[ExI] What Will Be Interesting in the Far Future

[Lee Corbin]

It's a wonderful feature of human life to be interested in something.
Anything, actually.

In what will the reigning intelligences of 10,000 A.D. be interested?

We abbreviate Kolmogorov Complexity to KC. Note that a deep drive
of highly cognitive life on Earth at this time (e.g. human beings) is to
discern patterns, and moreover to delight in such discovery. From 
backyard gossip to the profoundest scientific discoveries, intelligent
life as we know it revels in understanding.  We can probably claim
that such discoveries of truth, or patterns, or understanding, is data
compression, or, in other words, amount to an apparent reduction
of KC.

Discovering a pattern in a long string of 1's and 0's, to take the
archetypical example, is to achieve data compression of that string,
and it can be shown that except for extremely simple strings (we mean
data), an intelligence can never know for sure that the true KC has
really been identified---it may simply be that the apparently random
data has not yet been "broken" in the cryptographic sense, and 
even then may possibly be someday compressed even further.

What is "interesting" to an entity will have long, long ago been up
to the entity to decide. Even today we are surely only decades or
at worst centuries away from owning the capability of turning 
the "interesting knob" up or down on anything that we please.
But let's suppose that those entities *do* engage in something
analogous to a quest for knowledge, and that in some sense
they find it "interesting".  I'll now speculate on what that might
mean.

In 10,000 A.D. the ruling entities over some amount of physical
space could still be interested in science. Perhaps everything from
quantum computing to baby black holes could provide opportunities
for unlimited exploration. We really can't even guess. Mathematics,
however, is provably infinite in the sense that there will always be
patterns as yet undiscovered even among something so fundamental
as the positive integers. 

Darwinian survival, however, dictates that the discovery of yet more
advanced ways to self-organize, so as to be able to deploy at the 
boundaries of an entity  effective defenses against alien assimilation
will be "interesting",  (however strange will be whatever is then meant
by "alien", and maybe by "boundaries" or "entities"). 

Right now for us, however, it is more intriguing to posit that not
all of those entities' activities will be confined to attempts to survive.
We may succeed in passing on to our mind children the high valuation
of experience itself. If so---and they can afford that luxury---then in
addition to mathematics there should also exist art and philosophy. We
might suppose, along these lines, that "spiritual reorganization" would
also be a way to characterize their experiences and their search for
new experiences.

Getting back to a search for knowledge, however, consider that at
any time t an entity E(t) (with time on its hands, as just explained) 
will be interested in data compression.  A very large amount of 
known data or newly discovered data may or may not have low
enough KC for E(t) to be able to make progress in deciphering it
(at that time, of course).

(Some kinds of data will, a priori, have quite low chances of containing
real patterns, i.e., will a-priori be judged to be highly and irreducibly
random, and will not command attention. A very non-random source
of data, I would however suggest, would be *history*: especially the
history of the development of a particular entity E(t) as it looks for
clues to advance its own reorganization and its own search for more
"satisfying" experiences.)

But clearly E(t), that is, entity E at time t, is in the most interesting case
still growing, still advancing. The Busy Beaver problem in mathematics
gives some concrete indication of why and how. A quick look at the
tables in http://en.wikipedia.org/wiki/Busy_beaver  hints at what might
be possible by the addition of a single "neuron" to E.  Assuming, 
though, that by 10,000 A.D. entities have reached material constraints
---say that there is only a finite amount of matter or energy within the
grasp of E---the capability to reach more "states" of, for example, enhanced
spirituality, or more optimal number crunching, or better algorithms
in general,  will depend solely on internal reorganization.  But apparently, 
still not to worry! There are just *so* many possible internal states.

Conclusion: E(t) will find *interesting* in terms of new knowledge (for
knowledge's sake) breakthroughs in data compression made possible
at time t with E's capabilities at time t.   That is, if a somewhat structured
or entirely random data set has relatively low KC, and E is able to
discover that fact, then the data set or "theorem" will be interesting.

Lee