Mathematical models of the world — be they in physics, economics, epidemiology — capture only details that researchers notice and deem salient. Rather than objective claims about reality, they encode (and thus enact) our blind spots. And the externalities created by those models — microscopic pathogens invisible to the naked eye, or differences in the social network structures of two neighborhoods, or food webs disrupted by urban development — have a way of biting back when we ignore them. Structural inequality created by an insufficient model jeopardizes not just the ones left off the map, but the entire systems in which they participate. Science fiction author Philip K. Dick put it well when we said that “Reality is that which, when you stop believing in it, doesn’t go away.” Ultimately, ecological and social justice is dependent on our rigorous empiricism and our dedication to describing all the relevant dimensions of our complex world.
Welcome to COMPLEXITY, the official podcast of the Santa Fe Institute. I’m your host, Michael Garfield, and each 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.
In this episode, Santa Fe Institute President David Krakauer returns to talk about the latest essays in SFI Transmission series, to shed light on the crucial under-examined margins of our maps — and how good science both enables and demands us to do better.
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Read the essays we discuss in this episode:
David Krakauer and Dan Rockmore on out-evolving COVID-19
Jon Machta on the noisy equilibrium of disease containment & economic pain
Brian Enquist on how pandemics rapidly reshape the evolutionary & ecological landscape
Melanie Moses and Kathy Powers on models that protect the vulnerable
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Podcast Theme Music by Mitch Mignano.
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Mentioned in this episode:
Melanie Moses, Kathy Powers, Brian Enquist, Jon Machta, Dan Rockmore, David Krakauer, Michael Garfield, Edgar Allan Poe, Auguste Dupin, Dan Brown, Vera Rubin, Kent Ford, Fritz Zwicky, Robert Koch, Martinus Beijerinck, Charles Darwin, Jennifer Doudna, CRISPR, Cory Doctorow, Peter Singer, William Hamilton, Lauren Ancel Meyers, Caroline Buckee, David B. Kinney, Kurt Wiesenfeld, Chao Tang, Per Bak, Cris Moore, Sidney Redner, Manfred Laubichler, William Gibson, François de Liocourt, Andrey Kolmogorov, Geoffrey West, Andy Dobson, Jessica Flack, Steve Lansing, Nicolas Rashevsky, Darcy Wentworth Thompson, Mahzarin Banaji
Michael Garfield: All right, David, we are back for the seventh in this mini-series about the pandemic. And I feel like this one is also kind of timed very well for the crisis in a legitimacy and inequality and justice that we're seeing around the world right now, because this week we get to talk about the obvious realities that are really only obvious in retrospect that have been hidden in plain sight and, and what it means to bring those things into visibility. So, where do you want to dive into this?
David Krakauer: Yeah, I do. We have to remark on the current moment and just that we are living in a very complex world, and it's more important than ever for us to face up to, as you say, the reality that has been in plain sight, but we have treated as if it were hidden. And I think that, to the best of our ability in our work, we try and address these issues. Actually, as you know, I edited a book of essays called Hidden in Plain Sight, and I was very inspired in that title by a short story that many people will know by Edgar Allan Poe called the Purloined Letter. It's a very interesting short story, and the detective in that short story is the great Auguste Dupin. It's the absolute opposite of the standard mystery. The standard mystery is something like a Dan Brown mystery, where the secret is elaborately hidden, and it requires some kind of torturous ingenuity to so to solve. But, what Poe did is he subverted the genre by saying, you know, the hardest crime, the one that's truly difficult to solve, is the crime that's right in front of your eyes. And of course, I'm not just editorializing by pointing out that in the, in the larger, more expansive sense, that's what society is dealing with now: the crime that has been there right in front of their eyes, but is extremely difficult to solve. And scientists love puzzles, you know, we like to solve the hidden mysteries. And we discover things like subatomic particles and devise ingenious machines to allow us to see them. But, I think today's discussions are going to be about the kinds of ideas necessary to see the forces that have been shaping both the biological and cultural world around us. I just wanted to make that introduction.
So, the first contribution I guess, to discuss is the one that I wrote with Dan Rockmore, in this particular case. We were just talking about this interesting analogy between how the forces that shape evolution have been hidden in the way that the forces that shaped the universe have been hidden. In the 1930s, an astrophysicist Fritz Zwicky pointed out that there is a discrepancy between the amount of gravitational force needed to account for the movements of the galaxies, in terms of the visible luminous matter, and the invisible matter that he called the dark matter. And this was confirmed much, much later by Vera Rubin and Kent Ford who used more detailed spectrographic data to show that in fact, most of the universe is made up of both dark matter that accounts for gravitation, and dark energy, that is the pressure that's moving everything apart. And so, we're living in this very strange world now where physics for all its extraordinary contributions, can only account for 5% of what we see.
Dan and I got very interested in that and said, you know what we see in the living world, how much of what we see can be counted for by what is visible to the naked eye. And an interesting observation to make is that when Darwin wrote the origin of species in 1859, he had no idea that there was a microbial world. If you look through that book very carefully, you might be surprised to find not one mention of a bacterium, or certainly not one mentioned virus. And that's because they weren't discovered until several decades later. In fact, for most of our history, certainly not in the 19th century, but certainly in the 16th and 17th, people believe that small things like ants and flies were spontaneously generated. That they didn't need an explanation beyond the fact that they just sort of mutated into existence spontaneously.
And it was in the 1880s that Koch and Beijerinck discovered bacteria, and then viruses. The point that we wanted to make in this contribution is that the evolution of complex life, multicellular life, the kind of life that Darwin described, is deeply entangled with the evolution of simple life. And that the evolution of scientific ideas is deeply entangled with the plundering of microbial innovations. And –– this is the interesting factor of the world –– that the complex world that we now recognize would not exist if it were not for viruses. I guess we'll go into that, but moreover, many of our technologies of molecular biology, of genetic engineering are essentially direct borrowing from innovations that viruses have come up with over hundreds of millions of years.
Michael Garfield: Yeah. I've been talking about this for quite a while, the discovery of CRISPR by Jennifer Doudna and her lab, and how this is such a perfect example of…you have a list of biotechnologies that were found in this kind of way, but it draws attention to the way that so much of human innovation is just accidental or intentional biomimicry. And so, when we're talking about dark matter, there's something about how it links to this broader theme. We want to unpack in this conversation how the models that we make of the world are made at the timescale of the systems adapting to the world that they're modeling; which is the brain, which is the human lifespan, at the human scale, and the social environment that dominates our attention. So, it's dark matter when we're talking about cosmology, because 95% of the cosmos is irrelevant to the human timescale, to the human social world. And, this points me toward humility, because evolution and the cosmos…evolution as a distributed intelligent process has made a lot of discoveries because it's operating at a different time scale. I guess what I'm saying is that we have this way…like IP Fest veteran Cory Doctorow talks about the ridiculousness of “Terra Nullius,” this idea that we invent things out of nothing, that we can take credit somehow for our inventions. When really so much has to be said about being in the right place at the right time, and having our search through the space of possible innovations directed by the agency of our landscapes, and the evolutionary pressures of our moment. This question comes up in the Facebook group a lot about whether emergence is an epistemological or ontological question. Does complexity really emerge, or do we just notice it? And, I think a lot of this conversation is about how, really, we're not inventing these things or creating them. In many cases, there's a good argument that we're simply discovering what was already there because the times call for it. And that’s a shot-call on Brian Enquist’s piece later in this conversation, but I'll pin it there.
David Krakauer: Yeah, I think that there are some very intriguing discussions to be had in the interstices of your remarks. I was very taken by Singer's Darwinian ethics. I've always believed that a deep familiarity with evolutionary thinking changes your ethical responsibilities in the living world, because we come to an understanding that we basically are primates –– we’re almost indistinguishable from chimpanzees and gorillas, and were very closely related to invertebrates and into the trees. And that awareness of the common origin of all living things should extend deeply our sympathies and empathy to the nonhuman world. I think your argument is correct. The same argument should apply to human ingenuity. And, you're right, I think CRISPR is a beautiful example. I make these kinds of remarks and people think I'm nuts, but I stick by them…I believe that if Doudna and others were to win the Nobel prize for CRISPR, they should share it with prokaryotes who invented it. They just tinkered with a solution that the bacteria discovered. And I think that's really true. I think if people understood how much of our science –– certainly in the biological sciences –– is essentially a repurposing of discoveries made by evolution, that would change the way they think about creativity in this networked world, right?
Human intelligence is a part of a larger ecological system and it shouldn't be separated from it. Let me just give some examples, because I think it's important that folks understand what we're talking about here. In this paper we go through the history of genetics itself; that genetics would not exist as a science if it wasn't for the endonuclease enzyme. And that came directly from the restriction enzyme system of bacteria, it is the basis of most cellular biology, and certainly molecular cloning. CRISPR, as you pointed out, is based on an immune system that bacteria have to deal with viruses that might turn out to be the most important source of gene therapy ever appropriated from the natural world. Our own immune system, the adaptive immune system that is helping us fight off this horrible COVID virus and other viruses is actually based on a system called the RAG system, which was essentially stolen from a virus, and placed in a human, and now as the basis of immunotherapy. You can go on and on and on, for example, modern cancer therapies where you target preferentially cancer cells are borrowing the cellular tropism of viruses, in order to deliver appropriate drugs. So, it's extraordinary the extent to which engineering ingenuity has relied on viruses, but then you actually have to think about life itself.
Sex. There's a very interesting hypothesis that the late William Hamilton proposed, which is that the reason we have recombinational sex is to generate diversity to fend off pathogenic viruses. If it wasn't for the variability of the virus, we wouldn't have required a system to generate variability to counteract it, and so, we would be asexual. So, you know, even at the level of our own lives and the meaning we derive from our relationships, there's a deep evolutionary origin in our relationship to microbes.
Michael Garfield: I feel like there's a thread here that links us to the next piece by Jon Machta, which is about how –– as David Kinney talked about when he was on the show, about explanatory depth and the way that different disciplines of science seem to focus at different scales, it's because the requisite explanatory depth to explore the world at that scale comes with a certain metabolic cost: the cost of fine graining things, or course graining, and seeing them as big as is required, that there are differing computational loads and energetic investments required at all of these different scales. And it's been convenient, historically…I love that you used the word “appropriation” of the products of evolutionary search…because, again to call back to the piece on Terra Nullius and intellectual property, appropriation is easy when the systems that you're looking at have been conveniently reduced to featureless points. You can talk about a network, but if you're talking about a COVID transmission network, that transmission network is made out of people, and it's easy to forget if you're tuning things for convenience, for a parsimonious epidemic model, that there are other crucial dimensions involved in the way that that disease will spread. And, one is that the network is made out of people who are making economic decisions, that they have their own incentives. This has been a big piece of a huge amount of the work that's been going on at SFI with agent-based-modeling, and a huge piece of the kind of models that people like Lauren Ancel Meyers and Caroline Buckee have been doing. But Jon's got an interesting take on it, so why don't you unpack that?
David Krakauer: Yes, so Jon brings us back to that enigmatic hieroglyph, R0, this critical epidemic parameter that when greater than one tells us that an infection will grow exponentially, and when it's less than one, it will peter out. The technical terms for that are supercritical and subcritical. And what Jon asks, exactly as you said, is what dictates the value of what R0 is? Part of what dictates the value of the R0 is the transmissibility of the pathogen, so biological factors. And part of what dictates it are social, behavioral, and cultural factors, like social isolation and quarantine. So R0 captures both of these contributions, and what he goes on to point out is that the tension between these two contributions makes R0 hover around 1. I want to make this point more broadly, because it's such a key idea in complexity science, that it's worth investigating the history of this idea a little bit.
So just consider water, think about the ocean. The average surface temperature of the ocean is about 60 degrees Fahrenheit, and it boils at about 212 Fahrenheit. Now, the ocean isn't poised at the critical point, where water would vaporize. That would be a disaster, right? Because if there were a tiny fluctuation in the temperature, the oceans would vaporize, and that would be the end of it all. In complex systems, though, the opposite things happen. These critical points where you observe phase transitions –– like the R0 for an epidemic to it being contained –– are attractors that attractors of the dynamical system, that's naturally where the system wants to live at this extraordinary unstable point, which is very surprising. And there's data, by the way, from physiology, 20 years of data on the study of the brain, that shows that neurons are tuning themselves to near critical points, to a sort of order/disorder transition.
In 1987, Per Bak, Chao Tang, and Kurt Wiesenfeld wrote a paper in Physics Review Letters, a very famous letter, where they introduce the idea of self-organized criticality, and this is the term we use to explain why a system would be driven to the critical point. So, John's explanation is the one that you described, which is that the biology of the pathogen wants R0 to be very large because the virus spreads very widely. Human society wants to drive that down. So what happens, as we approach R0 = 1 equals is, well, as R0 falls below one, all of the news agencies and all of the government agencies and the media say, look, R0 is below one, so we can now go out and socialize, and we can return to work, and restore the markets. But, as soon as we do that, the biology takes over, and it drives it above 1.
And then, when it's driven above 1 culture takes over, and it drives it below 1. And it just oscillates back and forth around 1. And at that value –– take the contributions that say Cris Moore made, and Sid Redner made on long tails kick in –– because one of the characteristics of hovering by a critical point is that you get power law scaling of outbreaks. In fact, in the original paper of Per Bak and his colleagues, they looked at what's called the sand-pile model. That's what made this field famous. Imagine you have a level surface and you slowly pour sand onto it, it accumulates into a little sand mound, and it reaches what's called a minimally stable state with a fixed angle. That is, the slope, if you like, of the sand pile reaches a fixed value. And at that value, you get avalanches of sand of different scales that follow a heavy tail distribution. That was considered to be the correct idealized model for all systems that attract to critical points. Of course, it has its limits, but I think this is a very important point for complex systems generally, because it means that the interplay of the biological and cultural factors will make it extremely difficult for this disease to ever go away. And it's one of the mechanisms that will lead to endemism.
Michael Garfield: So, we’re talking about sand piles, and cascading collapses, and life poised at the edge of chaos, which is exactly what we're seeing here in the U.S. and around the world as the Coronavirus has revealed the inequities of what for people of privilege was an invisible environment, an invisible evolutionary landscape. We talked about this a lot in episode 29, when we were talking about mass extinctions and the relationship between crisis and creative opportunity. I like you're calling forth of Cris Moore’s piece, because his writing on how you take a fine grain look at R0, reveals the heterogeneity of our networks and how opportunity is unequally distributed in space and time. But Brian Enquist has this really cool piece, which calls back to Manfred Laubichler’s piece on the evolutionary fitness landscape. And it reminds me of a statement I saw from William Gibson, who was quoted apocryphally as saying that the future is distributed unevenly. And, he recently revised it to say that dystopia is distributed unevenly, not just in space and time, but within a single ecosystem or society for agents capable of reaching different affordances –– capitalizing on available free energy, or evolutionary opportunities.
So, there's the sense in which the opportunities available to generalists after a mass extinction, the opportunities available to the virus with its high beta mutation strategy, and the opportunities available to us now, socially, are described by the same mathematics. And Brian's got a really beautiful example of this from landscape ecology, and from trees, and how over the history of the human era, we have contributed to a series of radical regime changes in ecological settings that are not always as obvious to us: that this kind of mulching and boiling of possibility and creative destruction is going on in these areas.
David Krakauer: Yeah. I mean, I think your introduction there covers both Melanie Moses’s and Kathy Power's contribution, and elements of Brian's piece. Let’s just jump to Brian's, because I think it fits in with this larger question of the human relationship to the natural world. Because it's not just us, and it's certainly not just animals, it's also plants…the world that sustains us. What Brian is doing is drawing a really interesting parallel between the effects of COVID-19 in our time, and the 1904 blight of Chestnut trees. He makes this point that the first God, if you like, of pathogens was a Roman God of rust, a fungus that infects all sorts of wheats and ryes and apples and so forth, many people are familiar. But I thought that the parallels that Brian drew are extremely interesting at multiple different levels reveals a different kind of complexity, I think.
So, this blight was a fungus that seemed to have originated in Southeast Asia. It was transported via trade networks that were global. The primary tissue that this parasite attacks is the vascular tissue thereby reducing the respiration capability of the plant. And it's interesting that the American Chestnut tree defined the American forest. In his telling, it survived for 40 million years, and then in the space of 40 years, it effectively disappeared. And the Chestnut tree interestingly also touched American economic life –– that the wood of the tree is soft and light, and easy to split, it’s very resistant to decay –– it was the basis for construction and the barns and homes on the East coast of America were made from Chestnut. The nut of the Chestnut Tree was a significant source of protein, and very important in rural economies. And so, the Chestnut pandemic was not only about a biological disease that took down the Chestnut tree, but ramified out into culture to have a significant economic impact on the Eastern United States.
So that's the first parallel, which I thought was actually rather fascinating. It just makes it very clear, once again, that you can't really separate the impact of biology from the impact on the economy, and the impact on culture. That we have to come to a much better understanding of the entangled nature of reality, and stop pretending in our departments and disciplines that everything can be modularized, because it cannot. So, that was very important to me. He goes on to point out in the extension of the paper that he wrote, which you have linked on this page, he introduces some more technical concepts, which touch on the power law-like results that Per Bak and Jhn Machta describe.
In the late 19th century, a Frenchman, François de Liocourt, published a paper called the Management of Silver Fir Forests. And in that paper, he presents the distribution of tree sizes in the natural state. It's what we would now call, and has have called in our previous episodes, null models. In other words, this is the distribution of tree sizes that you would expect if the system were healthy. And it wasn't until the 1930s that the great Russian mathematician, Andrey Kolmogorov wrote down the equations which describe that distribution using his diffusion equations. And they become now the baseline against which we can measure deviations that are diagnostic of the disease state. And I think that's also very that, Brian points this out, that we always need to understand how far we've moved from the distribution that defines the healthy, and it's no less true for plants, as it is for animals.
Michael Garfield: To use that piece on the distribution of tree sizes, I've read elsewhere that we have clear signature that forests around the world are getting younger and shorter. And if we think about, Geoff West’s work on evolutionary networks following a space filling algorithm, that a young, short forest is not filling the available space, filling the opportunity of sunlight as efficiently as an older mature forest. And, there's a way to look at this in a kind of a geopolitical sense as a disrupted regime. This calls to Andy Dobson's remarks recently, on how our rampant development around the world has led to a quadrupling of zoonotic animal origin infections over the last 50 years. That by disrupting wild ecosystems, we're inviting quote unquote revolution from agents that are ordinarily kept in check by the incumbent regimes, like the mature trophic networks.
We just issued our institutional statement on current events last night, and we included a link to Jessica Flack’s work on nonviolent power: her study of primate dominance, hierarchies, and policing. You know, there is a way to look at violent policing as an attempt to impose a kind of order that is a system that has not effectively encoded environmental information, and sort of releases these invisible monsters, these invisible troubles, in a way that is very similar to the way that our development and our attempts to exert a kind of technocratic management over the natural world has released all of these infections upon us.
David Krakauer: Well, I would just say, I think that Jessica's work or Steve Lansing's work on the beautiful ritualized water irrigation system for the Subak in the Balinese Highlands is an example of that. I think what François de Liocourt did and what in fact Brian has been doing recently is giving us a sense of the invisible order that we're perturbing. It's one of the problems with climate, right? In other words, it's very difficult for the naked eye and the timescales, as you described earlier in which we live, to observe the impact on the system. And we require complexity analogs of microscopes and telescopes and mass spectrometry machines to see the world, properly. And then we need mathematical models to tell us what the equilibrium states of that world are, and what effect we're having on them. I think it's very important to understand that it's very difficult to see the order in a forest with a naked eye, you need to do more work. And one of the things that Brian is saying is that these kinds of models that de Liocrout and Kolmogorov have developed with the necessary microscopes to understand healthy States of complex reality.
Michael Garfield: Absolutely. And this brings us, I think, really gracefully into Melanie Moses’s and Kathy Powers’s piece, because what we're really talking about here is better math and science for fairer social outcomes and justice through empiricism.
David Krakauer: Yes. I think this is a very, very timely contribution, a very important one. And I do want to relate it to exactly the point you just made, and to Brian's point, and to previous contributions which is how we, those of us trying to understand the complex world with highly idealized, mathematical and computational models, remain faithful to it, and just in our projects. I want to give a bit of history here, because I think it's a very important area to understand, so just some of the nuts and bolts: One of the pioneers in mathematical biology, that is the use of mathematics to understand biological phenomenon, was Nicolas Rashevsky and Rashevsky was born at the end of the 19th century in Ukraine, was educated at the university of Kiev. He was an immigrant to the United States where he got a job at Westinghouse Labs in Pittsburgh, and eventually went onto the University of Chicago, where he became a professor in the department of physiology.
And in the 1920s and 30s, he read a book that we could have several programs about, Michael, by Darcy Wentworth Thompson, called On Growth and Form, which is one of the defining Vertex of complexity science published in 1917. And in response to that book, which presents a physical theory of the biological world, he wrote his book called Mathematical Biophysics: Physical Mathematical Foundations of Biology. And now, when we look back on that book, we have several very major criticisms of it. One is that it's too idealized. Another is that it's too beholden to the parsimonious dream of physics. Another is that it's a little too concerned with presenting almost a Platonic view of reality, and insufficiently concerned with the complications of reality. Out of Rashevsky’s work came models, or more like chess games inspired by reality than tools for comprehending reality. And this I like to use Rashevsky when I teach, because he represents a persistent challenge to the work we do, because as you move away from the sort of simple description of orbits and charges and fields –– the world that physicists work on –– it just gets worse and worse, and your models slowly metamorphose into metaphors. And this is often true without the practitioners being aware. And you're ultimately left with these rigorous, vacuous, vaporous statements. And I think at this moment in history, numerous well-intentioned people are writing down mathematical models with enormous deducted rigor and absolutely no value. What Melanie and Kathy describe is how the standard model of the epidemic, the SIR model or the SIRS model and so forth, has neglected elements of reality. It's neglected elements of reality in such a way that they are in some endogenous sense, justly, racist, right? And let me explain that.
They point out in their article that African-Americans, as we know, are dying from COVID-19 at a rate that are two or four times higher than White Americans. And that per capita cases are higher on the Navajo reservation in our own state, Michael, than in every other U.S. state.
Why is this? They go on to point out, well, African Americans tend to live in very dense urban areas. They live in multigenerational households…and as we know, older individuals are more susceptible to this disease. They're less likely to have paid sick leave, and health insurance. And they have a larger number of preexisting medical conditions, such as diabetes and so forth. And exactly the same arguments go for the Native American population: extreme inequalities of health and economic circumstance, a lack of basic services, running water, access to healthcare. And as a consequence, the native population is 17 times more likely to be diagnosed with this disease than the White population. And that's just the facts. And you could argue, look, mathematics doesn't care. You can't accuse a mathematical model of being in some sense, racist because it's just the math. But it's not really true because when you formulate a mathematical model, you make the decision about what to include and what to throw away.
The reason I mentioned Rashevsky, who is quite rightly pilloried by my community for oversimplifying the natural world, is I think we should be criticized for not dealing with the critical factors that would allow our models to help those communities at greatest risk. I think what Melanie and Kathy ask is, how should we do this? I will say that the Santa Fe Institute, to be honest, is perhaps one of the places that's been most aware of the importance of these factors –– as you pointed out agent-based models are models that do allow us to include things like the zip code, which is a primary determinant of susceptibility, unfortunately. Network theory allows us to look at the more structured interactions amongst populations instead of treating a population as fully mixed or well-mixed –– so, we have been working on formalisms that allow us to address the factors that models are designed to help us explain and treat. But, I do believe this is a very important interface between the power of mathematics in helping us understand the world, and the hidden ethical suppositions or social assumptions that go into our thinking about our mathematical models.
And there's no point in denying that complexity, Melanie and Kathy are right to make us respond to this debate, now more than ever, without compromising the rigorous, empirical quality of the work that we do.
Michael Garfield: Indeed, just as a way of linking back to a super important conversation we've had on the show before, when I had Rajiv Sethi on for episode seven, talking about his work on stereotypes and criminal justice, and then also, Mahzarin Banaji’s 2012 study on the development of racial stereotypes in children: these are examples of too-simple-to-be-useful models, now. The maladaptive over-simplicity of our models has been revealed by this situation, and nobody has the luxury to ignore these realities, anymore. You know, we need new norms because a lot of these things that…again, for convenience, for parsimony, we’ve regarded things like health as a private good, and it's become obvious that it's a public good, and the same can be said for social justice. So, really, what I hear in this is just that we can do better than three-year-olds.
David Krakauer: Yeah. And I think, for the Institute, that we address these very deep issues. I raised Rashevsky for a reason. He was so enamored with the simplicities of physical law and their power to enable the human mind to grasp non-living reality, that he hoped that you could apply the same simplicities to humanity into the living world. And behind that was a kind of aesthetic impulse, as you pointed out, simplicity, but behind models, just as easily there can be an ethical impulse. And, that's what we're describing here, that the move towards these more sophisticated models that encompass some of these essential facts of life should go into how we model and how we formalize complex systems. That doesn't in any way detract from their objectivity, and their mathematical rigor, it just said that the reason we made the decision to include that variable in our models, that we then subject to all of the analysis that we would any variable in the model, is because it's important. It's part of what we're trying to explain. And that's, I think the argument that's being made in this contribution, and it's one that we should all be very aware of.
Michael Garfield: Indeed. And lest we do a disservice to the articles that we've discussed here today, I would really suggest to everyone, if you haven't read these essays yet, or if you haven't gone to the website and looked at the research that we’ve bundled together in our statement on social justice, I really encourage you to do that. Now that you've kind of seen the aerial overview, it's good to land down, and walk around, and get a sense for things in their detail.
Do you have any more you want to discuss?
David Krakauer: No, that's it. Thank you, that's great. And thanks everyone for listening, and for taking seriously, the contributions that this community has been providing.