Some Thoughts on the Teaching of Mathematics -- ten years later

I describe some deep-seated problems in higher mathematical education, and give some ideas for their solution -- I advocate a move away from the traditional introduction of mathematics through calculus, and towards computation and discrete mathematics.Comment: 10 pages, to appear in Notices of the AM

On Abandoning XLISP-STAT

In'98 the UCLA Department of Statistics, which had been one of the major users of Lisp-Stat, and one of the main producers of Lisp-Stat code, decided to switch to S/R. This paper discusses why this decision was made, and what the pros and the cons were.

Amorphous Computing

The goal of amorphous computing is to identify organizationalprinciples and create programming technologies for obtainingintentional, pre-specified behavior from the cooperation of myriadunreliable parts that are arranged in unknown, irregular, andtime-varying ways. The heightened relevance of amorphous computingtoday stems from the emergence of new technologies that could serve assubstrates for information processing systems of immense power atunprecedentedly low cost, if only we could master the challenge ofprogramming them. This document is a review of amorphous computing

How Downwards Causation Occurs in Digital Computers

Digital computers carry out algorithms coded in high level programs. These abstract entities determine what happens at the physical level: they control whether electrons flow through specific transistors at specific times or not, entailing downward causation in both the logical and implementation hierarchies. This paper explores how this is possible in the light of the alleged causal completeness of physics at the bottom level, and highlights the mechanism that enables strong emergence (the manifest causal effectiveness of application programs) to occur. Although synchronic emergence of higher levels from lower levels is manifestly true, diachronic emergence is generically not the case; indeed we give specific examples where it cannot occur because of the causal effectiveness of higher level variables

What to Read: A Biased Guide to AI Literacy for the Beginner

Acknowledgements. It was Ken Forbus' idea, and he, Howie Shrobe, Dan Weld, and John Batali read various drafts. Dan Huttenlocher and Tom Knight helped with the speech recognition section. The science fiction section was prepared with the aid of my SF/AI editorial board, consisting of Carl Feynman and David Wallace, and of the ArpaNet SF-Lovers community. Even so, all responsibility rests with me.This note tries to provide a quick guide to AI literacy for the beginning AI hacker and for the experienced AI hacker or two whose scholarship isn't what it should be. most will recognize it as the same old list of classic papers, give or take a few that I feel to be under- or over-rated. It is not guaranteed to be thorough or balanced or anything like that.MIT Artificial Intelligence Laborator

The mathematical components of engineering expertise: the relationship between doing and understanding mathematics

this paper are extracts from our interviews with engineers.) Where, then, is the complex mathematics that certainly exists in modern engineering? Throughout all aspects of engineering design, computer software has an overwhelming presence. Also, in the particular firm that we visited, there a small number of analytical specialists (a few per cent of the professional engineers employed) who act as consultants for the mathematical/analytical problems which the general design engineers cannot readily solve. (In general in structural engineering, such specialist work is often carried out by external consultants, eg. academic researchers

5 Months of Haskell : Programming languages as just other programs. Contribution toward a field of computer science education.

The following is understood as a contribution toward a field of com- puter science education : a reflection of 5 months of learning the functional programming language Haskell; out of which has emerged for us that pro- gramming languages are ‘just other programs’. This lesson, so important, is never felt more than in a functional language like Haskell, we defend. It has for principal benefit to bring down the barriers between creators and users of programming languages, i.e. “programmers”, both are the same; a psychological-sociological fact not without revolutionary characteristics