Zipf's, Heaps' and Taylor's laws are ubiquitous in many different systems where innovation processes are at play. Together, they represent a compelling set of stylized facts regarding the overall statistics, the innovation rate and the scaling of fluctuations for systems as diverse as written texts and cities, ecological systems and stock markets. Many modeling schemes have been proposed in literature to explain those laws, but only recently a modeling framework has been introduced that accounts for the emergence of those laws without deducing the emergence of one of the laws from the others or without ad hoc assumptions. This modeling framework is based on the concept of adjacent possible space and its key feature of being dynamically restructured while its boundaries get explored, i.e., conditional to the occurrence of novel events. Here, we illustrate this approach and show how this simple modelling framework, instantiated through a modified Polya's urn model, is able reproduce Zipf's, Heaps' and Taylor's laws within a unique self-consistent scheme. In addition the same modelling scheme embraces other less common evolutionary laws (Hoppe's model and Dirichlet processes) as particular cases.
IN WATCHING the flow of events over the past decade or so, it is hard to avoid the feeling that something very fundamental has happened in world history. The past year has seen a flood of articles commemorating the end of the Cold War, and the fact that "peace" seems to be breaking out in many regions of the world. Most of these analyses lack any larger conceptual framework for distinguishing between what is essential and what is contingent or accidental in world history, and are predictably superficial. If Mr. Gorbachev were ousted from the Kremlin or a new Ayatollah proclaimed the millennium from a desolate Middle Eastern capital, these same commentators would scramble to announce the rebirth of a new era of conflict.
And yet, all of these people sense dimly that there is some larger process at work, a process that gives coherence and order to the daily headlines. The twentieth century saw the developed world descend into a paroxysm of ideological violence, as liberalism contended first with the remnants of absolutism, then bolshevism and fascism, and finally an updated Marxism that threatened to lead to the ultimate apocalypse of nuclear war. But the century that began full of self-confidence in the ultimate triumph of Western liberal democracy seems at its close to be returning full circle to where it started: not to an "end of ideology" or a convergence between capitalism and socialism, as earlier predicted, but to an unabashed victory of economic and political liberalism.
August 29, 2018 at 09:37AM
Building on this, could we create a list of governments and empires and rank them in order of the length of their spans? There may be subtleties in changes of regimes in some eras, but generally things are probably reasonably well laid out. I wonder if the length of life of particular governments follows a power law? One would suspect it might. ❧
August 29, 2018 at 09:43AM
Highlights, Quotes, Annotations, & Marginalia
The triumph of the West, of the Western idea, is evident first of all in the total exhaustion of viable systematic alternatives to Western liberalism. ❧
August 29, 2018 at 08:53AM
What we may be witnessing is not just the end of the Cold War, or the passing of a particular period of postwar history, but the end of history as such: that is, the end point of mankind’s ideological evolution and the universalization of Western liberal democracy as the final form of human government. ❧
What if, in fact, we’ve only just found a local maximum? What if in the changing landscape there are other places we could potentially get to competitively that supply greater maxima? And possibly worse, what if we need to lose value to get from here to unlock even more value there?
August 29, 2018 at 08:56AM
Hegel believed that history culminated in an absolute moment – a moment in which a final, rational form of society and state became victorious. ❧
and probably not a bad outcome in an earlier era that thought of things in terms of clockwork and lacked the ideas of quantum theory and its attendant uncertainties.
August 29, 2018 at 08:59AM
Believing that there was no more work for philosophers as well, since Hegel (correctly understood) had already achieved absolute knowledge, Kojève left teaching after the war and spent the remainder of his life working as a bureaucrat in the European Economic Community, until his death in 1968. ❧
This is depressing on so many levels.
August 29, 2018 at 09:05AM
Paul Kennedy’s hugely successful “The Rise and Fall of the Great Powers”, which ascribes the decline of great powers to simple economic overextension. ❧
Curious how this may relate to the more recent “The End of Power” by Moisés Naím. It doesn’t escape one that the title of the book somewhat echoes the title of this particular essay.
August 29, 2018 at 09:18AM
But whether a highly productive modern industrial society chooses to spend 3 or 7 percent of its GNP on defense rather than consumption is entirely a matter of that society’s political priorities, which are in turn determined in the realm of consciousness. ❧
It’s not so much the percentage on produced defense goods, but how quickly could a society ramp up production of goods, services, and people to defend itself compared to the militaries of its potential aggressors.
In particular, most of the effort should go to the innovation side of war materiel. The innovation of the atomic bomb is a particularly nice example in that as a result of conceptualizing and then executing on it it allowed the US to win the war in the Pacific and hasten the end of war in Europe. Even if we otherwise had massive stockpiles of people or other weapons, our enemies could potentially have equaled them and dragged the war on interminably. It was the unknown unknown via innovation that unseated Japan and could potentially do the same to us based on innovation coming out of almost any country in the modern age.
August 29, 2018 at 09:24AM
Weber notes that according to any economic theory that posited man as a rational profit-maximizer, raising the piece-work rate should increase labor productivity. But in fact, in many traditional peasant communities, raising the piece-work rate actually had the opposite effect of lowering labor productivity: at the higher rate, a peasant accustomed to earning two and one-half marks per day found he could earn the same amount by working less, and did so because he valued leisure more than income. The choices of leisure over income, or of the militaristic life of the Spartan hoplite over the wealth of the Athenian trader, or even the ascetic life of the early capitalist entrepreneur over that of a traditional leisured aristocrat, cannot possibly be explained by the impersonal working of material forces, ❧
Science could learn something from this. Science is too far focused on the idealized positive outcomes that it isn’t paying attention to the negative outcomes and using that to better define its outline or overall shape. We need to define a scientific opportunity cost and apply it to the negative side of research to better understand and define what we’re searching for.
Of course, how can we define a new scientific method (or amend/extend it) to better take into account negative results–particularly in an age when so many results aren’t even reproducible?
August 29, 2018 at 09:32AM
FAILURE to understand that the roots of economic behavior lie in the realm of consciousness and culture leads to the common mistake of attributing material causes to phenomena that are essentially ideal in nature. ❧
August 29, 2018 at 09:44AM
“Protestant” life of wealth and risk over the “Catholic” path of poverty and security. ❧
Is this simply a restatement of the idea that most of “the interesting things” happen at the border or edge of chaos? The Catholic ethic is firmly inside the stable arena while that of the Protestant ethic is pushing the boundaries.
August 29, 2018 at 09:47AM
Hence it did not matter to Kojève that the consciousness of the postwar generation of Europeans had not been universalized throughout the world; if ideological development had in fact ended, the homogenous state would eventually become victorious throughout the material world. ❧
This presupposes that homeostasis could ever be achieved.
One thinks of phrases like “The future is here, it just isn’t evenly distributed.” But everything we know about systems and evolving systems often indicates that homeostasis isn’t necessarily a good thing. In many cases, it means eventual “death” instead of evolving towards a longer term lifespan. Again, here Kauffmann’s ideas about co-evolving systems and evolving landscapes may provide some guidance. What if we’re just at a temporary local maximum, but changes in the landscape modify that fact? What then? Shouldn’t we be looking for other potential distant maxima as well?
August 29, 2018 at 09:52AM
But that state of consciousness that permits the growth of liberalism seems to stabilize in the way one would expect at the end of history if it is underwritten by the abundance of a modern free market economy. ❧
Writers spend an awful lot of time focused too carefully on the free market economy, but don’t acknowledge a lot of the major benefits of the non-free market parts which are undertaken and executed often by governments and regulatory environments. (Hacker & Pierson, 2016)
\August 29, 2018 at 10:02AM
Are there, in other words, any fundamental “contradictions” in human life that cannot be resolved in the context of modern liberalism, that would be resolvable by an alternative political-economic structure? ❧
Churchill famously said “…democracy is the worst form of Government except for all those other forms that have been tried from time to time…”
Even within this quote it is implicit that there are many others. In some sense he’s admitting that we might possibly be at a local maximum but we’ve just not explored the spaces beyond the adjacent possible.
August 29, 2018 at 10:08AM
For our purposes, it matters very little what strange thoughts occur to people in Albania or Burkina Faso, for we are interested in what one could in some sense call the common ideological heritage of mankind. ❧
While this seems solid on it’s face, we don’t know what the future landscape will look like. What if climate change brings about massive destruction of homo sapiens? We need to be careful about how and why we explore both the adjacent possible as well as the distant possible. One day we may need them and our current local maximum may not serve us well.
August 29, 2018 at 10:10AM
I feel like this word captures very well the exact era of Trumpian Republicanism in which we find ourselves living.
August 29, 2018 at 10:37AM
After the war, it seemed to most people that German fascism as well as its other European and Asian variants were bound to self-destruct. There was no material reason why new fascist movements could not have sprung up again after the war in other locales, but for the fact that expansionist ultranationalism, with its promise of unending conflict leading to disastrous military defeat, had completely lost its appeal. The ruins of the Reich chancellery as well as the atomic bombs dropped on Hiroshima and Nagasaki killed this ideology on the level of consciousness as well as materially, and all of the pro-fascist movements spawned by the German and Japanese examples like the Peronist movement in Argentina or Subhas Chandra Bose’s Indian National Army withered after the war. ❧
And yet somehow we see these movements anew in America and around the world. What is the difference between then and now?
August 29, 2018 at 11:46AM
This is not to say that there are not rich people and poor people in the United States, or that the gap between them has not grown in recent years. But the root causes of economic inequality do not have to do with the underlying legal and social structure of our society, which remains fundamentally egalitarian and moderately redistributionist, so much as with the cultural and social characteristics of the groups that make it up, which are in turn the historical legacy of premodern conditions. ❧
August 29, 2018 at 11:47AM
But those who believe that the future must inevitably be socialist tend to be very old, or very marginal to the real political discourse of their societies. ❧
and then there are the millennials…
August 29, 2018 at 11:51AM
Beginning with the famous third plenum of the Tenth Central Committee in 1978, the Chinese Communist party set about decollectivizing agriculture for the 800 million Chinese who still lived in the countryside. The role of the state in agriculture was reduced to that of a tax collector, while production of consumer goods was sharply increased in order to give peasants a taste of the universal homogenous state and thereby an incentive to work. The reform doubled Chinese grain output in only five years, and in the process created for Deng Xiaoping a solid political base from which he was able to extend the reform to other parts of the economy. Economic Statistics do not begin to describe the dynamism, initiative, and openness evident in China since the reform began. ❧
August 29, 2018 at 11:58AM
At present, no more than 20 percent of its economy has been marketized, and most importantly it continues to be ruled by a self-appointed Communist party which has given no hint of wanting to devolve power. ❧
If Facebook were to continue to evolve at it’s current rate and with it’s potential power as well as political influence, I could see it attempting to work the way China does in a new political regime.
August 29, 2018 at 12:04PM
IF WE ADMIT for the moment that the fascist and communist challenges to liberalism are dead, are there any other ideological competitors left? Or put another way, are there contradictions in liberal society beyond that of class that are not resolvable? Two possibilities suggest themselves, those of religion and nationalism. ❧
August 29, 2018 at 12:19PM
This school in effect applies a Hobbesian view of politics to international relations, and assumes that aggression and insecurity are universal characteristics of human societies rather than the product of specific historical circumstances. ❧
August 29, 2018 at 12:30PM
But whatever the particular ideological basis, every “developed” country believed in the acceptability of higher civilizations ruling lower ones ❧
August 29, 2018 at 12:37PM
Perhaps this very prospect of centuries of boredom at the end of history will serve to get history started once again. ❧
Has it started again with nationalism, racism, and Trump?
August 29, 2018 at 12:48PM
A mathematical model could lead to a new approach to the study of what is possible, and how it follows from what already exists.