Symbolic-Numerical Alliance

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 intelligence programming genuinely pleasant to work with.

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