[IAEP] Computation for thinking with (was IAEP] Sugar Digest 2013-10-05)

Edward Mokurai Cherlin mokurai at sugarlabs.org
Sat Oct 5 18:22:49 EDT 2013

On Oct. 5 Walter Bender wrote:
> In the early 1960s, while studying with Jean Piaget, Seymour Papert
> had the insight that computation was a "thing to think with".

Ken Iverson's Turing Award lecture was titled Notation as a Tool of Thought.


He, of course, used examples from his own language, APL (A Programming
Language), which inspired the creation of Backus's functional
programming languages (described in his Turing Award lecture), and
many others.

He quoted

Concerning language, George Boole in his Laws of Thought [1, p.24]
asserted “That language is an instrument of human reason, and not
merely a medium for the expression of thought, is a truth generally

Mathematical notation provides perhaps the best-known and
best-developed example of language used consciously as a tool of
thought. Recognition of the important role of notation in mathematics
is clear from the quotations from mathematicians given in Cajori’s A
History of Mathematical Notations [2, pp.332,331]. They are well worth
reading in full, but the following excerpts suggest the tone:

          By relieving the brain of all unnecessary work, a good
notation sets it free to concentrate on more advanced problems, and in
effect increases the mental power of the race.
 A.N. Whitehead

Ken's son Eric organized the annual Tool of Thought Conference to
follow up on that idea. You can see an example applied to our work
with Sugar, in Iverson's algebra textbook, which I have updated at


as part of the Sugar Labs program for Replacing Textbooks (with Open
Educational Resources). Of course it would help if we could get the
language concerned, J, packaged for Fedora and Sugar.

In mathematics, the otherwise contentious Sapir-Whorf Hypothesis, that
the structure of language sets limits on what is readily thought, is
simply understood as a given. Of course, it does not mean that we
cannot go beyond those limits, just that it is very, very hard, and
that in some cases we have to invent more language so that more people
can do it. Historically, the clearest example is the difference
between the Newton dot and Leibniz d notations for calculus. Due to
the nationalist furore over precedence between Britain and Germany,
British mathematicians refused to use the Leibniz d notation until
Charles Babbage founded the Analytical Society to "replace the dot-age
of England with the d-ism of the Continent".

Thus the proliferation of mathematical notations and of programming
languages and paradigms ever since.

There is a good deal more to this story, including the fact that
Turtle Art tree-structured programming is superior in Computer Science
terms and for children's use to textual programming, but I will leave
that unless somebody asks me.

Edward Mokurai (默雷/निशब्दगर्ज/نشبدگرج) Cherlin
Silent Thunder is my name, and Children are my nation.
The Cosmos is my dwelling place, the Truth my destination.

More information about the IAEP mailing list