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. http://www.jsoftware.com/papers/tot.htm 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 admitted.” 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 http://booki.treehouse.su/algebra-an-algorithmic-treatment/ 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. http://wiki.sugarlabs.org/go/Replacing_Textbooks _______________________________________________ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep