# Encounters

By cjohnson | October 18, 2005 5:36 pm

I was sitting on the bus this morning while it took me to work, and I was working out a computation on the back of the paper I’m editing, scribbling furiously, pausing every now and again to look around at the people. In other words, one of my usual morning activities….

I look up at one point to see a little African-American girl in a cute bobble-hat (I’m guessing she was about 6, or 7?) carrying a pencil and a large notepad, sit down next to me. When I look up again, she’s continuing whatever it was she was doing when she got on the bus wth her mom (sitting elsewhere) – she’s doing a computation! She writes (in really large, confident, pencil marks):

25 x 10 = 250

Then she thinks for a bit and writes:

29 x 10 = 290

Then she looks at what I’m writing for a moment or two, then turns back to her own (obviously more interesting) work and thinks for a bit more and writes:

24 x 10 = 240

At this point I’m feeling a bit self-conscious but very pleased about the picture the two of us must make, sitting at the back of the bus heads down calculating. I carry on. So does she. I notice after a while (I’ve got the corner-of-my-eye thing down to a fine art in case you’re wondering) that she’s decided that her multiplications need no further sharpening (or whatever she was doing) and turns to a new page and starts drawing a flower.

So now I’m frantically thinking of something to do to bring her back to the mathematics. (Nothing wrong with drawing a flower, but so much more unusual to see little girls absorbed in mathematics on their own like that) My stop’s coming up, so trying to start doing a silent reply to her work on my own page (perhaps a series of multiplications by 100?) -which would probably work eventually- would not work in time. Then I turn over my work to reveal a page which had one the paper’s figures on it. Her eyes flicker over to it for a moment and I see my chance. I tear out a square with the figure on the right on it and give it to her. Our silence is broken for the first time with a little “thank you” from her.

She immediately turns it over to the blank side and starts doing more multiplications by 10 on it.

My stop is really coming up now and so I just have to hope that she’ll eventually turn it back over and find something interesting about the other side. When I gave it to her, I was hoping she might have noticed how interesting it is that the curves all go through the same point. As I’m about to retrieve my bike from under our seat, she turns the square back over and asks me what she should do with it. So I point out the feature of the common point. So she says “oh, there are seven of them” and promptly draws a set of seven curves near the old ones, also decaying to the right, but now all going through the number 2!

* * *

Sorry if this is boring to you, but I just thought that was great! It really made my day, in fact. I’ve no idea what (if anything) will come of our encounter, and will not pin any great hopes on it, but it certainly is one of my favourite public transport conversations of all time….

-cvj

• Moshe

Really lovely story Clifford. Did she purposefully sit next to you and started imitating, or was it coincidental?

(also, now you are ready for all the proud stories about my daughter, not all of which involve bowel movements)

• citrine

Cute story, Clifford! It makes *my* day. Hopefully, she will continue to pursue Math (and Art, too) with the same enthusiasm the rest of her life!

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Thanks guys!

I think it was just accidental. Rather full bus, not many places to choose from. Also, it would be hard to see from far away that I was writing unless I was holding it up high, which I was not.

Cheers,

-cvj

• http://motls.blogspot.com/ LuboÅ¡ Motl

And after 2 more minutes, she wrote 31 x 16 = 496 and Tr(F^6) = C.Tr(F^2).Tr(F^4) for SO(32). Then she decided that her anomaly cancellation was perfect enough and she returned to her blog with Shakespeare.

• erc

That is really sweet.

When I was studying for my A-levels I baby-sat a lot, and there was one little girl who was just starting school and loved her work. Her mother bought extra work books for her, and she would always make sure she had something to do when I was there. Once her little brother was in bed, we’d both sit at the table, and get out our books. She would do hers (addition, multiplication etc), and I’d do mine (maths, physics, chemistry), and then we’d compare. I would show her what I was doing, and then explain what it meant – that I was working out how fast something would move if you threw it so hard, or that everything was made of tiny particles that were too small to see etc. I never knew how much she understood of course, but she was fascinated. She was the easiest child I ever had to look after.

• ljs

very sweet clifford! i assume this is why you love what you do! to capture the innocence of a child or anyone else and possibly change the course of their lives through education.

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Yes, Lubos, I made that joke to myself too…I did consider showing her some multiplications of some interesting numbers, (and definitely decided against showing her that the sum of all integers from 1 to infinity is in fact -1/12) but there was just not enough time….

ljs, I would not be so presumptious as to be wanting to “change the course” of anyone’s life, but if I can help someone realize that it’s ok to sit on a bus (or anywhere) and do their mathematics, who knows what they’ll realise it’s ok to do? Run for president? Become a scientist? Teacher?

erc, maybe that kid went on and continued to study maths, and maybe is doing science now…great!

I also like the idea that one day maybe 5 or maybe 20 or 40 years from now she’ll be searching the web and find this blog and this post and remember the encounter… and during her acceptance speech for her Fields Medal or Nobel prize she’ll wonder what happened to that guy….

-cvj

• Sam Gralla

I used to do calculations on the schoolbus! I remember one day particularly where I made a spectacular derivation: a “superformula” which gave the y(x) equation for a line in terms of the cartesian coordinates of two points that defined it! I showed it to Emily Chi, who I always sat next to on the ride home, and she was impressed. I had lots of fun doing math with Emily Chi. That is, until she discovered boys were more fun, anyway 😛

(Emily, are you out there?)

• http://www.3quarksdaily.com Josh Smith

That’s got to be one of the best things I’ve read in a long time. I mean, I browse the internet a lot, and there have been a lot of interesting reads lately. But by no means was that boring. Rather inspiring.

That’s what Idiot America really needs. Thanks for doing what you did.

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Josh. Thanks!

-cvj

• http://www.pyracantha.com Pyracantha

This reminds me of one of my favorite passages from Leon Lederman’s THE GOD PARTICLE (Delta Paperbacks, New York 1993). On page 382 Lederman recounts this story:

“…Of course, there are those bright moments when people surprise you. Several years ago, on Manhattan’s IRT subway, an elderly man sweating over an elementary calculus problem in his textbook turned in desperation to the stranger sitting next to him, asking if he knew any calculus. The stranger nodded yes, and proceeded to solve the man’s problem for him. Of course, it’s not every day that an old man studies calculus next to the Nobel-prize-winning theoretical physicist T.D. Lee on the subway.”

I hope that perhaps I could be (like) that old man someday.

• http://xenobiology.blogspot.com indrax

Awesome!

Maybe someday you’ll be watching the Nobel acceptance speech and the winer will tell a story that happened to her on a bus as a child.

• jprime

Why did you feel obliged to note that she was African-American? I mean, if she was white, would you have still blogged it and felt the same way?

Your intentions may be the best, but it still amount to judging someone by the color of their skin…or gender.

• Richard

Not boring at all! This is by far the most uplifting thing I’ve heard all day. I think that even small interactions with kids like this can be very positive for them, and it’s fun for us to watch those light bulbs light up in the their brains.

A few months ago I saw my seven year old niece for the first time almost two years. Out to dinner with the family, the kids were solving mazes before the food arrived. I pointed out the obvious path in a maze, but she thought it too trivial, and said she wanted to find a non-trivial solution, and proceeded to do it very quickly. I thought to myself “hmmmmm,” and felt delighted the rest of the evening.

• Herb

jprime,

probably for the same reason that he felt obligated to mention the bobbie-hat…

But for me, the story is BETTER because the child was black and female – these are two groups who are typically not encouraged to exceed in math.

• Sam Gralla

jprime: because african-americans are statistically less likely to have parents that will encourage interest in mathematics; because african-americans have very few professional examples to encourage them that they can do mathematics; because most of the country although it doesn’t admit it still looks at african americans and thinks “not smart, at least not left-brain smart”; because most of the USC campus assumes Clifford (who is black) is a student even though he dresses and acts like a proefssor.

In other words, because african americans face adversity. And seeing the genuine interests of a little girl blossom over that adversity is, well, inspiring.

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

jprime. I made no judgement of anyone. (If I missed it, pleaase point it out to me.) I just reported what I saw. As Herb pointed out (thanks Herb), and as noted in other places on this blog, two of the groups that are repeatedly told by society that they are not supposed to be able to do mathematical subjects are women and black people. Actually, I belong to the latter group, am still implicitly and sometimes explicitly being told that I’m not supposed to be able to do this, and so I know what I’m talking about. So jprime, it is important to me that she was African-American, and at that age when she has not started to be told by society that she’s not suppposed to be able to do this, or that she should be embarrased to be seen “thinking” and “doing school work” in public (such as on a bus) because it’s “geeky”, “nerdy” or “not cool”.

Best,

-cvj

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Sam Gralla,

Thanks for helping to make the point. Saw your comment after doing the one above.

-cvj

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

jprime: Sorry, I forgot your other question:

Because children in general suffer from being told that it is not cool to be interested in things like that, I would have blogged about it if she were neither female nor black. I would have blogged about it were she an adult too. Of any gender or race. Because society also sends adults that message too. Also, I would have blogged about it if they turned out to be a fellow scientist too, since it would be nice to make a connection with a stranger over maths and science, as opposed to the usual….. Sport, or Britney Spears, or…. (not that there’s anything wrong with those…)

Cheers, and thanks for asking, because it’s an important issue I care deeply about.

-cvj

• janet

Great story. For a child, simply having an adult notice what you’re doing and take it seriously can be a big deal.

Cool story.

Every now and then my younger brother asks me a math/physics question, at which point i have to try really hard not to drown him with too many pieces of information.

What is with physicists and trying to encourage others to learn these things?! (my guess is that we know what they’re missing out on ;-P).

Truely lovely story! I really enjoyed it.

Hopefully she could continue to love math (and all the beutiful things around her).

It’s times like that which add sparkle to our lives, isn’t it? They are also good moments to hold onto when someone else comes along and says something to bring you down. She may not explicitly remember that encounter, but maybe she’ll remember that someone else was doing fancy math, and that maybe it’s okay to study it.

• the one Intelligently designed

Realy lovely and cute story

• http://wearestillhere.blogspot.com Claire

what a lovely story!

• http://eskesthai.blogspot.com/2005/09/cft-and-tomato-soup-can.html Plato
• http://ofteninerror.blogspot.com/ Urbano

Very nice! I really liked it!!! Congratulations for this piece of writing!

• Lee

I think it’s especially important that you took her efforts so seriously. Too often, I see adults treat young children condescendingly when it comes to their academic pursuits. Of course, the numbers she was writing were elementary multiplication problems that most any adult, much less a professor of physics at USC, would know. Yet, too many times, the response to the child, either verbally or by manner, would have been, “Oh, that’s so obvious” when to the child, it is a big deal that she’s learned that much. And, I don’t believe that people are encouraged to learn more about anything when their efforts are so disparaged.

Instead, you responded by attempting to encourage her inquisitiveness by providing her with something that was reasonably designed to pique her interest. She may or may not follow up on that diagram, but I have a feeling she probably appreciated the way you treated her. And, maybe she left with the impression that academic pursuits of any type are not as geeky as she might have thought before she boarded that bus.

• ed hessler

Ah, such moments; sometimes they are the very essence of life distilled down. These experiences are a gift in receiving and in hearing. I loved imagining the two of you doing your maths, each no doubt encouraging the other as well as knowing that the other was a learner, too.

There was a wonderful Australian/New Zealand (?)teacher, Sylvia Ashton-Warner, who started each day with a word bigger than many of us would think kids interested in, alas, capable of, but she had learned that kids like such “power” words, learning what they mean and feeling them roll off their tongues. I’m reminded of Henry McPhail’s wonderful book for very young “to be read to’s,” titled “Henry Bear’s Park.” Henry’s Dad was no mere balloonist; he was an “ascensionist.”

• Quibbler

that’s a great story.

there were a few people in my childhood and adolescence who caused me to realise that science/math could be both interesting as well as aesthetically elegant; and generally these realisations took the form of seemingly “little” occurences such as your bus ride, but they certainly made a difference to me.

the approach makes a huge difference. very often the approach is “that’s obvious”, as Lee said. but girls and underrepresented ethnic groups often don’t even get that attitude. instead, they’re being interested in math/science is treated as “cute” but in a patronising way, rather than an endearing way.

thansk for posting this, Clifford. made my day.

–Q

• http://arunsmusings.blogspot.com Arun

The world may not be magic and there may not be any ineffable mysteries; nevertheless we cannot know what we might wish to know, such as what is going on in a little girl’s head, and what might come of a chance meeting in a bus.

• http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

Very nice story. Kids are naturally interested, we just have to feed the interest rather than scaring them off or boring them to tears. I remember my first intro to Pythagoras’s theorem — an eye-opener.

But Clifford, don’t you carry around signed copies of D-Branes to hand out on just such occasions?

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Hmmm, interesting idea there. Bit heavy to tote around though…..
-cvj

• http://blogs.discovermagazine.com/cosmicvariance/joanne/ JoAnne

Indeed, these small things can make a huge difference to a child. I distinctly remember when my father’s cousin taught me (at an early age) the powers of 2: 2, 4, 8, 16, 32, 64, etc. I grasped it immediately and was thrilled beyond belief. I made a point of rattling it off to my friends (geesh, I must have looked like a total geek!). She was the only relative who bothered to teach such facts, and perhaps it stands out that she was a *she*.

• robert

Tales like yours always lift the spirits. I’ve a couple, more or less in the same vein. The first is of a colleague who was reviewing a laptop animation of hydrodynamics results on a trans-Atlantic flight. In the next seat was a young boy who, after some minutes, chipped in with ‘Here mister, your game’s not that good is it, do you want to try one of mine’. And the other, of a wild child who dropped out from conventional education for a year or two, then decided to get back on track. I helped her out with a bit of math and science tuition. I remember her Eureka moment, when she realised that maths really did make contact with the real world. Four year’s on she contacted me, with a first class honours degree in econometrics and a ‘proper’ job in the bag. A happy ending? After one year she packed it all in to devote herself to the joys of surfing.

• citrine

Soon after reading Clifford’s post, I checked one of my credit card accounts online.

http://www.merrickbank.com/

When I saw the first pic after the Merrick Bank header, I couldn’t help smiling yet again, thinking of Clifford’s encounter.

• citrine

Oops. wrong url.
Here’s the right one.

https://logon.merrickbank.com/

• http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

Thanks Citrine! -cvj

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