A reaction changes something into something else. A chemical
reaction changes one or more substances into other substances and
a physical reaction changes one or more substances into another
form of the same substance(s). For example, melting ice changes one
form of water into another form. It’s a physical reaction. Burning
paper changes the linen rag in the paper into carbon, carbon dioxide,
and other substances. It’s a chemical reaction. Condensing steam or
dissolving sugar in water are physical reactions. A burning match or
a piece of rusting iron are undergoing chemical reactions. (Note:
There are also nuclear reactions, but those need special hardware,
like a sun, a nuclear reactor, or a particle accelerator.)
A network is a set of nodes together with links between
those nodes. The nodes can stand for anything and the links between
them can stand for any relationship between those things. For example,
nodes might be oil refineries and links might be pipelines connecting
them. Or nodes might be words and the relations between their
definitions, or between their spellings, or between their lengths.
Nodes can also be ideas and links might be associations among them.
Or nodes might be molecules and links might be chemical reactions
between them. Nodes might also be chemical reactions and links might
be catalytic connections between them.
A reaction network is a set of reactions in which any
one reaction can affect (start, stop, increase, decrease, modify)
some other reaction in the set. The reactions can be treated as
nodes of a network and the interactions between them as its links.
Extracting oxygen from air, digesting an apple, or creating vitamin
C from glucose relies on many biochemical reaction networks. All
known life-forms depend on many reaction networks.
non-linear reaction network
A reaction network is non-linear if the behavior of its
reactions can’t be expressed as the sum of any subdivision of the
network into parts. That is, no matter how anyone groups its nodes and
links, the way each such subgroup’s behavior changes over time is
affected by at least one node not in its subgroup. Thus, the only way
to treat the network is as a whole. It has no well-defined subparts.
For example, imagine carving a turkey at its joints. A non-linear
turkey would have no joints. No matter how it’s sliced, the behavior
of each part would depend on something in at least one other part.
For a slightly more technical definition, imagine changing some
part of a reaction network and watching the result. If changing the
same part just a bit more yields slightly more of the same result,
and that’s true for every part changed, then the network
is linear. For non-linear networks, though, the second small change
might have completely different results than the first such change.
Many reaction networks in physics, chemistry, and biology
are non-linear. All reaction networks described below (and in this
book) are non-linear. (Note: there can be a distinction between a
network that is non-linear and a network that grows
non-linearly. That is, non-linearity can be in space or time, or both.
Much of what is called ‘non-linear’ in math, physics,
and engineering is really about non-linear growth, not non-linear
structure. Much of what is called ‘non-linear’ in economics, finance,
and planning (for example, economies of scale, or the economies of
big cities, or non-linearity in financial networks) is about
non-linear growth but is caused by non-linear structure, which leads
to non-linear growth.)
An autocatalytic (‘self-helping’) reaction produces
more of its own catalyst. It thus catalyzes itself and thereby
creates conditions for itself to continue.
synergetic reaction network
A synergetic (‘jointly self-helping’) reaction
network creates catalysts for all its reactions. Thus, they
together act to reinforce each other. (Note the distinction between
‘autocatalytic’ and ‘synergetic.’ Every autocatalytic reaction is
This sense of the term ‘synergetic’ is a specialized term in this
book although the word is in common use in the general sense of
‘working together.’ In chemistry, a more common phrase for the same
idea is ‘collectively autocatalytic.’)
closed reaction network
A reaction network is closed, or has closure, if
it produces, or procures, or attracts, things that it needs to persist.
There may be, however, different kinds of things that it needs, which
leads to different kinds of closure.
For example, sucrase, a catalyst, breaks down sucrose, a resource,
into glucose and fructose.
That reaction, as a reaction network by itself,
isn’t catalytically closed; if it were,
the operation of breaking down sucrose would itself produce more sucrase.
That reaction also isn’t resource closed; if it were,
the operation of breaking down sucrose would itself induce more sucrose
to enter the reaction.
That reaction also isn’t operationally closed; if it were,
the operation of breaking down sucrose would itself produce more sucrase
and would also induce more sucrose to enter the reaction
However, in a large enough and diverse enough reaction network,
many reactions might work together so that the network as a whole
has various kinds of closure—catalytic, resource, operational.
(‘Closure’ is a mathematical term, usually used mostly in set theory or
topology, but it is redefined in this book
to apply specifically to reaction networks rather than just any set.
In this view, the network’s reactions are its ‘operations,’
as a mathematician understands the term.
When it comes to molecular networks, such reactions
can have catalytic closure (that is, synergy) or operational closure,
and the latter includes the former. That is, they
might produce all the catalysts they need, or they
might produce all the catalysts they need
as well as all the resources they need
that aren’t already provided by the network’s surroundings.
In the book, the term is used more loosely when it comes to human networks;
those might have operational or political closure—that is, they
might produce everything they need,
or they might try to use red tape or trade barriers or military barriers
or other barriers to bar loss of the resources they need.)
autopoietic reaction network
An autopoietic (‘self-preserving’) reaction network is a
operationally closed reaction network
enclosed in a semipermeable membrane, which its reactions themselves
maintain, which allows in energy and materials and expels wastes.
That is, its parts interact
so as to maintain themselves, their links, and their collective
membrane. A cell, for example, is autopoietic. In some sense,
so, too, is a termite colony—even though individual termites may wander
too far away from the nest and so die.
stigmergic reaction network
A stigmergic (‘self-building’) reaction network is a
self-changing one. It has two kinds of nodes: active and passive
ones. Its active nodes have transient catalytic links to its passive
nodes. Its active parts act on its passive parts to build, rebuild,
or extend them. The name comes from stimulation of workers (transient
parts) by the work they have already achieved (passive parts).
For example, termites following a scent trail to food, are acting
stigmergically; as termites on the trail are rewarded with food at its
end, they lay down scent on the trail, which encourages more termites
to walk that same trail. (Note: That’s also a simple autocatalytic
reaction, but laid out in space as well as time.) (This sense of
the entomological term ‘stigmergic’ is a specialized term in this book.)
ecogenetic reaction network
An ecogenetic (‘jointly self-building’) reaction network is
a stigmergic network whose passive nodes encourage new active
nodes to form. No one species of active nodes in it need necessarily
itself be stigmergic (unlike, for example, termites). The catalytic
reactions between its nodes either: 1/ create new nodes or destroy old
ones, 2/ create new links between nodes or destroy old ones, or 3/ they
modify the current catalytic links among its nodes. A food web, for
example, is ecogenetic. New species enter it and old ones leave,
each changing its structure over time, which thus changes which
new species can enter it next, and which old species will leave it
next. A city is also ecogenetic. (‘Ecogenetic’ is a specialized
term in this book. A more common term for it in ecology might be
reaction network phase change
A reaction network undergoes phase change when it experiences
a relatively rapid change of state. Its behavior or structure then
changes a lot. For instance, when a solid gets so hot that it melts
into a liquid, or when a match gets so hot that it ignites, or when a
nuclear reactor crosses the cutoff point for neutron production,
they are phase changing. The term originally comes from physics,
but many networks can phase change. For example, a food web under
ecogenetic stress can grow to support species that it couldn’t have
before. On the other hand, it can also collapse and thus fail to
support species that it did before. Both are phase changes.
Recursion happens when an operation is applied (‘recurs’)
within its own definition. Defining an operation in terms of
itself might sound like time-travel, as if someone could be their
own parent, but one way to think of it is in terms of
bootstrapping. Given a certain set of capabilities, someone
might use them to bootstrap themselves into different capabilities.
Recursive processes occur often in computer science and math,
but appear to be rare in real life. However, they are common in
biology (biochemistry, molecular biology, ecology, systems biology).
An autocatalytic cycle,
for example, is really a form of recursion since its current actions
affect its future actions. Synergy is similar, as is stigmergy,
autopoiesis, and ecogenesis.