How do you raise a child as a rationalist? I can't say that that was exactly what I had in mind but it seems to make for a fitting title here. A more precise title could have been: "How to deeply educate a child such that it fun and natural".

Today I'd like to tell you about the lullabies I sung and to what that led.

When my firstborn was very young I adapted a classic German lullaby "Schlaf kindlein schlaf" to numbers. It started with with only a few verses but grew over time (in part by the need to cover longer times until he slept).

I did sing it in German but I tried to translate it here to give you a better idea. It goes to the melody of "Schlaf Kindlein Schlaf which you may not know but can google easily (note that in German there are nicer rhymes for 100, million, googol):

Sleep, baby, sleep!

Thy father counts the sheep,

One, two, three and four

Little baby sleep some more

Sleep, baby, sleep!

The refrain repeats and the verses are replaced as follows: 

Five, six, seven, eight - Tired at the dreamland gate.

Nine, ten and eleven - Sleeping in the number heaven.

Twelve, thirteen and fourteen - Sleeping babies have you seen.

Fifteen up to twentyone - Dreaming baby sleep is done.

Twentytwo to hundredtwo - Baby I will care for you.

Hundredthree to thousendfive - Caring for you all your life.

Thousandsix to millionthree - Of your dream you can break free.

Millionfour to one googol - Dreaming of a giant ball.

Googol-one to googolplex - Steaming in the dreamland tracks.

Googolplex to infinity - I will always care for thee.

I get slower during the song and very slow with infinity - mostly they slept then.

I have dreams of this song where sheep accumulate to larger and larger blocks until the block number thats raising in blocks and everything ends in white noise.

I do no longer sing it to my older sons but they accompany me sometimes when singing it to my youngest (two years old). And they do know what googol means already.

I also have a bed ritual where I let them give the number of times I put the blanket on their face (they like it). When they give too large numbers I use blocks. These tended to get high too.

One time I asked for lower numbers (that was when my second oldest already knew halfs and quarters) which led to gaming for unusual fractions and ultimately to his insight that "There is no larger fraction than one half that can divide one" (by a seven year himself).

It seems to have put numbers so deeply in their mind and interest that my seven year old can do simple fractions, exponentials and roots in his head. I tried hard to avoid too much arithmetic before school lest they bore of math in school and that worked for his older brother (who nonetheless tops his class in math) but he just asks and asks and I have just given up and keep just answering his questions and posing comparable return questions at his Zone Of Proximal Development.    

There are dialogs that run like this (contracted):

He: "In school we had to give tasks to get 50. I was allowed to give 5*10"   

Me: "Can you give some other examples?"

He: "2*20+10" thinking a bit "20 time 2 and a half equals 50"

Me: "What about division?"

He: "100 divided by 2 obviously. Or 50/1."


Me: "How long is the side of a cube containing one litre?"

He: "10?" (omitting centimeters)

Me: "How do you know that?"

He: "You have told me." (*I* can't remember when; must be month's)

Me: "And how long is the side of a cube with 27 liters?"

He (dividing 27 then adding or something like that): "18,5?"

Me: "No. How did you get there?"

He: "There must be some number multiplied to get 27" (or something like that)

Me. "Yes, the side time the side times the side." (expecting him to try some numbers)

He: "What is the root of 27?" (he has picked up that root is the reverse of times the same number)

Me: "Good idea. Here whe have three times or a number to the 3rd power - so we need the 3rd root." 

He: "And what is the third root or 27?"

Me: "Try it."

He: "2*2*2 equals 16 no 8" (he seems to remember a few powers of 2)

Me: "Yes. That is too small"

He: "5^3? 5*5*5?"

Me: "That is 125 - too large"

He: "3?"

Me: "Yes."


He: "What is 10*10*10*10*10?" 

Me: "You mean 10 to the 5th power? That's hundred thousand"

He: "What 10*10*... [lots of 10s)?"

Me: "You mean 10 to the 30th power? Thats nonillion."

He: "What is 10 to the 100th power?"

Me: "That is called googol. A 1 with 100 zeros."

He: "What is 10^100^100^100?"

Me: "Do you mean 10^100 and that to the 100th power or 10 to the 100^100th power?"

He: Somehwat confused asks differnt questions, dialog levels off.

(note that in German "to the xth power" is simply "hoch" thus much easier to concatenate)

I have to say that I am quite proud of my children and wouldn't be surprised when you called me overly so. I have to add that we, my wife and I, invest significant time into our children, so just singing this song may not be enough. And it also may be that I was lucky that they are (partly) gifted with math (like me). But I have to emphasize that we did no rote memoization or repeated training whatsoever (and left that to school).

There are other things we do for 'rationalist training' which I will try to post some time soon.  


- Bed time stories with complex patterns (endless stories, simply nested stories, parallel stories, forking stories).

- Everyday Experiments for young children.

Note 1: I place the lullaby under creative commons as checked below. You may adapt and I recommend finding better rhymes/meter.

Note 2: This is my first real post here. Please feel free to tell if you think it inappropriate, too long or too much showing my probable pride. 

EDIT: fixed typos.
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Reminds me of one of my favorite quotes from the quotes thread.

At home there was a game that all the parents played with their children. It was called, What Did You See? Mara was about Dann’s age when she was first called into her father’s room one evening, where he sat in his big carved and coloured chair. He said to her, ‘And now we are going to play a game. What was the thing you liked best today?’

At first she chattered: ‘I played with my cousin . . . I was out with Shera in the garden . . . I made a stone house.’ And then he had said, ‘Tell me about the house.’ And she said, ‘I made a house of the stones that come from the river bed.’ And he said, ‘Now tell me about the stones.’ And she said, ‘They were mostly smooth stones, but some were sharp and had different shapes.’ ‘Tell me what the stones looked like, what colour they were, what did they feel like.’

And by the time the game ended she knew why some stones were smooth and some sharp and why they were different colours, some cracked, some so small they were almost sand. She knew how rivers rolled stones along and how some of them came from far away. She knew that the river had once been twice as wide as it was now. There seemed no end to what she knew, and yet her father had not told her much, but kept asking questions so she found the answers in herself. Like, ‘Why do you think some stones are smooth and round and some still sharp?’ And she thought and replied, ‘Some have been in the water a long time, rubbing against other stones, and some have only just been broken off bigger stones.’ Every evening, either her father or her mother called her in for What Did You See? She loved it. During the day, playing outside or with her toys, alone or with other children, she found herself thinking, Now notice what you are doing, so you can tell them tonight what you saw.

She had thought that the game did not change; but then one evening she was there when her little brother was first asked, What Did You See? and she knew just how much the game had changed for her. Because now it was not just What Did You See? but: What were you thinking? What made you think that? Are you sure that thought is true?

When she became seven, not long ago, and it was time for school, she was in a room with about twenty children – all from her family or from the Big Family – and the teacher, her mother’s sister, said, ‘And now the game: What Did You See?’

Most of the children had played the game since they were tiny; but some had not, and they were pitied by the ones that had, for they did not notice much and were often silent when the others said, ‘I saw . . .’, whatever it was. Mara was at first upset that this game played with so many at once was simpler, more babyish, than when she was with her parents. It was like going right back to the earliest stages of the game: ‘What did you see?’ ‘I saw a bird.’ ‘What kind of a bird?’ ‘It was black and white and had a yellow beak.’ ‘What shape of beak? Why do you think the beak is shaped like that?’

Then she saw what she was supposed to be understanding: Why did one child see this and the other that? Why did it sometimes need several children to see everything about a stone or a bird or a person?

Doris Lessing, "Mara and Dann"

Sounds a bit like the What do you see games that we play. And a bit like the Why-game (which always in the end leads to "because of physics" or "because somebody wants it"). But not all games work for all children.


And a bit like the Why-game (which always in the end leads to "because of physics" or "because somebody wants it").

I don't personally have children and don't know how much they are capable of understanding these things or being interested in it anymore, but I still have to ask - is there any particular reason why you have to stop at that point? Those sound more like semantic stop signs EY has talked about, and not real explanations. For example, you could still try to explain why people generally want these things in certain situations maybe even using cognitive science and psychology as help.

I have thought that if I ever have children and they ask me these "why" questions and I have some spare time, I will continue to answer until the child is not interested in doing it anymore, all the way down to quarks, probability arrows or whatever. Actually I'd love to do it. If I don't know much about some subject, I could learn more about it myself from books or the internet and it'd be pretty cool even if the kid was asking just for the sake of it.

Oh I didn't stop at "because people want it" on the first round. I did continue answering that people feel this and that way. But you cannot explain psychology too deeply to a five year old - there is just not enough terminology you can build on (and using to detached words will not do). So you are bound to appeal to empathy (which children have) and the second time around the answer is really "don't you feel that way too?".

As for the physics. The answer is not litereally "physics" but physics at a level where you also have no more words you can build on. There is a point where analogy to waves can get you only so far. Sure sometime the correct terminology has to be used. And a why game can be such a point. But then this really leaves the "and why that" chain and goes into story mode or experiment mode or physical phenomenon mode.

There is a difference between saying "because that's just how it is" (semantic stop sign) and saying "because of reasons that you can't understand yet, but will when you grow up". How do you make sure you are saying the second, and do you think your children understand that?

Because I do not really stop at that point. I may stop in the chain of a why game. But the topics will come up again and again in different locations. For example when my sons ask how many is "million times million times million times million" I will not just answer "septillion" (*) but e.g. try to illustrate this with an example like "water particles within a spoonful of water". Or if we heat sugar in a pan to make caramel I might note that the sugar partical hpentagons break up or form new structures. Or if we speak about respiration I will (building on oxidaition in fire) to explain that the lung equalizes oxygen and CO2 levels of air and blood.

  • Note that in German this is "Quadrillion" nicely verbalizing exponentiation via 'quad'='four' times multiplication of million.

Now I'm venturing into off-topic territory, but:

Note that in German this is "Quadrillion" nicely verbalizing exponentiation via 'quad'='four' times multiplication of million.

I didn't know that. German is my own native language (and AFAIK many others work the same). I'm not very good with large numbers (I usually count them: "million, milliard, billion, billiard..."), so that helps.

It is easy. For example Avogadros number is roughly 10^-24 (for the purpose of estimating numbers of particles in natural phenomena) thus 24=4∙6 thus million^4 thus "Quadrillion" in German. And one googol is 10^100 and 100 = 16∙6+3+1 thus 10 "Sedezilliarden" (from 16=sedecem) albeit all this doesn't work in English at least not so easily.

Eventually you do need to come to a stop sign, because you shouldn't always ask 'why' one more time even though you could.

Once you've gotten down to bedrock physics seems like a good time to stop. There are better wordings than the one you provided.

Incidentally, while I love that quote (and used the game in my MLP fanfiction), the book it comes from is not one I'd recommend.

I'm also not sure how empirically valid it is (i.e. does asking this game actually make the children more curious and perceptive?), and am not sure what balance parents should strike between questions and answers. Other stories of childhood development seem to focus on parents always surprising their children with new things to notice and think about; the example that comes to mind is Feynman's father often bringing things to his attention, and a question game may be suboptimal for that goal.

This method of asking children to remember and describe their experiences has long traditions and was praised by Charlotte Mason in her Home education series (link to the whole text). Charlotte Mason considered this a great way to teach children perceptiveness and excercise their recall, as well as provide information about the environment (compare volume 1 pages 46-52).

Though her pedagogy is sometimes laughably wrong (blame the state of knowledge about human body and development in late 18th century) it is still generally relevant and, in consequence, popular among homeschoolers (a quick google search will confirm).

If you take into account that by asking questions you focus on some areas of development but not on others, then Feynman senior's method might be a good complement to it.

Now that you mention Feynman I recollect that I actually used one of the games/stories from Feynmans autobiography for my children: A story of some very small dwarfs that wandered thru a strange land of regular red and blue trees: Ants on a carpet. It was very interesting for my second son who has a very high interest in plants and animals and who after I told the story took his pocket microscope and looked at the capet and said: 'it looks like grass'.

I have edited your title to "Raising numerate children" since numeracy, rather than general rationality, is the subject of your post. You are welcome to edit the title again, but more specific titles are usually better.

Yes. I agree. I initially wrote a much longer post that included more (unfinished) aspects which are more clearly associated with rationality. When shortening I kept focus on 'numbers' because that gave a uniform picture and a kind of story arc. I just hinted at these aspects with the lookout at the end. But I see this as part of a larger picture where numeracy is one part of rationality. You can't have rationality without numeracy or can you? And for me numeracy was the first step toward rationality. For me it really was an important part with an aha insight about continuous functions. I already started to move my sons from numbers to functions. Functions representing states in the world (e.g. a smart five year old can use numbers to quantify how happy he is). I want to write further posts that will follow up on this. I wonder if there is some way to bind these posts together under the heading "How do you raise a child as a rationalist?"

I was wondering about that-- avoiding "because I said so" is probably as important as math skills.


it also may be that I was lucky that they are (partly) gifted with math (like me).

Peer reviewed papers suggesting math skills are inherited:

Peer reviewed paper suggesting how parents discuss math influences child math skills:

Jean Piaget had so many American parents ask him how to accelerate their child's development that he came to call this "the American question." I do not think Gunnar is an American, but I believe it is the American question being asked here. I do not know Gunnar or his children, and the only general statement I can make about them is it appears he is a good parent and has clever children.

The question of the subject is too dense and should be partitioned. Some ideas for auxiliary questions:

  • Do there exists attempts at classifications of parenting styles? (So that we may not re-invent tread tracks)

  • Is parenting or childrearing an activity that supports the existence of relevant goals? Do there exist relevant values? Or is parenting better approached as a passive activity sans evaluation with no winners or losers? (So that we may affirm this question is worth answering)

  • Given affirmative answers to the above questions (and having achieved some epistemic rationality in this domain), and assuming a choice of parenting style(s) and/or values, what specific steps can be taken to activate those values in meatspace (so that we may gain instrumental rationality in this domain)?

  • The above kind of direct onslaught will likely lead to overzealous suggestion, so we can also consider stepping back and asking: what are some strategies for generating candidate actions without concurrently assuming premature preferences? [1]

  • Potential answers to the above queries will always be accompanied with degrees of uncertainty. How do we determine when to stop researching and move towards implementation? How does the domain of parenting differ here from the general solution (productivity / to-do systems like GTD or strategical thinking )?

  • Are there tangible contributions that can be made in the general case? If we went through this much work and make significant progress in answering some of these questions, and we have been surprised by some of the answers, is it our duty to make an attempt to inform other parents? What are the best ways of doing so? Joining a local club or school district assembly? A blog? Submitting to an editorial? Your lullaby above is wonderful and could make some serious universe-changing modifications to reality (e.g., a child grows up to assume a mathematical or scientific vocation) but we do not feel the wailing alarm in our head that assigns it the appropriate significance. Effective parenting is one of the most accessible optimization processes Joe Schmoe has access to, so how can we make meta-improvements on a large scale?

If you are serious in your attempt to answer the original query, I recommend selecting one of the above questions or something even finer-grained and re-submitting to Discussion. (By the way, I am interested.)

[1] Say that a naive answer is the banal "brainstorm," to make a list of relevant large-scale projects to relevant values (e.g., figure out a consistent system of reminding my kids to be compassionate to those around them (name 3 examples of specific compassionate actions) if we value empathy and mindfulness). Then a follow-up question is to locate where your candidate actions are in behaviorspace for this domain: collate several "brainstorm" lists by independent parents who seem to have similar values and styles. Are there academic resources? Potential analytics to be done? Are there quantitive variables that correlate to success? Can we data-mine historical sources over these variables? (e.g., if we are determining whether to raise kids vegetarian or omnivore, what do long-term studies in the literature say about follow-up health?)

Our parenting bibliography (sorry for most of it in German; I tried to find corresponding english ones but got few):

Each one starts with a line with the following ratings:

1) applicable age (for which age we do consult these books) 2) practical tips (P0: none; P++: many good tips) 3) theoretical/philosphical explanations (P0: none; P++; proper scientific research) 4) my personal recommendation (P0: do not use; P++: highly recommended) "?" means I don't known because only my wife read the book

0-1.5;+;+;+ Oje ich wachse, Hetty van de Rijt et al English: The Wonder Weeks

0-1;++;?;0 Spiele für alle fünf Sinne, Karin Mönkemeyer

0-6;P++;?;R0 Fingerspiele und andere Kinkerlitzchen: Spiel-Lust mit kleinen Kindern von Raimund Pousset

0-25;P+;T+;R+ Spielzeugland, Verbrauchenzentrale

1-3;?;?;? Kinderspiele, BZgA

1-10;?;?;? Spiele mit kleinen Kindern und Babys, Münchmeier

1-18;P+;T0;R+ Knaurs Spielebuch, Johanna Preetorius Note: Our editions is the original edition of 1968 which contains lots of old childrens games.

3-10;P++;T+;R+ Was Jungen brauchen: Das Kleine-Kerle-Coaching, von Alexander Bentheim und Monika Murphy-Witt

3-7;P+;T+;? Spielerische Sprachförderung von Gabriele Fischer, Christine Langner und Ursula Schlieter

3-14;P+;T0;? Das große Ravensburger Natur-Spielebuch: Über 190 Spiele für Kinder von Uli Geißler und Birgit Rieger

0-6;?,?,? Lieben, lachen und erziehen in den ersten sechs Lebensjahren von Steve Biddulph und Shaaron Biddulph English: Complete Secrets of Happy Children: A Guide for Parents

11-16;P+;?;? So macht lernen Spaß, Wolfgang Endres

5-11;P++;T0;R+ Die 50 besten Spiele fürs Selbstbewusstsein von Rosemarie Portmann

5-11;P++;T0;R+ Die 50 besten Spiele für mehr Sozialkompetenz von Rosemarie Portmann

5-11;P+;T0;R0 Die 50 besten Spiele rund um Zahlen von Rosemarie Portmann

5-15;P+;T?;R? Verrückt spielen, W. Kobl

5-16;P++;T0;R++ Ravensburger Gartenbuch für Kinder. Kleine Gärten im Zimmer, auf dem Balkon und im Freien von Diana Simmons und Elinor

6-13;P++;T+;R++ Denk dir die Welt: Philosophie für Kinder von Brigitte Labbé, Michel Puech, Jacques Azam und Anne Braun

8-25;P++;?;? Spielen Denken Lernen. Duelle auf dem Papier von Walter Diem

6-10;P+;T+;R++ Kinder können mehr. Anders lernen in der Grundschule von Fee Czisch

9-16;P++;T0;R++ Wie man einem Außeririschen begegnet, ein Floß baut und in der Wildnis überlebt ..., von Johnny Wilkens

7;P+;T++;R+ Weltwissen der Siebenjährigen: Wie Kinder die Welt entdecken können von Donata Elschenbroich

5-16;P0;T++;R+ Das kompetente Kind von Jesper Juul und Sigrid Engeler English: Your Competent Child: Toward A New Paradigm In Parenting And Education

4-14;P0;T++;R0 (outdated) Die Entwicklung des Zahlbegriffs beim Kinde von Jean Piaget und Alina Szeminska (1972) English: Child's Conception Of Number by Piaget Jean

0-3;P+;T+;R+ Warum Babys weinen: Die Gefühle von Kleinkindern von Aletha J. Solter und Karin Petersen

3-14;P+;T+;R++ Leitfaden für faule Eltern von Tom Hodgkinson und Heike Steffen English: The Idle Parent: Why Laid-Back Parents Raise Happier and Healthier Kid

8-12;P+;T++;R+ Praktisches Philosophieren mit Kindern: Konzepte, Methoden, Beispiele von Thomas Ebers und Markus Melchers

(somewhat incomplete; these are the ones I found in our shelves today)

Though I do not raise children, nor plan to do so in the near future, but plan to in the far future, would you be willing to make a lukeprog-style main post about parenting for rationalists? The bibliography is already there. I know that "parenting" is a mind-bogglingly large field but you could focus on seperate aspects as defined by age or subject.

In time I may. For now I will continue with short pieces to get a feel for the expectations and style. These can be wrapped up or restructured later. Or is that discouraged? The 'bibliography' is really not as deep as it looks. Most of the books listed are parent guide books which are often shallow on theory. I posted the list to show that I did my homework and as recommendations for other parents.

Wow. That is not a comment but a post in it's own right. I'm somewhat blown away of what to make out of it.

I will try to address the raised points:

1) Our approach to parenting can be classified as authorative/propagative (according to Baumrind's Three Parenting Styles) but with a non-extreme damand level. It is rather not Concerted Cultivation (which in our opinion puts to much pressure on the child and has it's own inefficiencies (and doesn't really lead to rationality). Instead we rather fall into the Natural Growth pattern. We didn't invent most of the methods we apply. You could say that we did a meta study on parenting and took the best of it. I will provide a parenting bibliography below. The lullaby is my own invention, but singing lullabies is one recommended method, as is reading and discussing bed time stories. Teaching via dialog of wuestion and answer is also a traditional teaching method going back to Socrates I believe

2) Is parenting a no-win activity? I'm not sure what this is diving at. I wonder if this takes the view that parenting and education should be left to specialists and that doing parenting oneself is inefficient any way it is done. Even if that may be true on average there are the following exceptions (some of which apply to our case):

  • Availability of professional care (we do use a wood kindergarten for outdoor, musical and social education)
  • Trust into the quality of professional care (compared to the alternatives)
  • Personal preferrence (our utility functions rank high on affection to our children)
  • Personal experience (my wife is a teacher)

3) I though much about 1) even before we had children and we compared multiple options regarding 2). Otherwise I'm not sure what to make out of this paragraph.

4) If with 'onslaught' my intense advancement of numeracy is meant, then I have to assume that you imply that I am jumping to conclusions by proposing my specific parenting style as a general model.
I do not. I recount personal experience. You could call my post an opinion piece. But I have to stress that this specific style results from very careful and long time planning, continuous adjustment, success control and it is even controlled in so far as we have basically 'run' the same 'program' with all our four sons so far. And it appears to be successful for all of them (if one can say that of 2 and 5 year olds).

5) When to move to implementation? I goess this is meant as a question for non-parents. For parents the point is usually the birth. And I can assure you that my wife has run this program with her usual productivity scheme she uses for all 'tasks'.

6) The tangible contributions I am just making, or am I? I was pleasantly surprised by our success. I was prepared to see more or less average achievement by my sons due to regression toward the mean (but I cannot completely rule out filtered awareness due to parental pride). And beside 'success' on some popular measureables like IQ or grades I see that my children are healthy, balanced and happy. Our parenting method gives us concrete positive feedback and I assume that it helps making us happy too.

Speaking of "nested stories", I remember I had a brain-shaking time as a kid the first time I read the Neverending Story and realized I was a boy reading a book in which a boy was reading book that spoke about boy reading books/imagining stuff. It was awesome and I think it's a good preparation to reading "Gödel, Escher, Bach".

Apparently there is a bedtime math movement which tries to promote this approach. There is a book and a study shows this to be very successful (sample size 587).

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Googling for 'numerate children' actually turns up an optimum hit:

Key messages

  • pre-school children's experience of number is not always built upon when they come to school.
  • Counting is an effective basis for the early years number curriculum.
  • Young children can use isiosyncratic symbols to record small numbers but standard numerals are more helpful in solving problems.


  • The knowledge that children bring to school needs to be built upon.
  • Children need experience of counting in a variety of social contexts.
  • Young children need to feel free to use a variety of ways including conventional numerical symbols to support simple problem solving.