Shape

155 Background
again. My eyes are stitched all over with the certainty that what’s been given before
doesn’t change. There’s simply nothing new to see. It’s just counting out. But then
there’s nothing new to design.
Background
Most of the material from William James is found in a pair of sections, ‘‘In Reasoning,
We Pick Out Essential Qualities’’ and its successor, in chapter 22—‘‘Reasoning’’—in
The Principles of Psychology. 1 The quotation on genius is in chapter 19. 2 It concludes
an account of how our conceptions of things alter by being used and how old fogyism
inhibits the assimilation of fresh experiences. ‘‘Old-fogyism, in short, is the inevitable
terminus to which life sweeps us on.’’ I like to think that visual calculating is a useful
antidote. The longish quotation on numbers and experience is in chapter 28. 3 James
talks about concepts and perceptual experience in Some Problems of Philosophy. 4 Kierkegaard’s
saying is found in James’s Essays in Radical Empiricism, and is followed immediately
with this observation.
Understanding backwards is, it must be confessed, a very frequent weakness of philosophers, both
of the rationalistic and of the ordinary empiricist type. Radical empiricism alone insists on understanding
forwards also, and refuses to substitute static concepts of understanding for transitions in
our moving life. 5
Fixed descriptions don’t work in life or in calculating with shapes. Static concepts and
the structure they imply are no substitute for rules and embedding. James’s descriptions
of the six-pointed star are in Pragmatism. 6 But also see his discussion of Lotze’s
descriptions of the star in chapter 11—‘‘Attention’’—in The Principles of Psychology.
James’s Talks to Teachers is worth reading from cover to cover, given the misplaced
emphasis in schools today on basics, standards, and tests. It also contains some nice
material on Francis Galton—I mentioned him in the introduction—and his seminal
work on mental imagery and visual imagination. (Again, there are antecedent sections
in The Principles of Psychology.) I have recorded James’s delightful remarks on old fogyism
and conversation. 7
R. Narasimhan describes Evans’s grammar and how it applies to his shape in the
first chapter, ‘‘Picture Languages,’’ in the book Picture Language Machines.
Recently, Evans has discussed a ‘‘grammar-controlled pattern analyzer’’ which he has implemented
in LISP. ‘‘The inputs required by the analysis program consist of: (1) a grammar, and (2)
an input pattern in the form of a list of lowest level constituents, with any desired information
attached for later use in the analysis process. The output will be a list of all of the objects defined
by the grammar which can be built out of the list of constituents forming the input pattern.’’
The following example taken from Evans’ paper should give an idea of how such an analyzer
would function: ‘‘Supposing we have a straight-line drawing as in Fig. 1, and wish to find
all of the triangles (16, in the case shown). Suppose the input is to be the list of vertices (9, in
this case) with, attached to each, a list of the others to which it is connected by a line of the drawing.
The grammar rule we need to define a triangle might look like: