🚀 go-pugleaf

malin@esther.la.asu.edu (Mike Malin) writes:

>This problem is intimately linked to the problem of how much of the
>spacecraft's mass available for payload.  Clementine got 7.5 kg of
>science payload to the moon on a 240 kg (dry) spacecraft for ~$75
>million. [compared to scenario of Observer class lunar orbiter]

The interesting thing here is that while the Observer Class
returns much more scientific data per dollar, it is not clear
that it returns incrementally more scientific _value_.
The Clementine radar experiment (an inexpensive afterthought
of an experiment on an inexpensive afterthought of a mission!)
may have been enough to discover lunar ice.  Most of the scientific 
value is derived from doing new experiments from new points of view, 
for example Clementine's lunar polar orbit (as opposed to Apollo's 
equatorial orbit that missed the lunar poles), and the addition of 
the radar experiment to the photograpny.  Getting a vast 
amount of extra data from the same instrument and same point of 
view can be important, but usually it has much lower value than 
the fresh, original data.

Traditionally this kind of issue has been considered 
very subjective, but let me be so bold as to propose a formal
measure, to use as a starting point for estimating incremental 
scientific value, and bringing more objectivity to cross-discipline
comparisons and research funding decisions.

This measure based on the incremental Kolmogorov complexity of the 
scientific data to be returned.  Briefly, Kolmogorov complexity is 
Kolmogorov complexity is the size of the smallest possible independent 
representation for a piece of information.  More formally, it is the 
smallest possible Turing machine that, when run, gives the data.  

With Kolmogorov complexity we can formalize many notions of 
"complexity" vs. "simplficity" that have long been intuitive and 
not always satisfactorally answered by tradtional information theory.
There are deep relationships between Kolmogorov complexity and
scientific induction, via a formalization of Occam's
Razor (see Li & Vitanyi for a thorough discussion).   In
this formalization science is the process of observing the
widest range of data and explaining it with the most concise
models.  New, original data has a large Kolmogorov complexity;
it leads to the discovery of new patterns of regularity, new
scientific theories.  Redundant data can be derived by the same model 
that gave us the previous data; it does not lead to 
new scientific models or theories.

Since random noise also has a large Kolmogorov complexity, we
need to modify our measure to strip out this noise, yet
leave in interesting new regularities.  To a first approximation
this can be done be putting a high value on regularity
(low Kolmogorov complexity) within the new increment, and
low regularity (high Kolmogorov complexity) between the 
regularity in (ie, scientific theories that can be derived
from) the current increment and the regularity in previous 
increments.

While it's impractical (indeed, impossible) to precisely
measure the Kolmogorov of largely unknown data, 
estimating the redundancy of additional data to be gathered
in terms of its potential for discovering new generalizable
scientific phenomenon, might go a long way towards evaluating its 
incremental scientific value.  For example, it's easy to see that
taking gigabytes of additional measurements of the orbit of 
Mars without higher precision probably won't contribute very
much to our knowledge of Mars.  That's an an easy example for
many of us to understand, but there are many other kinds
of proposals whose lack of productively are just as clear to 
scientists in the field, but next to impossible to communicate to
politicians or even scientists in other fields.   And yet more
areas where the merit is subjective enough that political
considerations can come to dominate funding decisions.

Without good measures, such as the proposed redundancy measure, 
it's extremely difficult to communicate the value of experiments 
to politicians or the lay public, or indeed between scientists themselves
in different fields.  The resultiing allocation of resources 
between experiments ends up being preposterously inefficient.
A measure of general scientific value based on Kolmogorov
complexity, while not a panacea, could make a valuable contribution 
to establishing our research priorities, a process that otherwise
is becoming more and more political, subjective, and inefficient.


Ref:
Li & Vitanyi, _An Introduction to Kolmogorov Complexity 
and Its Applications_, Springer-Verlag 1993
-- 
Nick Szabo					 szabo@netcom.com
"If you want to hit the moon tommorrow, aim for London today."