Science and Lutherie
It is a truism that no two guitars are alike. Nor are any two luthiers’ outputs indistinguishable. This in spite of the fact luthiers act like scientists in a fundamental way: we all work by trial-and-error. We typically have an aural vision of the finished guitar and we have an hypothesis about how to achieve this vision. In the course of construction we test that hypothesis and when it comes up a little short we refine our hypothesis and try again. This way our instruments improve, slowly, over many attempts. Of course this is not a fully scientific program, in part because there are no controlled experiments, as we usually work with a sample size of one or two; and in part because we each have unique, personal aural visions of what a guitar should sound like. We each work with a unique set of assumptions and apply unique expressions of intuition. Consequently we don’t all make the same scientifically optimized guitars.
The Bayesian View
Let me elaborate a little. Among philosophers of science there is a school of thought about the nature of scientific reasoning that is sometimes called Bayesian inference, or Bayesian induction. In essence, it claims that scientific reasoning and everyday reasoning are conducted in probabilistic terms. Though belief is a subjective matter, it describes how we, unconsciously or otherwise, apply probabilities to our degrees of belief in a proposition. For example, based on your experience you may hypothesize that a better sounding guitar can be made with heavier braces. In a sense, you are betting that, in the quest for a better guitar, the odds are in your favor if you make your braces heavier. We make these kinds of judgements all the time. We may then build a guitar with heavier braces and modify our original hypothesis accordingly. The prosaic name for this is “trial and error”. Scientists call it “scientific reasoning”.
This is really no different than how a scientist operates, even if he thinks otherwise. A scientist may draw from a broader and deeper range of information when calculating the odds of his hypothesis. His testing procedures may be more sophisticated and undoubtedly better funded. Nonetheless, the Bayesian view is that we are all employing scientific reasoning in our work. In this sense there is nothing mysterious or unattainable about science. Scientists are not members of a priesthood. Inductive reasoning is what we all do in virtually the same way. Scientists have the advantage only to the degree they are more explicitly rigorous in formulating and testing hypotheses.
Unfortunately, our lack of rigor in a complex world makes things a little more difficult for us luthiers. The guitar is a highly non-linear system. By this I mean, for example, that if you’ve discovered some aspect of construction that increases volume – say, making the top thinner – then you might wish to make it thinner and thinner and continue to register gain in volume. In all likelihood, besides all the other undesirable side effects, eventually the guitar would cease to be louder and in fact will begin to lose volume. This is true for every aspect of sound quality. Furthermore, there are usually tradeoffs to contend with. Chasing one desirable attribute, say volume, may undermine sustain, for instance, and at the same time it may degrade sound quality. Finding the right balance of attributes accounts for much of what we strive to do, and every luthier will elaborate unique solutions.
To consider one implication of this I would like to introduce a related idea borrowed from Population Genetics called an Adaptive Landscape. Visualize a 3-D landscape with many hills and valleys of all heights and depths. This vertical dimension is a measure of the “fitness” of a particular guitar design. Now actually, because of tradeoffs and varying tastes and needs among musicians, this single dimension really represents a composite of all sound qualities of the instrument. In essence, the higher the peak, the better the guitar. The two horizontal dimensions of this adaptive landscape – the compass directions – represent all possible ways in which to build a guitar.
Suppose you set out to build a guitar and you pick a design at random, without regard to its merits as a musical instrument. It is shaped like a guitar and has six strings, but it may have a top an inch thick and no braces, whatever… It will probably suck, but something about it may be intriguing, so you tinker with the design here and there and subsequent guitars start to improve. Eventually they may actually sound like a musical instrument. You have been moving, in this process, through the landscape from the point you started in some deep valley of low fitness and been moving by fits and starts up a nearby hill. Eventually you may reach the top of the hill. It might even be the tallest hill in the neighborhood, but it almost certainly isn’t the Mt. Everest of the guitar landscape. If you persevere you will eventually reach the limits of that basic design. To reach a position of greater fitness you will need to start over with a different design concept – a different point in the landscape – and hope that the local terrain ultimately leads to a loftier summit.
All of us luthiers are climbing our local hill like this. We have the advantage, though, that we didn’t start with an arbitrary design. We copied one that was already at a pretty high level of fitness. The problem we face is that we are somewhat blind to the landscape around us. We cannot see whether we are at the peak of some piddly hummock or are valiantly scaling a huge mountain. Our only knowledge of the landscape comes from the successes and failures of our own guitars as we travel on this journey, as well as conjecture based on seeing and hearing the successes and failures of others. But the luthier who makes a better sounding guitar with a thicker top than yours is likely not on the same local peak as you because he does a hundred other things differently as well.
We are all climbing different mountains and we are each at a different elevation of fitness on our respective mountains. We each started from a different place and worked our way up from there. Whether any of us will reach the top and whether my mountain is higher than yours is part of what motivates us. I may be climbing a peak in the Torres Cordillera. My colleague may be scaling Double-Top mesa, or she may be toiling in LatticeLand. Choose your path carefully or you might find that you can’t get there from here.