[From Bill Powers (2002.09.18.1230 MDT)]
Mike Acree (2002.09.18.0931 PDT)--
>Wolfram's cellular automata are following a rule set by him in his
program >Mathematica. When hydrogen and oxygen combine to form water, they
could also >be said, I suppose, to be following a rule about what H and O
are supposed to do >when they come together. But I wouldn't have said they
were operating at the >seventh level in PCT. I don't see any evidence that
Wolfram is thinking of these two >kinds of "rules" as the same, and I'm not
sure why you do.
Because that is how he talks about them consistently throughout the book
Page 8, para 3: "Existing methods in theoretical physics tend to revolve
around ideas of continuous numbers and calculus -- or sometimes
probability. Yet most of the systems in this book involve just simple
discrete elements with definite rules. And in many ways it is the greater
simplicity of this underlying structure that ultimately makes it possible
to identify so many fundamentally new phenomena. "
Simple discrete elements with definite rules. That is the digital-logic
approach as opposed to the analog approach involving continuous
variables. It is precisely the sort of operation I attribute to level 9
(if I said 7, I misspoke).
Page 22, paragraph 4: " Any program can be thought of at some level as
consisting of a set of rules that specify what it should do at each step.
There are many possible ways to set up these rules -- and indeed we will
study quite a few of them in the course of this book. But for now, I will
consider a particular class of examples called cellular automata, that were
the very first kinds of simple programs that I investigated in the early
1980s."
"What it should do at each step," of course, implies a series of discrete
operations carried out one after another, which is what generates the
patterns attributed to cellular automata. When he speaks of "programs" he
means exactly what I mean: tests for conditions leading to a choice of one
action versus another. That is how I have defined level 9 to work.
Unfortunately, in devising his new science which among other things is
supposed to apply to biological systems (see pages 7-16), Wolfram has
noticed practically nothing about his own properties as a human being,
properties that must exist before one can even consider the kind of model
he describes. Consider page 24, paragraph 2.
"The cellular automaton consists of a line of cells, each colored either
black or white. At every step there is then a definite rule that determines
the color of a given cell from the color of that cell and its immediate
neighbors on the step before."
Ah, a line of cells. How does a person perceive that elements form a
"line?" Obviously the person must be able to recognize that kind of
configuration (level 3), distinguishing it from curves and closed figures.
Then there is the matter of "black" and "white." This requires the ability
to sense at least light intensities (level 1), and perhaps, if shades of
gray or colors are involved as they are later in the book, sensations
(level 2). And what is the "neighbor" of a cell? Is that not a concept of
spatial relationship (level 5)?
Then we get to the first rule: " A cell should be black in all cases where
either of its neighbors was black on the step before." This is clearly a
rule based on tests and choices (level 9). Is the cell on the left
black, or is the cell on the right black? If so, then make the cell in
question black. That is an elementary program in exactly the sense of level
9. And is not the operation of making a cell that was white into a black
cell an event (level 5)?
There is another problem here: the rules are not stated clearly. Suppose I
have five cells to start with and indicate white by 0 and black by X. We
start with step 1 of the figures shown on page 24 at the top left (if
Wolframs is so well-acquainted with how papers are written for the
peer-reviewed literature, how come he doesn't label his figures so you can
refer to them as, for example, "Fig. 1"?).
00X00 (Start)
Now we have to examine the cells and apply the rule to each one. Cell 1 has
no black neighbor so it remains white. Cell 2 has a black neighbor so it
turns black, and we have, so far,
0XX00
Cell3 has a black neighbor oin its left now so it remains black. Cell 4
turns black because cell 3 is black, and we have
0XXX0
Now we have a problem: cell 5 now has a black neighbor on its left, so it
should turn black, too:
0XXXX
But that's not what happens in the next figure down in the book. Instead,
we end up with
0XXX0
How can that be? The answer is that we are not making "a cell" either black
or white. Instead, we are creating a NEW ROW OF WHITE CELLS and looking at
the row above it, which remains unchanged, to see whether each new cell
should turn black or be left white. We are, in fact, creating a _sequence_
(level 8) of rows, and applying the rule to each new row in turn. This is
not just a series of steps being applied to the same set of cells over and
over. It is a series of rule-driven operations which use the state of one
row as a means of determining the state of the next row in sequence.
Wolfram does not discuss the significance of the second dimension in his
diagrams, as far as I have seen. He speaks of the row above as being the
"previous step," but in fact that row has to be left in place, unchanged,
in order to construct the next row in sequence below it. The factor he is
overlooking here is memory: if we hold the state of the row of cells in
memory, we can now make a new row by applying the rule to each cell in
relationship to the _previous_ states of all the cells. Of course we can
also "remember" the previous row by drawing it.
So finally we can see all that is involved for a person to apply the
cellular automaton rules and generate the patterns we see in Wolfram's
book. If a person can already perceive sequences of relationships among
events involving transitions of configurations of sensations made of
intensities, and remember the appropriate experiences or write them down,
then the rules can be applied. Remove any one of those perceptual
abilities, and the cellular automaton cannot work. Wolfram sees his
approach as explaining everything: how does it explain all the levels of
variables and processes that underly the application of the rules?
I said that Wolfram's concept of discrete operations on discrete variables
is adhered to consistenly throughout the book. I just let the book fall
open in the middle, and found this on page 528:
"A defining feature of any particle is that it can somehow move in space
while maintaining its identity. In traditional physics, such motion has a
straightforward mathematical representation, and it has not usually seemed
meaningful to ask what might underlie it. But in the approach that I take
here, motion is no longer such an intrinsic concept, and the motion of a
particle must be thought of as a process that made up of a whole sequence
of explicit lower-level steps."
In other words, EVERYTHING consists of discrete states occurring in steps,
one after another (which Wolfram calls a sequence, correctly in terms of my
definitions). He speaks of "updating-events" which cause successive states
of something to change from one step to the next. "When particles move
faster they have more nodes associated with them", he says, where a node
results from slicing time. At each node, the discrete state of the particle
is "updated." By what? He never says.
I have seen this kind of theorizing before. It happens when for some reason
a person gets hung up on a single simple idea and starts trying to make it
account for everything. The problem is, it's ALWAYS possible to account for
everything if the only rule for accepting an explanation is that it seems
reasonable to you. If you never doubt the reasonableness of any of your own
ideas, theorizing is just a matter of imagining a plausible explanation.
Somehow, you never seem to come up with anything but good ideas.
I see Wolfram's book as a sad example of what can happen even to a
brilliant mind.
Best,
Bill P.
···
>Wolfram thinks that because
>he can perceive and state rules and program a computer to run by them, the
>rules exist outside his head as properties of the real world. The idea that
>such things are perceptions first, and only problematically and
>incidentally properties of Reality, is not part of his system. He has
>focused on one very narrow aspect of human experience, not only excluding
>everything else, but projecting it into the real world without any
>justification.
I read Wolfram as more sophisticated, in his chapter on psychology, than
the simple-minded objectivist you make him out to be; but your criticism
(and Rick's) is at least directed to the content of Wolfram's theory,
unlike the typical reviews I was pondering.
Thanks.
Mike