UNIVERSALITY: OR WHY THERE ARE SEPARATE SCIENCES
The reason is the existence of universality at many levels.
Let's start in the middle, where universality is most familiar.
- The basic computer components are universal. Whatever can be
built from transistors can also be built from vacuum tubes, relays,
fluidic elements, McCulloch-Pitts neurons, connectionist neurons, or
from any of the other kinds of neuron Marvin Minsky proved universal
in his 1954 Princeton PhD dissertation.
- On the biological level, molecular biology doesn't tell us what
kinds of animals exist. There could be six-legged mammals.
Apparently DNA could encode for them.
- Atomic physics is more closely linked to chemistry until you
get to organic chemistry. The simple compounds that can exist mostly
do exist, and the strengths of a chemical bond is determined by
quantum mechanical calculations to the extent that these calculations
are feasible. However, the complex organic compounds that exist in
nature are only a small subset of those that could exist. Which ones
occur in nature depends today on DNA encodings of the enzymes that
- Quantitatively, chemistry is determined by the nuclear atom
with a heavy positive nucleus and lighter electrons. It helps
somewhat to know about neutrons and protons, but most isotopes are
very similar chemically.
- The neutrons and protons are built from quarks and gluons, but
quantum chromodynamics is apparently not something designers of
nuclear power plants needs to know.
That's going down.
- I'll make the controversial assertion that intelligence will
take essentially the same forms in machines as it takes in humans.
The little green men from Arcturus will also have qualitatively
- Up another level, economics has most of its content independent of
psychology. The little green men will need to trade among themselves
and with us, and if their desires conflict among themselves or with
us, game theory will be relevant independent of their psychology.
Of course, psychology leaks into economics, as economists have
- Politics is interesting, because what happens is not just a
statistical result of the millions of citizens. Particular individuals
get high office, and then their peculiarities matter. People have
likened politics to the chaotic weather systems in which a seagull's wing
flutters in the Gulf of Alaska can be amplified to affect a big storm
in the Eastern US. However, politics resembles electing a chief
seagull for a term of four years.
Thus particle physics, though fundamental structurally, is only a
small part of science, as is chemistry or economics - to sample
The opposite intellectual sin to wanting to derive everything from
fundamental physics is holism which makes too much of the fact that
everything is ultimately connected to everything else. Sure, but
scientific progress is made by finding where the connections are weak
enough to allow separate theories.
Leakages and amplifiers
- Neutrons leak into chemistry a little bit, because chemical
reactions and equilibria depend slightly on the isotopes involved.
This permits small differences in concentrations of isotopes to be
used to study the history of a chemical substance in the sea or in
- Physics and chemistry leak into biology a lot.
- The spectacular leaks are in human affairs. Psychology
strongly affects sociology, economics and politics. Some of this is
at the level of averages, e.g. on the average women buy different
things than men do.
- However, the most important reason individual psychology affects
large scale social events is that most organizations require leadership by
an individual. The US has a president and so do corporations and
universities. Army units require leaders ranging from sergeants to
generals. If an organization must make a sequence of actions quickly
in a co-ordinated way, an individual has to be in a position to make
some of the major decisions. Attempts to avoid this have always
failed when the organization has to compete with others. Fortunately,
it isn't usually necessary to have a dictator, and the power of the
individual can be limited by what American political jargon calls
checks and balances.
- Which people get influential positions depends on competition.
- Whenever an individual is in charge his peculiarities and his
interaction with other individual can affect large scale events.
- Ideas are also amplified. The formal mechanism for this is
publication. Which ideas are amplified also depends on
- A plant or an animal at the level of a sea anemone or a jellyfish does
not require a decision making center. A tree bends toward the light,
because the individual branches bend. However, a mobile animal must
move as whole in some direction and requires a central mechanism to
decide on when and where to move and to make other decisions.
Universality in computer science and mathematical logic
All present stored program computers are universal. Any can do any computation
that can be done by any other and can simulate any other. We ignore
memory limitations. Taking them into account would require a more
All general purpose programming languages are universal. A program can
be written in any of them to simulate any other. Lisp and Prolog have
access to their own abstract syntax, and maybe this constitutes an additional
kind of universality.
- As Goedel showed, Peano arithmetic with axiomatized addition
and multiplication is universal in the sense that any recursively
enumerable predicate is representable by a first order logical formula
with one free variable, where the argument takes on Goedel numbers of
formulas as value. With just addition, Peano arithmetic is not
- The bare theory of car, cdr, cons,
and atom is not universal. I doubt that adding just
append would make it universal, but I don't know what
would. Adding eval would suffice but surely would seem
to be overkill.
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