Sir Roger Penrose on the nature
of conscious cognition
This present post is really a footnote to my Thinknet series. In that series I am
exploring a computerised simulation of connectionism in the hope that it might throw light on the subject of intelligence/mind. So having embarked on a series investigating
the nature of thinking with the foundational assumption that intelligence is a process that can be simulated
using algorithms, at the end of part 1 I asked the following question:
There was another question that
was waiting for a rainy day: Where does Penrose’s work on mental incomputability
fit into all this, if at all?
In his books The Emperor’s New
Mind and Shadows of the Mind Roger
Penrose suggests that incomputability is a necessary condition (but presumably
not a sufficient condition) for
conscious cognition. That is, according to Penrose what sets apart human
intelligence from algorithmic intelligence is that the former somehow exploits incomputable
processes. But not everyone is happy with Penrose’s proposal. For example Wiki quotes Marvin Minsky :
Marvin Minsky, a leading
proponent of artificial intelligence, was particularly critical, stating that
Penrose "tries to show, in chapter after chapter, that human thought
cannot be based on any known scientific principle." Minsky's position is
exactly the opposite – he believes that humans are, in fact, machines, whose
functioning, although complex, is fully explainable by current physics. Minsky
maintains that "one can carry that quest [for scientific explanation] too
far by only seeking new basic principles instead of attacking the real detail.
This is what I see in Penrose's quest for a new basic principle of physics that
will account for consciousness."
I wouldn’t say that I’m too chuffed myself about Penrose’s proposal; if it
is true then it puts the blocks on all attempts to find algorithmic simulations
addressing the problem of intelligence that use standard connectionist models of
the mind such as we see in De Bono’s The
Mechanism of Mind. Penrose is also challenging positions like that of John
Searle who believes that whilst conscious cognition is algorithmic,
algorithmics alone is not a sufficient condition for it: For according to
Searle a sufficient condition for conscious cognition is that its algorithms
are realised in biological qualities. Therefore constructing a formally correct
structure of say “beer cans” (as Searle puts it) would only amount to a simulation and not the-thing-in-itself So,
although Searle believes that conscious cognition requires a specialist biological
ontology he nevertheless believes that that ontology has an algorithmic formal structure.
Even if one should propose that the human mind is some kind of quantum computer
(in itself a radical proposal that is very controversial) human thinking would
still classify as a classically algorithmic process and that simply doesn’t go
far enough for Penrose! Penrose is nevertheless
making a serious proposal that needs evaluating.
So what then is incomputability? In his book Algorithmic Information Theory, Gregory Chaitin (following Turing) has a back-of-the-envelope
proof of the existence of incomputable numbers….. see the picture below:
Chaitin's proof of incomputable numbers (Click to enlarge)
As Chaitin notes above Turing’s halting theorem and Godel’s
incompleteness theorem follow on as corollaries from his Cantor diagonal slash
proof of the existence of incomputable numbers (See picture above).
In his proof Chaitin allows his computations to generate numbers of
indefinite length. For example, he permits an obviously computable periodic number such
0.123123123123…etc which disappears off into the infinite distance. Chaitin also doesn’t put a limit on the number
of possible computations (or algorithms) that might exist. However, in practice
we know that physical limits constrain both the size of the numbers an
algorithm can generate and the number of possible algorithms. So let us assume
that practical constraints imply that both the number of algorithms and the number
of digits generated have roughly the same value and let’s call that value n. This value n will give us a square of n
x n of digits. The finite computable
numbers that form the rows of this square can be thought of as configurations
of digits. Clearly then the n x n square contains n configurations of digits of length n. But Cantor’s diagonal
slash method shows that it is very easy to construct a configuration that
doesn’t appear in this rather limited set of practically computable numbers and the reason for this are also fairly
obvious – the square contains a mere n
numbers, but of course given a configuration of length n it is actually possible to construct a much larger number of
configurations and this number is quantified by an exponential of form:
~
A exp[kn]
(1)
….where it is clear that:
A
exp [kn] >> n
(2)
It follows then that there are far more conceivably constructible
configurations of digits than there are practically
computable configurations. Of course, we can continue to extend the value
of n, but according to (2) the set of
practically incomputable configurations increases in size much faster than n and this goes on into the infinite
realm where we find absolutely incomputable
configurations.
The foregoing tells us that as
n increases there is a spectrum of incomputability
running from progressively impractical levels of computability right through to
the absolute incomputability at infinite n.
Given this spectrum it seems to me that Penrose’s proposal identifying absolute
incomputability as a necessary condition of conscious cognition is a little
arbitrary; for perhaps the condition for conscious cognition emerges at some finite point along the road to absolute incomputability? However, if
we give Penrose the benefit of the doubt then according to Penrose incomputability
of process is one of the conditions that sets apart biological intelligence
(and which presumably applies to a wide range of animals such as primates, cats,
dogs, dolphins etc) from classical algorithmic intelligence. In particular in
his book “Shadows of the Mind”
Penrose constructs what he believes to be a specific example demonstrating the human
ability to think beyond computability; an analysis of his reasoning here is on
my to do list. But for the moment suffice to say that the
example he gives supporting his notion that humans have knowledge of the
incomputable does not entirely convince me: Incomputable knowledge pertains to
information about those complex and infinite incomputable patterns. But at no point
in Penrose’s example did I feel I was party to anything other than knowledge of
fairly regular patterns. Still, I really need to look at his reasoning more
closely.
There is, however, one relatively prosaic way in which the human mind
could tap into an incomputable process. In Edward De Bono’s book The Mechanism of Mind it is clear that
in his models the action of thinking modifies the brain’s memories and conversely
those memories effect the way thinking develops. So thinking effects memories and memories effect thinking – in short we have a feedback
system here; that is, nonlinearity is part of the brain’s natural processing. This
raises the possibility of complex chaotic behaviour which in turn has the
potential to amplify up the randomness of the quantum world. Randomness, if understood in its absolute sense, is incomputable and it is
possible (although never absolutely provable) that random quantum leaping delivers incomputable configurations
to our world. If the mind is chaotically unstable enough to tap into these random
configurations its behaviour therefore becomes incomputable. In fact it is
quite likely that this kind of common-or-garden incomputability is present in
the brain anyway – it doesn’t require the mind to tap into some new and exotic
incomputable physics or even for the mind to be a quantum computer. This kind
of incomputability, however, is clearly not a sufficient condition for conscious
intelligence: After all, the asteroid Hyperion is tumbling chaotically
and may well be sensitive to random quantum fluctuations, but that doesn’t make
it conscious!
Although I’m not particularly comfortable with Penrose’s proposal it is,
nonetheless, worth entertaining as a possibility. The fact is we still don’t
really know just what are the sufficient physical conditions (i.e. the
conditions as observed by the third person) which entail the presence of that
enigmatic conscious first person perspective of biological brains. If on the
other hand Penrose is wrong and incomputability is not a necessary condition for
the first person perspective then as Penrose points out in his book Shadows of the Minds it then becomes
possible in-principle to at least simulate
human intelligence using a sufficiently powerful algorithmic computer. For those
who reject the first person as a valid perspective then a simulation of this kind, which would presumably be thorough enough to pass the Turing test, classifies as
fully sentient by definition. It is true that nowadays computerised simulations
of all sorts are looking increasingly realistic and one can imagine
improvements to such an extent that these simulations could fool a lot
of the people a lot of the time. But there remains a deep intuition that
appearances, no matter how good, are never logically equivalent to a genuine
first person perspective, a perspective that is otherwise inaccessible from the third
person perspective.
AI expert Marvin Minsky would prefer to think that the quest for an understanding
of human sentience is purely a question of understanding its formal complexity
and that the ontology which reifies that formal complexity is not relevant.
Although I am unsure about Penrose’s proposal that incomputability is a necessary
condition of sentience I nevertheless agree with his feeling that the existence
of the kind of conscious cognition which is at the heart of practical levels of intelligence
points to something about our world which we don’t yet fully understand. That
I’m at one with Penrose on this question is indicated by the following quote
taken from a post where I criticise IDist Vincent
Torley:
Stupidly, to my mind, Torley even claims that
an intelligent agent might be insentient: To date this seems highly
implausible. A designing intelligence would have to be highly motivated; our
current understanding is that all highly motivated goal seeking complex systems
are the seat of a motivating sentience: For example, it is a form of irrational
solipsism to suggest that the higher mammals are anything other than
conscious/sentient. Notably, Roger Penrose book "Shadows of the Mind"
is based on the premise that real intelligence and consciousness go together.
Following John Searle I’m inclined toward the conclusion that
intelligence is not just its formal structure: Viz: A correctly arranged formal structure made of beer
cans wouldn’t be a practical manifestation of intelligence – in fact no simulation
would be practical, any more than we would expect an aircraft simulator to
actually fly! It follows then that we never could have the insentient
intelligence that Torley speaks of because any real practical level of
intelligence would need to exploit whatever processes deliver sentience and conscious
cognition. It is for this reason that I believe we should respect high levels
of biological intelligence in all its forms; dogs, cats dolphins primates, elephants
and, in my opinion, also human embryos. .
Be all that as it may, there is one thing I am fairly sure about: In the
connectionism sketched out by Edward De Bono in his Mechanism of Mind we are starting to see an uncovering of some of the important principles
required for intelligence, although I guess there is whole lot more to discover:
As physicists are all too aware, the disconnect between gravity and quantum
mechanics is a sure sign that our knowledge of the world about us is still very
partial.
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