## Happy Second Birthday Lily

Two years ago, I blogged when Lily was born.  Today I can blog that she runs, climbs, swims (sort of), constructs 3-word sentences, demands chocolate cake, counts to 10 in both English and Hebrew, and knows colors, letters, shapes, animals, friends, relatives, the sun, and the moon.  To all external appearances she’s now conscious as you and I are (and considerably more so than the cat in the photo).

But the most impressive thing Lily does—the thing that puts her far beyond where her parents were at the same age, in a few areas—is her use of the iPad.  There she does phonics exercises, plays puzzle games that aren’t always trivial for me to win, and watches educational videos on YouTube (skipping past the ads, and complaining if the Internet connection goes down).  She chooses the apps and videos herself, easily switching between them when she gets bored.  It’s a sight to behold, and definitely something to try with your own toddler if you have one.  (There’s a movement these days that encourages parents to ban kids from using touch-screen devices, fearful that too much screen time will distract them from the real world.  To which I reply: for better or worse, this is the real world that our kids will grow up into.)

People often ask whether Dana and I will steer Lily into becoming a theoretical computer scientist like us.  My answer is “hell no”: I’ll support Lily in whatever she wants to do, whether that means logic, combinatorics, algebraic geometry, or even something further afield like theoretical neuroscience or physics.

As recent events illustrated, the world is not always the kindest place for nerds (male or female), with our normal ways of thinking, talking, and interacting sometimes misunderstood by others in the cruelest ways imaginable.  Yet despite everything, nerds do sometimes manage to meet, get married, and even produce offspring with nerd potential of their own.  We’re here, we’re sometimes inappropriately clear, and we’re not going anywhere.

So to life!  And happy birthday Lily!

### 88 Responses to “Happy Second Birthday Lily”

1. Peter Says:

I’ve heard that one sign of the iPad generation is that they try to pinch-zoom ordinary printed text and get confused when it doesn’t work. Is this something you’ve noticed?

2. Scott Says:

Peter #1: Well, she’s not really reading printed text yet. But I can report that at 6 months, she tried to “swipe” a fish tank at a restaurant, like she was used to doing with an app where you swipe fish that float across the screen; and she also once looked behind the iPad when we were doing a video chat with her grandparents to see if they were there. But she no longer gets confused by anything like this: she does have printed books, and she knows perfectly well that they’re not iPads or smartphones.

3. Serge Says:

Happy birthday Lily!

Don’t forget to expose her – besides algebraic geometry 🙂 – to music and foreign languages as well. Hebrew’s fine of course, especially if it’s her mother’s first language.

I think the level of consciousness we’re able to perceive in other beings depends on our own form of consciousness. For a cat it’s probably the other cats who’re the most conscious living beings – even more, presumably, than any human baby.

4. Nick Says:

In what way is her access to the internet controlled? Is there some software that filters for educational content? Do you try to direct her in any way in her choices? I ask because I am interested in what exactly makes the difference for such kind of media to have a positive effect on the child.

5. Shmi Nux Says:

Happy Birthday, Lily!

> I’ll support Lily in whatever she wants to do, whether that means logic, combinatorics, algebraic geometry, or even something further afield like theoretical neuroscience or physics.

You know, some readers might take this statement at face value…

6. Shecky R Says:

Luv it! And looking forward to reports at 3, 5, 10 and 15, by which time she’ll no doubt be writing this blog herself, having taken over for her dad.

7. Richard Says:

Any chance that you might give a few examples of the best iPad apps for her? I’m sure that your (and Dana’s) judgment in selecting has helped.

8. James Gallagher Says:

There is the argument that modern tech makes it too easy for kids to get a satisfying feedback for very little effort.

But my own daughter is excelling in music, sports and academia and she spends a lot of her time on tech platforms.

So the argument isn’t a very worrying one it seems…

(I guess we’ll see when this generation grows up)

Happy birthday Lily!

9. Scott Says:

Serge #3: Well, she’s being raised bilingual in English and Hebrew, which is about 0.7 more languages than I currently speak. 🙂 And like most toddlers, she loves listening to music, or attempting to make it with whatever instrument is available.

10. David Speyer Says:

Mazel tov!

11. Scott Says:

Nick #4: We choose apps to download for her; then she picks which ones to play with. Since she can’t type yet, she’d have a bit of trouble downloading her own apps. As for YouTube, we start her on some video she likes (say, Elmo or Swedish Chef or Barney or Frozen); then she picks other related videos from the sidebar on the right, and so on recursively. So far, it’s never happened that this procedure has led her to any violent or sexual content—though if it did, I assume she’d simply be bored and annoyed by it (where’s Barney??). In general, my philosophy is that she’s allowed to learn anything whatsoever she wants, at whatever age she expresses interest in doing so.

12. Michael Bacon Says:

Your might think about Chinese, or orienteering (pun intended) her toward Asian languages (I’m partial to Japanese). But regardless, congratulations, enjoy! Your deserve it, your wife derives it, and your child (assuming you keep up the good work 😉 ) will enjoy the benefits of all of your joint efforts: loving, intelligent, diligent and relaxed parents. Congratulations.

13. Scott Says:

Michael #12: I studied Mandarin for a year when I lived in Hong Kong, but was a mediocre student (I passed the class only by writing a Mandarin-learning video game for extra credit), and then quickly forgot all of it. Maybe Lily will someday have better luck. (Maybe I could even dig up that 20-year-old game to help her… 🙂 )

14. Scott Says:

Richard #7: Starting when she was an infant, her favorites included Talking Tyler, Peek-a-Zoo, I Hear Ewe, Baby Aqua, Counting 123, and PaintSparkle.

At a more advanced toddler level, she likes EduRoom, Fisher Price Laugh & Learn, Yo Gabba, ShapeBuilder, Pepi Bath, AbbyPuzzle, … and I was just going through it to look up what the others are, but then she started screaming that she wanted the iPad, so it will have to wait.

In any case, the apps are like $1 or$2 apiece, so the right strategy is just to download every single one that looks vaguely appealing, then let the toddler decide which ones she likes (and when you find out, you can get more similar ones). One warning: do not download any of the free games, because they’re basically just advertisements trying to get you to buy other games.

15. Sniffnoy Says:

Happy birthday Lily!

16. physpostdoc Says:

There is something quite heart warming about this post! Best wishes for your daughter on her birthday.

17. dom Says:

I don’t completely agree with you. Giving any option might make her play dumb repetitive games that she learns nothing from. Your logic would also apply to letting her watch TV all day, choosing which channel she wants and that we know to be pretty bad. We also let our daughter play a lot, but enforce some control on the games. Surprisingly, still her all time favorite is to just draw – we have like three drawing apps and she keeps on switching from one to the other if she gets bored with one…

18. John Kerr Says:

Happy birthday Lily. May you discover an innate talent for fine art, scunnering your old man.

19. Tom Says:

20. arden.arboles Says:

A nerd like her daddy?!

What the heck, she is a knockout!

Mazel tov, preciosa Lily.

21. Scott Says:

dom #17: Believe me, we do control how much time she can spend on various activities, largely for reasons for logistics (e.g., she now needs to take a nap, or go to daycare). And she does complain extremely loudly when we do.

When I met with David Deutsch a year ago, I told him that for a long time, my dream had been that if and when I ever had kids, I would give them complete freedom to do anything they wanted—as advocated by the Taking Children Seriously movement in which Deutsch is active (one of his main interests outside quantum physics). It took having a kid for me to realize that, often, the bigger issue is whether the kid will give you any freedom. 🙂

22. Roger Says:

There is an article on Jezebel attacking you for refusing to let your toddler choose to be transgendered if she wants to be, as what happened to Shiloh/John Jolie-Pitt. Just kidding.

23. dom Says:

You met Deutsch a year ago and your daughter is two – you should get your story straight…

24. Scott Says:

dom #23: Yes, that’s right, Lily was 1 when I met him. Believe me, she was plenty old enough then to be restricting our freedom, and also to have her own freedom restricted. 🙂

25. dom Says:

Oh, sorry, then I misunderstood you because my english is not that good – instead of “my dream was” shouldn’t it be “my dream had been”?

26. Scott Says:

dom #25: You’re right, “had been” is preferable. Thanks; fixed.

27. aravind Says:

Happy Birthday Lily! You and your parents are mutually lucky to have each other in your lives. Have a wonderful year ahead! (From a professor who mostly lurks here and greatly admires your Dad’s writing style and his work.)

28. rrtucci Says:

That cat looks just like you!

(Okay, I know you will censor this too. I am resigned to my fate)

29. Rahul Says:

Hey Scott, as occasional babysitter of another almost-two-year-old, two questions:

(1) How did your get her past the Ipads-are-meant-to-be-banged-and-thrown-and-nibbled-on stage to actually doing something productive with them?

(2) How did you teach her to sort-of-swim.

30. asdf Says:

Scott #9, I’ve heard that kids have an amazing ability to learn new languages quickly, that they lose at around age 12 if they’re raised monolingual or bilingual, but they retain it permanently if they’re raised speaking 3 or more languages. So maybe you should speak Chinese with her sometimes. OTOH I’ve also heard it’s best if they speak just 1 language with each person they have regular contact with, e.g. English with you, Hebrew with Dana, Russian with Uncle Boris, French with Aunt Natalie and so on. Those last two are made-up characters, of course. I think Derek Bickerton has written about this.

https://en.wikipedia.org/wiki/Derek_Bickerton

31. Gil Kalai Says:

Mazal tov, Scott. Also the picture here as well as those from LHC post are splendid. The choice between the land of the squirrels and the land of the cats may be difficult but I hope the decision will bend toward the east 🙂

32. Serge Says:

Gil #31: As far as I’m concerned, the jet lag is no longer in favor of the European commenters when the blogger has moved towards Schrödinger’s cat (but I’m not trying to influence their decision in either way).

33. Scott Says:

asdf #30: As I said, I don’t remember even the tiny amount of Mandarin I once knew. Yes, if we had an easy way to immerse Lily in additional languages, we’d probably do so—but given logistical constraints, she might be fated to grow up “merely” bilingual, rather than trilingual or quadrilingual.

34. Serge Says:

asdf #30: The average American being mostly monolingual, two’s already a lot. 🙂 To me, what counts the most is to become aware at a young age of the possibility of naming the same things differently, of viewing our world from different perspectives, and so on…

35. Scott Says:

Incidentally, since I put up this post two days ago, the part about “constructing 3-word sentences” is already obsolete. This morning she came out with, “Lily sit down in car. Daddy sit down in car too.”

36. Scott Says:

Rahul #29:

(1) She was interested in what was on the iPad screen (or other computer screens) since she was 2 months old. But yes, she does sometimes abuse her iPad, so the key is that we keep it inside a soft protective case. (Incidentally, laptops are harder. She’s destroyed more than one laptop keyboard by ripping off keys, which is a real inconvenience until the laptop gets fixed—you find yourself composing sentences that meticulously avoid a certain letter or punctuation mark!)

(2) Well, she’s loved splashing in shallow water, etc. since she was 6 months old. And she now “swims” with a large flotation device, and also loves “jumping” into the pool if I’m there to break the “jump.” I’m not sure yet how we’re going to teach her to swim for real.

37. Michael Bacon Says:

“The average American being mostly monolingual, two’s already a lot.”

Heard a joke in Japan. If you speak three languages your trilingual, if you speak two languages your bilingual, and if you speak one language, your an American. 🙂 Parfaitement dit

38. Douglas Knight Says:

asdf, that is predicated on a false claim. Adults learn foreign languages faster than children.

The only linguistic task that children are good at is understanding and producing sounds. That they lose that with age. People that learned a large inventory of sounds as children (which is not the same as a large number of languages) have an advantage in learning new languages because it might not have new sounds. It wouldn’t terribly surprise me if they maintain flexibility.

But avoiding an accent is a very small part of learning a language. And for every other aspect of language learning that has ever been studied, adults learn faster. See here (gated) or here (public, but big).

39. Serge Says:

I believe every adult willing to learn a new language should have a try at Esperanto first. It’s still very alive on the Internet. As for me, learning Esperanto in three months gave me great confidence with the other languages. Then I tried to improve my English, and afterwards I started to learn Spanish. Well, all roads lead to Rome…

40. a Says:

Blonde baby! Black haired parents! I can believe P=NP also! Congratulations! Happy Birthday!

41. Scott Says:

a #40: Thanks! But my hair is brownish, not black—and it was blond, just like Lily’s, when I was a kid. And Dana’s hair is dark brown now, but it was also blond when she was a kid.

42. aviti Says:

Now, this is something I envy. I am serious here.

43. JimV Says:

I don’t usually understand most of the posts here in detail – too lazy to learn the math assuming I’m even capable – but I read them anyway for the excellent writing, which has me saying, “I see what you did there … and there … and there …!”

I do think cats have a consciousness, though, but we don’t always understand their communications. Another blog I sometimes read (“Way of Cats” or something like that) says that a cat kiss (or gesture of affection) is to look at you and slowly close and open its eyes, so you should do it back, if you feel affectionate. See also the “cat rescues a toddler” video.

44. Nilima Nigam Says:

Happy Birthday, Lily! It’s a strange world out there, and there will likely be gadzillions of opinions on how you should make your way through it.

Fortunately, you’ve got some awesomely supportive parents. (At least they will seem thus until you reach double-digits, when they may strangely morph into creatures who don’t understand anything, or you, and are just plain embarrassing. My children affirm this happens.)

So, whatever path you choose- may you be granted health and strength, and may you find much happiness and many friends along the way!

45. Serge Says:

Michael Bacon #37: Yes I’d heard this joke but with a French instead of an American! 🙂 Indeed, French was once a lingua franca in Europe after the slow decline of Latin. Now this role is being played by English, like everywhere else. So we haven’t had a long tradition with foreign languages either, even though the situation is rapidly changing with the younger generations who grew up with the Internet and globalization like my 20-year-old son. But you may also choose to invest your linguistic abilities into your own native language, which is what most writers do (and I wish I could express myself in French like Scott writes in English!)

46. s.vik Says:

The current gen has lots if computer and phone apps but will not product any real programmers in c or Fortran for real industrial or science applications.

47. BigKibitzer Says:

My children enjoyed Pingu, a claymation series available on Netflix and (in pieces) YouTube. The best part is the universal penguin almost-language. I often asked my kids “What did the penguin just say?”

48. Anonymous Says:

Douglas Knight comment #38:
“And for every other aspect of language learning that has ever been studied, adults learn faster”?! I’ve never commented on this blog before, but I can’t let that statement pass. Linguists have spent a lot of time thinking about the “critical period hypothesis”, which you may want to read about. The paper you linked to deals with second language acquisition, not first language acquisition. Raising children in a bilingual/trilingual environment almost always refers to first language acquisition. Every linguistics professor with whom I’ve had this discussion has strongly recommended raising infants in a multilingual environment; very small children have no trouble becoming fluent in three or four languages very quickly, and I don’t think anyone can say the same about adults.

49. Null Says:

What about something against usual academic values, like an investment banker or model?

50. Scott Says:

Null #49: Model, fine. But investment banker?? 😉

51. Bill Kaminsky Says:

In line with the cavalcade of comments about inculcating multilingualism while the kiddie’s neurons are still highly plastic, allow me to say:

No me culpen por favor, Lily (y Scott y Dana), por olvidarme de tu cumpleaños. ¡Feliz cumpleaños aunque sea un poco tarde!

And on that note, especially as my wife and I are thinking of a starting a family very soon, does anyone here have opinions — anecdotally supported, if not scientifically supported — on how to teach kids multiple languages?

For example:
– How many languages are too many?

– Only stick to ones that parents and regular caregivers can speak fluently? Or is exposing to children to age-appropriate foreign language media that the parents don’t really understand also worthwhile?

– Having settled on the languages to be attempted, should each parent and regular caregiver choose just one language in which he or she individually will always use to speak to the child? (I distinctly remember reading somewhere that there was some at least pseudo-scientific evidence in favor of this being optimal.)

– When the child is old enough to play with blocks and read along in picture books, should multilingual literacy be attempted, or just oral multilingualism?

– And so on…

Thanks 🙂

52. Greg Kuperberg Says:

Null – Or an investment banker *and* a model. She will have a short skirt and a long jacket. You will meet accidentally when she borrows your pen…

53. Darrell Burgan Says:

As a parent of four, I’ll kick in my own advice: generalizations about children are a fool’s errand. The only thing you can be certain of is that the journey will have many forks in the road, and parents can influence only so many of those direction changes.

With that said, the best a parent can do is prepare their children with as many tools and opportunities as they can. And then stand back and let them find their own way in the world.

Happy birthday to Lily!

54. Anonymous Says:

Bill Kaminsky #51:
– How many languages are too many? Anecdotally, three is absolutely fine. I have heard that four and (I’m much less sure about this) even five can be taught to infants as first languages. I’ve never come across a paper about this though.

– Only stick to ones that parents and regular caregivers can speak fluently? Yes. That’s what all acquisition researchers seem to advise. In the literature, I only remember a study that showed that 9-month old American babies could learn Mandarin (sounds) only from live speakers, not from Mandarin TV. It was probably a 2003(?) paper by this person: http://ilabs.uw.edu/institute-faculty/bio/i-labs-patricia-k-kuhl-phd

– Should each parent and regular caregiver choose just one language in which he or she individually will always use to speak to the child? Yes. It’s called the “one-parent-one-language approach”, which supposedly works well. Children are supposedly very good at figuring out which language is called for in which situation. I was advised against speaking two different languages to children.

55. Bill Kaminsky Says:

To Anonymous #54: Thanks! Thank you so much!!

56. a Says:

Scott @41 So $\exists$ jewish people whose hair ages brown instead of white?

57. Yoni Says:

Mazel tov Lily

Scott – I have heard many arguments against allowing young children too much screen-time, but never that it “will distract them from the real world”. Typically the reasons given are behavioural or developmental. I have been lead (admittedly by news articles rather than by a review of the academic literature) to believe that academic research supports limiting screen time in under-twos to zero and toddlers to maximum 1-2 hours per day.

58. Scott Says:

a #56: Well, maybe it will also age white—give it time! (Indeed, I may have developed white hairs just within the last month…)

59. Jr Says:

Congratulations.

60. Douglas Knight Says:

Anonymous 48, asdf made a false claim about second language acquisition, so I responded with real data about second language acquisition, which I explicitly labeled as about foreign languages. asdf claimed that children lose their “amazing” ability to learn languages around age 12. This is completely false. 8 year olds are slower at learning new languages than 14 year olds, who are slower than 20 year olds.

I have read about the “critical period hypothesis.” There is a critical period for the recognition and production of sounds. Linguists often make the very narrow claim that there is a critical period for learning a first language, meaning merely that if a child does not learn any language before, say, age 12, then the child will never learn a language. This claim is plausible, but based on very little data. It is also not relevant to anything.

If you claim that there is a critical period for first language learning says something about the difference between learning one language and learning two, not the difference between zero and one, can you say what you mean? Many people make such a vague claim, but no one has ever made a concrete claim to me. When I push linguists and psychologists on it, they usually retreat to the two standard hypotheses, or admit that they have no idea what the textbook was talking about. Nor has anyone provided me with data from which I can extract my own claim.

And if you do want to claim that very young children are good at learning languages (outside of sounds), you have to be very careful what you mean. By naive measures, they are terrible. An adult immersed for six months in a foreign language will have a greater vocabulary than a five year old native speaker. Is it fair to say that the adult learned 30x as fast? Mainly the child was learning the very concept of language and the abstractions behind those words. The adult will use more complex grammar and make fewer grammatical mistakes, which is a more fair comparison, but still problematic. If you just want to say that it is a miracle that the child learns a language while simultaneously learning what language is and learning so much about thew world, sure, whatever. But that says nothing about whether learning additional languages is a good idea.

61. Sniffnoy Says:

FWIW, here’s what Mark Rosenfelder has to say about the subject: http://www.zompist.com/whylang.html

(Not really competent to evaluate this, but thought it might be worth introducing.)

62. Eggo Says:

Scott, re. your #36, floating on your back in a nice deep bath is a great way to get comfortable being in water without floats; it solves the taking-off-the-training-wheels problem that can make learning to swim unaided quite scary.
She might be a little old for it now, and some people just aren’t buoyant, but it really helps build confidence.

Much better than learning to kick around in floaties, then getting scared when it’s time to take them off, which I’ve seen a lot of kids have trouble with.

63. GASARCH Says:

I have often asked parents of a 1-year old, jokingly, if the child is good at math.

At what age can you tell if a child has talents at Math? Music?
Other things?

At what age can you tell if a child has an interest in Math? Music? My little Pony? Other things?

64. Michele Says:

Douglas Knight comment #48: “An adult immersed for six months in a foreign language will have a greater vocabulary than a five year old native speaker.” I am not sure.

My experience (which is statistically irrelevant): when I was 6, me and my family went to France (from Italy). We spent 2 years there, my father working at the University, my mother caring about me and my little brother (and constantly interacting with French people speaking French *only*), and myself attending grade school. My French vocabulary quickly grew from 0 to N (very large). Of course I could not learn words and expressions “for adults only”, but in general my vocabulary quickly became richer than my parents’ one (and their vocabulary did not start from 0!).
My brother was 1 when we wen to France. At 3, he was able to speak French, him too (not to write or read complex statements, of course). Later, he studied French at school in Italy (I did not! I chose English). Today, we both speak, read and write in French very well (we practice with French friends, sometimes).

In 2013, I spent 6 months in France, as a visiting researcher (history repeating..). To French people I met, I always had to tell I am Italian, as the usual impression was that I was French – just coming from another French university. I am neither a genius, nor particularly talented for languages. I strongly feel that my French could not be so good, if I had to learn it at 10, 20, or 30. Maybe I am wrong, but I think an important aspect is the “accent”. When you are a little kid, you do not have (yet) any particular accent. So, if you interact with people speaking different languages, you may learn (for life) their different accents more easily.

@ Scott, wonderful post and congratulations!

65. Bill Kaminsky Says:

Apropos of GASARCH #63, I recently came across the following intriguing publication of the American Mathematical Society:

Math from Three to Seven: The Story of a Mathematical Circle for Preschoolers by Alexander Zvonkin (Université Bordeaux I, Talence, France), AMS-MSRI Publications, 2011.

You can see large chunks of it at Google Books:

Quite a bit of highly nontrivial mathematical concepts are introduced to the kiddies, providing some actual basis for those good ol’ Cold War hyperbolic worries that at least some Russian kindergarteners were more mathematically proficient than the median American undergrad.

Sidenote: This *was* a general fear, right? I cannot have been the only American undergrad to have heard his professor half-jokingly-yet-half-ruefully exclaim: “This is simple! SIMPLE! Russian kindergartener could do it!”, can I?

Seriously though, here’s the introduction written by the book’s translator:

This book is a captivating account of a professional mathematician’s experiences conducting a math circle for preschoolers in his apartment in Moscow in the 1980s. As anyone who has taught or raised young children knows, mathematical education for little kids is a real mystery. What are they capable of? What should they learn first? How hard should they work? Should they even “work” at all? Should we push them, or just let them be? There are no correct answers to these questions, and the author deals with them in classic math-circle style: he doesn’t ask and then answer a question, but shows us a problem–be it mathematical or pedagogical–and describes to us what happened. His book is a narrative about what he did, what he tried, what worked, what failed, but most important, what the kids experienced.

This book does not purport to show you how to create precocious high achievers. It is just one person’s story about things he tried with a half-dozen young children…

I’ll close just by saying that while those last 2 sentences must be borne in mind — i.e., the book fundamentally is “just” a detailed diary of one mathematician trying a bunch of things over the course of 4 years with 6 children — the mathematician in question is well-read in some child development literature and is quite observant himself, and so the fact this is all anecdotal doesn’t mean it ain’t highly interesting.

66. Anonymous Says:

Douglas Knight #60:

If we’re talking about second language acquisition, children gain fluency much faster, and I’ve seen living evidence of this everywhere around me throughout my life. Try talking to immigrants with children (assuming they immigrated to their new country before the kids reached puberty): I expect all of them to tell you that their children became fluent in English in very little time while their own (adult) English never reached a comparable level even though they started out knowing (significantly) more English than their kids did. I’m one data point myself: I knew no English in the first few years of elementary school, and then it became my dominant language in grade 5 (one to two years after I left my country of birth) to the point where I stopped speaking my native language at home, whereas my parents still speak broken ungrammatical English to this very day (almost two decades later) even though they’ve had no less exposure to English. I don’t recall actively “trying” to learn English because I didn’t memorize words or grammatical constructions; hearing the language around me for a year was simply good enough. My parents, on the other hand, still couldn’t gain grammatical competence despite attending English universities and living in an English environment, and my family’s story is unremarkable because it’s the same as everyone else’s. I therefore believe that there is a critical period for acquiring grammatical competence.

If you’re looking for more scientific evidence, I remember some relevant papers that I read a while ago for a course on bilingualism. My interpretation of the “critical period hypothesis” is not the same as yours; maybe there are different versions of it floating out there. Just now, I looked up the papers that I was thinking of:

– Newport, E. L. (1990), Maturational Constraints on Language Learning. Cognitive Science, 14: 11–28
(http://onlinelibrary.wiley.com/doi/10.1207/s15516709cog1401_2/abstract)

– Lardiere, D. (2006) Establishing ultimate attainment in a particular second language grammar, in Z.H.. Han & T. Odlin (eds.) Studies of fossilization in second language acquisition, 35–55. Clevedon: Multilingual Matters

I think the latter article looked at how an adult’s grammar became fossilized, and here’s a snippet from the first paper above: “Normal language learning occurs only when exposure to the language begins early in life. With exposure beginning later in life, asymptotic performance in the language declines: the effects over age of first exposure are approximately linear through childhood, with a flattening of the function in adulthood.”

67. Michael P Says:

Douglas Knight comment #48:

The value of learning more than one language in early childhood goes very far beyond the usefulness of the learned language.

The child learns how to look at things from different (verbalized) viewpoints; learns the difference between the concepts and the names of the concepts thus learning instinctively a bit of philosophy and becoming less likely to be fooled by a wordplay; gains the ability to understands things that are better expressible on one language than the other, etc.

IMO the ability to speak another language is just a pleasant side effect of the cognitive benefits provided by learning the second language, as in Sapir-Whorf http://en.wikipedia.org/wiki/Linguistic_relativity

68. dorothy Says:

Bill Kaminsky #65. It’s a lovely book but if you haven’t, read the end notes about what came of the children. The upshot is that the children of mathematicians went on to do math or math related things and the others didn’t. One moral for me is that you don’t teach your children so that they will learn what you have taught them. The point of the lesson is the lesson itself.

69. 27chaos Says:

Adorable! That cat deserves a medal.

70. Michael Bacon Says:

Dorothy,

Among the children who didn’t go on to do math or math related things, were there any discernible correlations or patterns in the work they did end up doing?

71. EE John Says:

Another data point – I moved from California to Oslo at the age of about 37 after marrying a Norwegian girl. I speak only English to our 3 kids and the wife speaks only Norwegian. It worked beautifully. Around the dinner table, the kids answer in the same language they are spoken to. No accent in either language.

I, however, am instantly identifiable as a native English speaker in the same way that we instantly picked out the German or Russian bad guys in 80s Hollywood action movies.

On the other hand, I help the kids with their Norwegian homework. It seems that my vocabulary is better in some areas, and my grammar is generally better than the kids’.

I did not learn by “immersion”, I went to classes at night for three years. I think people learn in different ways, and a pedagogical classroom approach was the right one for me. Immersion got me from 80% to where I am now (95?) but it didn’t work until I could grasp a lot of what was flying by.

72. James Gallagher Says:

Yoni #57

technology is developing much too fast for any “academic research” to be reliable re children’s interaction with it. Quad-core processors allowing VERY smooth interaction with a tablet screen have arrived in just the last two years for example, making a qualitative difference to the experience.

Obviously children should also interact with many other real children – that’s what public schools enable. But simplistic dictates like “no more than 2 hours screen-time” are just silly – especially when the tech experience is evolving so rapidly.

What should they do instead? Play with wooden toys?

73. Bill Kaminsky Says:

To Dorothy #68 and Michael Bacon #70,

First, thanks Dorothy. I hadn’t read the epilogue as I haven’t gotten my hands on the actual book, but rather just the official, 33 page book excerpt from the American Mathematical Society website:

http://www.ams.org/bookstore/pspdf/mcl-5-prev.pdf

and what I could see via the Google Books link I mentioned in #65.

But checking Amazon’s “Look Inside” feature, I’ve now been able to read the first page of the epilogue.

I’m not sure if later pages of the epilogue mention what happened between age 7 and working adulthood, but my take on the fact that only the children of the mathematicians ended up in math-related careers is as follows:

a) Overall, I’m not surprised. The children of mathematicians, presumably, got a lot of direct and indirect encouragement and education at home in math over and above the unusual experience of participating in a “math circle” while in preschool.

b) The bigger question for me — and, given the limited amount of the epilogue I can read, I’m not sure it’s one the epilogue answers — is whether most of the children eventually obtained an accurate sense of “true” mathematics (say, math of the sort one would find in the usual analysis, algebra, and geometry courses for college undergrads majoring in math) before they chose their careers. I say this since I myself am fine with my potential progeny choosing careers far away from math/CS/theoretical physics/etc. I just want them to have an accurate sense of the wonders of these fields before they decide to devote their lives elsewhere. (Additionally, though perhaps needless to say, I wouldn’t trust 99.9% of primary and secondary schools in the USA — be they public or private — to instill that sense.)

In closing, let me answer (to the best of my ability given the limited portion of the book I’ve been able to read) your question, Michael, about which child ended up where:

** Of the boys in the math circle **

Dima (the author’s son) — Indeed becomes research faculty in mathematics at one of the Universities of Paris

Andy (presumably revealed to be the son of a mathematician friend of the authors at some point, yes Dorothy?) — Got a degree in international economics and became a quant at a financial trading firm

Pete (presumably revealed to be the son of a non-mathematician at some point, yes Dorothy?) — Majored in Japanese as an undergrad and became an interpreter for a time in Japan, but now back to grad school for a degree in psychology

Gene (mistyped in the epilogue as “Jane” by the translator*, at least in the printing seen on Amazon, and also presumably revealed to be the son of a non-mathematician at some point) — Works with a tourist agency for domestic Russian tours of Moscow and St. Petersburg

[*Perhaps neurotically overcomplete sidenote: Rather than using a direct transliteration of the Russian names, the translator used American equivalents. Thus, Evgenii became “Gene”. But the author’s daughter, Evgenia (“Jane”) is also in the math circles. The translator’s mistake likely arose because both Evgenii and Evgenia in Russian get the nickname Zhenya.]

** Of the girls in the math circle **

Jane (the author’s daughter) — Got a PhD in film studies

and, alas, that’s where Amazon’s preview of the epilogue ends, and so I don’t know the eventual careers of her friends Sandy, Sasha, and Dinah are revealed.

74. Raoul Ohio Says:

All time best picture of a smart kid?

75. Arko Bose Says:

I am just a bit worried that she might develop carpal tunnel syndrome in her hands, from such an early use of touchscreens. 🙁

76. quax Says:

Too cute!

Does she yet get impatient with you when you are not fast enough on the ipad? My three year old is at that stage when silly papa cannot ever quite quickly enough navigate to her desired Netflix show. I usually just let her do it herself now, as she wants to take the ipad away from me as soon as she figures I am not doing it right.

As to David Deutsch does he have kids? Mine are about the most stubborn and headstrong creatures the world has ever seen. A strict TCS approach would by now probably have resulted in them withering away from malnutrition. And then there is the teeth brushing dilemma. Problem is that teeths need to be brushed before you can actually reason with a child.

77. Scott Says:

quax #76: Yes, she often gets impatient when it takes too long to set up a video for her. And no, David Deutsch does not have kids.

78. Anonymous Says:

quax #76 polish the rocks in the mouth. Scott, what do you think about the comment Jews like Mozart, Gentiles like Bach?

79. Scott Says:

Anonymous #78: I never heard that stereotype before, and it sounds totally made up—like “Lutherans like real analysis, Episcopalians prefer complex analysis.”

80. Vijay D'Silva Says:

Scott #79: And apparently algebraists eat corn in rows while analysts eat in spirals and non-mathematicians don’t care because they eat it with salt.

81. Nick Read Says:

I can haz consciousness?

82. Bill Kaminsky Says:

If there’s any interest in returning to the topic of giving children maximal freedom (up to constraints of them inflicting or suffering significant harm due to their relative ignorance about the world), then perhaps people would be interested in the discussion of various famous alternative pre-, primary, and secondary schools.

To take an extreme example that’s local to us here in the Greater Boston region, there’s the Sudbury Valley School. Sudbury Valley is a school of all ages from preschool through high school that’s run in the style of direct democracy known as “New England Town Meeting.” All major decisions—up to and including the hiring of staff and formulating what little there is in the way of a general curriculum—are made in a weekly school meeting in which all students and all adult staff (of which there’s only 8) may vote, one-person-one-vote regardless of age. (Thus, the adult staff is an insignificant voting bloc.) Execution of major decisions and the making and execution of minor decisions is done by committees chartered in the weekly school meeting with membership often randomly assigned by lots. The vast, vast majority of curriculum choices historically have been left to each individual and her or his ambitions, interests, and whimsies.

The school’s site — http://sudval.org/

A recent profile in the New Republic by Mark Oppenheimer — http://www.newrepublic.com/article/116015/sudbury-valley-school-alternative-education-right-my-kids

A recent interview of Sudbury Valley co-founder (and former physics professor at Columbia in the 1960’s) Daniel Greenberg done by the aforementioned Mark Oppenheimer —

83. quax Says:

Scott #77, it’s of course a cheap shot to assume that David Deutsch may reconsider his stance if he was a dad, but at any rate it would be interesting to see him try his approach in practice.
Bill #82, thanks for the link! Astounding that this works. Gives me back some hope for humanity. This kind of school would work well for my little boy (at 10 I guess he’s not that little any more). He is slightly autistic and hates when school makes him do something that he’s not interested in.

Then again if left to his own devices he’d never learn German, raised him kinda bi-lingual and he understands everything. But he doesn’t want to speak (unless he has to with other kids who don’t know English). He also thinks that the whole word should just switch to English so that the problem of foreign languages would be neatly solved.

84. jonas Says:

Re #78, I’m a counterexample to that.

85. quax Says:

Jonas #84, this is complete BS anyhow. Mozart is OK but really a bit overrated (his later stuff is much better than his early work, so he probably may have continued to grow as a composer). Goethe who had the pleasure to listen to both, Mendelssohn as well as Mozart, when they were child prodigies, commented that the former was more impressive. And frankly JS Bach is in a league of his own.

86. Alexander Says:

Don’t own an iPad, and even if I had one that would not be sufficient, because I have twins.

87. David Says:

My daughter was born two weeks before your daughter and it’s pretty cool to read about your experiences.

My daughter likes watching me solve chesstempo problems. She likes to quickly find the pieces, count the number of pawns, etc. She obviously doesn’t play the game yet but she seems very curious about it. When she was not yet two, she held up the iPad to a random lady on the plane and said that she was playing chess. The lady was quite surprised by all this!

But I agree with you, the iPad is a great tool for kids. I can’t see how it would be harmful but I have come across parents who think it’s irresponsible.

88. Cal Says:

We recommend the song “Mandy is two” by Johnny Mercer.