devlin

"soft maths" (immersive 3D environments)

At the other end of the economic spectrum, the immersive, three-dimensional virtual environments developed by the gaming industry make it possible to provide basic mathematical education in a form that practically everyone can benefit from.
 * [|We Will Finally Get Mathematics Education Right]**

We have grown so accustomed to the fact that for over two thousand years, mathematics had to be communicated, learned, and carried out through written symbols, that we may have lost sight of the fact that mathematics is no more about symbols than music is about musical notation. In both cases, specially developed, highly abstract, stylized notations enable us to capture on a page certain patterns of the mind, but in both cases what is actually captured in symbols is a dreadfully meager representation of the real thing, meaningful only to those who master the arcane notation and are able to recreate from the symbols the often profound beauty they represent. Never before in the history of mathematics have we had a technology that is ideally suited to representing and communicating basic mathematics. But now, with the development of manufactured, immersive, 3D environments, we do.

For sure, not all mathematics lends itself to this medium. But by good fortune (actually, it's not luck, but that would be too great a digression to explain) the medium will work, and work well, for the more basic mathematical life-skills that are of the most value to people living in modern developed societies.

Given the current cost of developing these digital environments (budgets run into the millions of dollars), it will take some years before this happens. We can also expect resistance from mathematics textbook publishers (who currently make a large fortune selling a product that has demonstrably failed to work) and from school boards who still think the universe was created by an old guy with a white beard (no, not Daniel Dennett) 6,000 years ago. But as massive sales of videogames drives their production costs down, the technology will soon come within reach of the educational world.

This is not about making the learning of mathematics "fun." Doing math will always be hard work, and not everyone will like it; its aficionados may remain a minority. But everyone will achieve a level of competency adequate for their lives.

Incidentally, I don't think I am being swayed or seduced by the newest technology. Certainly, I never thought that television, or the computer, or even artificial intelligence, offered a path to effective math learning. What makes immersive 3D virtual environments the perfect medium for learning basic math skills is not that they are created digitally on computers. Nor is it that they are the medium of highly seductive videogames. Rather, it is because they provide a means for simulating the real world we live in, and out of which mathematics arises, and of doing so in a way that brings out and confronts the player (i.e., learner) with the underlying mathematical structure of our world. If Euclid were alive today, this is how he would teach math

books by Keith Devlin (amazon review are fairly critical) [|The Math Gene: How Mathematical Thinking Evolved and why numbers are like gossip]

[|Infosense: Understanding information to survive in the knowledge society]
 * Why people, not computers, are the most effective way to transfer knowledge

[|Goodbye Descarte: The End of Logic and the Search for a new Cosmology of Mind] Much of the book is a critique of symbolic logic. Invented by Aristotle, it was merged with algebra and became a branch of mathematics and its most recent applications have been in artificial intelligence (AI) as well as the liguistic of Chomsky. What these disciplines have in common - what is "cartesian" about them - is their attempt to "captur[e] patterns of reasoning...in a pure fashion, isolated from context" and even meaning. In this view, computers are the perfect logic machines, processing info by manipulating symbols without understanding what they are doing.

The failure of AI to meet its original goals demonstrates, in Devlin's view, what is wrong with this approach. AI (or an "expert system") lacks common sense, whatever its diagnostic capabilities, and cannot make judgments when unforseen or ambiguous situations arise. Consequently, AI cannot operate outside extraordinarily narrow confines and hence are unreliable in many applications. Computers have also failed to produce a human-like language. This is proof, Devlin says, that the human mind is more than a logic machine ("Smart meat" as the Wired crowd might argue) that acts according to rigid subsystems of logical rules: context and meaning matter. These arguments are convincing and cogently argued.

Unfortunately, Devlin's arguments of where to go from there are far weaker than his analyses of past failures. The last third of the book is a loose jumble of ideas and speculation. He wants to create a "soft math" to incorporate context, meaning, and the qualitative into the study of the human mins, but does not get beyond saying we need it. This is a research agenda, but too vague to be of much use in my opinion. - Robert Crawford amazon review

Ch 1: Patterns of Mind There is a need to overturn the momentum of a 2000 year history of the power of logic Aristotle's logical inference: All men are mortal Socrates is a man Socrates is mortal
 * Notes about 'Goodbye Descartes'** - Bill Kerr 16Feb07

The idea that the Mind is a calculator which follows certain rules Historical trace: Plato, Aristotle, Leibniz (17th C), Boole (19th C), Gottlob Frege (20th C), the logical positivists (1930s), Chomsky's views on language, classic AI (1950s) - Logic has hit a wall

Ch 10. The Chesire Cat's Grin //"All right said the Cat; and this time it vanished quite slowly, beginning with the end of the tail, and ending with the grin, which remained some time after the rest of it had gone."// The Lewis Carrol quote is a great statement about the embodiment of knowledge, that the grin remains after the body has disappeared!! It's bizarre that information could exist outside of context.

Ch 11. Goodbye Descarte