"Randomness" in different branches of science

Loren Haarsma (lhaarsma@retina.anatomy.upenn.edu)
Mon, 23 Feb 1998 11:31:07 -0500 (EST)

Moorad Alexanian wrote:
> In quantum mechanics there is a dynamical theory that indicates the possible
> outcomes of given experimental measurements and the associated probabilities
> for such outcomes. Can someone tell me what is the dynamical theory that
> tells us what are the possible outcomes and the associated probabilities in
> evolutionary theory? Any theory that uses the notion of randomness must
> makes such issues clear; otherwise, it is not a scientific theory and are
> mere words

What about the optometrist who told me that I have twice the usual
probability of developing gloucoma during my lifetime because of an eye
injury when I was sixteen? He didn't have a dynamical theory, but I'd
still say that he was being "scientific." What about researchers
claiming that moderate alcohol consumption reduces the risk of heart
disease, or the more recent report that above-moderate alcohol
consumption increases the risk of breast cancer? They have only a few
clues about underlying mechanisms, which might or might not be correct.
But it sounds like science.

Different sub-branches of science use randomness in slightly different
ways, depending on how much empirical detail is known about the
underlying microscopic mechanisms..

In quantum mechanics, as currently formulated, results of measurements
*in principle* are undetermined and probabilitistic.

By contrast, in classical mechanics of complex systems the underlying
mechanisms are very well understood and deterministic, but in practice
the initial conditions cannot be specified exactly enough to allow the
final state to be determined. By use of general principles (e.g.
conservation of energy) and/or by Monte Carlo calculations,
probabilities can be assigned to final macrostates.

Different still, medical researchers can often assign probabilistic
outcomes to scenarios --- based on observational studies --- while
having only the vaguest ideas (if any) about the mechanisms underlying
the effect.

Most of biological research is somewhere between classical mechanics and
medical studies. For example, in my last research project I measured
changes in electrical conductivity in a single neuronal ion channel. By
measuring conductivity changes as a function of voltage, time, etc. I
could build a dynamical model of its behavior and learn something about
how many distinct structural states it had. I can't tell you much about
the actual structural states --- which amino acids shifted how far
relative to each other. I can only tell you by observation how the
channel's conductivity changes stochastically, and what the rate
constants are. But given only that much knowledge, about this and other
channels, without knowing the underlying structural dynamics, we can
build exquisite models of how nerve cells fire and propagate action

Historical sciences cannot have more detailed empirical/predictive
content than the experimental and observational sciences upon which they
are based. Consider a very simple experiment in microevolution: a dish
of bacteria grown from a single cell line, subjected to mutagens and/or
environmental stress. How will the bacteria evolve? We don't have a
dynamical theory to predict the outcome. We can measure the average
mutation rates from different doses of mutagens, but then we're stuck,
because we don't have dynamical models of how even single cells work.
I'm hopeful that within four to ten decades we will have detailed,
empirical models of cellular physiology, at which point we can predict
the consequences of a single mutation in a single-celled organism.
Imagine how much more difficult it will be to empirically predict
changes in multi-cellular organisms, or whole populations living in a
complex environment.

If that's the case, of what use are the historical sciences? Quite a
lot, in turns out. By starting with what is known about the
deterministic and stochastic processes, building models, and comparing
it to observation, constraints can be put on those underlying processes
and, sometimes, spectacular predictions can be made. Cosmologists used
particle physics and astronomical data to contrain how many different
types of leptons and hadrons could possibly exist --- something the
particle physicists couldn't determine by particle-smashing alone.
Before the discovery of nuclear energy, geologists who measured the age
of the earth could tell astronomers that some unknown mechanism was
needed to supply energy for the sun. Evolutionary biologists can make
predictions about genetic homologies amongst different species.


When I started learning quantum field theory, my professor put this diagram on the board:

Classical ______________ Quantum Mechanics Mechanics | | | | | | Classical Quantum Field ________________ Field Theory Theory

His point was that you could get from the intuitively understood classical mechanics to the truly weird QFT (my words, not his) in two resonable steps by two pathways. You can transform mechanical variables (energy, momentum, etc.) into classical field variables, the convert those field variables into quantum field operators; or you could first convert mechanical variables into quantum mechanical operators, then convert those operators into field operators.

When thinking about the different natural sciences, I like this diagram:

Experimental Observational Historical Physical ------------ Physical --------- Physical Sciences Sciences Sciences | | | | | | | | | Experimental Observational Historical Biological ------------ Biological -------- Biological Sciences Sciences Sciences

Consider the vastly increased complexity when going from physical to biological sciences. Consider the necessary changes in methodology and empirical content as you move from experimental to observational to historical sciences. Scientifically, it looks to me that the evolutionary biologists (when they talk science and not metaphysics) are using "randomness" in appropriate ways for their sub-discipline. Theologically, if God can providentially guide simple, every-day physical systems like the casting of lots, how much more over complex biological systems over long periods of time.

Loren Haarsma