Digital Revolution

Stephen Wolfram's Principle of Computational Equivalence is a landmark in complexity study. Even though it's wrong at large, it did show how seemingly simple programs can exhibit extremely complex behavior. The fallacy results from the desire to generalize without proper scrutiny. For example, it claims that complexities in different dimensions are similar. But, topology and geometry make very striking distinctions between dimensions. In 2D, we have Poincare-Bendixson theorem. In 3D, we have knots. All are specific to dimensionality. Unless we are going to say these constructs do not reflect complexity, we are forced to accept that complexity is much more than computation and things like geometry should be a subject of study. The field is still very young. A theory to rank knots is a good beginning. There is good reason to speculate that final results will involve vast new areas like statistics, and will provide insights into deep philosophical questions like rationalism vers...

Most people argue about symbolic computation versus numerical computation. There are plenty of advantages and disadvantages in each camp, which suggests the way out may be to forge a symbolic-numerical alliance that would provide the rigor of symbolic computation and the performance of numerical computation in a single package. It's not as trivial as simply adding two apps together. The underlying programming language has to be dramatically redesigned to express the alliance in a elegant and powerful way. So far, there is a trend for symbolic packages like Wolfram Language to adopt more numerics, and for numerical packages like Matlab to adopt more symbolics, but neither is a satisfactory alliance that fully integrates the two. The advantages of such a alliance are easy to see. Artificial intelligence often employs both worlds, like symbolics for knowledge representation, and numerics for data fitting, to say the obvious. A symbolic-numerical alliance would make artificial intellig...

There are many reasons why PC's aren't as good as Macs. But vast population doesn't understand them. Regulators attempt to regulate a market where they have no expertise. Apple's PR encourages magical thinking that further obscures the dynamics of its own success. Thus it seems appropriate to analyze the differences between PC's and Macs to find out what Apple's approach is really successful and why regulators' fashionable Apple-bashing is dangerous. One object that works very differently on PC's and Macs is function keys. On PC's, function keys are rarely used beyond F1 for help documentation. Their bindings are arbitrary and hard to figure out. Comparatively, Macs build function keys into the OS for display brightness, Expose, Launchpad, etc. Each with explicit purpose and properly decorated, function keys on Macs serve as fast shortcuts to frequently used OS controls. It's clear that Mac's function key design offers much better utility th...