Dynamics of Hierarchical Systems: a reaction

e[From Bill Powers (920912.0700)]

As I write this very sketchy and abortive review of Nicolis' _Dynamics
of Hierarchical Systems_ (recommended by Martin Taylor), I feel much
older than I am, which is already old enough. I have this uncomfortable
vision of a crotchety wrinkled old person living in the past, dubious of
everything he doesn't understand, hanging onto simplicities of an older
time and complaining about new-fangled and incomprehensible developments
beyond his grasp. This does not generate much confidence. The fact that
I've had much the same feelings about physics since about 1948 doesn't
bolster my confidence a lot; perhaps I was as prejudiced then as I am
now. Perhaps I have had one year's experience 40 times since my
undergraduate days in physics.

On the other hand I've watched developments every year since that
first course in "Atomic Physics" with the strong sense of deja vu.
Nothing really important seems to have happened in physics since that
Bomb went off. The main fallout of that explosion seems to have been a
sense among physicists that they must now have the key to all the
answers: after all, it worked, didn't it? In the light of that first
nuclear dawn, physicists looked into each others' faces and saw a new
race of superscientists. Mankind had progressed to a new level of
understanding of the universe, or at least certain intellectually-
favored members of mankind had. In physics lay all secrets of matter
and energy, in whatever forms they might appear. The only voice of
caution was that of Einstein and he was helpless before the wave of
hubris that overtook his science. Suddenly abandoned, he fell silent.

In the preface to his book, Nicolis says this:

"My intention is to start from "scratch" if possible, keeping the
reasoning heuristic and tied as closely as possible to physical
intuition; I assume as prerequisites just basic knowledge of
(classical) physics (at the level of the Berkeley series or the
Feynman lectures), calculus, and some elements of probability theory."

This, to Nicolis, is starting from scratch. What he means, of course,
is starting from the vast structure of suppositions and inventions
that marks physics as different from other natural sciences. He is
speaking to those who are already of the right faith. One knows
immediately that he is NOT going to start from scratch in analyzing
living systems, any more than the Pope is going to start from scratch
in analyzing morals.

In Chapter 1 he says this (with allowance for typography):

"_Structural_ hierarchy theory ... aims at reducing the quadratically
(N**2) rising number of switching elements as a function of the input-
output number N needed to perform a given task to the theoretical
minimum Nlog(N). This figure comes simply from the fact that N! is the
minimum number of states that a network should possess in order to
handle N input-output connections. If this is implemented via S
switches, the maximum number of states is 2**S."

[** means exponentiation in Fortran]

So the mind-set behind quantum mechanics takes its place as part of
"physical intuition." The cage begins to take shape; the bars are the
1s and the spaces between them are the 0s. The hardware of the
organism is assumed immediately to consist of switches that are in
states. Anyone familiar with the quantum mind-set knows that we are
preparing a universe of categorical things and events in which the
only choice is between "it occurred" and "it didn't occur" and in
which the only concession to continuity arises from statistics. This,
despite the fact that neurons are structures on such a gigantic scale
that quantum effects are swamped by continuous relationships.

This book, however, is not about structural hierarchy theory; it
simply assumes structural hierarchy theory.

"_Functional_ or dynamical theory, on the other hand, deals with
evolution of large-scale systems from stable subassemblies, and
studies the way these systems may _change_ through the exchange of
energy and information with their environment."

These exchanges, you can be sure, will be quantized sequences, not
continuous processes.

"In .. a communicative transaction, 'hierarchical' _coding_ and
_decoding_ are again instrumental in reducing the exponentially (2**N)
rising number of decoding steps (as a function of the length N of the
transmitted time series) down to an algebraic rate N."

"We will deal essentially with the problem of mutual _simulation_
between two dynamical hierarchical systems, and especially with the
problem of _compressibility_ of the information which a given system
receives from its partner. We proceed, however, in steps."

The systems of which he speaks are assumed, of course, also to
"proceed in steps." Step by step, the intellectual cage is built up,
the rules of conduct within it are laid out, and the nature of the
possible conclusions is shaped to fit the confines of the argument.

If one happens to be looking for it, the organism itself will be seen
to be strikingly missing. Starting from scratch clearly doesn't entail
watching an organism doing something. Even more to the point, it
doesn't involve an organism called Nicolis noticing what it, itself,
is doing. We who do notice the organism can see that we are looking at
the output of a brain. We are seeing a brain categorizing the
continuum of experience into packages, putting the packages into
sequence, and weaving the sequences into logical patterns that depend
on imagined perceptions, otherwise known as premises. We can see that
such patterns can indeed be built up to enormous complexity, and that
if they are allowed to develop in isolation from the rest of
experience, they can easily pass over into delusion. I think that
physics has been transforming itself gradually, over the past 40 or 60
years, into a systematic delusion.

The main thing I was looking for in starting to read Nicolis' book was
his concept of hierarchy. It's clear that he has one, but it's also
clear that he doesn't know exactly what it is. If he did know, he
would describe it unambiguously and plainly. Instead, he speaks from
certain assumptions about hierarchy, but the assumptions are largely
unconscious, so he speaks around and from these concepts without
looking AT them and describing exactly what they are.

One hint comes from the concept of a system composed of switches, so
that the whole system is in "a state" at a given instant. This implies
that the collection of switches comprises the whole system at its most
detailed level of physical organization. Whatever hierarchy exists,
then, must exist within this collection as various separable aspects
of its overall state. The whole system, apparently, participates in
all hierarchical aspects of its organization.

Another hint comes from a distinction made in passing:

"In the first place, the system must be hierarchical, i.e., possess at
least a hardware (H)(energetic-structural) level and a software
(S)(cognitive) symbolic, functional level."

It does help to have a different place to stand. Nicolis' concept of
hierarchy clearly has nothing to do with a _hardware_ hierarchy. The
hardware of the whole system is simply one level of the hierarchy.
What the hardware DOES is another level. This is very different from
the HPCT concept, in which the hardware itself is organized into
levels, and what the system does is different at each level as
dictated by the nature of the hardware at each level. This doesn't
mean that the hardware determines content; only that it makes possible
certain computations that could not be done at a different level of
the hardware.

The above quote is immediately followed by this, where S stands for
Software and H stands for Hardware:

"Information, in the form of discrete time-series emanating from the
S-level of system II (S2) [systems I and II are interacting] impinges
upon level H of system 1 (H1), where a set of convolutions (cross-
correlations) takes place between the time series received and the
intrinsic dynamics of system I at level H. The result of such
convolutions is the emergence of a _collective property_ possessing
far fewer degrees of freedom than S2 or H1."

Hierarchical levels, therefore, seem to be "collective properties" of
the physical system, separated not in space but in concept. And the
commitment to a discrete universe is set in concrete.

By page 5 in Chapter 1, Nicolis is dwindling out of sight as he goes
further and further into his imaginary universe, where I refuse to
risk being trapped. By the bottom of page five he is talking about
attractors and cascading bifurcations. At the top of page 6 he is
telling us we will be considering how a signal is encoded into
spherical waves and what happens when those waves, after passing
through a stochastic medium, deliver their information to a finite
aperture. He is pointing out that because perception is ambiguous, we
must deal with the entropy of an information-carrying spherical wave,
and that this of necessity takes us into statistical physics and
formal information and coding theory. To Nicolis, this is evidently
familiar and comfortable territory. He has no problem with these
analogies, because he is not trying to explain any particular behavior
of any real organism. He is exploring the properties of a world that
exists in the imagination, that has only those connections to real
systems that he assumes, through free subjective association, that
they have. The real world, the world of direct experience, has become
the dream, and this world of hypothetico-mathematical entities and
relationships has become the reality. That way lies madness, and I
will not follow.

I said that this review would be abortive. It aborted on page 6. In
order to follow the argument further, I would have to brainwash
myself, throw myself under the wheels of this blind machine, abandon
all questions and adopt the faith. The thought of doing to myself what
would be necessary in order to follow where Nicolis' brain wants to
lead me fills me, in fact, with horror. There's no other word for it.
I can see a slippery slope that descends at an ever-steepening angle
into an abyss. Venture too far down it, and there is no return. The
mind can't free itself from such a trap. Or if one can, it would be a
better mind than mine.

All this, of course, could be a feeble defense against admitting my
own intellectual failings and the fact that the world is full of
people smarter than I am -- considerations that are easy to document.
What I feel, however, is not embarrassment or despair at not being
able to follow further, but fear at knowing that I could. I've been on
this slope before and scrambled back to level ground only by luck, not
even knowing at the time that I had rescued myself (or that someone
had rescued me).

Ideas are inside us, not outside us. What we think about the world
isn't what makes it work, or even what makes it what it is. When we
begin to let our ideas take precedence over direct experience, we
start losing our grip on that tenuous connection with the real world,
and take the first steps into a waking dream in which all is
comfortingly consistent and solid -- but imaginary. Be Here Now, the
man said. Whatever else he said or did, that one was a zinger.



Bill P.