Who believes in the concept of a 'singularity'?

Question

Singularity as in Ray Kurzweils law of accelerating returns, not singularity as in dense point of space time.

Answer 1

Although I have not read Kurzweil's book, an important area of work for me in my research are singularities.

Singularities have been discussed since calculus formed. Most singularities are minor in practice. Some have large cascading effects.

The principal issue with singularities comes from differential topology, in what has been nicknamed "catastrophe theory." It is an important area of mathematics.

Catastrophe theory is much like Euclidean geometry. It is true, within certain obvious boundaries. For example, there is no such thing as a triangle. Such a thing cannot actually exist in the Euclidean sense, but in practice there are triangle. Triangles are simply extremely close approximations of true triangles, but if you look at a triangle on a microscopic level there are discontinuities in the molecular structure and molecules are not precisely in a line and molecules in nature are in motion. There is no such thing as a triangle. Of course triangles appear everywhere, almost.

So, with the caveat that catastrophe theory describes perfect forms, it is very useful.

Remarkably, wikipedia has a decent article on catastrophe theory. http://en.wikipedia.org/wiki/Catastrophe_theory

Also see...http://home.swipnet.se/~w-48087/faglar/materialmapp/teorimapp/ekt1.html

http://www.ento.vt.edu/~sharov/PopEcol/lec13/catast.html

You can see a Zeeman machine at

http://www.math.sunysb.edu/~tony/whatsnew/column/catastrophe-0600/cusp4.html


My suspicion of what you are talking about with singularities using accelerating returns is an over expansion of the observation that an R&D firm suffers from diminishing returns on its investment, but as soon as other firms copy it, the industry suffers from increasing returns to scale, even though each specific firm still lives under diminishing returns.

This is important because, while society benefits, the firms do not. It passes through as income to the R&D personnel, primarily and competition drives out all but temporary profits to investors. Investors in heavily demanded businesses, like software, get above average returns, but not from the R&D directly, but from the demand indirectly.

Answer 2

It is certainly reasonable to believe that innovations in technology have increasing and maybe even accelerating returns. But, there is no reasonable way to profit from this fact other than to take the CONSIDERABLE risk of putting time and/or effort into R&D. But, the probability of actually acheiving such an outcome is very small. If it were large, then we would all be doing this instead of reading and writing Yahoo Answers!