reaction A reaction changes something into something else. A chemical reaction changes one or more substances into other substances while a physical reaction changes one or more substances into another form of the same substances. 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 require special hardware, like a sun, a nuclear reactor, or a particle accelerator.)

network 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.

reaction network A reaction network is a set of linked reactions in which any one reaction can affect (start, stop, increase, decrease, modify) another reaction in the network. The reactions can be treated as nodes of a network and the connections 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 living things depend on many large and complex 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 its nodes and links are grouped, the way each such group changes is shaped by at least one other node not in its present subgroup. Or to say it another way: The only way to treat it is as a whole. It has no well-defined pieces. Imagine carving a turkey at its joints. A non-linear turkey would have no joints. No matter how we sliced it, each part would depend on at least one other part. For a slightly more technically correct definition, imagine changing some part of a reaction network and observing the result. If you change the same part just a bit more and get slightly more of the same result and that’s true for every part that you can change, then the network is linear. For non-linear networks though, your second small change might have completely different results from your first such change. Almost all 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. Non-linearity can be of structure or it can be of growth, or both.)

closed reaction network A reaction network is closed, or has closure if it produces, or strongly attracts, all its own substrates (that is, the resources, as opposed to the catalysts, it needs to continue to exist). For example, the enzyme sucrase breaks down sucrose into glucose and fructose. Sucrase is a catalyst and sucrose is its substrate. That reaction isn’t closed, but if it were it would mean that the action of breaking down sucrose would itself induce more sucrose to enter the reaction. Closed reaction networks are much more complex than such simple reactions. (‘Closed’ is a mathematical term, redefined in this book to apply to reaction networks instead of mathematical sets. The network’s reactions are its ‘operations,’ as a mathematician understands the term. As used in the book, a human network can be politically closed or operationally closed with respect to its operations’ needed resources and the default meaning is of operational closure.)

autocatalytic reaction (‘self-stimulating.’) An autocatalytic reaction produces more of its own catalyst. It catalyzes itself and thereby creates conditions for itself to continue. (Note the distinction between ‘closed’ and ‘autocatalytic.’ Closure is a more general idea than autocatalysis. Speaking more technically, a ‘closed’ reaction is ‘substrate-closed;’ an ‘autocatalytic’ reaction is ‘catalyst-closed.’)

synergetic reaction network (‘jointly self-stimulating.’) A synergetic reaction network creates catalysts for all its reactions. Thus, they together act to reinforce each other. (Note the distinction between ‘autocatalytic’ and ‘synergetic’. Synergy is a more general idea than autocatalysis. Every autocatalytic reaction is synergetic.) (This sense of the term ‘synergetic’ is a specialized term in this book although the word is in common use in the vaguer sense of ‘working together well.’ A more common chemical term for the same idea is ‘collectively autocatalytic.’)

autopoietic reaction network (‘self-maintaining.’) An autopoietic reaction network is a closed, synergetic reaction network with its own enclosing membrane that its reactions themselves maintain. Its parts interact so as to maintain themselves, their links, and their collective membrane. A cell, for example, is autopoietic. So is a termitary. (An autopoietic reaction network is closed with respect to catalysis, but is not, and cannot be, closed with respect to materials or energy.)

stigmergic reaction network (‘self-building.’) A stigmergic reaction network is a self-changing one. It has two kinds of nodes: active and passive ones. The active nodes have transient catalytic links to the 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). Ants following a pheremone train to food, for example, are acting stigmergically. As ants on the trail are rewarded with food at its end, they lay down pheremones on the trail, which encourages more ants 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 term ‘stigmergic’ is a specialized term in this book.)

ecogenetic reaction network (‘self-assembling.’) An ecogenetic reaction network is a stigmergic network whose passive nodes encourage new active nodes to form. No one species of active nodes in it is necessarily itself stigmergic (unlike, for example, termites). The catalytic reactions between its nodes either create new nodes or destroy old ones, create new links between nodes or destroy old ones, or they modify the current catalytic links among its nodes. An ecosystem, for example, is ecogenetic. New species enter it and old ones leave, each contributing to its structure over time, which changes which new species can enter it next, and which old species will leave it next. (‘Ecogenetic’ is a specialized term in this book. A more common term for it in ecology might be ‘ecologically successive.’)

reaction network phase change A reaction network undergoes phase change when it experiences a rapid change of state (occurring at a critical point). It radically changes its behavior or structure, for instance, when a solid gets so hot it melts into a liquid, or when a match gets so hot it ignites, or when a nuclear reactor crosses the cutoff point for neutron production. A reaction network poised to change phase is said to have reached criticality. The term originally comes from physics, but many systems can phase change. For example, an ecosystem under ecogenetic change can grow to support species that it couldn’t have before. It can also collapse and thus fail to support species that it did before.

power law Distributions that obey a power law are extremely skewed. The most popular elements are far more popular than the next most popular elements, and so on down to the least popular. Technically: element frequency is determined by some power of a variable. (Hence the name, ‘power law.’) The set of all words in Shakespear’s plays, for example, follows a power law. So do the sizes of cites, income distributions among people, the number of earthquakes ranked by size, and so on.

scale-free network A network becomes scale-free if its number of nodes is growing and if the chance that a new node will link to an existing node is proportional to how highly linked the existing node already is. That gives a rich-gets-richer effect, and power laws of node linkage. It’s called ‘scale-free’ because if you take only a subset of the network it too has a power-law degree distribution. A few nodes are hubs, with high degree (that is, they link to many other nodes) but most nodes have very low degree (that is, they link to only a few others). Many biological networks are scale-free, as are many other naturally occurring networks.

recursion Recursion is a way to specify an operation in such a way that the operation being defined is applied (‘recurs’) within its own definition. A simple way to think of it is in terms of bootstrapping. Once you have a certain basic set of capabilities you can use them to boostrap yourself up to more extensive capabilities. Recursive processes occur often in computer science and mathematics, but is rare in normal life. Now that we’re gaining an low-level understanding of biology we’re learning that recursion is also deeply entwined into the fundamentals of both life and mind. 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.

exponential growth Something grows exponentially if it doubles at a constant speed. Computer hardware for example has been exponentially increasing in many dimensions (speed, memory size, connectivity, and so on) for decades. This is an example of traditional compound interest. Capital left in a bank at a constant interest rate will double in a certain time, then keep doubling for each succeeding time period.

hyperbolic growth Something grows hyperbolically if it grows proportional to the square of itself. For example, each doubling might halve the doubling time of the next doubling. Hyperbolic growth is far faster than exponential growth. One way to think of the difference between exponential and hyperbolic is that in exponential growth something doubles in a constant time, whereas in hyperbolic growth something is doubling but the time it takes to do so falls the more it doubles. For a long time the human species has been growing hyperbolically, but has since tapered off to exponential, and is now nearing its peak population.

reaction	A reaction changes something into something else. A chemical reaction changes one or more substances into other substances while a physical reaction changes one or more substances into another form of the same substances. 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 require special hardware, like a sun, a nuclear reactor, or a particle accelerator.)
network	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.
reaction network	A reaction network is a set of linked reactions in which any one reaction can affect (start, stop, increase, decrease, modify) another reaction in the network. The reactions can be treated as nodes of a network and the connections 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 living things depend on many large and complex 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 its nodes and links are grouped, the way each such group changes is shaped by at least one other node not in its present subgroup. Or to say it another way: The only way to treat it is as a whole. It has no well-defined pieces. Imagine carving a turkey at its joints. A non-linear turkey would have no joints. No matter how we sliced it, each part would depend on at least one other part. For a slightly more technically correct definition, imagine changing some part of a reaction network and observing the result. If you change the same part just a bit more and get slightly more of the same result and that’s true for every part that you can change, then the network is linear. For non-linear networks though, your second small change might have completely different results from your first such change. Almost all 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. Non-linearity can be of structure or it can be of growth, or both.)
closed reaction network	A reaction network is closed, or has closure if it produces, or strongly attracts, all its own substrates (that is, the resources, as opposed to the catalysts, it needs to continue to exist). For example, the enzyme sucrase breaks down sucrose into glucose and fructose. Sucrase is a catalyst and sucrose is its substrate. That reaction isn’t closed, but if it were it would mean that the action of breaking down sucrose would itself induce more sucrose to enter the reaction. Closed reaction networks are much more complex than such simple reactions. (‘Closed’ is a mathematical term, redefined in this book to apply to reaction networks instead of mathematical sets. The network’s reactions are its ‘operations,’ as a mathematician understands the term. As used in the book, a human network can be politically closed or operationally closed with respect to its operations’ needed resources and the default meaning is of operational closure.)
autocatalytic reaction	(‘self-stimulating.’) An autocatalytic reaction produces more of its own catalyst. It catalyzes itself and thereby creates conditions for itself to continue. (Note the distinction between ‘closed’ and ‘autocatalytic.’ Closure is a more general idea than autocatalysis. Speaking more technically, a ‘closed’ reaction is ‘substrate-closed;’ an ‘autocatalytic’ reaction is ‘catalyst-closed.’)
synergetic reaction network	(‘jointly self-stimulating.’) A synergetic reaction network creates catalysts for all its reactions. Thus, they together act to reinforce each other. (Note the distinction between ‘autocatalytic’ and ‘synergetic’. Synergy is a more general idea than autocatalysis. Every autocatalytic reaction is synergetic.) (This sense of the term ‘synergetic’ is a specialized term in this book although the word is in common use in the vaguer sense of ‘working together well.’ A more common chemical term for the same idea is ‘collectively autocatalytic.’)
autopoietic reaction network	(‘self-maintaining.’) An autopoietic reaction network is a closed, synergetic reaction network with its own enclosing membrane that its reactions themselves maintain. Its parts interact so as to maintain themselves, their links, and their collective membrane. A cell, for example, is autopoietic. So is a termitary. (An autopoietic reaction network is closed with respect to catalysis, but is not, and cannot be, closed with respect to materials or energy.)
stigmergic reaction network	(‘self-building.’) A stigmergic reaction network is a self-changing one. It has two kinds of nodes: active and passive ones. The active nodes have transient catalytic links to the 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). Ants following a pheremone train to food, for example, are acting stigmergically. As ants on the trail are rewarded with food at its end, they lay down pheremones on the trail, which encourages more ants 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 term ‘stigmergic’ is a specialized term in this book.)
ecogenetic reaction network	(‘self-assembling.’) An ecogenetic reaction network is a stigmergic network whose passive nodes encourage new active nodes to form. No one species of active nodes in it is necessarily itself stigmergic (unlike, for example, termites). The catalytic reactions between its nodes either create new nodes or destroy old ones, create new links between nodes or destroy old ones, or they modify the current catalytic links among its nodes. An ecosystem, for example, is ecogenetic. New species enter it and old ones leave, each contributing to its structure over time, which changes which new species can enter it next, and which old species will leave it next. (‘Ecogenetic’ is a specialized term in this book. A more common term for it in ecology might be ‘ecologically successive.’)
reaction network phase change	A reaction network undergoes phase change when it experiences a rapid change of state (occurring at a critical point). It radically changes its behavior or structure, for instance, when a solid gets so hot it melts into a liquid, or when a match gets so hot it ignites, or when a nuclear reactor crosses the cutoff point for neutron production. A reaction network poised to change phase is said to have reached criticality. The term originally comes from physics, but many systems can phase change. For example, an ecosystem under ecogenetic change can grow to support species that it couldn’t have before. It can also collapse and thus fail to support species that it did before.
power law	Distributions that obey a power law are extremely skewed. The most popular elements are far more popular than the next most popular elements, and so on down to the least popular. Technically: element frequency is determined by some power of a variable. (Hence the name, ‘power law.’) The set of all words in Shakespear’s plays, for example, follows a power law. So do the sizes of cites, income distributions among people, the number of earthquakes ranked by size, and so on.
scale-free network	A network becomes scale-free if its number of nodes is growing and if the chance that a new node will link to an existing node is proportional to how highly linked the existing node already is. That gives a rich-gets-richer effect, and power laws of node linkage. It’s called ‘scale-free’ because if you take only a subset of the network it too has a power-law degree distribution. A few nodes are hubs, with high degree (that is, they link to many other nodes) but most nodes have very low degree (that is, they link to only a few others). Many biological networks are scale-free, as are many other naturally occurring networks.
recursion	Recursion is a way to specify an operation in such a way that the operation being defined is applied (‘recurs’) within its own definition. A simple way to think of it is in terms of bootstrapping. Once you have a certain basic set of capabilities you can use them to boostrap yourself up to more extensive capabilities. Recursive processes occur often in computer science and mathematics, but is rare in normal life. Now that we’re gaining an low-level understanding of biology we’re learning that recursion is also deeply entwined into the fundamentals of both life and mind. 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.
exponential growth	Something grows exponentially if it doubles at a constant speed. Computer hardware for example has been exponentially increasing in many dimensions (speed, memory size, connectivity, and so on) for decades. This is an example of traditional compound interest. Capital left in a bank at a constant interest rate will double in a certain time, then keep doubling for each succeeding time period.
hyperbolic growth	Something grows hyperbolically if it grows proportional to the square of itself. For example, each doubling might halve the doubling time of the next doubling. Hyperbolic growth is far faster than exponential growth. One way to think of the difference between exponential and hyperbolic is that in exponential growth something doubles in a constant time, whereas in hyperbolic growth something is doubling but the time it takes to do so falls the more it doubles. For a long time the human species has been growing hyperbolically, but has since tapered off to exponential, and is now nearing its peak population.

Glossary