Review of 'Dialogue Across Chasm: Are Psychology and Neurophysiology Incompatible?'

On Making Sense of Science

The mystery of the world is the visible, not the invisible.

Oscar Wilde

Oftentimes my students begin to argue against something only to find themselves arguing for the same thing, somewhat like Marom (2020, p. 600, "we must accept a long due departure from the habit of neatly arranging things in a hierarchy" vs. "the study of complex hierarchical networks and their development are far more relevant", p. 602). This is diagnostic of a problem with many scientists who have the procedural knowledge of doing science without a declarative understanding of the science (cf. Lawvere, 1992, pp. 15-16; 2003, p. 213; Lawvere and Rosebrugh, 2003, pp. 235-236, 239-240, 245-246). Here is a primer on science for the working scientist.

What is science? Science is about aligning reason with experience. In doing so, more often than not, we find available conceptual repertoire inadequate, which propels the construction of novel concepts that fit the part(s) of reality that is the object of our study; thereby leading to an ever more refined scientific understanding of the reality (Posina, 2020, pp. 78-79). Do we have a scientific understanding of science? Yes, Professor F. William Lawvere's Functorial Semantics provides a mathematical account of theorizing and modeling a mathematical category of particulars (planned perception / experiments; Lawvere, 1963, 1994, 2003, 2004). Before we discuss functorial semantics and the scientific advances beyond Rosen's (1991) "Life Itself", which Marom (2020, p. 602) cites to claim: "We lack the comprehensive methodology to study such relational contexts, and more so when closed loops between dynamical entities at different levels of organization are involved", we show that the claim is false!

Category theory, with its constructs such as category, functor, natural transformation, basic shape, incidence relation, adjointness, and objective logic, constitutes a comprehensive methodology to study relations between universes of discourses (Lawvere and Rosebrugh, 2003; Lawvere and Schanuel, 2009; note that a universe of discourse is a cohesive body of concepts), including [seemingly disparate] neuroscience vis-à-vis psychology (see Posina, Ghista, and Roy, 2017 for a discussion of functorial semantics in the present context) and even more basic mechanism (change) vis-à-vis organism (unity), as Rosen (1958) envisioned: "The representation of biological systems from the standpoint of the theory of categories." Of course, the study of biological organisms and the attendant mind-brain relations from the standpoint of category theory did not stand still in 1958. Professor Andrée C. Ehresmann, beginning with her seminal paper: "Hierarchical evolutive systems: A mathematical model for complex systems" (Ehresmann and Vanbremeersch, 1987) and with her relatively recent book: "Memory Evolutive Systems: Hierarchy, Emergence, Cognition" (Ehresmann and Vanbremeersch, 2007, 2009) continues to explicate the relations between neuroscience and psychology by building mathematical constructs specifically designed to address problems encountered in the development of consciousness science (Ehresmann, 1997, 2002).

In the spirit of nurturing the universal yearning for understanding, let us first address our collective generalized anxiety: reductionism. Let us say, I want to show to myself that I understand how the laptop I am using works. One proof of my understanding of the workings of the laptop would involve two sequential processes: (i) taking apart the laptop into pieces followed by (ii) putting together the pieces into parts of the laptop; note that a part of a whole is both itself and its relationship to the whole (Lawvere, 1994, p. 53). So is the case with science in general and brain in particular, as Carla Shatz, the then Chair of Harvard Neurobiology department, clearly stated: "I think the challenge now is how to put the molecules back into the cells, and the cells back into the systems, and the systems back into [the brain] trying to really understand behaviour and perception" (quoted in Gershon, 2001, p. 4). Simply put, the reductionist analysis is a carefully considered scientific method of understanding (cf. Marom, 2020, p. 602). Analysis--taking apart a whole into pieces--is the first half of the struggle to make sense, which is followed by synthesis--putting together the pieces into parts of the whole--and the significance of the composite process in the advancement of science has been thoroughly established (Lawvere, 2003; Lawvere and Rosebrugh, 2003, pp. ix-x, 154-155). Algebraic modeling of a space begins with subdivision: a breaking of the space into small comprehensible pieces. For example, a line segment is broken into smaller line segments. Next, these pieces are put together: algebraic inverse to subdivision. The composite process--breaking apart followed by putting together--gives a reconstruction of the object of our study (Brown and Porter, 2003; see also Lawvere, 1986, pp. 9-16). Note that this scientific method--synthesis after analysis--is a deep-time-tested method, as is evident in the way our brain goes about representing the reality we are suspended in: "Tactile information about an object is fragmented by peripheral sensors and must be integrated by the brain" (Kandel, Schwartz, and Jessell, 2000, p. 451). Given our finite instruments of knowing in conjunction with the infinite reality, it is not at all clear to me how else can we know? Science--a product of the human brain--is a more modern testimonial of the productivity of the process subsuming neural activity and synaptic plasticity. We, the neuroscientists, owe the most basic rule of synaptic plasticity--"When two elementary brain-processes have been active together or in immediate succession, one of them, on reoccurring, tends to propagate its excitement into the other"--to a psychologist: William James (quoted in Albright, 2015, p. 144). With the authority inherited by virtue of being a quasi-descendent of Kuffler (--> Wiesel --> Lipton --> Posina), I categorically assert that neurons and synapses are not party to any cosmic conspiracies against the theoretical foundations of psychology (cf. Marom, 2020, p. 602). On a serious note, we the students of the brain, behavior, and experience focus on neuron guided by the brilliant insight of Sherrington: neuron recapitulates, in elementary form, the integrative action of the brain (Albright et al., 2000, S3).

We now address Carla Shatz's question: how to put together? Let us begin with a 'putting-together' that we all know very well: 1 + 2 = 3. But, why? Or, what is that we did in summing together the numbers: 1 and 2? We picked the number 3 from a collection of numbers. But, how? Or, what is the most basic property that an object--in a collection of objects--must have in order to lend itself to be chosen? In order to be chosen, an object, in a collection of objects, must be unique. However, the uniqueness is with respect to the operation of sum and the summands. Working our way along these lines, we arrive at the definition of SUM as a universal mapping property (Lawvere and Rosebrugh, 2003, pp. 26-29; Lawvere and Schanuel, 2009, pp. 265-267). Of course, abstract definition is not our objective. Our objective is to understand how properties of a whole relate to the properties of its parts. For example, a one-element set has 2 two-valued properties (2^1 = 2 functions with one-element set as domain and two-element set as codomain) and a two-element set has 4 two-valued properties (2^2 = 4; see Lawvere and Schanuel, 2009, pp. 81-85). Next, let us say we sum the one-element set and the two-element set obtaining a three-element set. Here the three-element set is the whole with one- and two-element sets as its parts. Given the properties of the parts (one- and two-element sets), what can we say about the properties of the whole (three-element set)? Going by the definition of sum, we find that for each pair of properties of the summands (one- and two-element sets), there is a property of the sum (three-element set). In terms of our example of two-valued properties, this means that the sum (three-element set) has 2^1 x 2^2 = 2^(1+2) = 2^3 = 8 two-valued properties. Of course, we are not content with knowing the number of properties of a whole, given the properties of its parts. Knowing the relations between properties, i.e. how one property of an object determines or is determined by another property of the object is much more interesting, all of which takes us to function algebra (Lawvere and Schanuel, 2009, pp. 68-70, 370-371). In addition to the case of a whole determined by its parts, the case of a whole influencing its parts can also be studied using the tools of category theory (Lawvere, 1994, 1999; Lawvere and Rosebrugh, 2003, p. 232). More importantly, in view of the fact that the brain is made up of neurons along with their synaptic connections, COLIMIT, a generalization of sum, which allows putting together of objects along with their relations (Lawvere and Rosebrugh, 2003, pp. 78-79), is better suited for theorizing about the brain, behavior, and conscious experience (Ehresmann and Vanbremeersch, 2007).

If none of the above is authoritative enough, here is Newton explaining the scientific significance of compounding after resolution:

"As Mathematicians have two Methods of doing things wch they call Composition & Resolution & in all difficulties have recourse to their method of resolution before they compound so in explaining the Phaemoena of nature the like methods are to be used & he that expects success must resolve before he compounds. For the explications of Phaenomena are Problems much harder then [sic] those in Mathematicks. The method of Resolution consists in trying experiments & considering all the Phaenomena of nature relating to the subject in hand & drawing conclusions from them & examining the truth of those conclusions by new experiments & new conclusions (if it may be) from those experiments & so proceeding alternately from experiments to conclusions & from conclusions to experiments untill you come to the general properties of things, [& by experiments & phaenomena have established the truth of those properties.] Then assuming those properties as Principles of Philosophy you may by them explain the causes of such Phaenomena as follow from them: wch is the method of Composition. But if without deriving the properties of things from Phaenomena you feign Hypotheses & think by them to explain all nature you may make a plausible systeme of Philosophy for getting your self a name, but your systeme will be little better than a Romance. To explain all nature is too difficult a task for any one man or even for any one age. Tis much better to do a little with certainty & leave the rest for others that come after you then [sic] to explain all things by conjecture without making sure of any thing"

Summing it all, if we begin with a thoroughly understood instantiation of the basic idea of 'putting together' or VERBINDUNG (borrowed from Kant) and gradually refine our understanding, then we might be better equipped to abstract fundamental concepts (e.g. receptive field) that can help advance our understanding of the brain, behaviour, and experience. A theory of mind unmindful of matter may appear courageous from some viewpoint (Marom, 2020, p. 600), but concepts that fit reality matter (see Lawvere, 1992, pp. 28-30, 1994, pp. 43-47, Lawvere and Rosebrugh, 2003, pp. 193-194, 239-240; Lawvere and Schanuel, 2009, pp. 84-85, Posina, 2016).