“What’s the difference between learning Physics and being a Physicist?” — Jerome Bruner
The most effective method of knowledge transmission for human beings is storytelling (Andy Goodman). Stories stimulate the listener’s minds; encouraging information retention, engaging diverse areas of the brain, and providing motivation. So, why does Mathematics obscure its stories in technical language? Mathematicians may argue that precise symbolic manipulation requires a technical vocabulary, but surely Mathematics requires understanding in human terms before manipulation of symbols is meaningful. By telling Mathematical stories in a more engaging and interactive way, we can narrow the gap between practicing Mathematics and comprehending its concepts.
So how does J fit in this discussion? Well, as a computer language and a language of mathematics it provides a pragmatic bridge to experiment with mathematical concepts on the path to becoming a Mathematician. Although J’s brevity can challenge the learner, I propose a scaffold for the language; a visual tree graph that would reveal both the relationships between parts of speech and their arguments as the user hovers their mouse over fragments of the J sentence. Combined with the current tutorial system, this information could contribute a valuable semantic layer to the language.
The future lies in tools that allow our stories to be as personal as a whisper and as powerful as thunder. J may provide opportunities for learning Mathematics in ways that haven’t before been possible; teaching us how to be while teaching us how to.