http://spinemasher.livejournal.com/ ([identity profile] spinemasher.livejournal.com) wrote in [personal profile] spoonless 2006-05-18 01:37 am (UTC)

I wouldn't be surprised if it was a discontinuity in the derivative. After all, there are far more physical objects which are sharply changing as opposed to smoothly changing than most physicists would like to admit.

Of course, I should say I know nothing about the technical theories put forth with regards to the future evolution of technology but I will also confess that I think it is all non-sense, only in that one cannot reasonably have access to the actual relative probabilities in the absence of a set of dynamical laws. In effect, my perception of the relative probabilities are completely tainted by my biased perception of human history and consequently any predictions I make will be so flawed as to be completely useless especially if the system exhibits chaos. In short, it is probably worse than trying to predict the weather. Of course, none of this is cause to abandon the attempts, after all that is what science strive for.

I am much more used to making sharp distinctions between point and surface singularities because in the real 4-space manifold the distinctions are vital as the lead to vastly different physical evolutions. If you have an entirely singular then you are dealing with a separated surface in the topological sense. This is different, of course, from a singularity in coordinates which can be transformed away. In fact, a singularity is a real or physical singularity in the rigorous mathematical sense if it cannot be transformed away. Though this viewpoint is neither necessary nor sufficient because the 4-space and the connection of its geometry to its matter via the Einstein equations requires a careful and rigorous definition. This definition was given by Schmidt and involves the termination of geodesics. Nonetheless, a surface being singular is also vastly different from a single point because the to 4-space are topologically distinct and physically distinct as well.

We seldom hear about the important differences in physics because unless someone is working in a very specific theory of gravitation/cosmology, rarely does any bother working out the physical significances of topologically distinct space-times. As an example, MTW cite an example where the arising of a singularity is due to the initial conditions of the universe in space known as Taub-NUT types.

Now which one of these greatly varied possibilities best describes the impending technological evolution is anyone's guess. I'm quite comfortable staying out of the whole business and saying that I simply don't know. But I will say this, from the biased manner in which I view history, I expect that nature is filled with surprises and I am guessing that no one will come even close to what actually unfolds.

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