Sunday, January 24, 2010

Continuity black hole

Twenty first century man travels much more freely than his forbears; where they negotiated rickety staircases with missing treads, rough ground, uneven pavements & met insuperable or impenetrable barriers, we have travelators, escalators, lifts, automatic doors & access ramps. We can even fly.

Eventually we do have to come back down to earth, almost always, with the help of a lot of clever mathematics, on a designated landing strip.

We think that, mathematically speaking, the universe is an undifferentiated mass of points without gaps, through which we may travel freely in any direction in space without let or hindrance, on a kind of travelator which passes through or over any point.

Sometimes we have minor accidents, we do not quite make it on to the runway as we should. But then we just say oops! & pretend that we did, after all, mean to land where we did. Sometimes the results are more disastrous, fatal even.

We depend on mathematical equations & models to navigate us through these days of computers, budgets, targets. Most of these use the kind of mathematics of continuous functions, which depend crucially on the assumption that any answer is possible, corresponds to something in the real. Where it does not we round or truncate to something which does, cheerfully pretending that the reality gap does not exist.

Most of our accidents have been minor (we think).

They may not always be so.

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