[Edu-sig] Re: Now I went and did it
Sun, 8 Oct 2000 19:09:06 -0400
Art <email@example.com> wrote:
> the historical development - for many reasons. Among them - the best
> have of the history of civilization is through some understanding of a
> of geometry's development. I would go further and say that in many ways
> precisely the importance of geometry study - and the same was true in
> Euclid's time. Euclid was a summing up, and a history lesson in its time -
Not wishing to open any previous debates, but here are my 'coordinates' in
this fascinating topic. Hope it'll help us work better together...
I agree history is essential [my father was historian]
And history of science no less.
But I am not sure first introduction to subjects should begin with history
follow our present versions of that history. :::maybe, maybe not:::
Any subject, especially 'history' itself, cannot be understood without some
personal experiences to relate to.
For example, history as taught in schools, is hard to grasp even with a good
teacher, mostly because
as young creatures, we have not lived much ourselves.
On the day we are born, one day is a lifetime [in free air minus womb]
At the end of our first week our sense of time has already shifted
After six months our sleep wake eat rhythms have transformed from rhythm to
By ten years old we are very conscious of 'years' and somewhat of seasons.
But historical time is still so hard to relate to..
We are taught about this or that events in human history and 'important'
people or developments, and we really can't scale to them, nor in most cases
to the emotions, logic or conditions behind them. Novels and films are
easier to relate because they personalize, albeit at the expense of detail
or correct sequence.. which of course makes historians crazy, but can
provoke us to want to know more..
When we ourselves or someone near us is dying [at whatever age] then we can
say. "oh that's what a lifetime is.."
The most readable historians I know who embody some of this are Simon Schama
and Fernand Braudel.
A History of Britain : At the Edge of the World, 3500 B.C.-1603 A.D by Simon
Citizens : A Chronicle of the French Revolution by Simon Schama (March 1990)
The Embarrassment of Riches : An Interpretation of Dutch Culture in the
The Perspective of the World : Civilization and Capitalism 15th-18th Century
by Fernand Braudel
The Structures of Everyday Life : The Limits of the Possible
The Wheels of Commerce
In the case of Science, Math and Geometry, I believe much the same applies.
We have not yet much experience and we need help relating that to the
formal. The 'history' of geometry is not only Euclid. One must go much
further back and ask how did Euclid come to this strange juncture. We should
also ask what form his source code took. Our modern Euclid passed through
Arab, Renaissance, Enlightenment and Victorian interpretations before it
reached , Dover, McGraw-Hill or <insert your favorite publisher here>
Since the Library of Alexandria was destroyed we shall probably never know
what we are missing.
But we can imagine by asking from the earliest times what did these people
Navigators, sailors and travelers, constructors of ancient monuments,
merchants, farmers, fishermen, weavers, potters, artists, Geometers
themselves [the ones who measured
This is why I say start with string and sticks, pen and papers, balls and
as they say ...'think Egyptian..
String and sticks in the sand will allow a huge amount of interactive
geometry to emerge.
The basics of symbolic algebra follow 'naturally' from building things. If
you want to cut a piece of marble or wood to fit against another, the most
accurate way is hold up the first and make a mark. But it may be too heavy
to move and already carefully postioned.
The most portable way is use a stick [or string if you don't stretch it] and
make a mark or knot.
The use of measuring units only enters the picture when you get very
ambitious or start worrying about cost, time, having enough material etc.
Since we don't
even know by whom, or how Stonehenge and the Pyramids were built, we are
missing a big chunk of the history of geometry. Not too mention other parts
of Africa and Asia.
As a sometime carpenter in my early 20s I was so brainwashed by school and
rulers [and love of them], that it took me a couple of years of hands-on
work, to learn when NOT to use a tape measure - thus getting more accurate
faster.. The same applies for moving pianos and any large heavy object like
lengths of lumber.. carrying them precisely by the center of gravity etc..
My main argument is if you are going to the history do it deeply and
question the history we have been taught to find the real history. I think
in this way the lessons of the past become the experiences of today.
The computer allows to crate virtual simulators for all of this. But we
must not ignore the value of direct manual contact and our own senses. Thus
Dig for the experience of fundamentals and then reach for the brilliant
formalists [Euclid etc]
Other examples are to do with counting and relationship of number and
For example how to count a lot of small objects, how to measure and compare
These are the things humans have needed to do for perhaps 50,000 years.
A fabulous book which covers this from the earliest roots is:
The Universal History of Numbers : From Prehistory to the Invention of the
by Georges Ifrah
Hardcover - 663 pages (November 19, 1999)
John Wiley & Sons; ISBN: 0471375683
Other Editions: Paperback
What is brilliant about Ifrah's book is its trans-culturalism. Not just
derived from classical Greece-Renaissance Europe, he really goes all over
the world and looks at fascinating comparative history of how humans have
used number. Especially in the world today and USA perhaps more than
anywhere because of its melting pot, we must look at these things in global
I know an experienced wise old Chemist who is of the firm opinion that the
best way to _start_ teaching chemistry is through cooking. Then start asking
questions and providing paradigm guidance and method. She insists this if
done right will form the right foundation. Among her arguments is that when
the children go home, the chemistry lesson will be waiting for them on the
dinner table and throughout the rest of their lives. She is a firm
believer in scientific method.
Returning to the classical Greeks - we must ask how did they do their
What tools did they use?
Likewise what their peers in China or elsewhere were doing.
Consider the multiple approaches to Pythagoras.
Paper and scissors are a great tool here.
Take a pile of stones as you sit on beach by a fire watching the stars.. at
any time in history
Does Euclid pop out ... or do tetrahedral numbers?
Take a some string, some shells some sticks.. start drawing circles in the
sand and marking interesting points made by your marks, the sticks and the
Does Bucky pop out or does Euclid?
I think what we need in addition to spending some time together on a real
beach, is a virtual beach, string, sticks, shells.. a computer could do
Jason CUNLIFFE = NOMADICS['Interactive Art and Technology'].DesignDirector