe bit manipulation operations too. These are the kinds of things that only get harder to learn with age. They are also a great way to buy some peace and quiet time for a teacher, as genuine practice gently drifts into mindless busywork.

  42. Nick Says:

    Also, could you add for each topic how she responded?

  43. AP Says:

    Useless factoid – the #2 regulator at the fda center in charge of vaccines is the sister of physicist edward witten. If string theory never pans out and this is just a trolly problem that her M.D. and math Ph.D. from Stanford provided the education to solve, history may have given this unknown bureaucrat a one time chance to surpass the legacy of her famous sibling.

  44. Scott Says:

    AP #43: I had no idea that Ed Witten’s sister was one of the people in charge of regulating vaccines at FDA! That … sounds like it’s a good sign?

    As I’ve mentioned here before, I had a lovely dinner with Witten when I lectured at IAS two summers ago. I learned that, while he’s far from a blog person, he’s at least well-aware of the existence of this blog, as people close to him sometimes send him posts. So Ed, if you happen to be reading this: you have my permission to forward this post to your sister! 🙂

    (Admittedly, I perceive two massive bottlenecks here along the path to saving the world: first, I’d need to convince Ed Witten that I, a quantum computing theorist, had any insight worth sharing about vaccines or medical ethics. And second, Ed Witten would need to convince his sister that he had such insight!)

  45. Scott Says:

    Chan Bae #40:

      What did you talk about in the lesson on Buffon’s needle and how did it go?

    We had recently introduced π. So, I wrote a program to simulate Buffon’s needle (with crude graphics), had Lily watch it for a short time, and asked her to estimate what fraction of needles were crossing a line. She guessed a half, or maybe a little more than a half. I then had the program do millions of trials, showed her that the answer matched 2/π to the first few digits, and told her it had been proved that it converges to exactly 2/π. (Even though there’s a totally elementary, calculus-free proof, it requires the concept of linearity of expectation and I didn’t think she would follow it.)

    Wow! This number that measures how far it is around a circle keeps showing up over and over, even when we least expect it! I think she was slightly impressed, although less than I hoped she would be. 🙂

  46. Scott Says:

    Nick #41:

      How about arithmetic in different bases? As a mediocre working programmer, that’s something I wish I had learned as a kid. And I don’t mean discussing the general concepts, I mean drilling and memorizing, just like traditional times-tables.

    That’s a wonderful idea! I did introduce base-2 arithmetic and showed her examples of it, but she only partially understood, and then I just moved on without drilling. I think the problems were:

    1. She hasn’t even memorized the base-10 times table yet!

    2. She hasn’t yet even learned the base-10 algorithms for adding and multiplying with carries, although in easy cases she can simulate them in her head. And I’ve been reluctant to cover this stuff, since I know school will drill it beyond the point of tedium anyway, once it reopens.

    3. Unlike at school, with me she feels extremely free to decline any task that she finds even slightly tedious.

    Still, I completely agree with you that arithmetic in other bases is well worth another try!

  47. fred Says:

    How do you test a drug that will be given to *everyone* for side effects on fertility, births, and child development?

    Time to (re)watch “Children of Men”?

  48. Scott Says:

    Nick #42:

      Also, could you add for each topic how she responded?

    Alright then:

    The Collatz conjecture — she enjoyed playing around with it, both by hand and with a program I wrote

    The powers of 2 — she understood the concept of exponential growth and why it was relevant to viruses, and learned the powers of 2 up to 128 (alas, not 1048576 like when I was a couple years younger than her 🙂 )

    Bits and bytes — she knows that a bit can be 0 or 1 and that computers use them to store information. She still hasn’t yet internalized, to my satisfaction, that there are 2n possible strings of n bits, or that you need log2(N) bits to store something with N possible states (well, we haven’t really done logarithms yet), but she can handle small cases when asked

    Conway’s Game of Life — she loved watching and experimenting with it

    Handwavy discussion of the butterfly effect, determinism, predictability, reversible vs. irreversible laws, entropy, free will and the strong AI debate — she could spitball about any of these things about as well as an average adult layperson, although of course she was missing a lot of the knowledge (Newtonian mechanics, how computer programs work…) that led to the modern forms of these discussions

    Factorials — she had a surprising amount of trouble understanding why they count permutations. Or rather: she seems to completely understand why there are 3!=6 ways to permute 3 things. But she then takes the fact that there are 4!=24 ways to permute 4 things as just something to accept on my authority rather than the obvious generalization.

    Letter substitution ciphers — she LOVED this, completely understood everything, and got obsessed with inventing her own ciphers to give to her mother and grandmother

    The one-time pad — she understood it quite well, better than I was expecting

    Hilbert’s Hotel — she completely understands how the hotel can fit 1 more person, and even how it can fit people labeled by the positive integers. She partially understands how it can fit people labeled by ordered pairs of integers.

    Cantor’s diagonal proof — she seemed to follow, and internalized the message that there are different kinds of infinity. But I doubt she could reproduce the proof now.

    Solving simple equations — she could do it under extreme duress, but it was like pulling teeth, rather than a fun mystery. Should I circle back to this? Or will school do it ad nauseum anyway?

    Commutative, associative, and distributive — she sort of understood what these things are, and that they’re true, but not why they’re true or why they’re important

    Pascal’s triangle and its applications (including an hour spent flipping coins) — she LOVED the coin-flipping experiment! And she can reproduce Pascal’s triangle on her own, and at least partly understood the reasons why it’s important

    Prime vs. composite numbers — she now understands and can tell them apart, although she sometimes gets the names confused

    Why there are infinitely many primes — again, she seemed to follow at the time, but I doubt she could reproduce the proof now

    Factoring — for some reason, she still has trouble with this. In particular, that when we ask “how many 2’s are in 24,” we mean multiplicatively rather than additively (so that the answer is 3, not 12). Will need to circle back to.

    Famous open problems about primes (Goldbach, twin primes, Mersenne primes) — she had no trouble understanding these. We even learned about a thing called the “Riemann hypothesis,” which says that a simple formula can very accurately estimate how many primes there are up to a given number

    Zeno’s paradox — she was totally untroubled by it, and I can’t say she was wrong to be!

    Infinite series — she gets why they can have finite values, but beyond that has only the haziest understanding

    Adding and multiplying fractions — she had a lot of trouble with this, although she understands simple cases (1/4+1/4=1/2, (1/2)*(1/2)=1/4). Again, I could circle back, but I’m a little reluctant to, since school will drill this anyway

    Rational vs. irrational numbers — She now knows that 1/2, 2/3, etc. are rational whereas π, e, √2 are irrational, but I don’t know how much of that is understanding and how much just regurgitating. Part of the issue is that she doesn’t yet really understand decimal expansions.

    Proving the Pythagorean theorem — She could rearrange the shapes to prove the theorem, but she still remembers even the statement of the theorem only with prompting, so I’m sure she couldn’t reproduce the proof.

    √2 and its irrationality — I don’t think she understood the standard proof, at all. I had a little more luck with the geometric proofs that φ and √2 are irrational.

    π — she’s now a big fan, and knows it’s slightly more than 3 and that it measures the distance around a circle.

    Why A=πr2 — She seemed to follow at the time, but I doubt she could reproduce it. Part of the problem is that she was never even drilled about the areas of simple polygons.

    Buffon’s needle — already covered in earlier comment

    e — she knows that it’s a little less than 3 and that it constantly shows up in math

    The secretary problem — she was a HUGE fan! I wrote a program to simulate “deciding which suitor to marry” (where you should reject the first n/e of them, then marry the first heartthrob after that), and she obsessively played it for hours, learning how to compile and run QBasic programs in order to do so

    The golden ratio — understood reasonably well, at least at the time

    The Fibonacci sequence — understood reasonably well

    The birthday paradox — understood reasonably well, especially after we did detailed simulations of it

    Hex — she LOVED it, wanted to keep playing it, and became almost competitive with me within a day

    Why the first player has a forced win in Hex — she sort of followed, but I doubt she could reproduce the argument, and she didn’t much care. She just wanted to play.

    Making math games in MS-DOS QBASIC — she loved brainstorming ideas for text games for me to code up; she’d then inflict the games on her mother and grandmother. She’s shown little or no interest in learning to code the games herself.

    Ruler-compass geometry — after a friend told me how transformative it was for him at age 7, I had high hopes. Alas, this one was kind of a dud. Maybe it would’ve been different had I been a master of it myself

    The wolf, goat, and cabbage puzzle — she understood and enjoyed

    The troll who always lies or always tells the truth — surprisingly to me, she completely failed to get this one

    The surprise quiz paradox — she understood the paradox, but immediately generated “solutions” that seemed like nonsense to me (in her defense, experts still debate this one!)

    Eulerian tours — she now knows how to find them when they exist, but has trouble with the concept of characterizing which graphs are Eulerian.

    Planar and non-planar graphs; embeddability on a torus — she understood well, at least at the level we covered these things

    Anyway, writing this comment has made it obvious that, as much as it pains and bores me, we’ll need much more review and drill of the stuff we’ve already covered!

  49. Gerard Says:

    Growing up in the 70’s arithmetic in other bases was something that I remember spending a lot of class time on. I don’t recall in what grades but I wouldn’t be surprised if it was first introduced when I wasn’t much older than 7. Unfortunately the practically useful bases: mainly binary and hexadecimal and their relationships were never really taught or emphasized so the whole thing seemed like a rather pointless exercise that did little to improve one’s practical arithmetic skills.

    My impression is that Scott is concentrating on topics aimed at stimulating and motivating an interest in mathematics rather than directly accelerating the acquisition of skills. That seems like a good goal. That aspect was sorely lacking from my early (and even later) mathematics education and I think it’s something
    the vast majority of primary school teachers would be completely incapable of doing.

  50. James Cross Says:

    First of all, I have done the first part of the challenge. I have taken the vaccine in a Phase 1 trial. I write about the details here.

    I’m certainly too old for the second part of the challenge.

    I thought initially challenge trials might be a good idea; however, I’m not so sure now.

    The problem is whether we are willing to subject enough people to the challenge trail to determine if the vaccine works as promised and doesn’t have downsides like the disease enhancement mentioned by Paul Beame in comment 5. How many would it take? I would guess that, if it is not a large number, then we can’t really be sure enough to roll the vaccine out on the massive scale. The last thing we want is an ineffective or actually damaging vaccine.

    The problems with coronavirus vaccines are large. See this interview.

  51. James Cross Says:

    One more thought.

    If the main people at risk are older, then challenge trials with young people might not provide enough information on effectiveness and safety to roll out the vaccine to older people.

    In other words, it wouldn’t advance the timeline signficantly.

  52. fred Says:

    On “Ender’s Game”, there’s actually a very popular VR multiplayer game heavily inspired by it!

  53. Raoul Ohio Says:

    What did you say about the golden ratio?

    I’m sure everyone has read and/or been told plenty about the golden ratio. For example, the most beautiful rectangle, the first google hit is “… means a beautiful person’s face is about 1 1/2 times longer than it is wide …”, etc.

    Raoul sez: “Sez who?”.

    I have an alternative (to magic, beauty, charm, …) reason why it turns up a lot:

    First, you probably have noticed that 1/2, 1/3, 2/3, 1/4 and so on turn up a lot in formulas. Why? Maybe because they are roots of equations of the form ax + b = 0 with low integer coefficients?

    What about irrational numbers you ask?

    How about roots to x^2 + ax + b = 0 with low coefficients, such as a = 0, b = -2, or maybe a = b = -1? Can’t get much lower than that.

  54. Nick Says:

    Gerard #49

    My understanding is that multi-base arithmetic was introduced as part of an effort to reform math education. In contrast, I am not advocating for any major reforms. I am only advocating for a minor tweak, which is to make children learn hex arithmetic just the same way they are made to learn decimal arithmetic. Keep all of the existing arithmetic education infrastructure in place, just extend it to include hex. Addition tables, multiplication tables, drilling, flashcards, whatever, all the same, just with hex. Conceptual discussion and exploration are great, but the end-goal is that the kids can do simple hex arithmetic “natively”.

    Otherwise they might grow up to be programmers who can’t do hex arithmetic natively, in which case they will be required to do it the slow way:

    (defun +-hex (a b)
    (hex-to-dec a)
    (hex-to-dec b))))

    There is a tradeoff between lookup tables and computation, and when it comes to doing math in your head, the lookup-table approach is much faster. Take it from me, a mediocre working programmer who can’t do hex arithmetic natively.

    > My impression is that Scott is concentrating on topics aimed at stimulating and motivating an interest in mathematics rather than directly accelerating the acquisition of skills. That seems like a good goal. That aspect was sorely lacking from my early (and even later) mathematics education and I think it’s something the vast majority of primary school teachers would be completely incapable of doing.

    I agree with all that, but don’t throw the baby out with the bathwater. It’s important in life to be able to perform certain tasks quickly and easily and accurately, and in some cases the best way to facilitate that is to make kids memorize them at a young age. It’s the same with running scales in music, or shooting free throws in basketball. Sure, there’s a lot more to music than scales, and there’s a lot more to basketball than free throws, but all that other stuff comes a lot easier after you have the basics down, and boy you sure don’t want to find yourself struggling with them! Which leads to

    Scott #46

    I think a challenge that you may have to consider at some point is: are you doing math summer camp, or are you doing regular school? I guess that depends on how long the lockdown is expected to go. At some point in regular school, arithmetic has to get drilled. Really all I’m suggesting is to mix hex arithmetic into that same part of school. The trouble with hex arithmetic is that it’s too exotic for traditional education (traditional teachers themselves don’t understand it), while at the same time it’s too tedious for the hippy-dippy creative exploration approach to math. But it’s a useful skill, and I don’t think there’s any reason in principle why young children couldn’t learn it.

    (Of course, none of this is any criticism of how you’re doing things with your daughter, which is great. My girlfriend teaches ages 3-6, and trust me, neither parents nor teachers have a clue what the fuck is going on right now.)

    Scott #48

    > But she then takes the fact that there are 4!=24 ways to permute 4 things as just something to accept on my authority rather than the obvious generalization.

    “Obvious” is a word that’s best avoided entirely when teaching children! As a matter of fact, “generalization” might be bad too. Kids for the most part don’t have problems with executing explicit computations (hence the positive response to Collatz and GoL), but it can be hard for them to see the forest for the trees. It’s like the old joke where the physicist asks the mathematician how they visualize a 9-dimensional space, and the mathematician says “Easy, I just visualize an n-dimensional space and let n be 9”. Kids are like the physicist.

    You mention difficulties with factoring and fractions. Those likely have the same obvious root cause: “She hasn’t even memorized the base-10 times table yet!” Now, on the one hand, one might argue that it’s inappropriate to teach someone factoring when they don’t yet have basic facility with multiplication. On the other hand, maybe you will have an easier time convincing her to drill multiplication if you say “Remember when we talked about factoring and fractions? If you memorize your times-tables, those things will get way, way easier.” But that will involve, as I mentioned earlier, transitioning from math summer camp mode to regular school mode.

  55. Uncle Brad Says:

    Have you tried programming with Scratch for Lilly? I remember my kids loving Scratch when they were 7.

  56. Scott Says:

    Raoul Ohio #53:

      What did you say about the golden ratio?

    That it’s 1+1/(1+1/(1+…)), and also √(1+√(1+…)).

    That it describes the dimensions of a rectangle that can be subdivided into a square and a smaller, rotated copy of the same rectangle.

    That the ancient Greeks thought it gave the most beautiful proportions, or something, but I found that claim dubious.

    That it gives the limiting ratio between two successive Fibonacci numbers.

    That it’s irrational (we gave the simple geometric proof, which can be found for example on Wikipedia).

  57. Gerard Says:

    Nick #54

    “Otherwise they might grow up to be programmers who can’t do hex arithmetic natively, in which case they will be required to do it the slow way:”

    I’ve never really felt hampered as a programmer by not being able to do hex arithmetic in my head. Hex numbers of interest are likely to be 32 or 64 bit (8 or 16 hex digits) which would be too large for most people to work with easily even in decimal. A Python or Julia REPL (or whatever your favorite calculator program is) is a fast and much less error prone way of doing this when it comes up. Certainly familiarity with the hex digits and the binary patterns they represent is useful knowledge to keep at hand but I’m much more skeptical of the utility of hex arithmetic skills.

  58. Gerard Says:

    Scott #48

    “and learned the powers of 2 up to 128 (alas, not 1048576 like when I was a couple years younger than her 🙂 )”

    2^128 is a 39 digit number (in decimal). Since memorizing dozens of 30+ digit numbers seems like a herculean mnemonic feat for anyone, let alone a 7 year old, I wonder if you could provide a bit more insight into how this was accomplished.

    “Bits and bytes — she knows that a bit can be 0 or 1 and that computers use them to store information. She still hasn’t yet internalized, to my satisfaction, that there are 2^n possible strings of n bits”

    In my opinion the simplest way to explain this is to imagine an n bit register or number (let n be some reasonably small number for concreteness). Think of all the possible configurations of the n-bits and observe that each one of them corresponds to some integer representable by n-bits, hence in the range [0,2^n).

  59. Scott Says:

    Gerard #58:

      2^128 is a 39 digit number (in decimal). Since memorizing dozens of 30+ digit numbers seems like a herculean mnemonic feat for anyone, let alone a 7 year old, I wonder if you could provide a bit more insight into how this was accomplished.

    You’re joking, right? She learned up to 27 = 128.

      In my opinion the simplest way to explain this is to imagine an n bit register or number (let n be some reasonably small number for concreteness). Think of all the possible configurations of the n-bits and observe that each one of them corresponds to some integer representable by n-bits, hence in the range [0,2^n).

    Right, that will be easier once she really understands binary representation of integers.

  60. Scott Says:

    Nick #54:

      I think a challenge that you may have to consider at some point is: are you doing math summer camp, or are you doing regular school?

    I completely agree—this has been the central challenge since the beginning. For now, it’s math summer camp, for three reasons:

    (1) We haven’t even come close to exhausting the low-hanging math camp material!

    (2) Being merely her dad, rather than an official teacher, it is unbelievably hard to get her to do exercises and take them seriously.

    (3) The drilling/exercise part is also boring for me. Even when I teach undergrads, my teaching evaluations always say that I’m great on inspiration, storytelling, humor, making connections, etc. etc. but bad at actually walking through how to solve homework problems. And I’m learning that this is an even bigger problem when teaching a first-grader!

    Anyway, I agree that I need to beef up that aspect of Lily’s instruction—maybe by adding a “practicum” or “recitation session” to her daily schedule.

  61. Raoul Ohio Says:

    Fleshing out an idea from my college days, here is a demonstration that the golden ratio phi is in a 20 way tie for the 13-th simplest (real and complex) algebraic number.

    Define the Raoul Rank of an algebraic number by rank(x) = deg(x) + cont(x) where deg(x) is the minimal algebraic degree of x, and cont(x) is the absolute sum of the integer coefficients used in the minimal polynomial for x. Set deg(n) = 0 for integers if that is not the usual.

    The following is a list of numbers ordered by rank, with integers listed, otherwise the equation is listed with xx meaning x squared and +pm meaning plus or minus. The number in parenthesis is the total for that rank. Note that phi and rad 2 show up in the 5-th rank:

    0: 0; (1)
    1: 1, -1; (2)
    2: 2, -2; (2)
    3: 3, -3; (2)
    4: 4, -4, 2x +pm 1 = 0; 1xx + 0x +1 = 0 (6)
    5: 5, -5, 3x pm1 = 0, 1xx + 0x +pm 2 = 0, 2xx + 0x +pm 1 = 0, 1xx +pm 1x +pm 1 = 0 (20)
    6: (exercise for students: fill in the next 10 ranks)

    This supports my view that the reason phi shows up in a lot of formulas is because it has low rank, the same as rad 2, and only one higher than 1/2, another number that shows up a lot.

  62. asdf Says:

    Scott, the profiteering is unavoidable, so at minimum I want the pharma company CEO’s to get injected with the vaccine and the virus, if they think their vaccine is so great. Meanwhile here’s a rant that someone screenshotted on reddit, that seems to appear (I didn’t check directly) on Zack Cherry’s Facebook page, which might or might not be its origin:

    “The first places for open for regular business should be government buildings and offices. Starting in DC.

    If the White House isn’t doing public tours then the rest of the country is not ready to open.

    If your state’s capital building is not open to the public then the rest of your state is not ready to open.

    If your governor is not out shaking hands and kissing babies then it’s too soon for the rest of us.

    If your city’s court house and mayor’s office aren’t open for regular business then your city is not ready.

    If the governing body and lawmakers aren’t ready to take those risks then what does that tell you?”

  63. YD Says:

    Scott, are you planning on teaching any classes in the fall? If yes, can MIT students take it?

  64. Scott Says:

    YD #63: I’m planning to teach my undergrad Intro to Quantum Information Science course in the fall. But whether it’s in-person or online will depend on the state of the world at that time. In the former case, I know that the CS department was planning to videotape the lectures, for use in its online masters program. In the latter case, I don’t know what the policies will be, although I think UT has been pretty rigid about restricting its Zoom classes to UT students. In any case, I have a newly-revised set of lecture notes for the course that I’ll put on this blog very soon.

  65. asdf Says:

    I wonder if any of Vi Hart’s math-related youtube videos are suitable for 7 year olds (some are definitely too advanced). I haven’t watched many of them, but maybe “mathed potatoes” ( ) ?

  66. Richard Gaylord Says:


    just wanted to note that Singer is not the world’s most famous ethicist. several others, including both Jesus Christ and Ayn Rand (and even Immanuel Kant) are more famous – not necessarily more correct but, more influential

  67. gentzen Says:

    Raoul Ohio #38: I don’t think it is a parody. Not sure why you suggest so by saying:

    Just to lighten up the mood, check out this parody of a Quantum Computing Roadmap:

    For a long time, fusion has been the power source of the future. Maybe it still is, at least it is not dead yet. And quantum computing currently makes good progress, and the quantum information hype produces significant results (like a refutation of Connes’ embedding conjecture) independent of whether quantum computers are already useful (as suggested by D-Wave) or not.

  68. Scott Says:

    Richard Gaylord #66: Changed to “living ethicist.” (Should it be “living academic ethicist,” to exclude e.g. the Pope and the Dalai Lama?) Thanks.

  69. Scott Says:

    Uncle Brad #55: I know Lily did a little bit with Scratch at her school (they had an after-school coding club). I should look into it myself and see whether it’s worth incorporating into our lessons!

    For now, though, I still find QBasic by far the fastest way to translate a thought into something that actually happens on the screen—as I have since the age of 11. If and when I ever invest the time to learn a new language, I’m guessing it will be Python.

  70. Itai Bar-Natan Says:

    Raoul: A more mathematically natural way to define the simplicity of a polynomial is by its discriminant. Here too the golden ratio is a winner: Its discriminant of 5 is the smallest of any real irrational algebraic integer. However, if we extend to complex number there are simpler numbers, i (discriminant -4) and the cubic root of unity (discriminant -3), and I believe these are both more ubiquitous in formulas.

  71. John Figueroa Says:

    For what it’s worth, Bill Gates opposes human challenge trials for this, his reasoning being that it’s against the rules and for good reason (and it’s up to the regulators anyway):

    Ezra Klein
    Are there regulatory approaches we could do that would make this move much faster? People talk, for instance, about “human challenge trials” — does any of that seem possible to you?

    Bill Gates
    It’s up to regulators to decide. Mostly when you have a serious disease like this, it’s unethical to use human challenge trials. So I don’t think that will be used here. On paper, yes, that gives you a quicker way to see if your vaccine is effective so you could shorten the schedule. But who are those volunteers? Are they fully informed? For malaria that’s allowed because we have drugs that are entirely curative. But for TB, HIV, it’s not allowed. And unless there was some breakthrough innovation, it shouldn’t be allowed.

    It seems to me that this is an indictment of your King Gates plan, Scott—even even Gates, who was further ahead of the curve and demonstrated more competency on this than just about anyone, is making this mistake…

  72. Deepa Says:

    Each kid is different. Mine was so sensitive at 7 that he would only watch documentaries such as the ones in Bob Bullock state history museum (a beautiful Austin museum, by the way) or the Computer history museum in the bay area. We have had to walk out of “Cars” because one car was too rude to another. The Harry Potter book, first book first chapter, where the cousins are cruel to Harry, was too much for him at that time. He eventually outgrew this degree of sensitivity.

  73. Scott Says:

    John Figueroa #71: Over the years, it seems to me, Gates has been unbelievably cautious not to say anything that might provoke an outraged public reaction that would jeapordize his effectiveness. So while of course I don’t know, I wouldn’t put it past him to have a private view of these matters that differs at least somewhat from his public one.

  74. James Gallagher Says:

    dude, stop torturing your 7-year old daughter with math crap.

    Binge watch a dozen old classic disney cartoon movies with her, and discuss the political incorrectness if you want, but trust me, she wont ever want to watch those movies in 3 or 4 years time – lost childhood etc

  75. Scott Says:

    James Gallagher #74: Please believe me that in her short life, Lily has already watched most major Disney movies at least a dozen times, and a few (like Little Mermaid) at least a hundred times. And now that “school” is nothing more an occassional Zoom call, Lily spends almost half of every day vegging on the couch, watching princess cartoons or playing princess games on her iPad.

    All she does anymore that offers any mental challenge is:

    (1) A ~45-minute daily math lesson with me.
    (2) An even shorter daily reading lesson with my mom.
    (3) Playing strategy board games with my wife (if that counts).
    (4) Me reading her a chapter from The Adventures of Tom Sawyer each night.

    As I said, while some of my lessons bore her, she loves others, and it’s not so easy to predict which will be which. And she’s unbelievably good at refusing anything she doesn’t want to do, and she’s never once refused her math lesson (only goofed off during it, if it’s not one of the ones she likes).

    So … is this “torturing” my daughter? If it is, then isn’t normal school like some ultra mega North Korean torture? 🙂

  76. James Gallagher Says:

    Scott #75

    Little Mermaid isn’t one of “the classics”

    Sorry that your children will miss out on the fantastic creations of earlier generations

  77. Scott Says:

    James #76: Are you trolling? I mean, she’s also watched Snow White at least 70 times. And Dumbo, Cinderella, Sleeping Beauty, Alice in Wonderland, and Winnie the Pooh. To her generation, though, Little Mermaid, Beauty and the Beast, Aladdin, and Lion King are absolutely “classics” … even Frozen is slightly dated (!), having come out the year she was born.

  78. Deepa Says:

    Alice is wonderland is a cute movie. Very Disney. Sweet, but maybe Lewis Carroll would not have recognized his book in it!!

    I grew up on the poems in the book, and so I objected to the movie changing so much of it. Can anyone possibly improve upon “You are old, Father William” or “Jabberwocky”? No way.

    Maybe people who watch the movie first and then the book, don’t love the book, for legitimate reasons. In my case, we didn’t own a video cassette player until I was an old teen, by which time I’d read most children’s books. Disney could not get to me early enough :).

    Kids these days have so many choices in entertainment that they’re only mildly amused by things like the poetry in Alice, that opened up a whole new world to me (such as nonsensical poems). Edward Lear’s “A book of nonsense” is a nice buy after Alice! And so is Shel Silvertein’s “Where the sidewalk ends” (quite popular in America).

    And to meander back to the reason I came here now, here is a nice essay addressing your post :

  79. Deepa Says:

    Lily might love Asimov’s “How did we find out about computers?” It goes only up to 1985, but is riveting. It connects to things she has been learning and should be a prelude to a visit to the wonderful computer history museum in the bay area.

    And after reading the lesson list, I am thinking that if you read her Alice in Wonderland and the sequel, then you could read “Annotated Alice”, where Martin Gardener unravels and discusses the puzzles embedded in the Alice books (remember Lewis Carroll was a mathematician!.

  80. Shmi Says:

    > “how many 2’s are in 24,”

    I presume you explained it as “how many times can you halve 24 into equal parts” or something. There are indeed 12 2’s in 24!

  81. arch1 Says:

    Scott #36: Lily seems to have in common with many people (esp. very young ones) that she likes concrete stuff more than abstractions. FWIW Randall Munro (of xkcd fame) is another such person – at any rate, he said something like he has a hard time staying interested in pure theory or inclined plane problems, but “What If” questions (especially those of young kids) are a great way to trick himself into learning new stuff.

    That said, I think you have an opening on the abstraction front: You said that Lily understands P(3) = 3! but takes P(4) = 4! on authority. You can demonstrate (with objects) why the one implies the other, then convince her this argument extends without end, then help her do her own such proof in a very different domain, etc., and she *may* just end up convinced that she’s learned something better than magical – something real, and really powerful.

    Aside, in case you didn’t read “The Man Who Loved Only Numbers”: Paul Erdos (who loved spending time w/ epsilons, btw) was convinced of the wrong answer to Monty Hall, and couldn’t be argued out of it. It was only watching a computer simulation that got him unwedged. So if you can convince Lily of the correct answer without resorting to a simulation, you can tell her she did better than Erdos on that particular problem.

  82. nadbor Says:

    I have a 7 y.o. daughter that I’m trying to teach maths and your curriculum for your Lily made me feel embarrassed by how boring mine is in comparison. I think I’ll start incorporating more of the cool stuff that attracted me to mathematics decades ago and ease up on school-related topics from now on.

    Suggestion: Khan Academy has a place where you can write javascript and immediately see results on a canvas next to the editor. I found it to be a fantastic tool for introducing programming to people aged 7 to 57 (I used to run programming workshops out of my Uni for the general public). The student starts by writing code to draw simple shapes (routines like rectangle, ellipse are pre-loaded) then pictures of robots, trees, animals (kids love it). Then you introduce variables to parametrise the shapes, then functions to draw more of them, then loops, then animations, interactivity. It was a smash hit every time I tried it.

    Suggestion 2: Japanese animation from studio Ghibli. My daughter has of course watched all the Disney movies multiple times but she absolutely fell in love with My Neighbour Totoro and other Studio Ghibli ones. I won’t get into comparative analysis here let’s just say that both our little ones and their parents now prefer Ghibli to Disney. You should give them a try if you haven’t yet (they’re on Netflix now!).

  83. asdf Says:

    It looks like the virus is mutating rather quickly, reinfection is possible, a vaccine for today’s strain might not work on tomorrow’s, etc. :-(((((

  84. James Cross Says:

    Scott #73

    You can do all the trials you want on young and healthy volunteers but that isn’t going to tell you how a vaccine will work with the most vulnerable to the complications. How will challenge trials help if the first and primary people we want to vaccinate will be the elderly and the medically compromised?

    We also will would need to make sure the pool of volunteers has a representative sample of sex and ethnic groups in addition to age range in order to make a vaccine available for all.

  85. Gerard Says:

    I find it rather astonishing that according to polls Trump currently has a 44% approval rating. This in a year that is on track to combine the economic catastrophe of the Great Depression with the American death toll of World War II.

    You’d think that, if nothing else, that would be enough to convince a lot of these people that their chosen leader had lost the “mandate of Heaven”.

  86. Nick Says:

    My GF’s SIL’s father, a black man in his 60s in Brooklyn, died the other day from coronavirus. He spent several weeks in the hospital, during which time no family could see him. Prior to getting hospitalized, he was unable to get tested for over a week despite showing clear symptoms. Funeral homes there are booked solid.

  87. Scott Says:

    Nick #86: I’m so sorry to hear that.

  88. Scott Says:

    Gerard #85: I expect that, if Trump declared himself dictator today (using covid, or some imagined covid-related conspiracy against him, as a pretext) and cancelled the 2020 election, he’d retain at least a ~40% approval rating, and would have at least some support from Congress and the Supreme Court. Like seriously, I’d be willing to bet money on that statement (if money still mattered in a world where I could collect). That’s my basis for saying that we no longer live in a democratic society.

  89. Gerard Says:

    Scott #88

    Yes, it’s difficult to have a real democracy if almost half the people are fascists at heart.

  90. fred Says:

    If Trump is responsible for those things, then so are Macron, Johnson, Mattarella, Sanchez,… And I guess the people who support them are also all fascists?

    For reference, this is the actual current death toll *per capita*:

  91. Scott Says:

    fred #90: The US had the built-in advantages of lower density and extra weeks to prepare. And a time traveler from (say) the 50s or 60s would’ve expected us to be the world leader in these matters. Yet the best we can say is that we’re not literally the planet’s worst in covid cases or deaths per capita.

  92. Gerard Says:

    fred #90

    I never said Trump was responsible for the coronavirus situation, though he has taken actions and made statements that have certainly not helped things.

    I wouldn’t necessarily even call Trump himself a fascist, that would give him too much credit. He’s more of a reality TV caricature of a fascist, a cruel bully who appeals to the basest instincts of his followers, the desire for an authority figure to punish those they dislike and impose what they perceive to be their own will through force or coercion.

    I mean it’s true that this aspect of human nature is manifested to some degree through all governments, but Trump is practically the personification of it.

  93. Deepa Says:

    Nick : My sincere condolences. I did not realize things were this bad in NYC.

    My heart goes out to all the people in the family. The isolation that COVid19 patients have to grapple with in hospital, and the fact that many of them are older people (not super comfortable with technology) means they’re not receiving the emotional support their family could otherwise give them when they’re in hospital.

    Perhaps hospitals should tackle this by teaching them to use a simple app to stay connected to family and making sure their phones are charged, etc. Things that they might not have time for.

    Again, my heartfelt condolences.

  94. fred Says:

    Scott #91

    “would’ve expected us to be the world leader in these matters”

    The point is that with over a hundred countries dealing with this, we have a wild variation of flavors of leaders and approaches, and pretty much all of those countries are struggling with how to balance covid and the economy, because it’s all so damn new.

    So claiming that Trump’s approval rating should be at zero (and whoever doesn’t agree is a fascist) because the US isn’t at the very top of everything sounds either totally unfair (aka blame Trump no matter what he does) or like some simplistic case of old-fashioned American exceptionalism, which ironically is one of Trump’s beliefs. Basically Trump should be blamed because he’s not Trumpian enough… (America First, America’s the Best, Make America Great Again, etc) 😛

    One could claim just as well that it’s much harder to deal with this in the US because the US is so vast, and made of very different States, each with its peculiar economy and peculiar population.
    So one should really compare the US to the EU, which has shown close to zero effective coordination across its countries. Of course, it’s all very hard, so it’s not unexpected.

  95. fred Says:

    One last thing – in my book, local leaders are as responsible (if not more responsible) than POTUS.

    E.g. watch one of De Blasio (the NYC mayor) press conferences. The guy is as effective as a wet noodle. Good thing Cuomo is there to balance things out a bit.

  96. fred Says:

    Anyone losing sleep over Trump’s approval ratings being at 44% should find solace in the fact that G.W. Bush’s approval ratings after 9/11 were 90%, and that 70% of Americans were happy about invading another country.
    We now have 26% fewer fascists in the US!

  97. A1987dM Says:

    @fred #90: I think you mean Conte, not Mattarella. Mentioning the latter instead of the former would be almost like mentioning Elizabeth II instead of Johnson or Felipe VI instead of Sánchez.

  98. James Cross Says:

    Dana Milbank imagines how it would have been if Trump had run the Manhattan Project.

    One can imagine how things might have gone if Donald Trump had been the president who received Einstein’s letter: After two months, he would have congratulated himself for a “phenomenal job,” wound down his atomic task force and left the whole nuclear thing to the states.

    Texas would compete with Florida for uranium, while New Jersey and Ohio bid up plutonium prices.

    New York, making bombs, wouldn’t be in touch with Washington state, which would be retrofitting the B-29 without specs.

    J. Robert Oppenheimer, complaining about the lack of coordination, would be demoted and denied whistleblower protection.

    The bombs wouldn’t work properly in tests, the bombers would take off without enough fuel, Trump would blame the governor of Michigan — and we’d all be speaking Japanese.

  99. fred Says:

    Cross #98

    That’s not a very good analogy and quite silly. Groves “ran” the Manhattan Project, not POTUS.

    But what if anyone else than Kennedy dealt with the Cuban missile crisis?
    All of Kennedy’s advisors told him to attack, but he didn’t listen.

  100. Raoul Ohio Says:

    Arch #81:

    Lots of people are tricked by the Monte Hall problem, because it is a trick problem.

    A key part of the problem is that, after the initial choice, Monte Hall ALWAYS opens a door that is chosen using a strategy BASED ON THE FIRST CHOICE, and asks the person if they want to change. Only people who watch the show regularly know this fact. People who didn’t watch the show, which is most people in the world, don’t know why he opened a door and asked again. For all they know, maybe his strategy is to only open a door and ask again following a correct first guess, or maybe do it following a wrong guess, or maybe do that if the day in the month is a prime number.

    So in the usual presentation of MHP; you choose one of three doors. Then a surprise event happens about which you know nothing, and you get to rechoose one of two remaining doors. Without knowledge of the strategy used to select a door to open, the only thing you know is that your odds have improved from 1 in 3 to 1 in 2.

  101. matt Says:

    I never liked trolley problems for a reason I’ve not seen pointed out, though I’m sure someone has. The first time I heard a trolley problem it was phrased as “there is a fat man you can push onto the tracks. If you push him onto the tracks, it will stop the trolley and save 5 other people.” My reaction was: “would that work? will a single person, even very fat, actually stop the trolley if it hits him? Trolleys are very heavy compared to people. Even if it does stop the trolley, will it cause a derail, possibly causing people onboard to get injured?” I’m sure an expert on engineering could determine under what circumstances it would work, perhaps including a sufficiently slow, light trolley. However, in the heat of the moment, could one be confident that the engineering would actually work? This I think is one reason we need to be careful. In the context of the trolley problem you could reply “no, it’s just a thought experiment! Pretend it will actually stop the trolley!” However, I think one reason that we tend to be more careful about taking an action, such as pushing someone, rather than passively allowing events to continue, is that in the real world we don’t know what would happen.

    Anyway, does anyone know, would a fat man stop a trolley?

  102. arch1 Says:

    Raul #100: I agree that the Monty Hall problem statement must correctly describe the game (including that after the initial choice Hall ALWAYS opens a door not chosen, behind which there’s no grand prize). Like you, I’ve seen instances in which this wasn’t done. But most statements I’ve seen get it right, and even in those instances, most initial responses are incorrect (many quite adamantly and persistently so in the face of multiple clearly-reasoned arguments to the contrary).

    All of which doesn’t seem to explain Erdos’s lapse, because the computer simulation which finally convinced him *did* correctly model the game show, and in the descriptions I’ve read, Erdos had no objection to the simulation’s rules.

  103. arch1 Says:

    Scott, my #102 would be clearer with the following change:

    all of which -> That said, the “incomplete problem statement” scenario

  104. James Gallagher Says:

    Scott #77

    Blimey, she hasn’t even seen FANTASIA?!!! 🙂

    I was a bit drunk, so yeah, probably trolling accidentally, sorry 🙂

    Fantasia is still quite a good watch, although the uncut version is a bit too long for kids, and has some slightly grown-up scenes.

  105. Radford Neal Says:

    Raul #100:

    I don’t believe that ambiguity in the statement of the Monty Hall problem is the usual reason people get it wrong. If it were, we would expect them to ask for clarification, not adamantly insist that they’re right.

    I think the typical thought process is as follows. (1) Monty Hall can always open a door with a goat. (2) Therefore his doing so doesn’t tell us anything. (3) Therefore there’s no reason to switch.

    Steps (1) and (2) are OK. Step (3) is the problem. They really need to replace (3) with (3′) Therefore the probability that the door I chose has the car is unchanged (still 1/3). And then they need to go on to (4) Since I now also know _which_ door Monte Hall opened (unlike the fact that _some_ door with a goat was opened, _which_ is not a predetermined piece of information), I can switch to the other unopened door, increasing my probability of getting the car from 1/3 to 2/3.

    There may also be some people who go by the totally invalid rule that whenever there are two possibilities, with neither being impossible, they each have probability 1/2.

  106. Deepa Says:

    You’d said you plan to continue the math and CS fun exploration for Lily as long as the lockdown lasts. I have a humble suggestion! I know you might not have the time to spare, but just in case you do, how about expanding this to something like “Saturday Morning Math Group” that UT Austin’s math dept does, except in CS? There used to be something like that, called “Breakfast Bytes”, that just met a lot less frequently than SMMG. My son attended both regularly in the elementary and middle school years. He was drawn to the subjects and equally to the snacks they would have laid out. I would happily volunteer my time to help in any way with the revival of Breakfast Bytes, because every way I look at such a thing, it is super exciting. (One of those ways, is remedial lessons for me to pick up sneakily along the way, ha!).

  107. Deepa Says:

    p.s: A side benefit would be an automatic intellectual peer group for Lily, drawn from all over town, which could include her current peer group if they were interested in these subjects. The SMMG audience would happily show up! What a tremendous opportunity for all of them.

  108. Mitchell Porter Says:

    James Cross #98 mentions an article in the Washington Post… I managed to remember that the Post is owned by Jeff Bezos, and that Bezos and Trump don’t like each other. And then I realized:

    The richest man in the world owns the major newspaper, in the seat of government in the world’s most powerful nation.

    In a way that fact seems more significant, than the fact that he’s using it to attack the elected president nonstop. The more important fact is that the power of money and of oligarchs in the western world is this deep, this profound, this real.

  109. James Cross Says:


    Where’s the evidence that the Washington Post is attacking the “elected” President non-stop?

    The article I cited was an opinion piece. The Post regularly runs opinions of Hugh Hewitt, Marc A. Thiessen, and Henry Olsen who are regular Trump apologists as well as a number of other conservative commentators like Jennifer Rubin, George Will and Max Boot.

  110. Michel Says:

    Factorials for children: space three different marbles a marble apart, with matches spaced at both ends
    : | 0 0 0 | , and then ask in how many holes you can put the next different marble. Maybe she understands that for every possible permutation there are four holes to put the next marble in.

  111. Nick Says:

    Scott #60:

    > Being merely her dad, rather than an official teacher, it is
    unbelievably hard to get her to do exercises and take them

    I reported this claim to my GF, who, as I mentioned before, teaches a
    mixed class of ages 3-6. She said that many parents are saying the
    same thing, but that broadly speaking, the kids have been like this
    all along, and that teachers deal with the same problems! It turns out
    that they don’t get to school and suddenly do everything they’re told.
    Who knew?

  112. Scott Says:

    Nick #111: Right, but Lily’s teacher consistently reports that she behaves “perfectly” at school. And we’ve seen her behave at school completely differently from at home. In general, in each environment, she’ll do whatever she knows she can get away with!

  113. gabrial conroy Says:

    Scott doesn’t seem to address the arguments that these trials are actually an ethical brainer (and not no brainer). The above points, about potential dangers of a faulty vaccine or about the subtle coercion in supposedly “voluntary” trials, are ignored by him. He does address a tangential point about anti-vaxxers, but not the key point.

    That’s his prerogative, of course. It’s his blog. But I’d like to see his response.

  114. Nick Says:

    Scott #112:

    I reported your reply back too, and she said that I had mischaracterized what she said in the first place. What she really meant was that that scenario was a possibility, but not necessarily something that was likely. Whoops! Sorry about that.

  115. Marcel Müller Says:

    Good post, though I notice that I become increasingly allergic to rationalist humblebragging.

    “I’ve asked myself again and again over the last few months: why are human challenge trials for covid vaccines not an ethical no-brainer? What am I missing that all the serious medical experts see? And what are we waiting for: for 10 million more to die? 20 million? So it made me feel a little less crazy that the world’s most famous living ethicist agrees.”

    You know exactly what these experts see: A bunch of rules enacted in response to Mengele et al. and a lack of clear thought / moral courage to challenge them in combination with a condecending attitude in the medical system supposing that challenge candidates can never truly consent since they are too dumb to truly understand the risks involved.

    Sorry for my snarky attitude, but that needs to be said imho.

  116. Marcel Müller Says:

    While I would not call this “fruit of genius” but “obvious thing we just do not do”, this is my two cents on how to end Covid: Start mass producing reusable easy to use particle filtering masks now. (Not the surgical / community masks that may or may not be effective but something like this with P3 or N99 filters.) When / if the next wave starts distribute them to everyone or at least all people with a job that contacts many people. This will drive R far below one and can be done until consustent tracking is possible or eradication is achieved. Details here:

  117. Sandro Says:

    This is the trolley problem where the fat man wants to jump knowing his chance of death is below 1% and our decision is whether to stop him.

    The question is whether he actually knows and understands that 1% chance. You’re assuming a fat man with some appreciable understanding of engineeirng and physics in order to “know his chance of death is below 15”.

    Replace “fat man” with “10 year old child”, and you have the correct ethical conundrum faced by health professionals. Most people are fairly ignorant of basic biology.

  118. Scott Says:

    gabrial conroy #113: The very fact that we’re weighing the possibility of “subtle coercion,” or rare side effects, against the near-certainty of millions of non-subtle deaths along with a new worldwide Great Depression, encapsulates my argument for me. A train is bearing down on the human race, and the position of most of the world is “no, you don’t get it, we can’t just run out of the way, it’s way more complicated than that! Like, what if someone tripped while they were running? Even if they claim to understand the risk of tripping, can we be 100% certain that they do?”

    My position is that this is insane, and that history will vindicate me. But the very fact that this argument is taking place at all, with those who want to run from the onrushing train considered the “crazy” ones, means that I shouldn’t expect to be able to persuade by argument, at least not without going really, really, really deep to figure out the presuppositions that brought the other side to where it is.

  119. Tracy Hall Says:

    John #22: Thanks for the site name 1 Day Sooner. I signed up as well.

  120. Tracy Hall Says:

    Scott #48, re solving simple equations: You might try taking the tack that simple equations are a way of hiding secret numbers so that only people who know how to solve them are able to uncover the secret. And a pair of linear equations in two variables is the simplest form of a shared secret: If you give one equation each to two people, they cannot find one answer each working alone, but if they pool their information and work together, they can find both answers.

    Nick #41, Scott #46: When I was taught long division (at the age of 10 or 11, I think) I was discomfited by the fact that when dividing by anything longer than a 1-digit number, you have to guess how many times it goes in. To use a term I didn’t understand until much later, what they taught us was not algorithmic. Later on my discomfort was finally assuaged by learning that long division in binary is a perfectly good algorithm: If the number is less, it goes in once; otherwise it goes in zero times. (It would have helped if they had taught us a variant approach that I saw much later: Guess low and keep subtracting as necessary. In the limit, to make the base-10 algorithm entirely well defined, obtain the next digit in unary via repeated subtraction.)

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