I would need some information and references about the growth of the
number of scientists in the world over the last 300 years (on some
reasonable definition of who counts as a scientist). I?m mainly
interested in the ?big picture?, i.e., the number of scientists at
different points in time, e.g. 1700, 1750, 1800, 1850, ? 2005, or the
doubling rate over the last 300 years. De Solla Price famously claimed
in the 1960s that the number of scientists grew with a doubling rate
of 15 years over the last 300 years, and that ?80 to 90 percent of all
scientists who have ever lived are still alive today?. Is this still
true today?

Here is a superficial, and perhaps diverging comment:

Although, I am not sure of the numbers, I believe that people who can
formally be called "scientists" have increased as a proportion of the
population in the last 300 years. The reasons for this could be that
more and more communities are embracing rational thought and using
science/research as a primary tool in making money.

However, even as a PhD student in a reputed engineering college (among
top 10 in US), my observation is that mediocrity in science (as in
other fields) is becoming more and more endemic as more opportunities
are opening up for more people. What I mean is that even in good
universities, as the number of scientists is increasing, the average
quality of research and the proportion of fundamental and
path-breaking work is decreasing. With more precendents to follow of
how to do something, people who are not really trailblazers can enter
professions that required free-thought by following well-studied
examples. Or they start out as a brilliant scientist, but once
established, they quickly find a comfortable position where they can
indulge more in academic politics and nurturing their feifdoms, shying
away from further growth and learning. They also start cotries that
would reinforce their ideas rather than promoting people who can
challenge their ideas.

Anyway, enough rambling. But, you can see a disillusioned scientist
here. Well, not all is so gloomy as I potrayed... but I just wanted to
show one particular side of it.

PS: Someone told me that the amount of "knowledge" doubles every 17
years. I have no idea what he meant by "knowledge"... perhaps he meant
"written knowledge"

PPS: I am not a US citizen. I came here to learn and see a society
that is one of the most rational in the world. With the christian
revivalists talking about things like "intelligent design" to gain
backdoor entry into the world of science, I predict a loss of current
status of US as epitome of several things. Citizens of US, please save
your country and be vigilant about the murder of rationality that is
going on.

"The reasons for this could be that
more and more communities are embracing rational thought and using
science/research as a primary tool in making money" [please add] "and
improving lives."

Curious is on the right track.  There is inflation in what is called a scientist.
I just browsed a bunch of sites on the "Augustinerpater Johann Gregor
Mendel", often called the father of modern genetics, but the sites and
history don't call him a scientist or in German:  "Wissenschaftler". 
Ditto for many others:  people who designed clocks, discovered
chemical processes by experiment, inventors and engineers: "clever
craftsmen" who today would stand head and shoulders over a multitude
of people who call themselves scientists.
But the word ?scientist? is not so old, this from etymonline:
"scientist  
1834, coined from L. scientia (see science) by Eng. philosopher
William Whewell (1794-1866) by analogy with artist."

But, in their defense, it must be admitted that expansion of
scientific knowledge provides an expanding field for researchers.