When the auctioneer’s hammer went down, the violin sold for almost $16 million. It was one of the masterpieces of Cremona, the small northern Italian town that was the 18th-century center of violin-making. Ever since, the world’s best violinists have insisted that instruments made by Antonio Stradivari and his colleagues demonstrate a uniquely wide dynamic range and subtle tonal quality. So why can’t we make them like that now? Nobody really knows.

To begin with, the masters left no instructions. Some critics of trade secret law have cited Cremona as an example of progress “lost” because it was buried instead of published through a patent application. There are several reasons why that argument fails, but for today let’s consider the possibility that the violin makers couldn’t have passed on their secrets if they wanted to, simply because they didn’t know what made their violins sound so good.

Maybe they thought it was just their extraordinary skill. Stradivari, who worked until he was 92 and is credited with creating over 1,100 instruments, was not shy about promoting both his talents and his violins to royal buyers. His friend Guarneri was almost as commercially successful, and the Cremona luthiers as a group did nothing to dispel everyone’s assumption that the beautiful sounds were a product of nothing more than their superior individual craftsmanship. In any event, it was the result that mattered, even if no one could say what produced it.

Within the last century, as the remaining instruments were collected and prices began soaring, the search was on to re-discover the secrets of Cremona. For years, many credited the varnish. Recently, scientists discovered a particular bacterium had infested logs floating down river from the alpine forests, munching away enough of the interior of each cell to create an unusual resonance when the wood was dried and fashioned into a violin body.

So can you have a trade secret just because it produces results, if you don’t know how it works? The answer is yes; the law doesn’t require that you fully understand the mechanism that generates the effect. This is a good thing, since otherwise we might spend an inordinate amount of time peeling back the onion layers of causation in the search for the “ultimate” explanation.

In medicine, we long have used natural materials or drugs that are correlated with improvement or cure without knowing exactly how they work. Even when we think we know it, the human body’s systems, being almost infinitely complex and interdependent, laugh at us.

That doesn’t mean that the search for causation is a fool’s errand. Frequently, in trying to understand how we get good outcomes, we stumble on a related discovery that proves very helpful. This is what happened with the Cremona violins. On the heels of the revelation about cellulose-eating bacteria, researchers identified two types of fungus that perform roughly the same feat, after the fact. Applied to existing violins of lesser quality, these fungi do just enough of the right kind of damage to help the instruments approach the sublime quality of a Stradivarius.

A child, by trial and error, learns to ride a bike, but ask her how she does it and she can’t really explain. It has something to do with balance, but what is that? How many adjustments per second does she have to make? What role does speed play? (If you’re thinking none, then just compete with other family members to see who can ride the slowest without falling over.)

Machine learning, a kind of artificial intelligence, allows us to recognize patterns and establish correlations but not necessarily causation. Instead, multiple variables breed multiple hypotheses, and these become multiple opportunities for mining useful insights. A pattern extracted from big data can be applied by itself to improve the functioning of some systems, but it can also point us toward deeper understanding and even greater advantage. Discovering a secret often begs many questions, and leads to the discovery of more.

One lesson is that, when it comes to outputs, the assumptions we make about causation can sometimes mislead us, preventing us from using information about the phenomenon to developing new innovations. While we don’t have to know how our valuable trade secrets work, it usually pays to keep looking while we’re exploiting the advantages they provide. In fact, there may be some nuggets waiting to be uncovered by reverse engineering the good results produced by others. That is one of the ways that secrecy incentivizes innovation every bit as well as patenting.

We can enjoy the music at the same time that we try to understand how it’s made and why it moves us.