La distancia Lempel-Ziv y SSC

Human natural language requires a form of hierarchical processing, which it has been hypothesised involves the Merging of syntactic objects of increasing size. This sort of scale invariance is a distinctive feature of self-organising systems, and lends itself naturally to the dynamical interpretation. That sanguinity has been known for decades: Conjecture about Fibonacci sequences is more or less de rigueur in considerations of evolution of language. The other reason for favouring a dynamical interpretation is more recent and inspires considerably more confi- dence: EEG imaging has begun to provide strong evidence that the brain comes pre-equipped with a means for encoding multiply scalar dependencies. The basis of this progress is a deepened understanding of how homeostatic rhythms respond to input signals. The rhythms in question are the commonplace wave frequen- cies—beta, delta, theta, etc.—which emerge from the excitation and discharge of cortical structures. What is novel is the discovery of how interference patterns among these frequencies encode information. Patterns interfere with one another in much the same way as people do: The loudest ones cause the most disruption.

Another way of thinking about interference is to consider the waves cre- ated by displaced water from a pebble or the stern of a boat. Waves of greater magnitude—from heavier pebbles or faster boats—will consume ones of lesser magnitude. The same is true for brainwaves. A ‘louder’ wave with greater ampli- tude influences ‘quieter’ ones. This becomes of great significance when the rela- tionship between wave amplitude A and frequency f is plotted on a log scale. The result is a neat perfect line: A covaries almost perfectly with 1/fn_{. Neuroscientist}

György Buzsáki elaborates on why we should think this an important correla- tion:

[T]he inverse relationship between frequency and its power is an indication that there is a temporal relationship between frequencies: perturbations of slow frequencies cause a cascade of energy dissipation at all frequency scales. One may speculate that these interference dynamics are the essence of the global temporal organization of the cortex. (Buzsáki, 2006: 119; emphasis mine)

“Thus”, he claims a few pages later, “it should not come as a surprise that power (loudness) fluctuations of brain-generated and perceived sounds, like music and

14 _{This geometric character is particularly evident, for instance, in Kayne’s (1981) discussion of} ‘unambiguous paths’ in the binding of anaphora.

Optimality and Plausibility in Language Design 129 speech, and numerous other time-related behaviors exhibit 1/f power spectra” (Buzsáki, 2006: 123).15

There has been good confirmation of the hypothesis that cortical en- trainment of theta band oscillation responds to linguistically relevant syllabic units, with phase patterns observed to discriminate between actual and non- actual human natural language sentences (Ding et al., 2015). Poeppel’s lab has extended this significance to the phrasal level via precisely the mechanisms of rhythmic entrainment just described (Figure 9), showing that cortical responses closely track the temporal envelopes of phrase-level syntactic objects (Ding et al., 2015: 4). The interaction of different frequencies at varying spatio-temporal scales depicted in the figure allows for hierarchical structure in signal processing.

Figure 9: Cortical entrainment of temporal envelopes. The table on the left depicts ten distinct oscillating frequencies in the mammalian brain (Buzsáki, 2006:114). Top right is an illustration of low frequency delta waves overlaid by higher frequency theta and beta waves. The interaction of these different frequencies at varying spatio-temporal scales allows for hierarchical structure in signal processing (bottom right).

What this suggests is that one sui generis property of human syntax—its capacity for hierarchical embedding—is a consequence of the power law holding between different rates of cortical oscillation.

These findings have recently been developed into concrete proposals for the recent evolutionary history of human syntactic cognition by Murphy (2015, 2016a, 2016b) and Ramírez (2015) which provide a plausible explanation for sev- eral syntactic phenomena (Murphy, 2015). Murphy (2016a) describes how the coupling of higher frequency gamma and lower frequency theta waves could provide a kind of “binding memory” that preserves the complex wholes of phrases.

15 _{This gradient has been known since the mid-nineteenth century. For instance, Weber’s} Law—named for Ernst Weber (fl. 1830–40)—noted the basic configuration in the exponential ratio of ‘just noticeable’ perceptual characters to the strength of stimulus. Well-noted exam- ples include the phenomenological experience of heaviness compared to an object’s actual weight, and the perceived versus actual change in illumination of a light source.

M.R. Levot

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Figure 10: An ‘oscillatory tree’ demonstrating the alignment of syntactic-level phrases with oscil- latory frequencies (Murphy, 2016a).

An interesting corollary of this schema is that it may explain *XX (Boeckx, 2013) and *{t,t} (Narita, 2015; in Murphy, 2015: 13), violations in which elements of the same category (e.g., NP, VP, CP) cannot occur adjacently.

(12) ∗ JohnNP MaryNP ate apples.

(13) ∗ [which picture of the wall]i do you think that [the cause of the riot]j was {ti,tj}?

These patterns may occur, Murphy contends, because only a single binding from the high frequency gamma wave can be sustained at one time, adding further explanatory weight to the oscillatory framework.