(2016-11-31) Nielsen Thought As A Technology

Michael Nielsen: Thought as a Technology. Have you ever felt awe and delight upon first experiencing a computer interface? An interface that surprised you with its strangeness, with a sense of entering an alien world? (ThinkingTools)

My own first experience of this awe and delight was when I used the program MacPaint.

What makes an interface transformational?

I believe this is what made MacPaint so exciting to 11 year-old me: it expanded the range of thoughts I could think.

How can we invent new elements of cognition?

We can paraphrase Thurston as saying that mathematicians often don't think about mathematical objects using the conventional representations found in books. Rather, they rely heavily on what we might call hidden representations, such as the mental imagery Thurston describes, of groups breaking into formations of circular groups. Such hidden representations help them reason more easily than the conventional representations, and occasionally provide them with what may seem to others like magical levels of insight

what an expert person did when presented with a circuit… was quite different from what we tell [the students] to write down – the node equations… and then you're supposed to grind these equations together somehow and solve them, to find out what's going on. Well, you know, that's not what a really good engineer does.

I believe that for most subjects of any depth, experts have hidden representations that could inspire interfaces reifying those representations

much work on doing mathematics by computer has focused on automating symbolic computation (e.g., Mathematica), or on finding rigorous mathematical proofs (e.g., Coq). In both cases, the focus is on correct mathematical reasoning. Yet in creative work the supply of rigorously correct proofs is merely the last (and often least interesting) stage of the process

heuristics are often quick-fire rules of thumb, full of exceptions and special clauses, not rigorous proof techniques. They let experts sketch out arguments, and figure out what is likely true, and what is likely false. In short, they're a powerful way of exploring and obtaining insight

This shouldn't be confused for an argument that visualization is good, and algebra is bad. There is a cargo cult mentality which embraces visualization for the sake of visualization. In fact, there is no a priori reason a visual approach is superior. Rather, one must understand both the benefits and deficits of any specific approach

A good demonstration of this is the remarkable book Structure and Interpretation of Classical Mechanics, by Sussman and Wisdom. The book explains the ideas of classical mechanics through the medium of Lisp programs. In our terms, the book implements a Lisp-based interface to classical mechanics, complete with many new elements of cognition

Another example of this phenomenon is the program Photoshop, which builds in many deep principles of image manipulation. As you master interface elements such as layers, the clone stamp, and brushes, you're well along the way to becoming an expert in image manipulation. Similarly, someone who masters the interfaces in Structure and Interpretation of Classical Mechanics necessarily learns a lot of classical mechanics. By contrast, the interface to Microsoft Word contains few deep principles about writing, and as a result it is possible to master Word's interface without becoming a passable writer. This isn't so much a criticism of Word, as it is a reflection of the fact that we have relatively few really strong and precise ideas about how to write well.

An interface for projectile motion

explore two-dimensional projectile motion.

The fan of multiple trajectories and the wavefront of projectile positions are representations familiar to some experts, but are unknown to most students of physics


Many people implicitly or explicitly use this cognitive outsourcing model to think about augmentation. It's commonly used in press accounts, for instance. It is also, I believe, a common way for programmers to think about augmentation. (Augmenting Human Intellect)

A common informal model of augmentation is what we may call the cognitive outsourcing model: we specify a problem, send it to our device, which solves the problem, perhaps in a way we-the-user don't understand, and sends back a solution

In this essay, we've seen a different way of thinking about augmentation. Rather than just solving problems expressed in terms we already understand, the goal is to change the thoughts we can think

Kasper Peulen's Euclid: the Game, which builds up an interface using ideas from Euclidean geometry. Again, this heuristic is used widely, but Peulen's game shows it in a particularly well distilled form.

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