On Wed, 13 Oct 1999, John Clark wrote:
John commenting on Emlyn's interpretation of Moore's Law:
> That's a geometric curve not exponential, it can be described by a
> polynomial like (X^n) where n is a constant and X a variable.
> An exponential curve like (n^X) is not a polynomial. If n is only slightly
> greater than 1 then at small values of X it does not even look like a curve,
> it looks almost like a straight horizontal line, at medium values of X it
> looks almost like a geometric curve, at large values of X it looks almost
> like a straight vertical line.
>
> Moore's law looks geometric (but we can't be certain) not exponential
> so it's spectacular but we can deal with it.
>
John, I appreciate your posts because they sometimes (:-)) simplify things
to the degree that something that I "know" but am not sure I really
understand is expressed succinctly enough that I get an "aha" out of it.
>From now on I think I'll put you in the FO class (Feynman offspring).
To add add to the information base here, I've used Excel to fit various curves to the growth of Medline entries from 1965 to 1998. The data says:
2nd order Polynomial: y = 0.0004x2 - 5.0771x + 50386; R^2 = 0.9795 Exponential: y = 31685e^7E-5x; R^2 = 0.9805 Power (geometric?): y = 5E-5x^2.1719; R^2 = 0.9817
Now I'm no expert in statistics but the R^2 values (used to measure goodness of fit) are all *very* close. So I would say that it is impossible to know whether Medline information growth fits any of the above growth patterns. The best pattern would appear to be geometric, not exponential, but it is only by a very small margin. To get better data we would need to go get more historical records (pre 1965) or wait until we have more future records.
Looking at this on a graph, the trend lines virtually overlay each other. The actual annual variance in the number of Medline abstracts compared with the trend lines shows a cyclic pattern that I strongly suspect correlates with the growth and contraction of the economy (and therefore the scientific research allocation of health care budgets).
If I look from the start forward and from the end back, the knowledge (publication doubling time) has increased from 22 to 28 years so the rate growth of knowledge may be decreasing. However this is a very questionable perspective since it may be that we got the "easy" knowledge first and now each increment of knowledge is becoming more difficult to acquire.
One thing worth noting however with both Moore's law and health care "knowledge". Both hit limits. Moore's law is projected to hit limits now around 2010-2013, but even if they figure out ways around that, I know of no proposals that would allow classical computing with things smaller than single electron transistors. We definately hit those limits (assuming no slowdown) within 50 years. Similarly with health information (which is really a question of decoding blueprints of the machines we run on), we will at some point "fully" understand how the physical part of it works. When you get near those limits the phase space shifts. With Moore's law you get things like multi-value logic or quantum computing (for specific applications). In health areas you move from taking existing things apart to putting new things together.
Robert