Sadly we here observe a retreat within the simple language of mathematics. I am not decrying mathematics nor am I underestimating the great value of that language in extending knowledge of the physical world by bypassing the complexities and irrelevancies common to the natural languages.
It does, however, suffer from two major weaknesses:
Firstly, like all languages, it is capable of generating fictions - entities and scenarios which have no correspondence wit the real world.
Secondly, it is, like all reasoning or computational processes, raw data sensitive....
Unfortunately this entire discussion is deeply flawed.
Why? GIGO - Garbage in - Garbage out.
However good the logical systems used for processing information they are of no avail without meaningful input data.
Present technologies cannot be used as a basis for prediction because of the unexpected bifurcations and inherent non-linearities in technological developments.
Further problems stem from the use of the very inappropriate buzz-word "Singularity". Certainly a dramatic change is imminent, but this is better considered as a phase transition - t... (read more)