Some mothematical model of miners is READY!
First, look @
http://bitcoin.sipa.be/speed.pngConsider latest 2.5 months, we can see an exponential-like 'loop' in exponential axis 0Y:
a 'loop' (ROUGHLY) starts @ Mar 15, 2011 (700 000 Mhash/s), ends @ May 30, 2011 (3 500 000 MHash/s).
Note, there is also previous 'loop' of the same 'form' on the graph @ Dec 15 2010 - Feb 28 2011 (note, the same 2.5 months duration)
The latest 'loop' can be represented as a formula:
total_power (t, days, in MHash/s) = 250*(3162 + 2.5*10^ (0.0466*t)),
where
3162 - CONSTANT number of miners @ period Mar 15, 2011 - May 30, 2011 (our 'famous' ~ 10 000 miners)
250 MHash/s - typical power of GPU of single miner before upgrade @ Mar 15, 2011
250*2.5=625 MHash/s - typical power of GPU of single miner after upgrade @ May 30, 2011, where we observe a tiny 'fall' of total power
(note, compare with Mar 05 2011)
0.0466 - is norm koefficient, that all miners has upgraded their GPU till May 30, 2011, from 250 MHash/s to 625 MHash/s
I assume all miners observe how does total power increases with time. They are 'race participants'. And becouse they did not understand MY bitcoin society's crash theorem, they want to obtain max. profit, so they were forced to upgrade their GPU and continue 'racing'.
So, miners' 'total intelligence' is a classic system with positive feedback.
See the MODEL graph plotted:
http://www.wolframalpha.com/input/?i=plot+log_10+%28250*%283162+%2B+2.5*10^+%280.0466*t%29%29%29+t+from+0+to+100
total_power (0 = Mar 15, 201) = 794328 MHash/s (log_10 = 5.9)
total_power (75 days = May 30, 2011) = 3162227 MHash/s (log_10 = 6.5)
compare with data ACTUALLY observed:
total_power (0 = Mar 15, 201) = 700000 Mhash/s
total_power (75 days = May 30, 2011) = 3500000 MHash/s.
ALMOST 90% MATCH.
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If the number of miners were growing exponentially itself, we PRIMARILY observe LINEAR curve in the exponetial axis (0Y).
In fact, since Dec 15 2010, @
http://bitcoin.sipa.be/speed.pngWE DO NOT observe any growing LINEAR behaviour (in exponetial axis).
So number of miners = 3162 = const (t), since Mar 15, 2011 by evidence, and (may be) since Dec 15 2010 too.
If you still interested in, I may compute & model the Dec 15 2010 - Feb 28 2011 period too.