The Embodiment of Mind
What is a Number, that a Human may know it
and
A Human, that S/he may know a Number?
McCulloch (1965)
NUMBER: McCulloch (1965, p. 6) uses Russell’s definition of a number: “A number is the class of all those classes that can be put into one-to-one correspondence with it.” As an example, he notes that “7 is the class of all those classes that can be put into one-to-correspondence with the days of the week, which are 7.”
HUMAN: Neural Net (McCulloch and Pitts, 1943)
What is Formalism X, that a human may know it
and
A human that s/he may know Formalism X?
Emergence as a formalism
Every theory about the world, each formalism, every model and metaphor about emergence, or about any other phenomena for that matter, presupposes, typically unconsciously, some framework of the nature of being human. Often this presupposition is hidden and unexamined in the social milieu of the scientist espousing the formalism. McCulloch is proposing that this fundamental relationship between an idea and a framework about the nature of the being that proposes and knows the idea, largely ignored by scientists, be addressed explicitly.
The objective pretense won’t do. The theory is not out there, outside of us, to be validated or falsified by data collected out there. At the final moment, when a person decides a particular theory or model is relevant or useful or otherwise embraces it, it a human making a human judgment about a human construction. McCulloch’s double requirement that we be explicit about the relationship between the nature of the formalism and the nature of being human is critical. What is formalism X that it may be known by a human, and a human that s/he may know formalism X?
Turing: The Chemical Basis of Morphogenesis
E42: An N, K Boolean System
The first four columns (a to d) are four basins from the same dynamic system. The fifth column (e) is a basin from a different dynamic system.
These are static snapshots
Morphogenesis
--Emergence of Form
Is a ongoing, dynamic process
The development of biological structures
The Maintenance of a pattern of fur
Intuition as a legitimate methodology
Two Assumptions from the methodology of
Transformational GrammarFirst: the paradigmatic centrality of human judgment based on direct experience (what Chomsky calls intuition).
Second:Human behavior is rule driven; moreover, in the linguistic paradigm, it is assumed that native speakers have internalized the grammatical rules of their native language so that their intuitive judgments are based on these rules.
Algorithms (e.g., neural nets) drive human behavior
A FORMALISM for Emergence such
That a Human may know it
E42: N, K Boolean System
Kauffman: Processes of biology
E42: Processes of Epistemology
An N, K Boolean system consists of N nodes, each taking input from K other nodes. This input consists of either a 0 indicating that the other node is OFF or a 1 indicating that the other node is ON. At any time, T, every node in the system uses a logical operator whose arguments are its inputs to decide if it will be ON or OFF for the next iteration (T+1). For example, if a node has two inputs and its operator is the logical AND operator, then it will be ON during the next iteration (T+1) only if both its inputs are ON during the current iteration (T). If another node is using the logical INCLUSIVE OR operator then it will be ON at T+1 if either one input or the other or both are ON at time T. If a node is using the logical EXCLUSIVE OR (XOR) operator then at T+1 it will be ON if its two inputs are the different (that is, either {0,1} or {1,0}); conversely it will be OFF if its two inputs are the same (that is, either {0,0} or {1,1}). Any legal logical operator can be used and which operator actually is used by each node is decided pseudo-randomly when the system is first built.
How can we REPRESENT an N, K Boolean
system
that a Human may know it?
Historical Trace
Figure
2. Two Derivative-1 Categories |
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| Figure 2. Four basins from a pseudo-randomly generated dynamic system. Panels (a) and (b) are perceived as similar as are panels (c) and (d). | ||
| a
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b |
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Vertical Axis
Horizontal Axis
First Derivative Categories
Second Derivative Categories
Figure 3 Second
Derivative Categories |
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Second Derivative Category
A |
Second Derivative Category B |
|
First Derivative
Category 9 |
First Derivative
Category 1 |
First Derivative
Category 2 |
 |
 |
 |
Hierarchy of Emergence
3: The emergence of Meta-Categories of Form from
from the process of taking differences in differences in differences
2: The emergence of Categories of Form
from the process of taking differences in differences
1: The Emergence of Form (Turing) from process of transforming differences
Human Experience as Reference Point
Let us return to our epistemological frame with a quote from Bostic St Clair and Grinder (2001, p. 76):
“The linguist manipulates the syntactic, phonological, and semantic forms and judges and/or asks native speakers to judge whether the consequences are a well-formed sentence in the language, an ambiguous string or any one of an array of numerous other possibilities. The relevant reference point by the very nature of the research is internal to the bearer of the internal grammar – the native speaker himself.
“To put the matter in a somewhat different form, suppose that we succeeded in constructing an instrument that purportedly arrived at the same judgments for visual inputs as those possessed by normally sighted people.
“How would we know whether the instrument worked?
“The answer clearly is that we would accept the instrument as accurate if and only if the responses of the instrument matched those of normally sighted people. In other words, we would calibrate the instrument by using precisely the same set of judgments (intuitions) reported by the people involved that we presently use in the absence of such an instrument.
“Thus in fields where the patterning under scrutiny is patterning of the behavior of human beings, the reference point and the source of the judgments will necessarily be the human being.”
Integrate the 2 sides of of McCulloch's cybernetic question
What is Human Epistemology?
That a Human may know Emergence?
The transformation of differences across a richly connected network
Neural Nets
McCulloch & Pitts, 1943
Holland, 1975Bateson: Six Criteria of Mental Process
(1) Mind is an aggregate of interacting parts or components.
(2) The interaction between parts of mind is triggered by difference.
(3) Mental process requires collateral energy.
(4) Mental process requires circular (or more complex) chains of determination.
(5) In mental process the effects of difference are to be regarded as transforms (i.e., coded versions) of the difference which preceded them.
(6) The description and classification of these processes of transformation discloses a hierarchy of logical types immanent in the phenomena.
E42: (N, K Boolean System)
Designed to simulate
this Epistemological Framework
Human Judgments based on Direct Experience:
The relational reference point
for
Integrating the two sides of
of
McCulloch's Question
