Something I Learned in Kindergarten

Fifty years ago today there was a six-year-old at a kindergarten (“nursery school” in British English) in Oxford, England who was walking under some trees and noticed that the patches of light under the trees didn’t look the same as usual. Curious, he looked up at the sun. It was bright, but he could see that one side of it seemed to be missing. And he realized that was why the patches of light looked odd.

He’d heard of eclipses. He didn’t really understand them. But he had the idea that that was what he was seeing. Excited, he told another kid about it. They hadn’t heard of eclipses. But he pointed out that the sun had a bite taken out of it. The other kid looked up. Perhaps the sun was too bright, but they looked away without noticing anything. Then the first kid tried another kid. And then another. None of them believed him about the eclipse and the bite taken out of the sun.

Of course, this is a story about me. And now I can find the eclipse by going to Wolfram|Alpha (or the Wolfram Language):

Eclipse 50 years ago

And, yes, it was fun to see my first eclipse (almost exactly 25 years later, I finally saw a total eclipse too). But my real takeaway from that day was about the world and about people. Even if you notice something as obvious as a bite taken out of the side of the sun, there’s no guarantee that you can convince anyone else that it’s there.

It’s been very helpful to me over the past fifty years to understand that. There’ve been so many times in my life in science, technology and business where things seemed as obvious to me as the bite taken out of the sun. And quite often it’s been easy to get other people to see them too. But sometimes they just don’t.

When they find out that people don’t agree with something that seems obvious to them, many people will just conclude that they’re the ones who are wrong. That even though it seems obvious to them, the “crowd” must be right, and they themselves must somehow be confused. Fifty years ago today I learned that wasn’t true. Perhaps it made me more obstinate, but I could list quite a few pieces of science and technology that I rather suspect wouldn’t exist today if it hadn’t been for that kindergarten experience of mine.

As I write this, I feel an urge to tell a few other stories—and lessons learned—from kindergarten. I should explain that I went to a kindergarten with lots of smart kids, mostly children of Oxford academics. They certainly seemed very bright to me at the time—and, interestingly, many of them have ended up having distinguished lives and careers.

In many ways, the kids were much brighter than most of the teachers. I remember one teacher with the curious theory that children’s minds were like elastic bands—and that if children learned too much, their minds would snap. Of course, those were the days when Bible Study was part of pretty much any school’s curriculum in the UK, and it was probably very annoying that I would come in every day and regale everyone with stories about dinosaurs and geology when the teacher just wanted people to learn Genesis stories.

I don’t think I was great at “doing what the other kids do”. When I was three years old, and first at school, there was a time when everyone was supposed to run around “like a bus” (I guess ignoring the fact that buses go on roads…). I didn’t want to do it, and just stood in one place. “Why aren’t you being a bus?”, the teacher asked. “Well, I am a lamp post”, I said. They seemed sufficiently taken aback by that response that they left me alone.

I learned an important lesson when I was about five, from another kid. We were supposed to be hammering nails into pieces of wood. Yes, in those days in the UK they let five-year-olds do that. Anyway, she had the hammer and said “Can you hold the nail? Trust me, I know what I’m doing.” Needless to say, she missed the nail. My thumb was black for several days. But it was a small price to pay for a terrific life lesson: just because someone claims to know what they’re talking about doesn’t mean they do. And nowadays, when I’m dealing with some expert who says “trust me, I know what I’m talking about”, I can’t help but have my mind wander back half a century to that moment just before the hammer fell. The individual involved in this story is now a very distinguished mathematician… presumably using much safer tools.

I’ll relate two more stories. The first one I’m not sure how I feel about now. It had to do with learning addition. Now, realistically, I have a good memory (which is perhaps obvious given that I’m writing about things that happened 50 years ago). So I could perfectly well have just memorized all my addition facts. But somehow I didn’t want to. And one day I noticed that if I put two rulers next to each other, I could make a little machine that would add for me—an “addition slide rule”. So whenever we were doing additions, I always “happened” to have two rulers on my desk. When it came to multiplication, I didn’t memorize that either—though in that case I discovered I could go far by knowing the single fact that 7×8=56—because that was the fact other kids didn’t know. (In the end, it took until I was in my forties before I’d finally learned every part of my multiplication table up to 12×12.) And as I look at Wolfram|Alpha and Mathematica and so on, and think about my addition slide rule, I’m reminded of the theory that people never really change….

My final story comes from around the same time as the eclipse. Back then, the UK used non-decimal currency: there were 12 pennies in a shilling, and 20 shillings in a pound. And one of the exercises for us kids was to do mixed-radix arithmetic with these things. I was very pleased with myself one day when I figured out that money didn’t have to work this way; that everything could be base 10 (well, I didn’t explicitly know the concept of base 10 yet). I told this to a teacher. They were a little confused, but said that currency had worked the same way for hundreds of years, and wasn’t going to change. A couple of years later, the UK announced it was going to decimalize its currency. (I suspect if it had waited longer it would still have non-decimal currency, and there would just be a big market for calculators that could compute with it.) I’ve kept this little incident with me all these years—as a reminder that things can change, even if they’ve been the way they are for a very long time. Oh, and again, that one shouldn’t necessarily believe what one’s told. But I guess that’s a theme….

Posted in: Life and Times



    I wonder how correlated these things are to your genetics VS your life experience… I also find myself much more biased towards creating a tool to solve a problem then to solve the immediate problem… I wonder if there are genes relating to that behavior…

    Daniel Bigham

    Hi Stephen, thanks for sharing these great insights, I will read this with both my boys, our entire family frequently stumbles upon the same problems you had during kindergarten and “school” life…when enabling abilities thanks to technology would be so much easier or simply play lampost instead…I have one dyslexic son who has such tremendous creative potential and a very abstract thinker who would notice the difference in reflection too, actually I believe both of my sons would , and my trouble is, that it is so hard to fight for environments which allow them to do so …because it is so hard to play with hammers these days…THANK YOU for all you do and are….


    Daniel, like your thinking I am wondering along the same lines, I believe that myself I always felt insulted by the questions I was asked to solve, they bored, each time I struggled to understand what was requested of me, before that I had done what I thought had been requested, which I really loved and learned with only to find out that what was asked of me had been a very simple thing, unenthralling, which did not leverage any of my skill or talent and did not bring me into a zone of optimal learning. Whilst I am the first to understand that “solving the problems we want to solve”, might impede on learning and limiting things, it still bring out real solutions to real problems in the right environment because it breeds the right attitude, whilst the “solving only what one can solve trap” has to be avoided…

    It still means that it can bring people on the way to “question the question, because how do we ensure we ask the right questions, the idea is to stretch our thinking into acting and doing whichever from that takes ie, a tool or a work of art inspired by the problem at hand. The issue arises if we ask kids to solve the immediate problem because they get a brownie point instead of letting them explore how they would like to solve this or where this could lead them…in their understanding sense making or learning…


    I too was given a hammer, nails, and wood to play with in kindergarten. About 45 years ago. (It is a humble thing to share with Stephen Wolfram.)

    Perhaps someday Dr. Wolfram could discuss the persistence of the hexagesimal system in timekeeping/geodesy/etc

    Vince Virgilio

    Stephen, I recognize the story of my life. At times I can’t help to feel a bit lonely as nobody in my immediate environment is really interesred in the things that intrigue me. Fortunately there is the Internet.

    Bert Morriën

    I too remember the wonderful strangeness of the shadows under a tree during an eclipse. Only after stopping and looking at the shadows’ moon shapes did I remember that a partial eclipse was supposed to be occurring that day.


    Great stories, and highlights something I’ve often be struck by: how seemingly “minor” events during our childhood can shape our attitudes in later life. I remember encountering a very sick-looking rabbit on a country walk one day in the 1960s and my mum explaining it was dying from myxomatosis, deliberately used by farmers to control rabbits. It made me question “scientific” attitudes to animals, and I went on to write a widely-cited paper questioning the evidential weight provided by animal models in toxicity testing.

    My own kids have related similar small events that changed their attitudes in a highly non-linear way (which may explain how one’s kids can end up with some beliefs radically different from our own!).

    Anyhow, tanks for the thought-provoking stories.


    I like reading scientific materials that sound like a cool story. As they are exciting they easily stick in my memory.


    Awesome! I like how Wolfram is able to read almost anything you type into it! Thanks! Also, I have a question: How can I place a Wolfram widget on my website?