"Technological Progress Grows Exponentially and Reaches Infinity in Finite Time". This is a contradiction. The exponential curve reaches y=infinity @ x=infinity. So the referenced page fails to define exponential growth.
You can't have "infinite progress in finite time". I agree that this is impossible.
Alright then.
Keep in mind that the site just quotes the book on the subject. So this is an "official" position.
Lets define the singularity as "technology growth reaches the rate of x2 per day.". Do you think that this is impossible?
I can't tell if it is possible.
It also could 12233x per month or 0.12x per second or whatever.
But that's irrelevant hence the above definition of it. What you are proposing is something else, just a point on a slope not a singularity (hence the name (!) )
Well... a few weeks after that point, it will be x2 per second. So, close enough. It's just a trend line, not an exact mathematical exponential function.
I don't think "singularity" is meant to be taken literally. The idea is that growth, at some point, will be so absurdly fast that it will represent an unimaginably profound shift in society/human existence. Think of it in terms of "paradigm shifting events". See this resource to get an impression of this:
http://www.singularity.com/charts/page17.htmlAll it's really saying is that the next "event" is coming within our lifetime. Considering the exponential nature of technological growth (growth is proportional to size. f(x) = df/dx), it seems pretty inevitable to me.
Sorry for being so off topic.