One can argue for the singularity without making assumptions about the software complexity problem of getting from human to superintelligence. The reason is that with nanotechnology, so-called "weak superintelligence" would be sufficient. The argument goes like this:
The nanotech-uploading argument
In the first half of the next century, we get molecular nanotechnology in the sense of a general assembler. Using nanotechnology, we can upload humans. Nanotechnology also makes it possible to build computers that are fast enough to run an upload as high speed. Drexler has sketched out a simple mechanical nanocomputer the size of a sugar cube with a processing power one million times that of a human brain. Hence we can run the best human brains at a speed where after one day they will have experienced more than two thousand subjective years each. During this time they will almost certainly have managed to design more effective architectures such as electronic nanocomputers and quantum computers. Since the uploads can control a molecular lab at molecular speeds, they are not slowed down by having to rely on humans to carry out trial-and-error testing. If the uploads have a sufficient stock of raw materials, they can easily build themselves larger and faster computers to run on, and they can design and build machines that can get them even more raw materials. All this can happen in less than 24 hours. If the uploads so decide, they can of course go then on to quickly transform Earth into more computers and launch vehicles for von Neumann probes. It is perfectly possible that the singularity happens before uploading takes place, but this argument shows it will happen no later.
Nick Bostrom
http://www.hedweb.com/nickb n.bostrom@lse.ac.uk
Department of Philosophy, Logic and Scientific Method
London School of Economics