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We Have Imperfect Knowledge Of The World

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Posted by Jim Bergquist on January 10, 2001 21:39:34 UTC

I think that the biggest problem that we might encounter is our imperfect knowledge of the world or universe as a whole. You yourself imposed bounds on the sets representing the world. But I think that a more complete picture of the state of affairs is that we are limited by our unique point of view. In cosmology, our knowledge of the universe is limited by the velocity of light so we only know about the distant past of remote places. There is also a reduced resolution for remote locations. We only know of a slice of the observable universe although we might be able to compensate somewhat by treating this as a boundary value problem. One must also note that our knowledge of the universe is bias by those elements which do communicate information to us. We have to look for indirect evidence for dark matter for instance.

The use of a finite number of data points also presents a problem. We would be modeling the world with a 3D grid. One would then have to make a projection in order to get a continuous model. There may be flaws in going to the limit.

The rules should recognize that there are bounds to available knowledge. Some barriers may be insurmountable. Others may be filled in by explorers and analysts.

I think that multiplicity of solutions should be gone into in more detail. Some equations have more than one solution; take the binomial equation as the simplest example. This is the mathematical equivalent of the optical illusion. I think that you touched on this when you said that more than one function will fit a given data set. How can one discriminate among the possible solutions if they are of equal merit. I think that the economists have this problem when trying to optimize their results. There is the problem with local maxima. How can we be certain which state the economy is in?

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