Blockchain Papers

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Steven M Boker, Michael J. Wenger

In certain mathematical statistical circles, there appear to linger doubts about the soundness of latent variables, in particular common factors in factor models. In what follows we will show, to the best of our knowledge for the first time, that a common latent factor in a factor model can be conceived of as a genuine scientific construct obeying the usual formal criteria for such constructs. Following the discussion in Simon (1977, ch. 6 .6 ) it will be shown that a common factor in a factor model can be transformed into a network of regres­sion relationships between the manifest (observed) variables. Because this transformation is invertible, we end up with two strictly equiva­lent models; the factor model and a model without the factor. This shows that the latent factor in a factor model serves as a placeholder for a system of relationships between the manifest variables and thus obeys the most stringent criterion for valid scientific constructs (cf. Simon, 1977).In what follows, we present a complete constructive proof that the latent factor in a 1 -factor model can be transformed away, yielding a model composed of a network of regression relationships between the observed variables. Preliminary work in this direction can be found in a recent book by the first author that can be freely downloaded from internet (Molenaar, 2003). Also the paper by Rovine and Molenaar (2005) contains further elaborations. But in this chapter, we for 189 the first time present all steps in the proof in full detail and for the simplest possible situation, a 1 -factor model. Even though we take great care to explain the steps in the proof as clearly as possible, a lot is asked of the reader. We suppose that they have a working knowledge of structural equation model­ing, are acquainted with elementary matrix algebra, and are willing to work through some unfamiliar notions taken from time series anal­ysis. These efforts only can be asked if the returns are irresistible. And in our opinion the results presented in this chapter are quite revolutionary. For the first time a general technique, an invertible transformation, is presented with which one can remove latent vari­ables from a latent variable model without any loss of information. This makes explicit something basic about the scientific nature of la­tent variables: They are real and have solid groundings in the data. It turns out to be a matter of taste whether one wants to enter­tain a latent variable model, or instead, its equivalent representation without latent variables. Of course, latent variable models may be better interpretable (in our opinion, they almost always are) and we certainly do not want to advertise the unconditional use of our trans­formation technique. But a proof that latent variables, in particular common factors, can be reduced to functional relationships between manifest variables shows that these latent variables share all their for­mal and semantic qualities with other respectable scientific constructs like electromagnetic potential, entropy, and so forth. This is not only important from a philosophy of science point of view, but also for discussions about the status of well-known psychometrical constructs like reliability and validity (cf. Borsboom, Mellenbergh, & Heerden, 2003). Another implication of the proof to be given shortly is that all structural equation models can be shown to be nested. This par­ticular implication is not elaborated in this chapter, but details can be found in Rovine and Molenaar (2005) and in Molenaar (2003). To give one particular example, it can be shown that the latent growth curve model is nested under the latent simplex model (contra Rogosa & Willett, 1985; see also Mandys, Dolan, &; Molenaar, 1994). But the harvest is much bigger. If, as will be shown, it is possible to remove the factor from a 1 -factor model, then apparently it is possible to reduce the common latent dimension from one to zero. Because after the removal of the latent common factor (which defines the common one dimension in the initial 1 -factor model), there are no longer any common latent factors in the obtained equivalent model (hence the latent dimension in the latter model is zero). It is shown in Molenaar (2003) that this result holds in general. To illustrate, starting with a standard 2-factor model (where the two factors span up a two-dimensional common latent space), it is possible to transform this model to an equivalent model in which the common latent space is one-dimensional. Finally, the model obtained in the previous step can itself again be transformed into an equivalent model in which the common latent space is absent (zero-dimensional). This, of course, raises urgent questions about the proper definition of the dimension of a common latent space (like in statements such as “this psycho­logical test is indicative of two underlying dimensions”). There are additional important implications, although of a much more theo­retical nature. We mention only the direct relationship of the kind of result that we are about to prove with similar results obtained in mathematical system theory and statistical field theory (both of which are elaborated somewhat further in Molenaar, 2003). We hope and expect that sufficient reasons have been provided to carry on reading this chapter.

Ward-Steinman

An Invitation to Play:A Response to Patrick Schmidt's "What We Hear is Meaning Too:Deconstruction, Dialogue, and Music" Patrice Madura Ward-Steinman The aims of dialogue-as-deconstruction, as described by Patrick Schmidt, are concepts I have pondered as a result of a five-week sabbatical visit to Melbourne, Australia. My research focus there was improvisation, and early in my visit I attended two concerts at the premier jazz club, Bennett's Lane. There I heard twelve improvisers in a variety of ensembles, all in celebration of the seventieth birthday of their mentor, Tony Gould, who also performed. Gould is cited by John Whiteoak and Aline Scott-Maxwell as an "outstanding player who has never ceased to develop as an improviser" and who "as a pianist, records prolifically across a wide musical spectrum."1 While the music was jazz, it was freer and fresher than usual. There was striking interaction among the musicians, including facial expressions that reflected genuine ecstasy, and body movement that was naturally "in sync" with the music. I began to ask many questions, including: Is Australia's jazz different from that [End Page 82] in the U.S.? Is Tony Gould's influence as a teacher the reason for the difference? What accounts for the sensation of "freshness" in this music? And why is this musical experience so gripping, both aurally and visually? Serendipitously, I discovered answers through the opportunity to respond to Schmidt's aims of dialogue-of-deconstruction. I shall illustrate how those aims, namely decentralized power and conflict, multiplicity and meaning, and mis-listening may be met in the improvising music ensemble. Decentralized Power and Conflict The lifeblood of "free jazz" and "free improvisation" ensembles is de-centralized musical interaction, which may be considered a metaphor for dialogue-as-deconstruction. Case in point: the Tony Gould Quartet was an improvising unit with each musician contributing to the musical whole. The air was electric with each musician poised in both the anticipation of what the other might play and in the moment of creation. A recent trend in studies of organizational behavior is on "self-directed" or "self-managed" groups, as identified by Keith R. Sawyer.2 David Borgo3 explains that the characteristics of these "self-organizing systems" or "SOSs" are threefold: they operate without centralized control, they "exhibit both complex and adaptive dynamics," and they are comprised of autonomous individuals who demonstrate a high degree of connectivity. Both authors assert that an ideal SOS is the free improvising ensemble, where musical ideas are allowed to emerge and adapt, and even musical "mistakes" may be manipulated into the context, thus creating new directions in dialogue. However, SOSs have some inherent problems. For example, they are "slow to emerge. . . . The more complex they are, the longer it may take them to warm up: hierarchical layers have to settle down . . . and individual(s) have to acquaint themselves with one another."4 Borgo explained that even advanced improvisers often need to pursue a musical idea for a long while for it to achieve coherence. Philip Alperson adds: "As the number of designing intelligences increases, the greater is the difficulty in coordinating all the parts; the twin dangers of cacophony and opacity lurk around the corner."5 It seems that "interactional synchrony"6 can develop among musicians who have "good chemistry" after a warm-up period, but those with conflicting personalities, aesthetic dispositions, or musical styles may have a more difficult time of it. When members of the Tony Gould Quartet were asked how they are able to achieve musical unity, they explained that they have played together for many years, they "hang out and drink together" when not on the bandstand, and they trust each other. Even when one of the members feels "out of sorts," their improvisations are respected as authentic expressions. Others' differences are honored, [End Page 83] rather than felt in opposition to one's self.7 Ingrid Monson8 quotes several musicians who use the metaphor of marriage to describe the musical relationship during a peak performance; on the other hand, jealousy, competition, and even hostility on the bandstand are not uncommon and can destroy an ensemble. So, it appears...

Jeffrey Melnick

"Soul" Jeffrey Melnick (bio) Sometime in the mid-1990s, Steve Bernstein was asked by John Zorn to make a record for Zorn's Radical Jewish Culture series. Bernstein is a downtown New York avant-garde jazz trumpeter and bandleader—a member of John Lurie's Lounge Lizard's and leader of his own Sex Mob—a group that specializes in free jazz versions of James Bond theme songs and covers of Abba and Prince. Bernstein explains that he was initially puzzled by Zorn's invitation. He writes in the liner notes to Diaspora Soul, the record he finally made for Zorn: "I was left with an enigmatic question. How does a Jewish musician who has spent his life studying 'other' musical cultures make a 'Jewish' record, when, by nature, all of one's music is already 'Jewish'?" Bernstein, by his own account, struggled for three years with this question, and then finally had what he calls his "Gulf Coast epiphany":"I had been doing a lot of reading and listening for the past few months to the music of New Orleans, and had been developing a theory about the evolution of New Orleans marching band music not into what we call jazz, but into rhythm and blues."1 Those of us familiar with the discourses of Black-Jewish likeness see now where this is going, and forgive us if we are cringing: somehow Bernstein will punctuate this musicological genealogy with some definitive proof that the diasporic souls of Black folk and Jewish folk are linked and that these links take musical forms which, if not identical, exist at least in some kind of natural harmony. This is a line of thought that's been promoted for almost a century now: Alexander Woollcott said it about Irving Berlin, stride pianist Willie the Lion Smith said it about himself, Harvard professor Isaac Goldberg said it about George Gershwin, Mezz Mezzrow said it about himself . . . and the list goes on and on. In academic discourse this position was staked out most influentially by Irving Howe, in his World of Our Fathers, where he described Jews in blackface as sympathetic actors who used the Black mask as a vehicle to articulate their own woe. Amazingly, Michael Alexander, in his recent book Jazz Age Jews,2 pushes this insensitive argument even further: according to Alexander, [End Page 13] Jolson was so sympathetic to African Americans that he was willing to compromise his own upward mobility by donning blackface. Michael Alexander's Jazz Age Jews is only the most egregious and relatively recent expression of an ahistorical and politically dangerous axiom undergirding much of what passes for "Jewish Studies." The axiom is "We all know what 'Jew' signifies and we all know it is kind of a synonym for 'Black' anyway." Even the newer Jewish studies tends to make indefensible claims about the meaning of Jewishness—while these claims vary from place to place there are consistent assumptions being made that there is an audience out there in agreement that "Jew" still marks off some recognizable territory or activity. The purpose of my paper is to argue against unanimity, against consensus. My primary motivation is political: in an era when "Jew" too often signifies an "us" putatively opposed to "them" (Arabs) I want to suggest we take a break from imagining "Jew" as any kind of stable or singular identity. And as a cultural historian I want to take note of a new generation of cultural actors and activists—Jewish one way or another—who are busy inventing heretofore unknown ways of being, sounding, looking, and "acting" Jewish. These new Jews range from the immensely talented Jonathan Safran Foer, whose first novel3 offers a Ukrainian descendant of Nazi collaborators as its hero, thereby purposely denying the easy comforts of an us vs. them orientation, to the Jewish two-thirds of Sleater-Kinney, the all-woman band that redefined punk rock as a woman-centered activity in the 1990s and early 2000s, and the Jewish two-thirds of Northern State, who seem poised to do the same for hip hop. My standards are loose here: this is a Jewish "generation" only insofar as I say so...