In response to
my recent blog on evolutionary emergence and the fecundity of bottom up
localised decisions, a friend, and excellent blogger, Tim
Reeves, shared
his thoughts in the shape of his mathematical spongeom sketch of evolution, and in the shape of
a comment in which he claimed that:
"There is no way to distinguish between
right and wrong in the trial and error computation which ultimately must make
the appropriate selection, except to say that top-down transcendent constraints
skew the statistics in favour of certain classes of outcomes."
As Tim rightly
says, evolution requires a physical substrate of active information on which to
run, and a constraint of the physical laws to do so (this is something I've
written about in more depth before). However, I don't think the comparison is the best objection to
the social elements I covered in the evolutionary emergence blog. Let me
explain.
What’s
happening in biological evolution underneath that layer is that there is a huge
biochemical morphospace that has a connected structure through which
evolution’s reducible complexity can traverse. Take, for example, irreducible
complexity and reducible complexity - they refer to the arrangement of stable
organic structures in evolution’s ‘morphospace’, but they cannot most primarily
be understood at the level of the organism, because morphospace is not an
adaptive landscape where we visualise the relationship between genotypes (or
phenotypes) and reproductive success, and model fitness on the height of the
landscape.
Morphospace is
a mathematical model of the form of connectivity between patterns – so a
reducibly complex morphospace means that the biological structures that
populate the evolutionary landscape form a connected group. The notion of a
gigantic sponge made up of very tiny fibrils that connect the evolutionary
structure together sits fine with me. If the connection has no broken off parts
then the random walk of evolution can move across the whole structure.
In fact, this
is a particularly good illustration because sponges are composed entirely of
mobile cells which can move about between different layers of tissue and
reallocate themselves to take on different tasks. Sponges have totipotency,
which as you may know, is the ability of a single cell to divide and produce
all the differentiated cells in an organism. This allows any fragment of a
sponge to regenerate into a self-sustaining organism.
A good analogy for markets?
I'm afraid
though, the analogy of every tiny fibril representing the complete structure of
the entire world’s biochemistry causes me problems when we get onto markets. You
have to remember, no one is saying markets don't evolve without a top
structure. What is being said is that activity at a local level is, just like
natural selection, producing complex and sophisticated outcomes that look too
well cultivated to have occurred by Smithian localities, and there we find a
good analogy to the 'naturalism' of biological evolution.
You’ve
probably heard of the term irreducible complexity in relation to the debate
about intelligent design. The ID debate uses a fairly rudimentary definition of
irreducibly complexity in relation to the evolvability of organisms (as per my
definition above). At a deeper level, at the level of computation, if a system
can only exhibit the full extent of its output by running it then we can say
that system is computationally irreducible. Obviously we humans cannot
understand the full implications of this when it comes to the entire universe,
but the universe is a nexus of activity which has an underlying story that we
may define as being computationally irreducibly complex.
What this
means is that to simulate a like for like model of the universe would involve
computation of universe-size proportions, just as to simulate the whole history
of biological evolution would involve computation of the whole 4.5 billion
years of biological evolution.
Extending the
analogy to society, consider human history (let's call it H) as the sum total
of everything that has happened in the vast search space, just as morphospace
is the totality of the search space in the biochemistry that facilitates
evolution. If we imagine H to be a computational model representing every
piece of data and information linked to humans, then we can say that H is
computationally irreducible, because H is locked together by every contingency
(that is, all the constituent facts contained within H) so the removal of one fact
would change H to something that isn’t H.
I realise that if you're unfamiliar with this kind of talk, notions like computational irreducible complexity are going to be quite conceptually opaque to the mind, so hopefully a simpler illustration will help, in the shape of what's called a magic square. A magic square, if you not familiar with it, is a configuration of numbers that give a beautifully succinct illustration. If you look at the square of numbers below, you'll see that the removal of one number from a global size magic square would change the whole structure.
24 23 15 16 14 19
13 17 21 22 20 18
12 26 9 10 29 25
31 2 4 33 5 36
What’s
significant about the magic square is that its numerical structure totals 111
when summing columns, rows and the diagonals. When added together each sequence
of six will obtain 111 each time. Change any one of the lines and the magic 111
will be thrown out. In other words, altering the configuration will disrupt the
overall connectivity of the square. Mathematics has conceptual forms that
entail magnificent symmetry, and the removal of any of those proprietary parts
means it falls down like a house of cards in a gale force wind.
Returning to human
history (what we called 'H'), obviously H by definition can only be one
computational set because the only way to change that set would be to produce
an alternative history, and we can’t do that, because we are then talking about
some other kind of H. Altering the configuration of the magic square will
disrupt the overall connectivity of the structure – and that must be what the
human story is like – you cannot change one constituent part without changing
the whole.
Obviously,
constituent parts could be changed with seemingly no effect on the whole, but
that’s not really happening – it’s only because we see reality through the tiny
lens of our first person perspective that we don’t see the change to the
whole. Pretty much every word you speak to others, every decision you
make, and every course of action you take has implications far wider than you
can imagine.
Let’s take a fairly extreme example to illustrate. Say you go back to April 20th 1889 and kill baby Adolf Hitler; it is obvious that the whole human story will be inexorably altered from that point onwards. The 20th century would look unrecognisably different, even if at the time your act didn't appear to have global consequences. Using Hitler is only an extreme way of describing what would apply at smaller levels too. Suppose you just want to go back in time and stop the little girl who lives down the lane getting run over. Even that small intervention would have vast ramifications beyond your scope – you’d start a social butterfly effect that impinges on the rest of the human story.
The H we call
human history is irreducible, because the removal one component makes it
something other than what it is. History tends to be viewed first off at a
local level (one’s own history perhaps) and those local connections are woven
into the standard cause and effect relations that make up the bigger
picture.
Just recently
a young cyclist was knocked down by a car on the roundabout near where I live.
With local introspection it is hard to imagine that this event had any real
bearing in China or Brazil, but it would do – not immediately directly of
course, but given H it must have an effect somewhere down the line.
Because things are not immediately obviously connected to us, each event in the
global structure of H appears local and disconnected, whereas all events are
actually woven together in an interconnected whole. Clearly though not
every event has global relevance – if I suddenly scratch my nose for 3 seconds
that won’t have any bearing on China or South America will it (butterfly effect
notwithstanding).
I said that
reality is seen through its of conceptual layers – well just as overall human
history is incompressible, at the individualistic level the history of a
person's life is the same – change one bit of it and it is no longer that
unique system. So in that sense even the rubbing of my nose is part of a
unique personal history for me. I am in my 40th year of being alive on
earth, so my life's history amounts to around 14,500 days, or 350,000 hours, or
21 million minutes, or just over 1.2 billion seconds and counting.
Of course we
can work with a compression based on how much time I've been asleep in that
time, or eating, or driving, but just like with evolution, the history of my
life can only be fully analysed with the same 1.2 billion seconds computation
time. In other words, even if such a project were possible, to run a
program of my life to see how my thoughts, feelings and emotions had changed
and developed from birth to now would involve factoring in every single
experience and influence and neuronal processing, and that's what I mean at a
wider level by history being incompressible.
To change one
element of it means changing the totality of the whole thing. On a grander
scale the world's history of the socio-personal is the same - to set up a
computation mapping every event, the influence of those events on people, and
the cognita processing those influences would take a timescale of the same
length as the world's socio-personal history.
The perceived
format of the magic square and the irreducibly complex nature of mathematics,
the universe, evolution, human history, and whichever lens we choose to gaze
through, provides us with a great metaphor for life – reality appears to us
locally, and it can be extended into a much broader multilayered picture of
interconnected stories – be they social, historical, biological, physical or
mathematical. And what appear at the local level as a collection of separate
and somewhat disconnected mini narratives actually weave a global pattern,
which is itself embedded in an even bigger mathematical object that we only
sparsely sample through this brilliant narrative we call physical
reality.
Now we get to
the nitty gritty of Tim's question in relation to the freedom of markets and
where it's beneficial for them to be artificially interfered with. As a
reminder:
"There is no way to distinguish
between right and wrong in the trial and error computation which ultimately
must make the appropriate selection, except to say that top-down transcendent
constraints skew the statistics in favour of certain classes of outcomes."
What you have to really consider is what in societal terms is the overall
transcendental physical regime that constrains possible behaviours/outcomes?
Society is constrained by all sorts of overarching authority figures (rule of
law, regulations, mandatory exchanges of money, etc) but the question at hand
here is not to deny their existence, it is to locate areas where they are
excessive and counterproductively interfering in our beneficial transactions
and our liberties (as per my recent paper
on trade).
So to put it
in algorithmic terms, the debate is about whether the algorithmic means by
which the seek, find, reject and select computation is carried out in human
behaviour better at a local level, or whether it is better imposed by authority
figures. Given that local behaviour is concomitant with local knowledge and
local incentives, it is fairly evident that there are many areas of society in
which the authority figures are constraining the societal value (the consumer
surpluses + the producer surpluses) at a level lower than would be the case
without their interference.
Society is, of course,
subject to physical constraints – most notably, energy, labour and knowledge –
that limit the rate of progress and the directions society can take. But as we've covered before, many decisions made locally have knowledge-based and
incentive-based advantages that top-down command decisions do not have (see here for example)
Appendix
As a bonus, if
you don't mind ending on a tangent, the whole sponge is computationally irreducible notion also demonstrates what
is it that the Intelligent Design school have got wrong about irreducible
complexity about irreducible complexity being unevolable in biological
morphospace. Using the fairly standard scaffolding example that is often posited
as an illustration – once you've removed the scaffolding and the cranes from,
say, a Gothic cathedral, and destroyed any knowledge of cranes, cathedral
construction becomes irreducibly complex. If we look for examples of this in
biology and use a comparison between heavy stones in cathedrals and cells in
organs, whereas with the Gothic cathedral the stones are simply too heavy to
have been hoisted there, there are similar occurrences in biology where if
subsequent mutations remove the antecedents of symbiotic systems there is no
way to logically regress the path of a complex evolutionary adaptation.
If one
component was removed then it could not function, and this seems to be due to
two possibilities: The proteins (or protein complexes) have been modified
further since the addition of the hypothetically removed part. If such
modification creates dependence on this more recent part then its removal would
be detrimental. Secondly, as we’ve said, the structure evolved with
'scaffolding'. It is hypothetically possible that a structure could only be
stable when complete, but that it could also be stable if another structure is
present. Remove this second structure,
just as scaffolding is removed when building work has finished, and the first
structure remains stable. However, remove a single part of the structure and
the scaffolding is needed for support again, if it is not there the first
structure collapses. Both of these are
ways in which irreducibly complex structures can evolve – but crucially they describe
irreducible complexity in the biological patterns of morphospace, not in the
computational ‘sponge’ whole.
The problem with the IDists idea of irreducibly complex systems is that if morphospace does contain lengthy leaps that refute reducible complexity such large leaps taken would never be stumbled upon because they would be too computationally complex. You see, the Intelligent Design school is thinking of Irreducible Complexity in terms of subtraction of functional elements which leads to “instability” in the organism. But if we think back to our pattern of morphospace with the sponge, those concepts of “scaffolding” (and everything else in the biological patterning) will be embedded in such a complex configurational nexus that biological irreducible complexity could only be found in morphospace with a computation of the same length. So the IDists are barking up the wrong tree with their version of irreducible complexity.
N.B: Point of clarity: logical incompressibility is different
from morphospace because it is dealing with a different heuristic. Logical incompressibility
has to do with equations and algorithms used for data compression, although in
mathematical terms it is true that physics effectively defines a set of stable
structures in morphospace. The subject we have dealt with is tricky because we
are looking at how mathematical patterns are configurations of laws over
physical systems, and it is easy to confuse mathematical patterns with the
physical systems they support.
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