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April 01, 2005

Watch and Learn

We may never truly know what is really “real”, but it doesn’t stop us from explaining the world nevertheless. Theoretical development isn’t a search for the ultimate truth - or “The Theory of Everything” as its called, for theory is independent of truth. However, we would still want to apply it to practice. Practice has the problems of being imperfect, and subjective… that one would begin doubting it, that it is some kind of illusion.

But somehow we want to trust practice (up to a certain degree). So, I wouldn’t say that it produces illusion, but rather it can be deceitful (theoretical jumps), i.e our intuition leads us to false conclusions. However, this conclusions are only false when we go beyond the system (ω-incompleteness), and other forces begin to gain significance.

For instance, we all know that “the Earth is round.” But for me to make use of this, I would have to travel around the world. However, I obviously don’t do this very often, and on a day-to-day basis of zooming across Toronto, it is much more convenient of treating the Earth really as flat. And indeed, its true, at every point locally, the Earth really is a plane (hence a 2-manifold but thats besides the point).

So to know what goes on in a system, we don’t need the exact truth, we need good enough truth (i.e statements which are true and applicable in the system). We explain phenomena with the simplest available theory (a la Ockham’s Razor). When that system ends, another one begins. The bigger the picture, the more precise we need to be - the more complicated the model.

Experiments serve two purposes: First, they help in theoretical construction. Most of the time, we don’t know what is going on, and before we can describe it, we have to see it. Seeing is believing. The second purpose is to help verify theories. By verifying theories, it means taking care of the theoretic jumps. If the theory is falsified, we can blame it on the fact that we don’t know what is going on. A good self-saving clause, perhaps.

Think of them like a drawing. The graph of a mathematical function is an invaluable, irreplaceable aid for understanding the function, but by no means is a valid proof. It inspires Theory. Once we can see the bigger picture, we push theory in that direction. Without the practice, the Theory could never come into existence.

Posted by Oleg Ivrii at April 1, 2005 08:20 PM

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