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A Billion Vs a Killion

Ohlone Elementary is a school in Palo Alto with an amazing approach to imparting education. In mathematics, especially, I was struck by their insistence that we should not teach algorithms blindly to kids (carrys, borrows, etc.) I admit to being initially skeptical of this, until one day my suspicions were finally laid to rest. I wrote this letter to my son's teacher in appreciation.

Dear Ms XXX

Often when putting Panini to bed, we engage in a fun and silly game in
which we throw silly and ridiculous questions at each other and answer
them with similarly silly responses. Midway during this game last
night, after we had done due justice to his currently favorite themes
regarding the smallest spiders, greatest galaxies, biggest bombs and
the wealthiest people, Panini asked me ``Which is bigger, a billion or
a killion?'' I am ashamed to admit I was only half-attentive during
this ritual yesterday, being preoccupied with other things, and so I
said ``I don't know. 'Cos there is no such thing as a killion''.

To this Panini pressed ``Well if there IS such a thing as a killion,
then which is bigger?'' I said, again only half-thinkingly, ``I don't
think anyone knows the answer to this because no one knows how big a
killion is.''

At this point, Panini was silent for a few seconds and said ``I know
which is bigger.'' I thought we were still playing the silly game, of
course, and asked him how he could possibly know this, expecting an
equally silly response.

Panini replied ``Well, if you name all the numbers from one to a
billion, you'll see that a killion does not appear anywhere in the
list. And so...'' he continued unaware that he had already lost me to
astonishment, ``...a killion has to be bigger than a billion.'' My
total attention was suddenly brought down to earth in a riveting
realization of the simplicty and beauty of the argument he had just
advanced. He fell asleep soon afterwards, but I could not when I
tried to later. I don't know if you had taught this to him in class. But
even if that were the case, I was duly impressed with his apparent
appreciation of the problem. He had only said something of this
caliber once before which I had noted as a one-off occurrence, but
yesterday I felt that you would like to know of this too.

We know that you deemphasize the learning of algorithms in favor of
learning concepts and we try to support that at home whenever possible
by not sabotaging your efforts. Although we are sure that you are
confident of your methodology, I thought I would pass on this snippet
of an incident to you so you can rest further assured that whatever
you are doing seems to be working wonderfully. On occasions such as
this we feel rightfully relieved about our original decision to choose
Ohlone three years ago.

With grateful appreciation,

cc: Ms XXX, Principal


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Comments (3)

Very amusing, but how could panini outsmart you? :)

But what if killion is negative? hmmm?

Hi Alex,

Glad to see your comment! And a very good point (I mean the one about negative integers). Why don't you ask Panini yourself the next time you see him?



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