[Fis] Objects: Irreversibility of the Foundations

Some random thoughts:

1. Independent reinvention: another path to consilience

Two years ago, I have been trying to solve a particular problem in machine
learning, my field of research. Looking around, I found a particular
generalization of mutual information, which was constructed by my colleague.
I performed numerous experiments, and it performed well. Then I tried to
check if anyone thought of that before, and, empowered by Google, I was
surprised to find virtually the same formula (re)invented independently with
different names over the past 50 years in: biology (Quastler), psychology
(McGill), information theory (Han, Yeung), physics (Kikuchi,Cerf&Adami
arXiv:quant-ph/9605002), neuroscience (Brenner), robotics (Yairi et al), and
closely related notions in game theory (Grabisch & Roubens), complexity
theory (Gell-Mann), statistics (Darroch), and chemistry (Kirkwood). I could
go on, but I wonder how many I already missed. Most researchers, but not
all, arrived at it by employing the inclusion-exclusion principle outside of
strict context of set theory. That was my encounter with consilience: but it
was not a discovery of applicability of a different method in an unexpected
domain, but the independent discovery of the same hypothesis (actually a
tool) in a number of different domains: isn't this the same.

2. Hierarchies of sciences

Perhaps that is demonstration enough that vertical integration is beneficial
if not necessary. And here come in Pedro's diagrams of sciences. I do not
see a need for politically correct circularity. I also agree with the
optimistic viewpoint that there needs to be only a single vertical field
that provides the cognitive "tools" (which are, however, psychologically
feasible) to all the horizontal fields. Role models already exist: logic,
mathematics and statistics (and philosophy that studies their foundations).

As a side note, I found Pedro's reference to circle of knowledge very
interesting. There, religion and philosophy are in the center. Where is
religion today? While philosophy sets the framework for what and how to
think, religion answers the Why?. While some people could involve in the
infinite regress of why why why, most stop recursing at a certain level and
move forward. Religion is a formal setting of this direction, combining with
the informal herding behavior. Ultimately the quality of this direction is
judged by survival and growth of both the religion and its followers.

3. Objects reified

Mathematics and logic, for one, have been cast in stone. Nobody dares
question the fundamentals anymore, it would be unimaginable throwing all
that away. This seems like a proof of Stan's senescence. Mathematics and
logic are all discrete, based on objects and their behavior. Probability
theory, too, is discrete, with the division of the universe into discrete
events. And without probability theory, there is no statistical notions of
information or entropy. If you now look at the natural world, you don't see
objects: you see the fuzz of interlocking leaves, the swaying fur of grass,
the smooth gusting of wind, swarming of flies, the gritty mess of mud, soil
and pebbles on the ground, the swirling stream, the foamy foam.

Then you turn and look at a urban landscape: objects (discrete buildings),
objects (discrete chair), objects (discrete road-side signs), objects
(discrete potted plants), objects (discrete buttons), objects (discrete
humans), objects (discrete molecules of air), objects (discrete plant
species), objects (discrete knots of wind speed), objects (centimeters of
leaf surface area), objects (zeros and ones encoding the music on a CD),
pummeling of photons, cascading of electrons. We don't know what there is
inside an atom, but surely it's objects, and objects within them. Computers
are engineered so that everything is fully deterministic and predictable,
and there is nothing that is not an unnested discrete binary object, all
equal, all egalitarian.

We're trying to fit every aspect of nature to objects and to relationships
between them. The problems we have with concepts like continuity (what is
infinity? what is zero? what is divide-by-zero?), forces, fields,
relationships and interactions (are two particles interacting at a distance,
or are they really a single object? is a molecule of my body an independent
molecule or is it my body?) are a kludge retrofitted on objects that tries
to capture everything that objects alone miss. Indeed, our representations
have senesced, and all we will ever do will be in the context of objects.
*Can* we think in some other way than by reifying objects, or has our
cognition senesced a long time ago? If computers don't, do we still have the
freedom to think in non-objects? Fuzzy logic is not an answer: every fuzzy
variable is still an object: either it's hot or it is not, two values, two
objects. Just as in logic, a hypothesis is either perfectly true or
perfectly false.

You might wonder for a few seconds, perhaps admit it, but you would
certainly not want to work in this direction. Life's too short and that's
senescence.

Aleks

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Received on Thu Oct 7 10:50:24 2004