John O. Campbell
What are the
fundamentals of knowledge? What does it mean to say that one thing knows
another thing? Although human knowledge is one of our fundamental defining
characteristics we have only scant clues concerning the nature of knowledge.
The academic knowledge
industry has largely settled on a definition of knowledge only slightly
modified since it was first proposed by Plato: knowledge is justified true
belief. In my view this definition suffers from a possible implication that
only humans may have knowledge. However if we loosen the meanings of
‘belief’ to include non-human expectations and narrow the meaning of
‘justified’ to ‘justified by the evidence’ I cannot quibble with this definition.
More technically
information theory offers the concept of mutual information. If we know one
thing, X, with a certain degree of certainty, and X is correlated with another
probabilistic event Y then if we know X we also are more certain about Y. The
added certainty is mutual information. For instance if we know the sky is
cloudy we know it is more likely to be raining than if we did not know the
state of the sky. Knowing the sky is cloudy provides information about the
likelihood of rain.
From a human
perspective there seems to be a maximum amount of mutual information we can share
with any other entity. Even those who we love most dearly largely remain
mysteries. In many respects our inner selves are quite isolated; we are unable
to effectively communicate very much of our wondrous complexity.
One view of this
problem is that to know something requires a mental model of it. The degree to
which this model reproduces the known thing is the degree to which we know it.
However the world around us is much more complex than our individual human
brain; it includes numerous other human brains as well as numerous other
complex entities. Our mental models can be at best only rough sketches of the
true reality.
Recent neural
research shows that mental models consist of a hypothesis space which divides
the possibilities into an exhaustive and mutually exclusive list of hypotheses
and assigns probabilities to each. As new information is received the
probabilities are updated in accordance with the support their respective
hypotheses have received from the new information or evidence. This Bayesian
brain school of neuroscience has succeeded in explaining many of the brain’s
mysteries.
Perhaps
unsurprisingly it turns out that our brains are most adept at gathering
knowledge concerning other members of our species. In a way this is to be
expected as we are best suited to know other things that are similar to
ourselves but the mechanics may be surprising.
The brain
contains families of ‘mirror’ neurons. When for example we observe someone
smiling a family of neurons in our own brain fire. This is the same family of neurons
that fire when we smile and are correlated with the emotions we have when we
smile. Thus we gain understanding of the other person’s mental state; on the
basis of this information we judge some hypotheses concerning the other person
as more likely and others as less.
This brilliant
mechanism in some ways enables us to know others as we know ourselves. There
are however ambiguities. Even our self-knowledge is incomplete and a smile by
itself is somewhat ambiguous; it could mean many things.
We are not alone
in our problem of knowing. Another view of this conundrum is at the level of
fundamental physics. Here we see that information can be transferred between
entities in only four ways, through the four quantum forces of nature. For
example when we see someone smile the information is transferred from the
reflected light to our visual system via a quantum interaction in our retina.
Quantum
information transfer is hugely constrained. Only a minute portion of the
information that would fully describe a quantum system may be transferred to
entities in its environment. Quantum systems too are isolated.
Quantum systems
may be modelled in a hypothesis space or state space which is the set of
density matrices on N-dimensional complex Hilbert space (ref.: Information-theoretic postulates for
quantum theory). This technical description conveys some of the mind
boggling complexities of quantum systems; the density matrices are hugely
complex and the Hilbert space may approach infinite dimensionality.
Information
transfer between quantum systems and their environment takes place through
communication channels, the nature of which are beginning to be unravelled. It
appears that information regarding only a very small subset of the quantum
complexity may be transferred through these channels and that subset consists
of a simple probability distribution, it is the same probability distribution
which quantum theory provides for the outcome of measurements on quantum
systems (ref.: No-local-broadcasting
theorem for quantum correlations).
We may now see
quantum theory in a new light. Our physical reality is based on quantum systems;
however quantum systems are weird and spooky compared to the logical and
familiar classical world we inhabit. This situation exists because we (and all
other classical entities) may only experience a very small subset of the
quantum world, just a few measurable attributes, and again this knowledge is in the form of probability
distributions. These probability distributions form our best model and the best
knowledge we may have of the quantum reality.
A further
interesting point is that quantum communication channels can be viewed as
selection mechanisms; only certain aspects of the quantum system can survive
the transfer to the system’s environment. In this sense quantum information
transfer may be seen as a Darwinian process as described by the theory of
quantum Darwinism (ref.: Objectivity
Through State Broadcasting: The Origins Of Quantum Darwinism).
Once we note that life, neural models and cultural knowledge such as science may also be best understood as evolving via Darwinian processes, we are led to the stunning conclusion that reality is at base a nested hierarchical system of knowledge accumulation mediated by Darwinian processes.
While knowledge
is by its nature always incomplete and we may not be fully known to any other
entity, we may gain some solace from understanding that the rest of reality is
in the same boat with us. As our knowledge is based upon forms of quantum,
biological, neural and cultural knowledge we should understand that the reason
we may see further than other natural entities is because we are standing on
the shoulders of giants.
No comments:
Post a Comment