So to mix the four key ingredients together (honey, nitrates, charcoal and sulphur), when in fact there were literally hundreds of ingredients to select among, was basically a relatively improbable fluke. Mixing them together in the correct proportions (or close enough to get a significant result) was an even bigger fluke. Combusting them, another fluke. And publicizing the result, yet another.
In short, it's incredibly easy for the Chinese to miss out on gunpowder altogether.
If that was a disagreement with my post Dvaldron, it didn't say there was any independent development, in fact I said the opposite. Without the Chinese there would have been no European alchemy, and as far as we know non of the meso-american cultures developed alchemy (but they did develop some drug production).
One can look at your inprobability arguement in reverse, how likely is it for you not to combine the right ingredients together to make any one of the many explosive substances known about.
Let's just take gunpower and say there are 10 steps in creating it, right? and there are 100 different substances known with different chemical properties (they don't know this, but we do; there are more, but we are going to ignore the heayy rare ones);
The chance you pick the wrong substance is 99/100, and you pick incorrectly either 1, 2, or all 10 of them. Making the culmative binomial odds;
Correct Incorrect
1/100 99/100 P(corr.)*P(incorr.) = P(this combination) 1 0.01 0.9135172475 0.0091351725 2 0.0001 0.9227446944 9.2274469442792E-005 3 0.000001 0.9320653479 9.3206534790699E-007 4 0.00000001 0.9414801494 9.41480149401E-009 5 1E-010 0.9509900499 9.509900499E-011 6 1E-012 0.96059601 9.6059601E-013 7 1E-014 0.970299 9.70299E-015 8 1E-016 0.9801 9.801E-017 9 1E-018 0.99 9.9E-019 10 1E-020 1 1E-020
SUM of Probs: 0.0092283885
That you choose a combination with 1 or more wrong ingredients to success. Thus making the odds that you do pick a winning combination is 99%. Before you go; 'wait wat? that make no sense'
You'll realise that I left out all the combinations of ingredients that didn't have at least 1 correct ingredient. Is this valid to do? Well arguably yes, while I'm sure many different 'elixers' were made that didn't contain a single one of the right ingredients, eventually somebody is going to happen on just one of the right ingredients, at random and its going to be used over and over again.
Both Sulpher, Charcoal, Honey and cooking are very common, so its not without a stretch of the imagination that they do get combined in the 'right way' many many times over. Compared to say Rhino horn, which makes it into only 1% of all the elixers ever made.
My point being; if you assume that butterfly legs, and ground up dinosaur fossils are as commonly combined at random as say water and yeast are, then the odds are astronomical that you get the right combination. But the fact is, some combinations are going to be far more common than others. So it makes sense to assume that a decent percentage of the 'elixers ever made' contain at least one of the right ingreidents.
Indeed, your bacon and eggs that you might have cooked for breakfast contains all the ingreidents needed to make gunpowder.
The devil is in the correct amounts, which nobody can really estimate the probability/improbability for with ease. The question then becomes asking do we count all the combinations with trace amounts of this correct ingredient, or this one? Since few people are going to add a 'pinch of this' because it will hardly perturb the end result.
It will quickly boil down to 'equal amounts of each' being the realms of being the 'right orders of magnitude', at which point you could weight these for the avalibility at the time to be combined, thus while you loose possitive probalities due to extremes of combinations, you also would pick up possitive probabilities based on the avalibility of ingredients to experimented with. Thus allowing us to account for the rarity of powdered Rhino horn, or tears of a mountain lion.
Because we have little full knowledge about the process that went on in anicent China at the time we cannot really do this. Therefore we cannot say how probable or improbable it is that we reach the correct combination by random chance.
However we can say this with certainty;
Human experimentation is Baysian by nature; we do not obey random statistics.
Put in the form of science for the layman; if it goes boom, boink or fisses we want to do it again. That means any reaction, will likely receive much more attention than null results. Thus if somebody created an explosive, they are much more likely to create it again because 'its cool', and we are curious.
While I could have said this at the beginning of the post, thus saving myself some writing I wished to highlight why things that we might think are improbable based on random chance take into acount all manner of subtlies that can invalidate them, such a Rhino Horn being as avalible to hand as Charcoal.
This is more the lesson I wished to convey, rather than anything to do with the thread in general. Because your post gives the wrong impression of probability in invention and experiementation. Look up the Philosophy of Science for a bit more indepth discussion than presented here.