"physical limits to what can be achieved" A poster named Tony wrote in a previous post: "Projects like this make me think that there are physical limits to what can be achieved with computing." There are MANY physical limits to what a computer can achieve. As for Computing limits they are closer to those of human knowledge. The coilability of wire, was a problem that wasn't seriously tackled by mathematicians until chaos theory and fractal dimensions were widely accepted, and even then it took years for a team to tackle the problem computationally. The first custom-built computer that increased yields in production of springs wasn't even built until the late 90s. To this date and I guess well into the future, many of these kinds of problems remain unsolved by computing, because no human science comprehends them yet. The flow of air traffic, I guess, must have been modelled by some highly dynamical system and might, by now, be reasonably well understood. But the problem in this case is that it must be done in real time and I don't think any computer can do that kind of calculations in real time with enough accuracy to control the traffic flawlessly. A friend of mine works for a lab that builds simulators for jet engines. He mentioned the problem of turbulence, they can't computatinally model turbulence to a degree of "correctness" so they have to settle for approximations. I guess that climate prediction ("not weather, but climate") is a the top of computational complexity. Even weather prediction has been mathematically proved to be highly unreliable further than 4 weeks into the future. Does anybody here work on any project with such "physical limits"? π Saturday, September 28, 2002 There is a mind set that says we can model anything in the real world so long as we can measure it, digitise it.  However, in digitising it we can only measure so far, beyond that we treat the fractional bits as insignificant. In the Universe there are no insignificant bits. As in physics with the dichotomy between thinking of light as traveling in waves or particles.  In lots of ways thinking in particles makes it easier to solve certain problems but in behaviour a wave is closer in description. So unless we can hold things like the infinite series of PI, the infinitessimal edges of events we will always fall short to some degree in modelling the physical universe. Simon P. Lucy Saturday, September 28, 2002 There is this paper in The School of Niklaus Wirth: The Art of Simplicity, and it says "Historically a system grows until it is no longer manageable by current technology.  With the advent of a new technology a system can grow larger and further up, but ironically most of the additional performance and capacity will be spent on managing added complexity.  [...]  To make our life easier and to free our mental capacity for practical problems we must deliberately build simple systems which remain below the limit of complexity achievable by current technology.  If we do this a window of opportunity will open which we like to call the 'window of simplicity' as depicted in figure 1." -- Schulthess, "Lean Systems in an Intrinsically Complex World. Sammy Saturday, September 28, 2002 Cryptography is an obvious example. One limit is that software itself isn't physical and has only an indirect effect on the real (physical) world... it takes a lot of indirection to apply it to physical problems, such as preventing environmental degradation or feeding hungry people. Christopher Wells Saturday, September 28, 2002   Fog Creek Home