The Violin Problem: On Knowing More Than We Can Tell

We’ve spent three centuries trying to replicate a sound we understand but cannot explain.

There are roughly six hundred Stradivarius instruments left in the world, objects so singular in their construction and effect that they stand at the intersection of art, science, and myth. Individual violins command tens of millions, and their voice has resisted reproduction with a persistence that borders on the absurd. This resistance is not due to any lack of effort. Modern science has brought to bear upon these instruments the full weight of its analytical machinery: the wood subjected to chemical dissection, the grain mapped, the varnish interrogated, the density measured, the curvature modeled to tolerances of precision that Stradivari himself could neither have conceived nor required.

We have, in short, learned a great deal, and yet we have not closed the gap.

The natural inclination is to suppose that something remains undiscovered — a missing variable, or some hidden treatment — and that the problem is therefore one of incompleteness rather than misclassification. But this assumption already concedes too much. It presupposes that the knowledge in question is of a kind that submits to reduction, that what Stradivari knew might, given sufficient analysis, be rendered into a sequence of instructions.

It was not.

What Stradivari knew did not exist in propositions awaiting articulation, but in judgment accumulated through practice: in the selection of wood by feel, in the anticipation of how a given plate would respond before it had been shaped, and in the execution of innumerable small, irreversible decisions of thickness, tension, and form whose significance could be neither fully observed nor faithfully recorded. When he died in 1737 and the workshop tradition that sustained this way of knowing gradually dissolved, nothing was lost in the conventional sense. There was no formula misplaced or documents destroyed.

The knowledge did not disappear. It ceased to exist.

The same distinction, between what submits to articulation and what can only be embodied, reappears in Bach’s Partita №2 in D minor, composed for solo violin during the very years Stradivari was at the height of his craft. Its final movement, the Chaconne, stands among the most structurally and emotionally expansive works ever written for a single instrument.

Brahms, writing to Clara Schumann, confessed: “If I imagined that I could have created, even conceived the piece, I am quite certain that the excess of excitement and earth-shattering experience would have driven me out of my mind.”

Every note of the Chaconne is explicit. The score is complete, portable, and perfectly reproducible. It may be printed, transmitted, and studied.

And yet the performance remains irreducibly variable. Two violinists, working from the same notation on the same instrument, may produce experiences so distinct as to seem, at moments, entirely unrelated. The divergence lies not in what is written but in what cannot be written: in the pressure of the bow, the shaping of a phrase, the infinitesimal calibrations of timing and emphasis that occur too quickly and too integrally to be separated from the act in which they are embedded. The score tells the performer what to play. It does not, and cannot, tell him how.

Between the notation and the music, something intervenes.

It is to this intervening dimension that Michael Polanyi gave a name. A Hungarian-born chemist turned philosopher, Polanyi devoted the latter half of his career to a discrepancy so pervasive it had become invisible: the difference between how knowledge is described and how it is actually acquired and exercised. His formulation, offered in the opening line of The Tacit Dimension (1966), is deceptively simple:

“We can know more than we can tell.”

In its diluted modern usage, “tacit knowledge” has been reduced to a problem of incomplete documentation: the knowledge that practitioners carry but have not yet committed to manuals or systems. The proposed remedy is procedural: capture, codify, and store. With sufficient effort, the tacit is presumed to yield to the explicit.

Polanyi’s argument admits of no such resolution.

He was not identifying a deficiency in record-keeping, but a feature of what it means to know. Tacit knowledge is not explicit knowledge awaiting transcription; it is knowledge that resists articulation — not contingently, but necessarily. The difficulty does not arise from inadequate tools or insufficient diligence, but from the fact that making such knowledge explicit alters its function. What is made focal ceases to operate subsidiarily, and thereby ceases to function as knowledge in the original sense.

Polanyi arrived at this view as a practitioner. His early career in physical chemistry had already established him as a serious scientist, yet it was a visit to the Soviet Union in 1936 that redirected his intellectual life. There, he was informed that scientific inquiry would be subordinated to the needs of the state, that research would be planned and discovery organized in accordance with centrally determined priorities.

What Polanyi recognized at once was not merely the political danger of such a system, but its epistemic impossibility.

Scientific discovery depends upon a form of judgment that cannot be specified in advance: the recognition of significance where no rule yet exists, the pursuit of lines of inquiry that cannot be justified ex ante, and the abandonment of others without formal disproof. It is guided not by procedure but by a cultivated sensitivity to what might matter — a sensitivity that precedes articulation and cannot be recovered once articulation has displaced it.

From this, Polanyi derived a broader conclusion: that all knowledge, even in its most formal expressions, rests upon tacit foundations.

The structure of this claim is clearest in his distinction between focal and subsidiary awareness. When one drives a car, attention is directed toward the road — the traffic, the direction, the destination — while a host of subsidiary elements operate beneath: the pressure on the pedal, the positioning of the hands, the alignment of the mirrors. These are not unconscious, but they are not the object of attention. They are what attention leans on to be directed elsewhere.

Reverse this relationship — draw attention away from the road and fix it instead upon the subsidiaries — and the act begins to deteriorate. The violinist who attends, not in passing but in totality, to the bow, the fingers, or the mechanics of execution forfeits the very fluency those elements were meant to serve. The disturbance lies not in awareness itself but in its reordering: what should be indwelt is instead made explicit. Integration does not endure such inversion. It disintegrates under it.

It is in this integration that tacit knowledge resides. “We know a thing by relying on our awareness of it for attending to something else,” Polanyi writes in The Tacit Dimension — an act he describes as indwelling, in which the parts are not objects of attention but the means by which attention is made possible.

To render its components fully explicit is not to preserve it, but to disassemble it. The subsidiaries, once made focal, cease to function as supports and become objects in their own right, and the act they once enabled dissolves in the process. From this follows a conclusion Polanyi states without apology:

“A wholly explicit knowledge is unthinkable.” (Personal Knowledge, 1958)

Grant this, and the modern ambition to render the world fully legible through models, metrics, and machine intelligence is not merely incomplete but misdirected. It aims, however unintentionally, at the elimination of the very ground upon which all judgment stands.

The parallel to Hayek is not incidental. Where Hayek identified the dispersion of knowledge across markets, Polanyi identified its irreducibility in practice. In both cases, the error lies not in execution but in conception: the belief that knowledge can be fully articulated, collected, and redeployed from a position of central oversight.

As Hayek observed, “the knowledge of the circumstances of which we must make use never exists in concentrated or integrated form.” (The Use of Knowledge in Society, 1945)

More precisely, what Hayek located in prices, Polanyi located in perception. Prices coordinate dispersed knowledge without requiring its articulation; tacit integration achieves the same within the act of judgment itself. In both cases, what is known exceeds what can be stated, and what is coordinated exceeds what can be directed. To suppose that either can be replaced by explicit instruction is to misunderstand the very mechanism by which knowledge operates.

The development of modern finance may be understood as a sustained attempt to render knowledge explicit: to translate judgment into models, experience into data, and uncertainty into quantifiable risk. Each stage in this progression has yielded genuine gains, yet running beneath it is a largely unexamined premise: that what resists formalization is either negligible or merely not yet formalized.

Polanyi’s argument suggests otherwise. The tacit does not diminish under formalization. It withdraws — becoming less visible precisely as it becomes more consequential.

The attempt to render knowledge fully explicit does not merely leave something out; it alters what remains. We begin to treat what can be stated as though it were the whole of what is known, and what cannot be stated as though it were dispensable. What is lost is not only the tacit dimension itself, but the recognition that anything has been lost at all.

The limitation is not merely that such systems fail at the margin, but that in succeeding where they can, they alter the conditions under which judgment itself is formed. In displacing the need for interpretation in ordinary cases, they reduce the occasions on which interpretation is exercised at all. What atrophies is not the tolerance for error, but the capacity to recognize, correct, and ultimately learn from it. The risk, then, is not only that we rely upon systems that cannot replicate tacit knowledge, but that we gradually lose the capacity to generate it.

Tonight, I will sit in a concert hall in Louisville and listen to Itzhak Perlman play a violin built in Cremona in 1714 — the “Soil” Stradivarius, once owned by Yehudi Menuhin, widely considered one of the greatest violinists of the 20th century.

I have listened to Perlman long enough that the anticipation carries its own specific gravity. There is no violinist alive in whom the argument of this essay is more plainly audible: the technique so thoroughly inhabited that it has ceased to be technique, the interpretation so fully indwelt that nothing announces itself as interpretation. Among the works on the program is Morricone’s Love Theme from Cinema Paradiso — a melody so unguarded in its longing that its power seems unanalyzable. One can describe its harmonic structure, identify its intervals, and notate every instruction the score contains. None of it accounts for what the piece does.

The instrument has been studied, measured, and analyzed more thoroughly than Stradivari could have imagined. Its materials and dimensions are known, and in principle, nothing about it is hidden.

And yet what will occur in that room will not be contained in any of this.

The sound will emerge not from the wood alone, nor from the score, nor from any description that might later be offered, but from the integration — from the contact between bow and string, from the accumulated judgment of a lifetime, from the innumerable decisions made too quickly and too integrally to be separated from the act itself.

We will hear something we cannot explain, and understand it nonetheless.

There is an analog of this gap in investing. It does not present itself as a discrete insight. It appears instead as judgment: in the recognition that a client’s plan, though technically sound, will prove untenable under pressure; in the sense that market consensus has hardened into complacency; in the perception that risk resides not simply in the data, but in the uniformity of its interpretation.

What is at issue here is not mysticism, nor a plea for intuition unmoored from discipline. It is, rather, the claim that disciplined judgment itself depends upon forms of awareness that cannot be exhaustively formalized without distortion. One may describe the conditions under which such judgment emerges, and one may certainly refine it through experience, criticism, and rigorous analysis. But one cannot detach it entirely from the situated act of appraisal in which it has its life.

This, in turn, illuminates the Stradivari example. The measurements remain; the materials remain; even much of the relevant technique can be reconstructed with considerable faithfulness. What does not remain, at least not in any fully transferable form, is the integrated practical knowledge that once animated the workshop. It did not fail to survive transcription; it belonged to a mode of knowing for which transcription was never sufficient.

Polanyi’s enduring importance is most fully apparent at precisely this point. His argument was not that some residue of knowledge has yet to be formalized, but that formalization itself rests upon tacit acts of integration that cannot be made fully explicit without ceasing to function as such. To say that we know more than we can tell is therefore not to identify a temporary limitation in our methods. It is to describe a permanent feature of human inquiry.

That feature is readily obscured in an intellectual culture increasingly disposed to equate what is explicit with what is real, and what is measurable with what is authoritative. Yet the obscurity does not eliminate the dependence. In science, in art, and no less in investing, the most consequential forms of judgment continue to rest upon subordinated acts of perception, discrimination, and integration that resist, and will always resist, full articulation.

The argument, then, is not that explicit knowledge is unimportant, nor that models, metrics, and formal systems are dispensable. It is that they are insufficient, and insufficient not accidentally, but in principle. They presuppose a knower who can indwell a practice, integrate its elements, and discern significance before it has been made fully explicit.

We know more than we can tell.