What are the best practical tools for the mind, methods to organize work and thought, how to turn an idea into reality? Last night a group of friends gathered to wind our way around the topic.

No discussion on the display of information would be complete without Edward Tufte; his books were carefully salted around the room. Tufte is to visualization as Strunk & White are  to writing, or Knuth is to programming: bracing, original, unforgettable. Kevin Kelly says of this book: “It is a passionate, elegant revelation of how to render the 3 dimensions of experience into the 2 dimensions of paper and screen.”

On glancing through Envisioning Information, our next door neighbor  Christof noticed Oliver Byrne’s visual proof of the Pythagorean Theorem. Dating from 1847, the proof explains it by means of kaleidoscopic triangles on the page.

Is such a description understandable by the average person – or does this require expertise in the specialized symbols of mathematics? For that matter, what about the more esoteric knowledge of our time, quantum mechanics, superstrings, microfluidics? Is there a level of understanding that bypasses the common mind altogether – and perhaps even the specialized mind? This spurred a side trip, a description of the ground-breaking proof of Kepler’s Conjecture, a problem that, like the sword in the stone, had defeated legions of mathematicians for the last four hundred years. The problem is simple to state: what’s the best way to pack balls in a box? Answer: the common grocer’s pyramid. But can you prove that? For four hundred years, nobody could.

Then in 1998 Thomas Hales, then at the University of Michigan, dumped 250 pages and 3 gigabytes on the Annals of Mathematics. It was a solution both human and machine, a “proof” partly created by himself, partly by a computer program. In other words, he understood part, and the computer “understood” the other part. Four years later, after having dozens of the best minds in the world examine portions, the Annals declared that they were pretty sure the proof is correct.

For the first time, Hales had cracked the species barrier, by producing something that is true, but which nobody could understand, by collaborating with a computer. He used the mind-tools of mathematics, and a “machine-mind” tool (a program). History may look back on this as the first time that deep thought was achieved by a non-human.

But, wait a minute. Do we “trust” such a proof, if no human being can completely verify it? Do we accept it because a computer said so? Christoph (who specializes in the field of artificial intelligence called automated reasoning) explained that in mathematics such high-level proofs are really done through hierarchical levels of trust. We believe a basic set of premises, and a set of conclusions are based on the premises. Then at a higher level of abstraction, another set of conclusions or an entire logic is built up. Levels of trust. How do you know your car will work? You trust the mechanics, who trust the engineers, who trust the designers, who trust the physicists…

In Tufte we also found Charles Joseph Minard’s wonderful map of Napoleon’s march to Moscow and back. As an engineer of Roads and Bridges in post-revolutionary France, Minard was drawn to the physical world. This map prompted Tufte’s explorations into visualizing information.

Considering this intersection between the physical world and presentation, visualization and the thing depicted, we strayed into the realm of teaching. Schools are increasingly demanding the use of presentation software such as Powerpoint, rather than mere lectures. What does that mean for education, and the legions who are taught that a bulleted list is the best way to deliver information?  Another neighbor talked about teaching physical skills: how some students could grasp a verbal description, others needed to see a demonstration, and yet others needed to have their bodies go through the actions. This is called “blended” teaching/learning, a blending of styles. Reading, writing, recitation, practice, demonstration – even the sense of smell can be used, as nurses can confirm who have learned to spot C. difficile by odor alone.

Anara told of a student having trouble with a class, who was finally able to learn by reciting the material while running – similar to the discovery that music and song can be a way for certain people to learn. Maria Montessori developed a theory of teaching writing through the sense of touch, tracing out letters with the fingers before every picking up a pen.

Mind-tools… perhaps we should call them mind/body tools, since learning and understanding is done as much by the body as by the mind. And along with the body, emotions.

All of these tools are used to convey information or meaning from one person to another, which involves a certain degree of social skill, as anyone who has suffered through an obscenity-laced session of slam poetry will recognize. Then again, artists throughout history have often been rebels, outsiders, with little or no social skills. If van Gogh produced masterpieces, does it matter that he mailed his ear to a woman who jilted him? Perhaps the majority of artists are misfits, drunkards, unstable, eccentric?

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