TLDR version: the authors (philosophers mostly) who use that ineffable defintion don't measure anything. The authors (psychologists, economists) who do measure "tacit knowledge" use a much more tractable operational definition, generally defined as just not-yet-codified or non-doctrinal knowledge, which is measured like any other knowledge, starting with writing it down.
Frankly, the notion isn't anywhere near as clear or uncontroversial as (say) the Wikipedia article presents it. The fact that one encounters the notion more in management publications than in psychology ones... is a fair warning given the amount of management fads known to mankind.
Now quoting from a paper by Kabir, N. (2013) (whose only merit is that it ranked high a google search), "Tacit Knowledge, its Codification and Technological Advancement":
Several prevailing views regarding conceptual notion of the term tacit knowledge exist. The first view is that
tacit knowledge is part of knowledge that has not been codified as yet (Ambrosini and Bowman, 2001; Boisot,
1995; Davenport and Prusak, 1998; Leonard and Sensiper, 1998; Nonaka and Von Krogh, 2009). This
epistemological dyadic perception places tacit knowledge as a phenomenon directly opposite to explicit
knowledge.
The second view is tacit knowledge by very definition is tacit – ineffable. Any attempt to convert it to explicit is
a futile effort. Tacit knowledge is the background or subsidiary knowledge of the focal knowledge of the act at
hand. Because of this, it is not reducible to the level of explicit as it is only relevant to a specific context
(Tsoukas, 2006: 410; Tsokas and Vladimirou, 2001: 973‐93; Cook and Brown, 1999; Brown and Duguid, 2000;
Jones and Miller, 2007).
The third view that corresponds with our suggestion in this paper: In any context where knowledge is applied,
a part of tacit knowledge, which is overlaid on top of all the knowledge being utilized, will always stay ineffable
and cannot be codified. We can call this fragment of knowledge the “meta tacit”. Apart from this, most tacit
knowledge, depending on the degree of difficulties in codification, its viability of codification and the
availability of required resources could be codified. Collins shows eight different possible reasons or "Cannot"
ranging from inconvenience to impossibility to clarify what types of tacit knowledge are not explicable. (Collins,
2010 pp. 88‐96)
So yeah, pick your poison. And measure the ineffable or some such.
Another paper which calls out some of the (obvious) issues is by Lowney, C. (2011), Ineffable, Tacit, Explicable and Explicit:
Qualifying Knowledge in the Age of “Intelligent” Machines:
There would appear to be problems with any formulation of tacit knowledge, be it Collins’ or
Polanyi’s. First of all, to a critical reader, the term itself can appear to be an oxymoron. Isn’t all knowledge
necessarily explicit? If something is not explicit but somehow veiled in silence, can it properly be called “tacit
knowledge”? There is a second problem as well. If tacit knowledge, somehow operative in the background,
can be made explicit, can it then properly be called “tacit knowledge”? Isn’t the term merely a placeholder
for something unknown that, we hope, will someday become known? Putting both these problems together,
“tacit knowledge” seems to present a dilemma: either it is tacit or it is knowledge, but not both.
Collins begins mainly by addressing the second horn of the dilemma. He agrees with Polanyi that
“tacit knowledge” is not merely a way station on the road to explicit knowledge. For Collins, the proper use
of the word tacit, directly opposes the explicit—it is that which cannot in a strong sense become explicit.
Background knowledge and bodily skills that can become explicit are “explicable” and therefore are not
properly called “tacit” for Collins. So riding a bike or mastering a craft are not, in the end, proper examples
of tacit knowledge, although the experience we have when we ride a bike, drive a car, or learn how to make
a good pair of shoes can fool us into thinking those tasks are inexplicable
So yeah, according to Collins and his followers, Alice's example (bike riding) is not proper. So what is proper tacit knowledge for the purist then?
Collins [...] separates Relational Tacit Knowledge (RTK), e.g., learning
the skill of a master craftsman; Somatic Tacit Knowledge (STK), e.g., riding a bike; and Collective Tacit
Knowledge (CTK), e.g., knowing when it is appropriate to laugh at a joke. Collins rank-orders these phases
on a scale ranging from easiest to explicate (RTK), to more difficult (STK) or impossible to explicate (CTK).
But ultimately, for Collins, both STK and RTK are, in principle, explicable, so without a use for “tacit” as that
which may become explicit, there would be no relational or somatic tacit knowledge per se. Only collective
tacit knowledge would remain. Collins thus widens his use of “tacit” to include the explicable, but he will
occasionally remind us that the proper understanding of tacit comes from its contrast with the paradigmatically
explicit
This to me is reading far more like philosophy than science.
To conclude this, what's tacit knowledge in the military? Well it's
knowledge not well supported by doctrine or formal training
You can certainly measure that (first by writing it down, and then asking questions about it of others)... and they do just that. So it depends how you define it... philosophically or operationally.
And in fact, the latter definition is prevalent in economics as pointed out by Cowen et al., (2000):
Tacit knowledge thus has come to signify an absolute type, namely: “not codified” knowledge. As
such, however, the label now covers the implicit complement of a category of containing a
various forms of information and social knowledge, but which itself usually is left undefined and undifferentiated
So it depends who you ask.
Kabir, N. (2013). Tacit knowledge, its codification and technological advancement. Electronic Journal of Knowledge Management, 11(3).
Lowney, C. (2011). Ineffable, tacit, explicable and explicit: qualifying knowledge in the age of “intelligent” machines. Tradition and Discovery: The Polanyi Society Periodical, 38(1), 18-37.
Cowan, R., David, P. A., & Foray, D. (2000). The explicit economics of knowledge codification and tacitness. Industrial and corporate change, 9(2), 211-253.