COMPLEXITY: Physics of Life

W. Brian Arthur on Economics in Nouns and Verbs (Part 1)

Episode Notes

What is the economy?  People used to tell stories about the exchange of goods and services in terms of flows and processes — but over the last few hundred years, economic theory veered toward measuring discrete amounts of objects.  Why?  The change has less to do with the objective nature of economies and more to do with what tools theorists had available.  And scientific instruments — be they material technologies or concepts — don’t just make new things visible, but also hide things in new blind spots.  For instance, algebra does very well with ratios and quantities…but fails to properly address what markets do: how innovation works, where value comes from, and how economic actors navigate (and change) a fundamentally uncertain shifting landscape.  With the advent of computers, new opportunities emerge to study that which cannot be contained in an equation. Using algorithms, scientists can formalize complex behaviors – and thinking economics in both nouns and verbs provides a more complete and useful stereoscopic view of what we are and do.

This week we speak with W. Brian Arthur of The Santa Fe Institute, Stanford University, and Xerox PARC about his recent essay, “Economics in Nouns and Verbs.” In this first part of a two-part conversation, we explore how a mathematics of static objects fails to describe economies in motion — and how a process-based approach can fill gaps in our understanding.  If you can’t wait two weeks for Part Two, dig through our archives for more Brian Arthur in episodes 13 and 14.

If you value our research and communication efforts, please subscribe to Complexity Podcast wherever you prefer to listen, rate and review us at Apple Podcasts, and/or consider making a donation at You can find numerous other ways to engage with us — including job openings for both SFI staff and postdoctoral researchers, as well as open online courses — at

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Podcast theme music by Mitch Mignano.

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Related Reading & Listening:

• “Economics in Nouns and Verbs” by W. Brian Arthur (pre-print)
@sfiscience Twitter thread excerpting “Economics in Nouns and Verbs”
• “Mathematical languages shape our understanding of time in physics” by Nicolas Gisin for Nature Physics
• “Introduction to PNAS special issue on evolutionary models of financial markets” by Simon Levin & Andrew Lo
• “The Information Theory of Individuality” by David Krakauer et al. for Theory in Biosciences
• “On Coronavirus, Crisis, and Creative Opportunity with David Krakauer” on Complexity Podcast
• “The Erotics of Becoming: XENOGENESIS and The Thing” by Eric White for Science Fiction Studies
• “New model shows how social networks could help generate economic phenomena like inequality & business cycles” by INET Oxford on research by J. Doyne Farmer

Episode Transcription

W. Brian Arthur  (0s): Yeah, quite starkly economic theory was able to look at questions of what we call allocation quantities of this versus quantities of that. If the price of oil rose say 20% to reach a new equilibrium or balance, how much more hydro energy would Norway use or Sweden to substitute for the higher prices? The economics is wonderful, but a months and prices, unfortunately, economics is no rigorous theory or very little rigorous theory of where does an economy come from in the first place?

How does it develop and grow? How does innovation work? How does economic development itself work? There was no way to mathematize those. And so anything to do with formation and process within the economy has been orphaned.

Michael Garfield (1m 23s): What is the economy? People used to tell stories about the exchange of goods and services in terms of flows and processes, but over the last few hundred years, economic theory veered toward measuring discrete amounts of objects. Why the change has less to do with the objective nature of economies and more to do with what tools theorists had available and scientific instruments be they material technologies or concepts don't just make new things visible, but also hide things in new blind spots.

For instance, algebra does very well with ratios and quantities, but fails to properly address what markets do, how innovation works, where value comes from and how economic actors navigate and change a fundamentally uncertain shifting landscape with the advent of computers, new opportunities emerged to study that which cannot be contained in an equation using algorithms. Scientists can formalize complex behaviors and thinking economics in both nouns and verbs provides a more complete and useful stereoscopic view of what we are and do. Welcome to Complexity, the official podcast of the Santa Fe Institute.

I'm your host, Michael Garfield, and every other week, we'll bring you with us for far-ranging conversations with our worldwide network of rigorous researchers, developing new frameworks to explain the deepest mysteries of the universe. This week we speak with W. Brian Arthur of the Santa Fe Institute, Stanford University, and Xerox about his recent essay, Economics and Nouns and Verbs. In this first half of a two-part conversation, we explore how a mathematics of static objects fails to describe economies in motion and how I process based approach can fill gaps in our understanding.

If you can't wait two weeks for part to dig through our archives for more Brian Arthur in episodes, 13 and 14, if you value our research and communication efforts, please subscribe to complexity podcast wherever you prefer to listen, rate and review us at Apple Podcasts and/or consider making a donation at You can find numerous other ways to engage with us, including job openings for both SFI staff and postdoctoral researchers, as well as open online courses at

Thank you for listening. W. Brian Arthur it is a pleasure to have you back on Complexity Podcast.

W. Brian Arthur (3m 54s): I'm delighted.

Michael Garfield (3m 56s): So when we had you here the first time we spoke in very, very grand sweeping terms about the history and the future of complexity economics. This call, we have an opportunity to focus on something a little bit more granular, which is this pre-print that you've written Economics in Nouns and Verbs and the sea change or phase transition that you seem to believe is now necessary for us to adopt a more complete and comprehensive and practical approach to economic theory.

So why don't we start in the prehistory of this paper a little bit, and what motivated this line of thinking for you and what led to the development of these ideas in your case?

W. Brian Arthur (4m 47s): Somehow in the last five to 10 years, I got fascinated by computation. I should start out by saying I'm trained mostly as an applied mathematician, PhD in operations research, but that was all mathematics, very much trend in math and engineering. So my language of science, so to speak, is standard mathematics, but for some reason, some just sheer interest I got fascinated by computation 5, 10, 15 years ago. And then the last five years, I started to read some classics. What Alan Turing had written in 1936. I was reading Greg Chaitin’s ideas on algorithmic information theory, many other things, just trying to wrestle with what really was computation all about. And then I realized something else.

I began to realize that my own papers, and I think many of us at Santa Fe Institute could say the same 20 ago, 30, 40 years ago when I'm starting out my papers where mathematical, meaning expressed an algebra, calculus, linear algebra, and so on. And now I can say many things fluently, just like other people in complexity, but I tend to say them computationally.

And I started to wonder what had happened. And I began to realize that all the sciences are shifting in their means of expression from mathematics or standard mathematics to computation. I began to wonder why, so I don't want to say mathematics is dead, but I realized that there was a precedent for this in the 16 hundreds. So at the year 16 hundreds, in fact, for another 120 years after that mathematics was geometry.

But in that century, maybe 10 years before that, and 20 years after the 16 hundreds, algebra came in and started slowly to take over as mathematics or the language of science. And so I began to investigate that, and that was absolutely great fun. Algebra was bitterly opposed by Kepler. He called it gauche sometime around 1625. Thomas Hobbes, compared it to, as if chickens had been scratching on the page with all these silly symbols and Isaac Newton discovered called algebra, the analysis of bunglers didn't stop him using it, but I don't think he was too honest about it at least early on.

So when I talk about mathematics, I've noticed that the idea of what is mathematics keeps changing. So 1600 old geometry, 1720, 1750 it shifted, and now mathematics is largely taken to be algebra. What eventually came to be linear algebra as well, and the calculus. And of course there's many, many other parts of mathematics I need to say that are not algebra group theory, number theory, probability theory, all sorts of other branches of mathematics. What I'm talking about here as standard mathematics is roughly how theories are expressed in journals, whether they be physics engineering and in this case economics. And so that changed from being geometry to algebra.

In fact, I was quite amused that when Kant was starting to look at chemistry and must have been around the 1780s, if I recall, right, he chided it for not being scientific. And what did he mean? Well, he said it's not expressed in mathematics. And what did that mean? Well, it wasn't algebra, so there'd been a big shift. And I began to realize that we're in the middle of another shift at the moment, shift in language from seeing theory is being expressed first as geometry, then as algebra, and now as a computation, or I should say more precisely expressed algorithmically in some way where possibly a computer could handle that.

And there's similar resistance. There's similar outrage. And also I want to stress here at the outset that there isn't a final language I think for science, at least I hope not. We still use geometry heavily all over the place every time we write a graph down or show an image or something, some sort of tabulation, we often refer to geometry because it appeals to us in our brands visually. We do use algebra. I don't think that's going to stop, but we're getting a sort of third language alongside these two. And that language is computational. It used to be considered the following model. And then there'd be a set of equations. Now it's much more, let me put together the following model, assume, and then there'd be something algorithmic written down.

So I began to wonder where all that had come from and what it was going to deliver. And was this just fashionable? And was there a certain amount of just hyper BS or whatever that somehow we could all do computation. Everybody can do mathematics at least through trend in science, but I want to give you a quick story of where this really came from. My interest came from one single comment that a colleague made external member of the Santa Fe Institute, a good friend of mine.

I'd written a book about technology and how it evolves. And the book was written in plain English. My model was Darwin had written his book on species originate on how evolution works. And he had written that in planning this, that was my model. And at one stage I wrote down a sequence of steps by which technology has come about, replace previous technologies, like the railway train and railways replace canal technology. They're called forth further technologies, railways needed messages.

And so rail was called forth telegraphy the Telegraph. They called forth a lot of R and eventually steelmaking and so on. And railways became a component in overall transportation and they eventually changed the economy, changed society, and changed the way we do things all over the space of several decades. So I readjust this to a series of steps or what you'd call an algorithm. The comment, my good colleague, he blurbed the book.

He said, I love your book. I have learned an enormous amount from this book. He was all full of praise, but you know, Brian, he said this privately, he says, but it's not science. I said, what do you mean it's not science? Where are the equations? And so I had a what the bleep moment and I was offended and I don't know, bloody hell, this is science as much as anything else.

It was argued logically based on an offload of observations.  I went back. And I started to think if a theory or a story that we tell in science, how things form, if that is expressed in terms of algorithms, step one, step two, and so on, instead of equations, does that mean it's not science? And so I started to look at the whole question, could algorithms be science?

I'll give you more answers to that later on, but that's really what prompted me, got my goat and motivated the whole thing. I never told my colleague later, but I did send him the paper.

Michael Garfield (14m 7s): Well, that's actually great because in walking people through this, it seems like the right place to start is at the beginning where you set the stage with a little bit of the logic from the nature of technology, talking about the way that science proceeds as much by its instruments, as it does by our thoughts and the way that different instruments, you give the example of an MRI scan or a CT scan, reveal, different aspects of the world, reveal different phenomena. And that to draw term that you talked about in this book and you, and I think talked about in our first conversation, you just have Schumpeter and his idea of creative destruction and the way that when a new technological mileau, matures it not only reveals certain new affordances, but also forecloses on others.

And so there's the sense in which it's not simply a building on, it's a replacement of, and I like the point that you make in here that as you put it, I believe mathematics is powerful and economics and necessary, but I don't believe that it is suited to describing all that is interesting in an economy. In fact, I don't believe that given the complication of the economy and the humanness of the people who act within it, there is any privileged way to view the economy. So just starting there, which is a very large, you know, it's a grand philosophical claim, but it's a claim based on a rather robust pattern that you observe in your work.

And the way that if we think about math as a tool than different sub-domains of math, provide us different cognitive affordances. And then this is where if you care to comment on that, great, but this seems like a place where we can actually dive into the way that a noun based economics differs from an economics based on verbs as well like what the concrete distinctions are between the worlds that each of these tools disclose to us.

W. Brian Arthur (16m 5s): When I was writing about technology or the nature of technology, I spent quite a few years, probably a dozen or four years looking at technologies and really trying to understand them in great depth and trend in technology or in engineering. And in particular, I started to look at the history of science and I realized that science didn't proceed by wonderful theoretical ideas, followed by measurements, which is what we're told.

There's plenty of that, but really new instruments might come along almost randomly, so to speak. And then they would give us a new view of what was out there in nature. Classic thing is when Galileo makes his own telescope and points the heavens January 16, 10, and notice some fixed stars behind Jupiter and notices a few days later, when he looks again, the fixed stars, aren't fixed, they're moving.

And a few days later, he realizes, oh my God moment, that these are moons around Jupiter. And suddenly the whole world view shifts in that moment because everything in those days was supposed to revolve around the sun or the earth, depending on what fuel you took. And here are things revolving around Jupiter. So that was a sort of, oh my God moment.

And it came about because Galileo had a new instrument, telescope. Similarly, I noticed that I started to get into a nuclear magnetic resonance, MRI machines, and they can look at the same thing. There could look at your arm. It might have a fracture. MRI imaging and hospitals shows you in great detail, the soft tissue. So if you're looking in terms of maybe some sort of hernia or something, that's what you would want to use.

CT scanning by contrast looks at bones much better. So it was the same thing. You're looking at an arm, but one instrument was showing you soft tissue, the others showing you hard tissue or bones, bone structure. And that gives you a very different view, just two instruments. And then I took an interest in Helio physics, the physics of the sun. And yeah, you see the familiar pattern much as everyone from Galileo, a radiating sphere of energy and light with a few things going on in the surface, plasma injections and things like that.

But then I started to look at X-ray telescopes pointed at the sun, the images they were showing. And again, there was a moment where I was slightly shocked. The sun didn't appear normal. It had big fishers running through it more or less diagonally. And it looked almost as if it was ready to break in half. I think listeners should take a look for themselves far from perfect sphere and very peculiar looking, not at all uniform and just riven through by these gigantic fishers.

And so began to realize that different instruments of seeing are instruments of understanding or instruments of exploring showed you different things. It's an elementary point, but I realized too that when there are new instruments of looking, then they show you new things and science changes as a result. Now it's not the only way science changes, but that's certainly the history of science, I think, is more advancements in instruments of seeing or understanding than it is just thinking. If we had science that was just pure thinking, we'd have the science of the Greeks.

And we don't. The reason is now of course, we've particle accelerators. We have x-ray crystallography. We very advanced instruments for looking and those give us a whole world. And we have to adjust our worldview to what we see. I began to realize also that mathematics was an instrument of understanding. And that was also slightly a shock when we went from just using geometry to understand say the heavens and switched. So that would have been true on the time of Copernicus or Galileo. And we started to use algebra that Newton did. We see more precisely, we see different things. We get  new explanations that are detailed and quite accurate for planetary orbits being elliptical and so on. So mathematics then shows something different. It's not just a language that we use, algebra calculus or whatever.

It's actually more like an instrument that you're appearing through and what you see. So feel free to interrupt at any stage, but let me move on quickly to economics. Economics is very much based on geometry, not totally, but heavily based on geometry until, and an armchair speculation and just Oracle analysis up until about 18, seven years.

So, and then it became very much interested, slightly obsessed eventually by algebraic mathematics. Now I include all the modern stuff that was brought to this day. I'm talking about algebra, largely calculus, linear algebra. So the kind of mathematics we're taught to apply in graduate school. And I began to wonder what sort of economics to that give you. A few years ago, I wrote a book called complexity in the economy and I around about 2014, 20 5, I had been thinking heavily about algebra.

And I began to realize that algebra is wonderful. I'm a huge supporter because that's my toolbox largely. I began to realize that algebra as a language or as an instrument of seeing, or as an instrument of exploring dealt only with quantifiable objects. So if you say X plus Y equals 115, the X must be quantities, measurable quantity.

And so most of the Y because algebra is fundamentally a form of arithmetic. It's a means of arithmetic that's carried out partially symbolically. So you've coefficients, you've XYZ, symbols, you've plus signs. You can do arithmetic operations. You can take square roots of equations. You can get X to the power of an and all this sort of thing, but it remains a more general arithmetic.

In fact, I think it was in 1707 that Isaac Newton put his lecture notes together and published a book called Universal Arithmetic. But what he really meant was algebra. So if you set up anything in algebra terms, or we would not say mathematical terms, the things you set up had to be quantitative nouns, and almost without thinking economics adopted this, the 1870s on through to the modern day, theories started to become more and more mathematical.

And I had wondered earlier, why did economics deal nearly all was nouns? So quantities produced quantities consumed. Those are nouns. Rates of this and of that prices a month traded numbers of firms, economic growth. These are all nouns. And of course it could object and say, well, hang on. I read the newspapers and they've talked about firms going into chapter 11 and real events. OPEC doing something in the oil industry and so on, but doing something or carrying out something or some process isn't easily expressible in algebraic mathematics.

And so it gets dropped. And I began to realize there was a giant sieve in economic theory if economic theory is expressed in standard mathematics than anything that had to do with processes or events fell through the sieve. And the only thing retained for years were nouns,  rates of this and rates of that. And I sat down and I thought, what difference does that make to economics?

I began to realize, you know, I started to look at older writings and economics. I came across a lovely passage. I was quite familiar with actually by Alfred Marshall. Marshall is writing around 1890 and he was talking about why industry is custard. You know, why is there say a leather industry in Italy or even a violin industry in Cremona?

This is what Marshall says. When an industry has chosen a locality for itself, it's likely to stay there long. So greater the advantages from people following the same skill trade get from being near one another, it's as if the mysteries of the trade were in the air, good work is rightly appreciated. Inventions and improvements happen in machinery and processes. The general organization of the business have their merits promptly discussed.

If one man starts a new idea is taken up with, by others and combined with suggestions of their own and so on. So what he's talking about is not rates of this and the months of that. What Marshall's really talking about as a whole process of the formation of industry and how events, something happens, somebody discovers some new thing it's discussed down at the pub in his day. It's talked about by people in the same tread may be taken up.

It may be improved upon, but these are all processes. And then I started to look at passages from Paul Samuelson, the great economist who had more than anybody, in my opinion, mathematized economics. And this was in the 1940s and Samuelson was writing about how international tread could be expressed in terms of economics.

And he imagined the scientists trying to maximize the raw total of clothing production in Portugal and England subject to certain constraints. So the passage reads Z equals X sub two equals X, sub two, and X sub two prime is to be maximized subject to X one plus X one prime equals capital X one. And so on.

It's just pure algebra. It's actually what I would call linear programming. This sort of mathematics I specialized in, but what struck me about the passage was that there were no human relations in there. It was all nouns related to other nouns. There was no word in narrative. There is no idea of humans actually trading, no firms were mentioned and people and actions and events had been edited out just to sort of shoe horn, all of this into the algebraic sausage machine and the whole thing, I'm being somewhat snide.

But again, this is my stock and trade so I can say this.  This has been a shocker. If you hold those two passages alongside each other, Alfred Marshall was trained in mathematics in the 1860s. He was second wrangler if I remember, Lord Raleigh in the trippers in Cambridge member of Trinity College. So it was one, a hell of a good mathematician in his day. And a trend in mathematical physics became an economist, but his story is his theory as wordy something's in the air, children pick it up.

Ideas are discussed. That's processy, that's very be 60 or so years later, then we got Paul Samuelson, 50 years later, even who's got religion. He thinks that economics should be like theoretical physics. And we should take out all these silly stories and just concentrate on X sub one plus X prime sub one equals capital X.

Doesn't do it for me. I realized that we had lost something. So just to summarize all of this, using the language of algebra, calculus, differential equations, linear algebra, that sort of mathematics reduces economics to relations between quantities and in particular, then that rules out stories and it rules out events and it rules up processes.

And once I realized that I began to realize why I had because had been trained in mathematics, I thought it would be natural to study economics at Berkeley, actually under mathematicians. When I tried to do that, I couldn't stand the courses I was given. I specialized in those days in what's now called development economics, looking at what we'd call developing countries or in those days, third world countries and how they develop. Economic development think in terms of India at the time or countries in Africa, economic development was described in noun form as a country was developing. If its GDP, which is, was improving or increasing by at least 1%, after all his thoughts, I began to realize that that's like saying an embryo, like a human baby is developing in the womb.

You could say it's developing and turning into a human being. If it's volume or weight was improving or increasing by more than 1% in a given time, maybe in two weeks or something like that. And I thought, sure, it's a measure of development. It's not totally awful, but it doesn't tell you a single thing about what development is or how embryos for that matter develop. You can't just say it grows.

It fades away. We have a phrase and economics, we talk about up upsy downsy economics, quantities down, prices up, prices up quantities, doing something else. Unemployment up prices down. And so this is the way we think about economics. It's like, as if there's all these colored test tubes all in a row, and one of them says oil prices. And one of them says unemployment and the liquids in each are moving up and down.

And it seems to be the job of economics to connect these different non-quantities, using some ideas, but how they do connect and then working out of mathematics for what affects, what it's mechanical. It's completely quantity, a noun based. It's not wrong. It gives us plenty of insights and I don't expect this to change. But when it comes to any questions of formation, how does an economy form. How does a new technology form? How does the new technology come about?

How does innovation work? How is a new industry formed and set up when a set of new technologies comes along, think of mass production or automobiles or electronics, or the digital technologies, how do industries change? How does structural change? Those are all questions of formation. And there you start to look at those.

You realize those are all processes and processes require verbs, but you can't handle verbs in the standards, mathematical language, at least in standard algebra and calculus. So what do you do, you just talk about, well, there's more of this and there's less of that. This is growing. That's fading away. This is replacing the number of new firms is this. And so on. Most people would say that economic theory is theory expressed in standard mathematical form, but standard mathematical form reduces you to only quantitative objects or a quantitative amount.

So all of economic theory is based upon this amount affects that amount. Left out is process any idea that there could be events or it could be verbs, or it could be actions and interactions. There could be actions triggering other actions, or it could be actions, inhibiting other actions. And we could think about that. We could talk about that and people have, and people. Do Austrian economics for example, it's a school of economics has been around for a long time, thinks in terms of actions and processes and verbs, but it's ruled to the side because you can't express that and standard mathematics. Therefor it's not proper theory. Therefor it doesn't count. So this is, I think there are other missing thing. And let me just say here that, you know, if somebody says, okay, you know, are you anti theory or you anti mathematics and economics?

No, no, not at all. That's what I've done for most of my career. I'm not completely reformed either. I will continue to use mathematics, but I do think that it's a restrictive language. It restricts our thoughts to a months of this affecting the months of that. And it precludes us going inside. What is economic development? How does Silicon Valley change where the new inventions come from?

You can't look at that in a set of equations at all easily. And those are all processes that you can get inside the processes. And you can understand those processes. Economic development, for example, has an awful lot to do with new credit coming available. Simple banks being set up. It has to do with people setting up schools, setting up new things, trying something and failing, maybe buying trucks, delivering something, maybe new railway destinations being opened up.

So these are all processes. There are by no means deterministic. Something happens here. Something happens there. They kind of do follow a pattern, but that pattern isn't led down deterministically and yet countries to develop. So to put it quite starkly economic theory was able to look at questions of what we call allocation, quantities of this versus quantities of that.

If the price of oil rose say 20% to reach a new equilibrium or balance, how much more hydro energy would Norway use or Sweden to substitute for the higher prices? Economics is wonderful about amounts and prices. Economics had to bypass. Unfortunately, economics is new rigorous theory or very little rigorous theory of how, where does an economy come from in the first place?

How does it develop and grow? How does innovation work? How does economic development itself work? All of these had to be left out. They've all been explored of course, and where they form, but there was no way to mathematize those. And so they're kind of the orphans stepchildren. If that's not contradiction in terms of economics, anything to do with formation and process within the economy has been orphaned.

You say, well, isn't that true in all science? I mean, isn't physics about velocities and position and amounts and quantities of energy and mass, all this sort of thing.. Certainly up until the last several decades, but biology is all about process. Whether it's molecular copying of DNA or replacement of DNA or messenger RNA, things like that.

These are all processes. How cells form, how molecules replicate in particular at the DNA level, how embryos form, how neural processes work within the human brain, those are processes. And we're understanding them as process. And this explains to me why biology couldn't be mathematized. There's a kind of oddity. Yet i's all important. And it's becoming central in the science itself. So biology is an oddity because nearly everything that looks at including things like sequencing DNA, that's a process of synthetic biology. It's a set of processes. They can't easily be mathematized because what counts, isn't quantities or numbers of stuff, what counts is events, that trigger events. And so on.

Michael Garfield (40m 53s): So it occurs to me listening to you speak about this, that in the history that you present of economic thinking, all of the math is before the publication of the Origin of Species. And that like the reason that you keep turning to biology seems to be that biology made this transition. And the 19th century between basically a static taxonomy, a version of the world in which all of the species have been created and are timeless and permanent to a world in which species go extinct and species are created in an ongoing sort of innovation process.

So likewise algorithmic thinking seems to emerge through a kind of a Darwinian paradigm shift that you get this notion of the world as essentially an emanation of these eternal forms in the mind of God, to a world in which everything is in flux and the resistance that the theory has experienced and its various implications has a lot to do with the visceral discomfort that many people feel with the idea that the self and various other things that we take for granted as static as solid ground upon which to base our understanding of the world are in fact constantly in flux. I read a fabulous paper about this as relates to science, fictional horror, Eric White, The Erotics of Becoming: Xenogenesis and the Thing  where he talks about why it is that so many horror movies are about an ever-metamorphosing monster.

And that it's related to the discomfort that the world experienced at the idea that we had evolved from monkeys and that would have evolved into something else, that the human is not this archetypical perfect, you know, static crystal and thing. But it's just one point along an ever-shifting continuum of possible forms relating to each other. I liked the way that you continually draw people's attention in this work to the fact that an algebraic equation system does not endogenously generate new variables.

I mean, you said as much just now that it's pre-specified when you say, okay, this is you've already decomposed the system. You've already recognized all of the salient features of it. And it's funny because again, to view these different mathematical modalities as themselves evolutionary products that are like adaptations to a time and a place that this sausage machine that you're talking about of traditional economic thinking, it results in this particular effort to try and squeeze the universe into the shortest possible equation, right?

In a way it looks like these revenue models that try to maximize externalities, it's like let's make this efficient as possible and then build on those efficiencies and create these mature ecosystems where the winners are betting on efficiencies given by economies of scale. But you get to a point where there's a disruption from within or from beyond the ecosystem. And then suddenly those finely tuned equations no longer work to describe a world that is changing rapidly under the influence of say an asteroid impact or to give an indogenous, you know, rapid technological change caused by networked electronic technologies.

And at that point, David Krakauer, and I talked about this back in Episode 29 that you see when the equilibrium quote unquote is punctuated, you make a point that all of this math biases us towards equilibrium thinking. What's like, well, that makes sense if the world that you're living in, isn't changing in unexpected, freaky ways every day, but then suddenly you need a non-equilibrium model because the world that you're living in is clearly not in equilibrium. And you get these strategies, like he talks about the high mutation rates of viruses because the host body is always changing.

Their environment is always changing or the way that generalists tend to do really well or high beta investment strategies tend to do really well in periods of market crashes and mass extinctions and so on. So that's where we get this new epistemology of immutable self. You know, the Bucky Fuller, I am a verb. The Alfred North Whitehead’s process philosophy. And again, this was recently formalized deliciously in a paper I love bringing up on the show, Krakauer led this paper,Information Theory of Individuality.

It shows that the category of the individual is itself something that emerges out of these relational processes. It's informational integrity through time, or it's informational scaffolding by its environment. It's just funny how it's not just that the theories disclose new worlds, but that they themselves seem to be the precipitates of our interaction with the world. And that in a shift to an algorithmic economics, one that allows us to explain where new technologies come from and the way that our various relational processes lead to unexpected phenomena and the way that this helps us sort of strip ourselves of the bias of equilibrium and also of rationality, because you can't have perfect knowledge about a world that's always changing and about which you are learning everything through these relationships.

It's just funny that it seems that the tools required to make this methodological shift in the practice of economics are big data machine learning vastly in complex simulations, which are the theory itself as sort of the desired output. And again, Krakauer and other folks at SFI have written a lot about this in terms of the tension between prediction and understanding like it's really not important in the midst of a crisis to be able to understand what's going on so much as it is to be able to predict what's going to happen next.

You see this bifurcation in the 21st century. I mean, it's been there the whole time in one form or another, but you see it really pronounced in this split between the efforts to arrive at a general theory and the acceptance that really what we need to be doing is just generating as much knowledge from our data as we can. So, that's just a riff that I'd love to pass back to you and how that sort of shifts the emphasis from maximizing externalities to closing economic circuits, to understand these processes in their completeness, and then folding all those externalities back in where we may not understand what we're actually looking at anymore, or that's no longer sort of the ultimate goal.

But now we know at least that we don't have such a naive idea about value creation, where it's basically like some kind of cooking the books, this notion that value just emerges de novo out of it's like actually it's revealed to be something that was hidden by the very fact that we were using equations to think about these matters,

W. Brian Arthur (48m 31s): There's about a half a dozen or a dozen ideas in what you're saying. So let me see if I can comment on some of them. And I think you're getting it all the important things, just a one footnote to make sure facts are straight. Darwin published the Origin of Species in 1859. And coincidentally mathematization of economics really took off in the 1870s. And from there after Darwin's ideas, in fact, Alfred Marshall, who was part of that process of mathematizing economics famously said the Mecca of economics is biology.

He had read Darwin. He wanted an evolutionary economics and that evolutionary economics, he couldn't see how to do it. So he was very much instrumental in this equilibrium view and economics doesn't deny change. It just says, okay, we'll have a screenshot of the economy here. Then maybe firms electrified and stop using steam engines.

So we have another screenshot. We go from this cycle librium to that equilibrium. It's rather like saying that children grow up and that's age two that look like this and that age 11, they look like something else. It's fine. But it doesn't really explain any process of how things develop. And if you're looking at the developments of a system of arteries or of neural systems, it doesn't work in finite snapshots.

And I think Marshall knew this in the 1890s, but there wasn't much she could do about it. And yeah, there is a bias and standard mathematics. It's not quite insurmountable. All of this is just awkward. I think standard mathematics is I keep saying has been wonderful at explaining relationships in economics, how incentives arise, how different forces in the economy bring forth certain behaviors, how behaviors are related, how prices in one sector steel might be affected by prices of oil. Standard economics standard mathematics allows us to understand all of this extremely well.

What it doesn't do is show us how things evolve and come about.

Michael Garfield (51m 30s): Thank you for listening. Complexities produced by the Santa Fe Institute, a nonprofit hub for complex system science located in the high desert of New Mexico. For more information, including transcripts research links and educational resources, or to support our science and communication efforts. Visit