I've seen plenty of mathsy comp sci that was very much rooted in reality. A good example was a graph search algortihm for searching graphs which require 10 of gigs to store (DNA matching is one practical example). This algorithm took into account disk speed, memory speed, cache speed etc.

Many researchers developing these algorithms are also using them too. They can't ignore reality.

As for using symbolism. It's quite like the difference between talking about writing a complex program and actually writing one. It all seems so simple when you start but when you get right down to the details of what do I need to pass to ths function and where will I get it, you start to hit problems that you didn't see before. Similarly, analysing an algorithm mathematically and symbolically (hopefully) prevents you from skipping any details so although less people will understand it, those that do will be able to poke holes and find mistakes much more easily than if they had to perform all the analysis independently themselves.

Of course it's also a good idea to describe the algorithm well in a natural language but we'd all be sitting in the dark if Maxwell had just said "we have these waves, electric and magnetic and they go up and down and they're always perpendiular to each other..."

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