While Hahnemann had probably never heard of Avogadro's number (which was only determined half a century after Hahnemann published Organon der Rationellen Heilkunde in 1810) he surely must have realised that his dilutions were stretching even the limits of utter impossibility. However, Hahnemann had his own explanation for the skeptic using his potentization-dynamization theory. The vigorous shaking or pulverizing of a substance in between dilutions, he claimed, caused the substance to leave behind a 'spirit-like' essence which, although 'no longer perceptible to the senses', was nevertheless 'remembered' by the water, and thus retained healing properties.
A problem with that explanation, of course, is that such essences would remain from things that weren't in the original preparation. If it works for the 11 herbs and spices prepared by the practicioner, why doesn't it work for the trilobite spit or the coelacanth piss? And if it does work for those other things, then how can one do science on it?
It seems much more likely to me that homeopathy "works" when it does due to placebo effects and due to body finding a way to fight attackers on its own.
There are many deadly diseases, like [link|http://en.wikipedia.org/wiki/Ebola|ebola]. As deadly the Za\ufffdre ebolavirus variant is, 10% of people who get it survive. Estimates of survivability are always estimates. As you say, too many physicians memorize numbers and put much more faith in that than actual observation and thinking about the patient.
Cheers,
Scott.