On the nature of minds, or: truth and consequences

Abstract

Are minds really dynamical or are they really symbolic? Because minds are bundles of computations, and because computation is always a matter of interpretation of one system by another, minds are necessarily symbolic. Because minds, along with everything else in the universe, are physical, and insofar as the laws of physics are dynamical, minds are necessarily dynamical systems. Thus, the short answer to the opening question is ‘yes’. It makes sense to ask further whether some of the computations that constitute a human mind are constrained by functional, algorithmic, or implementational factors to be essentially of the discrete symbolic variety (even if they supervene on an apparently continuous dynamical substrate). I suggest that here too the answer is ‘yes’ and discuss the need for such discrete, symbolic cognitive computations in communication-related tasks.

Keywords:

• computation
• dynamical systems
• symbolic dynamics
• communication

Acknowledgement

Many thanks to Rick Dale and to Barb Finlay for detailed and insightful comments on a draft of this article.

Notes

Notes

1. How two unknowns can be recovered from a single measurement is an interesting question (Marr 1982; Edelman 2008) that is beside the point for the present discussion.

2. And perhaps even in physics and cosmology (Wolfram 2002).

3. The isomorphism between state transitions does not have to unfold in real time; cf. Grush 2004.

4. A mind is not confined to an individual's brain; rather, it spills over into the environment and in particular, into other individuals' brains (Dennett 2003, p. 122).

5. For an early proposal for a multi-level explanation of how the vertebrate retina may be solving the lightness problem, see Marr (1974). In this connection, see also the multi-level discussion of why the chicken crossed the road (Edelman 2008, table 4.1).

6. Note that quantum computation, which is super-Turing, is most probably not relevant to cognition (Tegmark 2000; Koch and Hepp 2006), even if it proves to be feasible.

7. A partition is ‘generating’ if refining it by resorting to progressively longer discrete representations allows arbitrarily small intervals of initial conditions to be singled out (Crutchfield 1994).

8. It may be continuous at other levels, as it was shown by Spivey (2006) for the case of processing of lexical items, for example; still, such continuous processing is periodically checked by discrete ‘milestones’  — just as a skier rushing down the slope ascribes a continuous trajectory, yet must pass either to the left or to the right of the tree that blocks her way.

9. To make this work, the segments that comprise the communication signal as it unfolds over time must, of course, be sufficiently distinct. This is true of spoken languages despite coarticulation (and the supposedly ‘blurry’ phonology; Port and Leary 2005), and even of sign languages (Sandler 2006).

10. It is worth reiterating here that given a particular process, what is up to interpretation is not whether or not it constitutes a computation, but rather which computation it constitutes. As noted in Section 2.2, multiple answers are usually possible, but their number decreases with the complexity of the process and of the computational interpretation that is being attributed to it.

11. In this connection, Jaeger (1999) writes, ‘I […] believe that neural dynamics, propped by billions of years of freewheeling evolution, intrinsically defies clean definitions  — mathematical rigour hardly being a fitness criterion in natural selection. As a consequence, I do not think that the notion of dynamical symbols can be mathematically defined’.

12. For a definition of explanatory reduction, see Dennett (1995, p. 195).

13. Unless Lloyd (2008) is right and ‘the universe [is], at bottom, digital’.

14. This is why the computer on which I am writing these lines is digital rather than analog. Even the kind of oscilloscope that I used as an undergraduate in the dynamical systems and control lab in the engineering school to plot limit cycles would these days be wholly digital, behind its analog-to-digital front end.