I offer the proposition that all models are inaccurate, some models are useful, and the usefulness of a model is in the balance between the accuracy and the ease of use.<p>Compared with floating point numbers in computing, and finite difference types of calculus, the model offered by the reals is much, much simpler to work with, and then modelling them with floating point nubmers is comparatively simple.<p>Doing the work directly with floats is hard, and detailed analysis and theorems are virtually impossible.<p>For a sound theoretical basis to many applications, it's easier to work with reals and then approximate with floats than it is to work with floats directly.<p>I further offer the observation made in another item that working directly with computer calculations is making science unreproducable<p><a href="http://news.ycombinator.com/item?id=1069808" rel="nofollow">http://news.ycombinator.com/item?id=1069808</a><p>Suggesting that we simply do the calculations and then work with the results has its drawbacks.<p>Finally, I'm doing some huge simulations at the moment, and every now and again they blow up.  The results are supremely plausible, but if I didn't have an underlying theory, rigorously developed in the world of pure math, I wouldn't know that.