So much for the Singularity

Wikipedia defines a technological singularity as:

the hypothetical future emergence of greater-than-human superintelligence through technological means. Since the capabilities of such intelligence would be difficult for an unaided human mind to comprehend, the occurrence of a technological singularity is seen as an intellectual event horizon, beyond which events cannot be predicted or understood.

The blog Cognitive Social Web has a post arguing that The Singularity is not coming. The post argues that a singularity requires an exponential rate of progress in science. In actual fact, according to the post, science advances in a linear fashion, not an exponential one. This happens because each area in science faces diminishing rates of return as their field progresses.

I would like to simply argue that scientific progress is in fact linear, and this despite the capitalization of past results into current research (“accelerating returns”), and despite an exponentially increasing population of scientists and engineers working on advancing it (resource explosion). And since I don’t want to argue in the realm of opinion, I am going to propose a simple, convincing mathematical model of the progress of science. Using the same model, I’ll point out that a hypothetical self-improving AI would actually see its own research progress and intelligence stagnate soon enough, rather than explode —unless we provide it with exponentially increasing computing resources, in which case it may do linear progress (or even better, given a fast enough exponential rate of resource increase).