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Math Guy
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Well, to take your second objection first, I certainly understand the need not to go picking data to fit one's thesis, but I really don't think I've done that.
I'm not making an accusation. I'm saying that I have not seen the proof of an objective method of data creation and analysis. From that, it follows that I morally have to disregard your claims. (I'm implicitly pointing you to OPAR ch. 5, except that, oops, I just made it explicit).
I would say the idea of a dynasty is one of the oldest, and most firmly established, in historical thought.
Well, Plato's epistemology is vastly more "established", yet I don't accept it. In general, I do not accept claims simply from social reasons such as "historians agree". That is especially true when the logical foundations of a science are as shaky as they are in the social sciences. In fact, I don't even know that historians agree. If indeed historians agree, and there is an objective definition of "dynasty", then it ought to be possible to state that definition of "dynasty", and show that it is not a taxonomic artifact. I'm (unfortunately, extremely) aware of the power of academic disciplines to invent concepts that don't refer to anything in reality, or which are only marginally connected to things in reality. The fact that historians have created such a term does not mean that it is indeed a true concept that refers to something in reality and has a definition. Thus I ask for that definition and the evidence that it relates to something in reality.
Your point applies to the next level up, where we string together successive dynasties ruling the same country.
I think you have the concepts organized the wrong way -- you seem to be saying that "dynasty" is primary and "nation" is secondary, whereas I would reverse the hierarchy. A dynasty is a series of rulers of a country, which are related in terms of legal succession.
Plus there just aren't as many cases to work with, which given that this is a statistical argument is a handicap.
What exactly is a "statistical argument"? I would say that, properly understood, statistics is a method of evaluating empirical data, that is facts such as "Henry VIII was King of England for 38 years". The facts have to be primary.
My rule with regard to data is that I don't get to pick and choose.
Okay; do you entertain questions from the audience? For example if I give you a couple of random countries, will you demonstrate how the facts of that country are supported by the facts?
But I'm not manipulating the data. It's up to other people, more expert than me, whether to list a given dynasty as ruling "Portugal".
My objection to that is that it abdicates responsibility for the relationship to reality -- it makes your claim highly contingent. Knowledge does not accumulate by the creation of weakly-founded claims, claims of the type "If we knew that X is true, then we could conclude that Y is true". Rather, knowledge accumulates by first establishing that X is true, and that Q is true, and that Z is true, and then integrating those established facts via the conclusion Y.

I don't doubt that there exists a mathematical method for modeling patterns that have a power law appearance; if you can establish that the data do have that appearance, then it raises the interesting question "What fact of reality causes this distribution?". But if there actually is no such distribution, then there is no thing requiring explanation.

The concept of "entropy", legitimately applicable in physics, does not apply to dynasties. Notions of "heat loss" simply don't apply to the duration of a sequence of kings ruling a country.

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I was telling a colleague about this at lunch today. The way I put it, I said the stability of any structure is more vulnerable as entropy increases. So it makes sense that in ever more complex systems (due to population increase for instance), even if those structures are institutions like monarchy, they will be less stable so in that case not last as long.

Is that anything like what you're saying?

That is a good way of putting it. I have a number of other stability measures that work the same way. For example, if you study election returns district by district, you will find a very regular power-law dependence of the result on the number of voters. Small districts tend to produce much more decisive majorities for the winner. Large districts produce weak majorities, or pluralities in a multi-party system. Once again the pattern appears to depend solely on numbers, not on culture or language or economics.

In effect, when you try to achieve consensus on a particular candidate, information entropy (uncertainty) increases with the number of voters. A group of 2,500 voters will give the winner 75 percent of their votes, and distribute the remaining 25 percent among the other candidates. It can keep that kind of consensus up for election after election. A group of 25,000 voters will almost never do that well. They might manage a 60-40 split on a regular basis. A group of 250,000 voters will be lucky to manage 55-45. And so on.

You can see the implications almost immediately. Large states or districts can't form strong consensus in favor of any one leader, and so they are more unstable. Small states or districts can stay with a policy or platform for several cycles with far less difficulty.

The perpetual 50.5-49.5 split between presidential candidates in the modern U.S. system is not, at root, a problem with ideology or culture. It is not the fault of the Republicans and Democrats that America is perpetually locked in red-versus-blue warfare. It's a consequence of the principle of maximum entropy.

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I'm not making an accusation. I'm saying that I have not seen the proof of an objective method of data creation and analysis. From that, it follows that I morally have to disregard your claims. (I'm implicitly pointing you to OPAR ch. 5, except that, oops, I just made it explicit).

My copy of OPAR is in a box somewhere and I haven't read it in a while. But I infer this has to be a reference to Peikoff's doctrine of "the arbitrary". Right? So I did a little searching on the Web under "arbitrary," just to make sure of the argument, and here's what Peikoff says:

An arbitrary claim is one for which there is no evidence, either perceptual or conceptual. It is a brazen assertion, based neither on direct observation nor on any attempted logical inference therefrom. For example, a man tells you that the soul survives the death of the body; or that your fate will be determined by your birth on the cusp of Capricorn and Aquarius; or that he has a sixth sense which surpasses your five; or that a convention of gremlins is studying Hegel’s Logic on the planet Venus. If you ask him “Why?” he offers no argument. “I can’t prove any of these statements,” he admits—“but you can’t disprove them either.”

And what, according to Peikoff, is one to do with such a claim?

In the absence of evidence, there is no way to consider any idea, on any subject. There is no way to reach a cognitive verdict, favorable or otherwise, about a statement to which logic, knowledge, and reality are irrelevant. There is nothing the mind can do to or with such a phenomenon except sweep it aside.

Okay, assuming for the moment that this is what you are referring to, let's next clarify what claim(s) you regard as arbitrary. I have made two distinct claims. One could perhaps break them down further but there are at least two separate ideas here:

1) If you consult Wikipedia's list of dynasties, and do some quick sums on the dates for each one, you will find that later hereditary rulers in a given dynasty on average had shorter terms than earlier ones. You will also find that the lengths of the dynasties themselves form a similar pattern.

2) The reason the terms of later rulers or the spans of later dynasties are shorter is because long series of hereditary rulers (and by extension, long series of party control in any system that transfers executive power) are governed by a power law, in conformity with the principle of maximum entropy.

I am not at all surprised if anyone is skeptical about claim #2. I haven't come anywhere close to establishing it in a handful of posts. For a reader of this forum who does not have access to my book, it is merely an interesting hypothesis at this point. Not an arbitrary hypothesis in Peikoff's sense, let me stress, but not proven either.

I am, however, surprised that you consign claim #1 to the status of "the arbitrary". Reading Peikoff's explanation of what that term means, I see no resemblance between it and what I am saying. It not only isn't arbitrary; I also have trouble even treating it as open to question. It is an observable fact.

I would say the idea of a dynasty is one of the oldest, and most firmly established, in historical thought.

Well, Plato's epistemology is vastly more "established", yet I don't accept it. In general, I do not accept claims simply from social reasons such as "historians agree". That is especially true when the logical foundations of a science are as shaky as they are in the social sciences. In fact, I don't even know that historians agree. If indeed historians agree, and there is an objective definition of "dynasty", then it ought to be possible to state that definition of "dynasty", and show that it is not a taxonomic artifact. I'm (unfortunately, extremely) aware of the power of academic disciplines to invent concepts that don't refer to anything in reality, or which are only marginally connected to things in reality. The fact that historians have created such a term does not mean that it is indeed a true concept that refers to something in reality and has a definition. Thus I ask for that definition and the evidence that it relates to something in reality.

Responding to this has taken me some time. First, to understand what you were saying here I had to Google "taxonomic artifact". In 30 years of busy intellectual life I have never heard anyone (Objectivist or otherwise) use that term, and I did not think merely breaking it down into dictionary definitions of "taxonomic" and "artifact" was going to be sufficient. Google gave me 175 matches in total -- not a lot -- and I reviewed every single one. Of these, 94 were footnotes or endnotes referring to a 1987 essay in Nature entitled "Is the Periodicity of Extinctions a Taxonomic Artifact?" The overwhelming majority of the other 81 were references to paleontology or evolutionary biology, since 1987. In one case, a liberal blogger referred to the Republicans calling themselves "the party of morality" as a "taxonomic artifact". In one other case, Noam Chomsky made an analogy between the biological sense of the term and an obscure distinction between certain passive and active verbs. A book on museums also used the term as a sarcastic metaphor, referring to the Crystal Palace exhibition of 1851 as condensing the whole of human endeavor into one glittering and senseless category, roughly speaking, "things ruled over by Queen Victoria."

That's all I could find. It is not a term in wide use even among paleontologists.

So then I spent some time sorting out what sort of thing a "taxonomic artifact" actually is. It turns out that among paleontologists it has several meanings. It has been used to refer to a classification scheme that treats unrelated species as belonging to a different family. That seems straightforward, except that I have also found authors using it in the reverse sense -- a classification scheme that takes minor differences in the same species as constituting evidence of multiple species. Thus it does not seem to mean much more than "classification error," and might be dismissed as not a particularly useful term even in paleontology.

However, the word "artifact" does have some significance here. It rescues the term from being redundant. Today's paleontologists quite often use statistical methods to assign classifications. They don't necessarily study the fossils by eye and form a reasoned judgment about them, finding such techniques both subjective and cumbersome. Instead they crunch numbers and let various scoring schemes determine what is a species and what isn't. So a "taxonomic artifact" arises specifically when you incorrectly classify fossils as a result of using an poorly chosen statistical procedure.

Whew. Okay. So now I have some sense of this term's literal meaning, but I remain unable to apply it (even metaphorically, as I must assume you meant) to my own work. I didn't assign rulers to dynasties on the basis of a statistical procedure, and neither did the various scholarly authorities that Wikipedia references. The basic data don't rely on any kind of statistical reasoning. They are the most elementary sort of observation, e.g. in 1483 Richard III became protector on behalf of the 12-year-old son of his brother Edward IV. You would have grounds to worry about specific dynasties being artifacts if my calculations had any impact on how dynasties are identified and classified, but my calculations all come well after the fact, and nobody else involved in the process ever made any calculations. The metaphor of "taxonomic artifact" just doesn't apply here. It is a kind of error that cannot occur.

I will deal with some of your other objections next.

Your point applies to the next level up, where we string together successive dynasties ruling the same country.

I think you have the concepts organized the wrong way -- you seem to be saying that "dynasty" is primary and "nation" is secondary, whereas I would reverse the hierarchy. A dynasty is a series of rulers of a country, which are related in terms of legal succession.

I'm not saying "dynasty" is primary and "nation" secondary. I'm saying "ruler" is primary in relation to "dynasty," since a dynasty is a collective noun relating to a number of rulers. A series of dynasties clearly is a derivative concept which requires both the idea of "ruler" and the idea of "dynasty" to make sense. It is still more derivative, hence my reference to it belonging on "the next level up". No epistemological error here.

Plus there just aren't as many cases to work with, which given that this is a statistical argument is a handicap.

What exactly is a "statistical argument"? I would say that, properly understood, statistics is a method of evaluating empirical data, that is facts such as "Henry VIII was King of England for 38 years". The facts have to be primary.

Yes, certainly the facts are primary. I'm not suggesting arguing from numbers unconnected to facts. But if I have 379 examples of a phenomenon to support one claim, and only 25 to support another, then all else being equal my claim with 379 examples is the stronger one. More measurements lead to a more precise abstraction about how the measurements are related. The larger the number of examples, the more convincing our estimate of, for example, the slope of a curve.

My rule with regard to data is that I don't get to pick and choose.

Okay; do you entertain questions from the audience? For example if I give you a couple of random countries, will you demonstrate how the facts of that country are supported by the facts?

I couldn't parse this sentence. You can certainly suggest countries at random for discussion, from the Wikipedia list. Here is the link: http://en.wikipedia.org/wiki/Dynasty

But I'm not manipulating the data. It's up to other people, more expert than me, whether to list a given dynasty as ruling "Portugal".

My objection to that is that it abdicates responsibility for the relationship to reality -- it makes your claim highly contingent. Knowledge does not accumulate by the creation of weakly-founded claims, claims of the type "If we knew that X is true, then we could conclude that Y is true". Rather, knowledge accumulates by first establishing that X is true, and that Q is true, and that Z is true, and then integrating those established facts via the conclusion Y.

I think saying I have abdicated responsibility for the relationship of my data to reality overstates your case by a long way. I was simply saying that I don't speak Portuguese, don't have access to the National Museum where the original source documents regarding the Portuguese monarchy are stored, and have not studied, for example, the long succession of treaties, surveys, tax censuses, and other documents that scholars use to define the ever-shifting borders of Portugal over the past 1,100 years. Much less do I speak Chinese or Russian or Swahili, or have access to the relevant national archives for their dynasties. If I must be responsible for proving all that firsthand, the project is impossible and secure knowledge of history is impossible.

If there were time, or if I could find suitable helpers, I would do a more in-depth investigation of the sources underlying the Wikipedia list, and build a longer and more authoritative one. In fact I did do a search of many hours for kingship lists not on the Wikipedia page, and found several (such as Assyria). However, including or excluding these items did not alter my conclusions, and the items I found omitted tended to be disputed by scholars, or incomplete, much more often than the items Wikipedia accepted. So my effort to criticize the Wikipedia list for the most part reinforced its credibility.

There is no absolutely secure position to take here. If I build a custom list of my own selections, I am open to accusations of cherry-picking my data. If I rely on Wikipedia, I accept responsibility for whatever flaws exist in their list. To maximize my credibility, I have chosen to cite Wikipedia but to do some independent work validating it.

I don't doubt that there exists a mathematical method for modeling patterns that have a power law appearance; if you can establish that the data do have that appearance, then it raises the interesting question "What fact of reality causes this distribution?". But if there actually is no such distribution, then there is no thing requiring explanation.

Yes. But this criticizes at least two distinct ideas while treating them as one. First there is the idea that later rulers have shorter terms. Never mind whether they obey a power law. Their terms are consistently shorter, in a very striking way. The question, "What fact of reality causes this distribution?" applies to that observation, that the later rulers stay in power for a shorter time. The power law is the start of an answer to that question. I maintain that the definition of "dynasty" behind the Wikipedia list is objective, that the data are reliable, and that the fact of a decline is firmly established. That is the correct starting point of the discussion: There is a decline, now how do we account for it?

The concept of "entropy", legitimately applicable in physics, does not apply to dynasties. Notions of "heat loss" simply don't apply to the duration of a sequence of kings ruling a country.

Historically, the idea of entropy was never strictly or solely about thermodynamics. That was its first and most spectacularly successful application, but it has many others. It began as a theory about enumerating the total number of possible states in a system. At that time (the late 19th century), the existence of atoms remained speculative. Details of their behavior were unavailable. So Boltzmann's arguments about entropy were on a very broad level. They referred, in effect, to the number of distinct moving parts (which might be atoms or molecules or something else altogether) and the number of states those parts could take on.

Since 1948, science has recognized the distinct field of information entropy, introduced by Claude Shannon. It has nothing to do with thermodynamics, but it very definitely refers to the number of moving parts or possible states in a system. Since 1957, science has recognized the principle of maximum entropy introduced by Edwin Jaynes. Again, it has nothing specifically to do with heat loss or thermodynamics. There are textbooks applying it, for example, to economics. I cited one earlier.

In writing about the principle of maximum entropy to an audience of lay readers, or even for scientists, it is best to be careful and start by assuming they know nothing about any other kind of entropy beyond the version governing thermodynamics. People are often surprised to learn that the principle even exists. But I thought that I already made that introduction.

An appropriate challenge at this stage of the discussion might be that you haven't read or heard of Jaynes, and find it difficult to believe that the same mathematical rules can be applied to people (or viruses, or falling bombs, or other entities) that apply to atoms. That is legitimate and reasonable, and moreover I consider it my burden in the discussion to explain how that can work. Happy to do it, in fact. But I can't keep going back to the very beginning as if I hadn't spoken at all.

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"A series of dynasties clearly is a derivative concept which requires both the idea of "ruler" and the idea of "dynasty" to make sense."

How many dynasties in 2009 really have any power? Until we can define a certain "amount" of power a dynasty had (and certainly in some cases we can say a dynasty lost power even before it was officially overthrown), it is little more than family lineage, which certainly would follow some mathematical patterns, as you've shown.

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"A series of dynasties clearly is a derivative concept which requires both the idea of "ruler" and the idea of "dynasty" to make sense."

How many dynasties in 2009 really have any power? Until we can define a certain "amount" of power a dynasty had (and certainly in some cases we can say a dynasty lost power even before it was officially overthrown), it is little more than family lineage, which certainly would follow some mathematical patterns, as you've shown.

Well, yes, that's certainly true in 2009. But the whole list of dynasties covers every major power throughout history, since around 3,500 BC. Apart from a few very brief experiments in democracy, hereditary monarchy was the standard form of government everywhere, right up to the 20th century.

So a decline in stability in hereditary monarchy might not be big news today . . . it affects places like Nepal or Saudi Arabia, and not much else. But it has huge implications for our study of history.

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I don't see any negative implications for free will in this work at all . In fact, if the numbers hold up (which I leave to those more expert to quibble about), I see precisely the opposite. What the models of dynastic decline look like to me are models for the failure of oppressive governments. A newly established dynasty, or political party, or even a new ruler within an established regime, typically has a great deal of popular support, but little real power (relative to the end of the previous administration) because the structure of the new regime has not yet been firmly established. As the new regime becomes better established, the rights of the citizens are more efficiently arrogated, and therefore more citizens will be unhappy with those in power, lending more support to any opposition. It makes sense that this pattern would hold just as well for longer time-scales, as each successive ruler within a particular system would necessarily be able to learn from his predecessors, thereby gaining power, and losing popular support, that much more rapidly. This looks very optimistic to me, as it implies that humanity is moving inexorably toward a freer society. This pattern would not be possible, or even coherent, without the existence of free will.

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I don't see any negative implications for free will in this work at all . In fact, if the numbers hold up (which I leave to those more expert to quibble about), I see precisely the opposite. What the models of dynastic decline look like to me are models for the failure of oppressive governments. A newly established dynasty, or political party, or even a new ruler within an established regime, typically has a great deal of popular support, but little real power (relative to the end of the previous administration) because the structure of the new regime has not yet been firmly established. As the new regime becomes better established, the rights of the citizens are more efficiently arrogated, and therefore more citizens will be unhappy with those in power, lending more support to any opposition. It makes sense that this pattern would hold just as well for longer time-scales, as each successive ruler within a particular system would necessarily be able to learn from his predecessors, thereby gaining power, and losing popular support, that much more rapidly. This looks very optimistic to me, as it implies that humanity is moving inexorably toward a freer society. This pattern would not be possible, or even coherent, without the existence of free will.

Ultimately I think the challenge to free will posed by curves like this can be met. I am not arguing that free will doesn't exist. But I think these curves do complicate the picture. The issues are subtle and far-reaching.

For governments to move systematically from lasting 600 years to lasting 8 years, is good news overall for the cause of individual freedom. But if the erosion of regime stability is truly inexorable, if it follows a predictable mathematical rule, then the question arises: Where do philosophical ideas enter into the story?

The decline in regime stability was evident several thousand years before Aristotle appeared on the scene. It continued in similar fashion after Aristotle, and after Augustine, and Aquinas, and Locke, and Kant. I cannot discern any acceleration or change in the pattern. The shape of the decline curve is the same throughout history.

This contradicts (or at least appears to contradict) the Objectivist premise that philosophical ideas move history. Ideas might well move other aspects of history, but not regime stability. These curves appear to transcend (there's that word again) philosophy, religion, language, any influence other than numbers.

I think the correct way to view these curves is as a manifestation of steadily increasing disorder. Early societies were extraordinarily uniform and predictable, at least as compared with the way we live now. Very little changed in any given year. There were no new language words, no new ideas, no economic improvements, and no political innovations. Thus regimes were very stable.

However, each new nation-state that was founded necessarily had its own language and customs, its own economic foundation,and its own unique vulnerabilities. Innovation wasn't impossible, merely uncommon. The pace of change gradually accelerated, the nature of politics changed -- but the amount of change at any given point was governed by statistical rules unrelated to the content of the ideas. Knowing what philosophical ideas were in play in a given society is necessary to predicting its future course, but ideas alone are not sufficient to explain what happens. There is, so to speak, a speed limit for change. Societies will only absorb so much change at any one time -- not more, and not less either.

Because these curves are so common (I have hundreds more to talk about), I think it is necessary to modify the Objectivist premise regarding the role of ideas. Ideas do drive history and social life, but only in a direction allowed by statistical laws, and only at the pace allowed by the size and complexity of social systems at that point.

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The reason is that that is how randomness actually works.

Randomness refers to a type of relationship between events belonging to a given set. If events are completely independent, we call it a perfectly random system. Randomness is a property assigned to the system, not the other way round. Randomness does not explain a behavior; randomness is a behavior.

Varying cumulative-averages merely imply that successive events in a given system are not completely independent. The "dependence" may be non-trivial or subtle; but it has to result from an existential cause. Now, if you are trying to identify the type of (existential) "causes" that are responsible for drop in cumulative-averages in the systems that you studied, that would be OK. But it seems to me that you are unconcerned about existential causes. Rather, you attribute the behavior of the system to the method of study itself - the mathematics (you call it the "mathematical metacause" here and here). This is dangerously similar to the interpretations of quantum mechanics that ascribe observed uncertainty (behavior) to the act of observation (method) itself. Unsurprisingly, they too use almost the same words as you: "that is how nature works".

Finally, I have some questions related to your approach. In case of the random walk, it is possible to "model" the system based on the existential nature of each individual event - probability, independence etc. It could be analytically proven that as the system size would increase, the distribution in this system would converge to a Gaussian. However, in case of your analysis, what is the proof that the systems are indeed governed by power laws? Since you don't say anything about the fundamental cause of change in cumulative averages, aren't you are basically curve-fitting?

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I never quite bought Rand's claims about the influence of Aristotle on history. Not to say I dismissed them, but rather found them hard to believe and furthermore not worth the study required to prove. Which is to say the Objectivist ethics held true for me regardless.

I have a question at this point:

You have mentioned that you have hundreds of examples to back up your argument. Obviously such a list can be convincing without being exhaustive. You do not have unlimited time to plot a curve for everything. So my question is, what qualities should I look for in finding more cases?

If I looked at the term of team managers in soccer leagues, for instance, would you expect me to find the same trend?

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Math Guy, this has been a very interesting thread, thanks for starting it.

For example, if you study election returns district by district, you will find a very regular power-law dependence of the result on the number of voters. Small districts tend to produce much more decisive majorities for the winner. Large districts produce weak majorities, or pluralities in a multi-party system. Once again the pattern appears to depend solely on numbers, not on culture or language or economics.

In effect, when you try to achieve consensus on a particular candidate, information entropy (uncertainty) increases with the number of voters. A group of 2,500 voters will give the winner 75 percent of their votes, and distribute the remaining 25 percent among the other candidates. It can keep that kind of consensus up for election after election. A group of 25,000 voters will almost never do that well. They might manage a 60-40 split on a regular basis. A group of 250,000 voters will be lucky to manage 55-45. And so on.

Wouldn’t a reasonable explanation be that it’s easier to achieve a stronger consensus with a smaller, more homogenous group of people located in a given geographic area than it is with one that is larger, more diverse, and more geographically dispersed? I’d like to hear more about what data you reviewed to come to your conclusions on this application of your theory. Which political races did you consider and over what periods of time?

You can see the implications almost immediately. Large states or districts can't form strong consensus in favor of any one leader, and so they are more unstable. Small states or districts can stay with a policy or platform for several cycles with far less difficulty.

The perpetual 50.5-49.5 split between presidential candidates in the modern U.S. system is not, at root, a problem with ideology or culture. It is not the fault of the Republicans and Democrats that America is perpetually locked in red-versus-blue warfare. It's a consequence of the principle of maximum entropy.

If we look at presidential elections, the recent close races are not unusual in our history, however we shouldn’t necessarily expect them to continue this way forever. We don’t have to go back too far in history to see that Reagan beat Mondale by 18%, and Carter by almost 10%. Nixon beat McGovern by 23% and Johnson beat Goldwater by a similar margin. I don’t see much of a pattern here other than we appear to have several close elections, then we have a landslide.
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Randomness refers to a type of relationship between events belonging to a given set. If events are completely independent, we call it a perfectly random system. Randomness is a property assigned to the system, not the other way round. Randomness does not explain a behavior; randomness is a behavior.

Varying cumulative-averages merely imply that successive events in a given system are not completely independent. The "dependence" may be non-trivial or subtle; but it has to result from an existential cause. Now, if you are trying to identify the type of (existential) "causes" that are responsible for drop in cumulative-averages in the systems that you studied, that would be OK. But it seems to me that you are unconcerned about existential causes. Rather, you attribute the behavior of the system to the method of study itself - the mathematics (you call it the "mathematical metacause" here and here). This is dangerously similar to the interpretations of quantum mechanics that ascribe observed uncertainty (behavior) to the act of observation (method) itself. Unsurprisingly, they too use almost the same words as you: "that is how nature works".

Finally, I have some questions related to your approach. In case of the random walk, it is possible to "model" the system based on the existential nature of each individual event - probability, independence etc. It could be analytically proven that as the system size would increase, the distribution in this system would converge to a Gaussian. However, in case of your analysis, what is the proof that the systems are indeed governed by power laws? Since you don't say anything about the fundamental cause of change in cumulative averages, aren't you are basically curve-fitting?

Hmm, these are excellent questions. It may take me several posts to deal with all the implications, so bear with me.

To start by getting terminology right, you identify "random" events as always being independent. I agree that that is the conventional way of looking at the problem, the classical perspective laid down by Newton and Pascal in the 17th century. But that is not how Jaynes approached it. We actually go back to a more basic level of argument in Jaynes' system. Random behavior, Jaynes would say, simply means the behavior of a system with a range of possible states about which one has limited knowledge. If I must guess which state the system will be in at a given moment, then by definition the system is varying randomly. Randomness is a relationship between the observer and the observed. The system itself "knows" what it will do, or is doing. It is determinate. It is my knowledge that is indeterminate. I have to specify a range of possibilities because I don't know which one will occur.

You may recognize that this is a Bayesian approach to probability. However, Jaynes then added his own innovation. He viewed probability as a branch of logic. He introduced the principle of maximum entropy as a kind of virtually all-purpose limiting case -- a logical axiom, if you like. The principle of maximum entropy is a supremely powerful principle because it is nearly always going to be applicable. Systems that are not at maximum entropy are the exception. Systems that are at maximum entropy are the rule. In everyday problems like economics or history, the principle of maximum entropy is even more useful than, say, conservation laws. There's no guarantee that the number of people in an economy will remain constant, or that the quantity of money will be conserved -- but there is every reason to think that disorder will always be at a maximum, no matter what sort of quantities we are measuring, whether any are conserved are not.

One consequence of this approach is that the idea of independence recedes in importance. We don't necessarily need to know if the elements of the system are independent, or dependent, and we don't build up a detailed model of the classical kind of what the system might be doing. We take a different route entirely. We know that dependent or independent, they are thoroughly disordered -- and the kind of disorder is itself meaningful to us. Jaynes didn't use the Objectivist terminology, but he certainly would have understood it if I said that randomness is an epistemological concept, not a metaphysical one. The system does what it does, and we do not know the details: instead of trying to model the details we apply a few broad logical rules about what it has to be doing and make estimates based on those.

It is possible to make a strong prediction about the behavior of very complex systems - that is, to specify a distribution curve that the observable system variables will obey -- using a very limited number of parameters, provided that the system does obey the principle of maximum entropy. The details of the system then remain unknown. One does not model the mechanics. One would instead compute what range of outcomes (what curve) would maximize the entropy -- that is, maximize the uncertainty of individual outcomes. This usually turns out to be a power law.

Jaynes limited himself to demonstrating this in chemistry and physics but he acknowledged, in a number of papers, that it could be applied to economics and to other phenomena as well. In the past fifty years, many people have since done so. The results are elegant and powerful, and sidestep entirely the dependent/independent problem.

So for example, if we sat down to estimate how elite incomes (the top 10 percent say) would be divided up in a society, we would immediately become bogged down in an insane number of details. What laws apply? What are the tax rates? What are the cultural imperatives? What sort of wealth does the society hold? Is it agrarian, industrial, post-industrial? Most people would shrug and say they have no idea how incomes are distributed. It would seem like an impossible task even to start building the model.

However, Vilfredo Pareto discovered more than a century ago that ALL societies, from the medieval era to the present, obey the same simple rule for the distribution of elite incomes. They always follow a power law. The arrangement is a geometric function: it might be 100,000 people with incomes of $50,000 to 99,000, and then 40,000 with incomes of $100,000 to $199,000, and then 16,000 with incomes from $200,000 to $399,000. You see the rule? For every doubling in income, in this country there are just 0.4 times as many people who earn the higher amount. In another country the fraction might be 0.35 or 0.27 or some other number. However, plotted on a log-log graph, these cohorts or bins closely approach a straight line -- always. The only variation between countries is the slope of the line.

Now, I contend, backed up by Jaynes, that the reason that Pareto's income curve works so neatly, and gives us this elegant power law, is because of the logical constraint of entropy. The set of all elite income-earners is large enough, the economy complex enough, and enough time has gone by, that you can ignore the details of the society and just assume that income uncertainty will be maximized according to the principle of maximum entropy. The range of incomes is not just very wide -- it is as wide as it can be, given the circumstances. It is maximally random. This makes it possible to estimate the distribution of incomes using a very simple curve despite the daunting social complexities involved.

That's a very, very compact summary of a complex idea requiring several chapters in my book. It's a very different approach to probability, and it requires serious thinking about before one can do it confidently. When I say the cause of Pareto's elite incomes curve is a mathematical meta-cause, I mean this: Despite the economy's incredible complexity, and all the myriad possibilities of free will, the end result is always this very smooth geometric distribution. There are all sorts of things we don't know about the economy, but there is one thing we are confident we do know: its measurable variables must obey the principle of maximum entropy.

So to answer your concluding question: Yes, I'm curve-fitting, but with a very powerful logical principle that says this shape of curve is privileged epistemologically.

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I never quite bought Rand's claims about the influence of Aristotle on history. Not to say I dismissed them, but rather found them hard to believe and furthermore not worth the study required to prove. Which is to say the Objectivist ethics held true for me regardless.

I have a question at this point:

You have mentioned that you have hundreds of examples to back up your argument. Obviously such a list can be convincing without being exhaustive. You do not have unlimited time to plot a curve for everything. So my question is, what qualities should I look for in finding more cases?

If I looked at the term of team managers in soccer leagues, for instance, would you expect me to find the same trend?

Yes. If you mean, should the very first managers of a team tend to last longer in the job, and later managers cycle through more frequently, then yes, that is what I would expect, though I haven't studied that case. It's true, for example, of comic books. A long-lived comic book will tend to keep its original creative team for many years, a decade or more. But eventually, when the founders leave, their replacements are on average less loyal, or less popular with the readers, or viewed as mere temp workers by management. In any case, they tend to have shorter tenures.

This same principle applies to customer loyalty in a lot of industries. Your first customers are your most enthusiastic and committed. The 100th or the 10,000th shows up later and leaves much sooner. I call this "loyalty fatigue" and it has a big impact on businesses dependent on charging annual support fees, or "upselling" established customers.

I've found a few counter-examples so far. It isn't true of mayors, at least not in the major American cities dating back to Revolutionary times. But the reason appears to be a massive change in the job description. Early mayors were unpaid, and were not elected. They were chosen by a committee and assigned the job. It was not unknown for even prominent citizens to move away rather than accept the honor. So comparing the tenure of modern mayors to 18th-century Boston is perhaps inappropriate. It's apples versus oranges.

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Math Guy, this has been a very interesting thread, thanks for starting it.

Wouldn’t a reasonable explanation be that it’s easier to achieve a stronger consensus with a smaller, more homogenous group of people located in a given geographic area than it is with one that is larger, more diverse, and more geographically dispersed? I’d like to hear more about what data you reviewed to come to your conclusions on this application of your theory. Which political races did you consider and over what periods of time?

You generally have to be careful to compare within a system rather than between systems, to look at many races taking place together at one time, rather than just one. So it works well if you compare small Canadian Parliamentary ridings (electoral districts) to large ones, or Senate races in small U.S. states versus large ones, or small districts in the City of London to large ones, for the same series of elections. It would not work, or at any rate the law would be much less apparent, if we created a grab-bag of different voter populations -- like mixing Greek, Ukrainian, and Iraqi election results in one data set. The law isn't that universal. It also doesn't work quite as well for presidential elections, where there is only one nationwide ballot. For more on this see below.

If we look at presidential elections, the recent close races are not unusual in our history, however we shouldn’t necessarily expect them to continue this way forever. We don’t have to go back too far in history to see that Reagan beat Mondale by 18%, and Carter by almost 10%. Nixon beat McGovern by 23% and Johnson beat Goldwater by a similar margin. I don’t see much of a pattern here other than we appear to have several close elections, then we have a landslide.

Yeah, you got me on that one. I was being a little sloppy in referring to the 50.5-49.5 split, and didn't spell out what I meant. First, there is a very noticeable difference between small states and large ones. Hawaii or Alaska will generally deliver bigger majorities than California, when the vote is held for governor or Senate seats. But there's also a trick that distinguishes the American system from most others. Most systems are genuinely multiparty, and that means it is possible to win with no more than a plurality. Multiparty systems thus tend to have a steeper curve. The strength of the consensus fades more noticeably as we go from 2,500 to 250,000 voters. The U.S. system so effectively excludes serious third parties that the winner nearly always has a genuine majority. The failure to achieve consensus is much less noticeable if there are two and only two choices, not 3 or 5 or what have you.

So the majorities are noticeably stronger in U.S. elections than in Canadian or European ones, and the curve isn't as steep.

Edited by Math Guy
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This is a good theory, but ultimately wrong. It is relatively easy to test. In a number of countries, one dynasty has followed another for thousands of years. Egypt, China, Rome, Byzantium, and other great states outlasted even their strongest dynasties by an order of magnitude. As many as 30 dynasties have succeeded one another in governing the same geographic region. So we can perform the same analysis as we did for the individual rulers, but on a wider scale.

We find that here too, there is decline. Later dynasties do not last as long as the early ones. The shape of the curve is the same; the average decline of 20 percent from the first half of the list to the last half is again evident.

Post your data for China--the names of the dynasties and their durations upon which you based your result. I'm fairly familiar with Chinese history and unlike you don't have to rely on the vagaries of Wikipedia for what constitutes a "dynasty." I'll add up front that I ran the same test and found results at great variance with yours--positive power-law exponents in all cases, regardless of how you define "dynasty" (for it's a vague term that meant different things at different times), provided you use only the dynasties for which the dates are actually solidly supported in the historical or archeological records. (Which excludes the Xia and Shang dynasties; it's ridiculous on the face of it if you know anything about Chinese history and culture to even consider including the Three Sovereigns and Five Emperors, who are purely legendary figures of the same sort as Adam and Methuselah and with much the same overinflated lifespans.) The existence of the Shang is at least established, though the dates are sketchy; if we include a duration of 540 years (the various figures are around that), then and only then do I get negative exponents--very small negative exponents in some cases, very small positive exponents in others, with correlation coefficients between 0.02 and 0.06. (The Xia is charitably described in many sources as "possibly legendary.") In other words, the data are such that you have to include one semi-historical dynasty about which virtually nothing of its history or its reign periods are known in order to support your thesis, and even then it's statistically nugatory. More generally, in fact, a discussion of the Chinese data would clarify many of the problems with your blithely relying on others to do your basic ground-clearing.

Two initial questions:

1. Do you fit your power-law curve to the number versus duration of each dynasty, or to the beginning year versus duration of each dynasty? (For me this doesn't matter; I get a positive power in all cases without the Shang and positive or negative but with very small absolute values with the Shang included. It's an important question though to pin down your methodology.)

2. Why haven't you reported your correlation coefficients? In all cases mine were less than 0.18, which is hardly impressive evidence.

Once I see your data, I'm sure I'll have a large number of questions about your principles of selection--though you've already admitted you most likely fobbed off the responsibility for answering them onto Wikipedia.

Edited by Adrian Hester
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I am sure some of you will be tempted, as I was, to hypothesize that this has something to do with limited human lifespans, and the vigor of youth, intergenerational dynamics, and the inherent limitations of hereditary rule. We might call it the "King Lear" effect...He delays until the last possible moment, in most cases until he actually dies. This means that he is succeeded by his adult son, or perhaps several sons, who have spent a lifetime waiting in their father's shadow.

More generally, if succession is from the father to the son, the if the father is long-lived the son will be fairly mature upon accession to the throne and simply in the course of things will not be expected to have as long a lifespan.

This is a good theory, but ultimately wrong.

Wrong? Or do you mean incomplete? Those are very different claims.

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Here is a breakdown of the data. It shows how many dynasties I found for that period in history, and their average durations.

# AVG

3050-2500 BCE 6 637

2499-2000 BCE 10 507

1999-1500 BCE 14 304

1499-1000 BCE 8 216

999-500 BCE 16 137

499-1 BCE 26 189

CE 1-500 27 297

CE 501-1000 61 184

CE 1001-1500 109 132

CE 1501-1800 73 107

CE 1801-2008 38 52

First of all, note that before about 500 BC, very few dynasties are recorded--the historical record is incredibly sparse for that period, and in many cases the king lists that you are relying on probably include many legendary and semi-legendary figures who were given reign periods that can't be checked and were probably fabricated out of whole cloth for cultural reasons. (Like the sage emperors in China.) Besides that, the only dynasties from that time we'd have records of are the ones so powerful and so long-lived as to make such an impact on later societies, for very few societies had writing then! The average durations you rely on for the period before 500 BC, in other words, are simply not at all comparable in completeness, accuracy, or reliability with later periods. Moreover, the period after 1800 saw republican revolutions throughout Europe and Latin America; that too renders their inclusion suspect since an entirely new ideological factor had come on the scene.

So, if we focus only on the years between 500 BC and 1800 AD, we find a general downward trend by number of dynasties: The average duration of all dynasties in years is 273.5-1.549*N (N=number of dynasties), with a correlation coefficient of 0.73 and error about the mean of 49.6. But even on your own terms, that makes sense: Thy're not all independent at all, but rather competing within larger geographic areas, so of course some win out at the expense of others, a process that is more intense the greater the number of dynasties. But you can't blithely disregard the serious problems of reporting either--the historical record is very spotty, so you have a general trend throughout the period of 1000-1800 AD of consolidation against a much greater mass of documentation from 1500 on; a similar pair of competing factors is at play for the period before the collapse of Rome.

You can see that on a detail level, the data are not absolutely uniform. The trend plunges downward steeply in the years approaching 500 BCE, then rises to a local peak in the early centuries AD, before plunging down again. But taking the cumulative average, we see a curve very closely approximating the previous two. We have zoomed out to an even more colossal scale, and the shape of the curve is the same yet again. History . . . is fractal!

What I see is that you have no idea of the factors at play on a true "detail level." The data simply are not comparable throughout the period; taking the cumulative average is a meaningless exercise without such detailed treatment.

There are plenty of issues that can be raised here about the quality of data. Do we know if the early kings referred to in documents from 4,000 years ago actually existed? Shall we trust the inferences of archeologists about the Pharaohs? Perhaps in those distant times there are empires completely unknown to us, that lived much shorter lives and died without records.

I see you actually do have a glimmering of the difficulties you've not addressed, but the fact that you treat them as open questions is significant.

But even if we discarded the data prior to 500 BCE as being untrustworthy, and took only those dynasties that were established since Aristotle, or since Christ, we'd still have the same basic result. Decline pervades the data set. It cannot be purged by removing a few unusual items, or postulating a few missing ones.

Ah, but I'm not "postulating a few missing ones," I'm pointing out systematic gross errors with strong time dependencies that knock your entire methodology into a cocked hat.

What this suggests is that long spans of history are tied together by a mathematical rule. If staying in power represents success, then throughout human history, hereditary dynasties have been inexorably growing less and less successful, and more and more unstable.

A result based in great part by including semi-historical and pre-historical (i.e., legendary) dynasties and ignoring basic questions of the reliabilityand completeness of the sources of your data.

The presence of the rule on the other levels suggests that on this level as well, the trend has real predictive and causal meaning. We don't know yet WHY this rule operates...

No, we don't even know THAT this rule operates at all.

What does this make you think of?

It makes me think of Hegel.

Makes me think of Toynbee--a vast historical schema to which he fit cherry-picked data with no regard for the historiographical difficulties at the base of his entire enterprise.

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First some examples of decline on the dynastic level:

Dynasties ruling Portugal, 868-present

Vimara Peres to 1072, 204 years, so for N=1, mean length 204

2nd County to 1139, 67 years, so for N=2, cumulative mean 135.5

Burgundy to 1385, 246 years, so for N=3, cumulative mean 172.33

Aviz to 1495, 110 years, so for N=4, cumulative mean 156.75

Aviz-Beja to 1581, 86 years, so for N=5, cumulative mean 142.6

Hapsburg to 1640, 59 years, so for N=6, cumulative mean 128.67

Braganza to 1853, 215 years, so for N=7, cumulative mean 140.71

Saxe-Cobourg Gotha to 1910, 57 years, so for N=8, cumulative mean 130.25

Braganza to 2007, 97 years, so for N=9, cumulative mean 126.6

Even though I know fairly little about Portugal, I still know enough to question the wisdom of treating the period of Spanish rule between 1580 and 1640 on the same level as native dynasties.

If you plot these on a spreadsheet and fit a power-law curve to them, you get an exponent of -0.178. My universal model predicts -0.30576. So this is a slightly shallower decline than expected, but then they cluster around -0.30576, they don't precisely match it every time.

"Cumulative mean"? So in other words you're basing vast claims about human behavior on the general phenomenon of regression towards the mean! Let's do this differently and take your same data with duration versus dynasty number. In that case you have a decline that is much less precipitate; if you fit a power law to it you get an exponent of -0.03149, with a correlation coefficient of 0.34. (Note that the number of digits I've kept is far greater than appropriate, but then you do the same.) It would be an interesting mathematical exercise to start with time series fitted to a power law with a low correlation coefficient and a low absolute power exponent, represent the expected cumulative mean as a time series, fit that to a power series, and find the expected power exponent for that; I suspect due to regression towards the mean you'd find the expected exponent to be negative and rather larger in absolute value for a wide range of initial parameters. So yes, another reason your methodology is entirely suspect--ironically, through the simple operation of randomness and the law of large numbers!

And in fact we can test this very easily with the Chinese dynasty data. Start with the data set that includes the Shang dynasty with a duration of 510 years (an oops above--that, not 540, was the duration I used throughout), breaking up the Eastern Zhou into the Spring and Autumn and Warring States periods (which is actually beneficial to your argument, since that tips the exponent from slightly positive to just very very barely negative), and including the Liao and Jin (non-Chinese dynasties ruling nortern China) rather than the two Song dynasties (native dynasties ruling south China in the same period), though the differences resulting from that last choice are entirely negligible. This set of choices, which still has many points to quibble about, gives an exponent of -0.0006763, based on my figures, with a correlation coefficient of 0.009. If you then calculate the cumulative means and fit a power law to that, you (or a least I) find an exponent of -0.022 with a correlation coefficient of 0.88. But you'll find that with a wide range of data sets; using the cumulative mean wipes out vast amounts of variation and greatly exaggerates the effects of earlier dynasties on the results. This we can see if we do a simple thought experiment: The geographical region of Utopia has been ruled by 20 dynasties; the first one lasted 500 years, the second 200 years, the third 30 years, and each of the subsequent dynasties lasted 10 years longer than the predecessor of its predecessor. (This gives a sharp initial drop followed by a slightly rising heavily jagging rise similar in very broad outline to the Chinese dynastic data.) The general trend is rising, and if fit to a power law has an exponent of 0.0084; however, if you fit the cumulative means to a power law regression towards the mean predominates and you have an exponent of -0.014. (Moreover, the correlation coefficients are 0.145 and 0.696, respectively, for the cumulative means wash out much of the variation in the actual figures, so that the power law fits the cumulative-mean data very much better.)

What is fatal to the trustiness of your method is that if we reverse the data we sometimes get much the same result! For the same Chinese data reversed, the cumulative mean when fit to a power law has, yes, a negative exponent, -0.012. So whether going forwards or backwards in time, you get a negative exponent either way! For the Portuguese data reversed, on the other hand, the shortness of the last two dynasties suffices to give positive exponents, 0.031 for the raw data and 0.0168 for the cumulative mean.

Dynasties ruling France, 843-1870

There are 14 dynasties in the series, from the Carolingians to the last of the Bonapartes. I'll give the lengths of each, and the cumulative means:

144 / 144

341 / 242.5

170 / 218.3

17 / 168

74 / 149.2

203 / 158.2

12 / 137.3

10 / 121.4

1 / 108

0.5 / 97.2

15 / 89.7

18 / 83.8

4 / 77.6

18 / 73.4

Stability in France declined a good deal more steeply than in Portugal. The best fit curve has an exponent of -0.385, a little worse than my universal model. Again, you can play with these numbers in various ways but I think the conclusion is always going to be a power law decline.

Well yeah, if you fit a time series to a power law, in lieu of other information you can expect the power law to be declining in half the cases. If you then add in regress towards the mean by relying on cumulative means, especially with small absolute values of the exponent, of course you're going to have a predominance of power law declines!

In any case, your French data are a mass of incompatible regimes--not dynasties since you're lumping in republics with empires and monarchies. Here is the second half of your data with the names of the regimes in question labeled and classified:

12 / 137.3 First Republic (usually divided into different regimes as follows: Constitutional monarchy, republic, the Directorate, and the Dictatorship of Napoleon)

10 / 121.4 First Empire (Bonapartist)

1 / 108 Bourbon Restoration following Napoleon's abdication (pre-revolutionary monarchical line)

0.5 / 97.2 Return of Napoleon from exile at Elba

15 / 89.7 Second Bourbon Restoration (pre-revolutionary line)

18 / 83.8 July Monarchy (Orleanist, an offshoot of the Bourbon line)

4 / 77.6 Second Republic

18 / 73.4 Second Empire (Bonapartist)

Not only do you lump in republics with dynastic regimes, you put the period from Napoleon's abortive return from Elba until his defeat at Waterloo on the same level as the Carolingians! Suffice it to say that's a sign of utter historical ignorance. Before the 1750s there was very little antimonarchical sentiment in Europe, but once it spread, then yes, there was a great deal of political instability in Europe, and particularly in France. This passel of regimes is a major reason for your results, but it's signally unclear it's fair to include them. If we exclude the First Republic and all later regimes, we find that the decline is much less marked (and in this case is obscured by taking the cumulative mean, thanks to the sagging middle): -0.064 for the raw data, -0.016 for the cumulative means (correlation coefficients of 0.26 and 0.31, respectively), versus by my figures -0.13 for the overall raw figures, -0.036 for the overall cumulative means (correlation coefficients of 0.65 and 0.93, resp.). For the reversed data excluding post-Revolutionary regimes, we find +0.064 for the raw data (as we should) and +0.014 for the cumulative means.

It would be interesting to take all of your data, reverse them in time, and fit the resulting cumulative means to a power law and see how many of them remain negative--given the low correlation coefficients for the raw data you've already presented, it's a toss-up, but that's because your method is fundamentally unsound for showing what you want to show.

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This we can see if we do a simple thought experiment: The geographical region of Utopia has been ruled by 20 dynasties; the first one lasted 500 years, the second 200 years, the third 30 years, and each of the subsequent dynasties lasted 10 years longer than the predecessor of its predecessor. (This gives a sharp initial drop followed by a slightly rising heavily jagging rise similar in very broad outline to the Chinese dynastic data.) The general trend is rising, and if fit to a power law has an exponent of 0.0084; however, if you fit the cumulative means to a power law regression towards the mean predominates and you have an exponent of -0.014. (Moreover, the correlation coefficients are 0.145 and 0.696, respectively, for the cumulative means wash out much of the variation in the actual figures, so that the power law fits the cumulative-mean data very much better.)

What is fatal to the trustiness of your method is that if we reverse the data we sometimes get much the same result!

As with the mythical state of Utopia. If we reverse the data, then for the raw data we find an exponent of -0.0084 and for the cumulative mean an exponent of -0.0081. So no, your method does not show what you want it to show; it's simply unsound.

Edited by Adrian Hester
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First, let me say I'm excited to be talking with a serious historian (or history buff) about this, and thank you for commenting. If my thesis seems naive and presumptuous and annoying, well, perhaps it is all of those things. I started by saying it was preposterous, and I'm not going to flinch if people are skeptical. But let us see.

The data for China that I used are (years duration first, then name)

628 Three August Ones and the Five Emperors

470 Xia Dynasty

554 Shang Dynasty

275 Western Zhou Dynasty

514 Eastern Zhou Dynasty

246 Spring and Autumn Period*

254 Warring States Period*

15 Qin Dynasty

215 Western Han Dynasty

16 Xin Dynasty

195 Eastern Han Dynasty

45 Three Kingdoms

52 Western Jin Dynasty

103 Eastern Jin Dynasty

161 Southern and Northern Dynasties

37 Sui Dynasty

289 Tang Dynasty

53 Five Dynasties and Ten Kingdoms

167 Northern Song Dynasty

152 Southern Song Dynasty

209 Liao Dynasty

119 Jin Dynasty

97 Yuan Dynasty

276 Ming Dynasty

1 Shun Dynasty

267 Qing Dynasty

4 Empire of China

If I omit everything up to and including Shang, I still get a negative slope of -0.29 for the cumulative curve. (I have a reason for using the cumulative curve, which I will discuss below.)

Wikipedia actually breaks down the Eastern Zhou into two partly overlapping sub-dynasties (shown with *), so if I use those instead of treating the Eastern Zhou as one, the slope becomes more shallow, and flattens noticeably at the end, but it's still -0.26. If I throw out the two rump dynasties (Shun in 1644 and Empire of China in 1912-16), there's a slight rise at the end which spoils the monotone shape of the curve, but it still doesn't get me back to the average of the first two accepted dynasties in the set. And at that point I would have thrown out 5 of my 22 data points. To get a positive curve I have to start with the Qin, which basically throws out everything in Chinese history prior to 221 BC.

It would not take much for your knowledge of Chinese history to vastly exceed mine. But it seemed from my study of the Mandate of Heaven that the Shang Dynasty had to have some real historical foundation, since the theory of the Mandate was used by the Zhou to justify their overthrow of the Shang. Plus there seem to be ample primary sources cited for the Shang -- the "Bamboo Annals," inscriptions on bronze artifacts, archeological digs of palaces and tombs. Wikipedia lists several different sets of dates that have been proposed for the length of the Shang, but none put it any shorter than 500 years.

Again, I'm not averse to doing the analysis independently of Wikipedia or some neutral source, assembling a custom data set. But coming from someone who is not a professional historian, I think the cries of "cherry picking" if I did it that way would be all the louder.

1. Do you fit your power-law curve to the number versus duration of each dynasty, or to the beginning year versus duration of each dynasty? (For me this doesn't matter; I get a positive power in all cases without the Shang and positive or negative but with very small absolute values with the Shang included. It's an important question though to pin down your methodology.)

2. Why haven't you reported your correlation coefficients? In all cases mine were less than 0.18, which is hardly impressive evidence.

First, about correlation coefficients, and confidence levels: In early drafts of my book, I actually computed all these, not just for the historical dynastic data but for all the various curves I presented. I took all that information out after about six months because 1) citing them all wreaked havoc with the flow of the text; 2) the coefficients and confidence intervals were typically good for large data sets but not as good for small ones; and 3) my particular method of presenting the data tended to force high correlation values in a way that a statistician would see as contrived.

Out of these, 2) was probably the strongest argument. In effect, the specific figures didn't actually convey much in a given case, beyond whether I was working with a lot of data points, or a few. I could write a book that would have stupendously high correlation and confidence scores for every graph, simply by dropping 70-80 percent of my examples and sticking with large data sets. But it wouldn't convey the idea I'm working on. If I wanted to write about the application of the principle to a very broad range of items, then I would have to accept the data sets as they came. For example, if I have a dynasty that consists of 8 rulers, I can play with different ways of calculating the likelihood of the last 4 being less long-lived than the first 4 -- but all the methods I might use give the same weak confidence level, because N=8 just can't do much for you.

I'm not expressing scorn for academic convention. It has its place. But this isn't a Popperian argument where I'm trying to falsify some proposition by showing the data lie outside an arbitrary confidence interval. Since the theme of the book is to illustrate the power of Jaynes' way of looking at probability, and since I'm arguing that these phenomena are invariably nonlinear, nonstationary, and don't obey the central limit theorem, it would be redundant to continually test, for each and every graph, the alternative thesis that they do obey the CLT and that the pattern is just random happenstance.

Now, in regard to your first question, I use rank number versus cumulative years to get average duration, and plot the decline in average duration. Why do the calculation based on the cumulative curve? Because the theory says that the pattern depends on increasing set size, or rank. We can certainly do it other ways and still get a decline -- as you did when you fitted a linear estimate to my table and got the downward trend of about 1.5 years lost per additional dynasty. But if you think the cause is entropy, then you want above all to see what the pattern looks like in a cumulative plot. That allows me to compare apples to apples when I look at disparate data types.

However, that also creates a strong auto-correlation effect. The scores for a cumulative plot are always good if the slope is even slightly downward. So if I were to cite correlation scores for the graphs the reader actually sees, it would be meaningless and misleading.

I hope that's clear. I'll deal with the rest of your points tomorrow, when I have more time.

Edited by Math Guy
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You generally have to be careful to compare within a system rather than between systems, to look at many races taking place together at one time, rather than just one. So it works well if you compare small Canadian Parliamentary ridings (electoral districts) to large ones, or Senate races in small U.S. states versus large ones, or small districts in the City of London to large ones, for the same series of elections. It would not work, or at any rate the law would be much less apparent, if we created a grab-bag of different voter populations -- like mixing Greek, Ukrainian, and Iraqi election results in one data set. The law isn't that universal. It also doesn't work quite as well for presidential elections, where there is only one nationwide ballot. For more on this see below.

Ok, I have no problem with the proposition that smaller groups will tend to reach a stronger political consensus than larger groups. However, I think that's relatively easy to explain, as smaller political groups are likely to be more homogenous and likely to have more shared experiences and values because they are less geographically dispersed, among other reasons. Given all of this, I don't see how this phenomenon is explained by a Power Curve and worse yet, I'm not sure what useful information a Power Curve or entropy or whatever we call it gives us when it comes to politics.

By the way, threads like yours are why I give money to support the O'ism Online forum. A big thumbs up to everyone who has contributed to this thread. This forum consistently has some of the most intelligent back and forth discussions you can find anywhere on the internet.

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First of all, note that before about 500 BC, very few dynasties are recorded--the historical record is incredibly sparse for that period, and in many cases the king lists that you are relying on probably include many legendary and semi-legendary figures who were given reign periods that can't be checked and were probably fabricated out of whole cloth for cultural reasons. (Like the sage emperors in China.) Besides that, the only dynasties from that time we'd have records of are the ones so powerful and so long-lived as to make such an impact on later societies, for very few societies had writing then! The average durations you rely on for the period before 500 BC, in other words, are simply not at all comparable in completeness, accuracy, or reliability with later periods.

I agree with these concerns, broadly speaking, but I don't regard them as a conclusive argument against including the data. On the level of analyzing individual rulers, I won't use semi-legendary figures who live 400 years; but given some circumstantial evidence I will accept a dynasty whose precise sequence of rulers is unclear or disputed as nonetheless having governed for X years in total. I see your concern about pre-literate societies but then we have to ask, if they had no records and could not themselves determine who had ruled in the past, does the concept of a "dynasty" even apply? Part of the basic idea of a dynasty is that it establishes the legitimacy of successive rulers by demonstrating their connection to the past. At the point where records do not exist, any argument about the stability of multi-generation rule starts to become moot.

I agree the early record may indeed be biased toward longer-lived dynasties, and that short-lived dynasties that did keep written records might have been overlooked. But to use this argument to exclude data items kind of begs the question. We're trying to discover what gives a society stability. If stability goes down as the size and complexity of a social system goes up, for example, then small kingdoms not in the historical record might actually have supported longer-lived dynasties. Obviously, we don't know, and I won't rule data in or out based on speculation.

Moreover, the period after 1800 saw republican revolutions throughout Europe and Latin America; that too renders their inclusion suspect since an entirely new ideological factor had come on the scene.

Yes and no. I considered throwing out everything after the start of the Industrial Revolution, for example, but I found it again begs the question. New dynasties formed after 1800 had lifespans averaging only a few decades. Existing dynasties made it through the century intact only to die in the Great War, or World War II. So under the pressure of republicanism, expanding literacy, steam power, capitalism, what have you, the early dynasties still behave differently from the late ones within that span of time. That's what we're testing for, so no data gets thrown out.

So, if we focus only on the years between 500 BC and 1800 AD, we find a general downward trend by number of dynasties: The average duration of all dynasties in years is 273.5-1.549*N (N=number of dynasties), with a correlation coefficient of 0.73 and error about the mean of 49.6. But even on your own terms, that makes sense: Thy're not all independent at all, but rather competing within larger geographic areas, so of course some win out at the expense of others, a process that is more intense the greater the number of dynasties. But you can't blithely disregard the serious problems of reporting either--the historical record is very spotty, so you have a general trend throughout the period of 1000-1800 AD of consolidation against a much greater mass of documentation from 1500 on; a similar pair of competing factors is at play for the period before the collapse of Rome.

Well, at this point you've thrown out roughly a third of my data, focusing on the extremes on either end, and yet there's still a downward trend. I agree that even after 1000 AD the list isn't complete, but again I'm reluctant to speculate about the statistical character of dynasties we know nothing about, and that may not even have existed. (Just for example, we now know that New Guinea supported a large population over the past several thousand years. There were enormous numbers of people living in the interior of the island that early 20th century explorers simply missed. But when first contacted, these previously unknown peoples didn't have large-scale political systems, or dynastic rule, or even written language. It seems unlikely that they had these things in the past, and lost them.)

I agree that apart from the Old and New Worlds prior to 1492, dynasties were never absolutely independent of one another, but I think the idea that the trend can be explained by them competing for territory is kind of vague. I wouldn't say China was seriously competing with Spain at any point in their histories, for example. The Silk Road trade no doubt allowed East to influence West and vice versa, but it hardly seems like a determining factor in regime stability. And anyway, merely being able to come up with an alternative hypothesis for why there is a decline trend doesn't show mine is unsound.

There are a bunch of remarks here that I've grouped together:

What I see is that you have no idea of the factors at play on a true "detail level." The data simply are not comparable throughout the period; taking the cumulative average is a meaningless exercise without such detailed treatment.

Ah, but I'm not "postulating a few missing ones," I'm pointing out systematic gross errors with strong time dependencies that knock your entire methodology into a cocked hat.

A result based in great part by including semi-historical and pre-historical (i.e., legendary) dynasties and ignoring basic questions of the reliabilityand completeness of the sources of your data.

Makes me think of Toynbee--a vast historical schema to which he fit cherry-picked data with no regard for the historiographical difficulties at the base of his entire enterprise.

I'm aware of the complexity of the story, and the problems with the quality of the data. However, the whole point of a maximum entropy curve is that it allows estimates to be made of the trend or the range of outcomes without knowing the details of how the system works. The data are sufficiently good to perceive that kind of simple trend (and sadly, as I observed, if kingship lists aren't good enough as data, then almost nothing from ancient history is).

It's a startling claim, as even Jaynes observed, but it works in physics problems and there is no obvious reason why it would not work here. That is what my research was intended to determine.

Toynbee makes a good point of comparison, as does Spengler. I don't think it's fair to say either man "cherry-picked" his data, just as I don't think that that complaint is true of me. If you want to accuse them of something, or me, I think a better charge would be overly broad generalization -- a theory that is excessively inclusive rather than exclusive. They intended to cover all the relevant cases and made a good-faith effort, but their arguments were too simple to explain all the facts. Mine starts with an apologia for why a very, very simple model might actually be sufficient. (And not to be snarky, but I think Toynbee and Spengler both stand up quite well as scholars and historians in comparison with Rand's "Attila and the Witch Doctor" essay.)

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The data for China that I used are (years duration first, then name)

628 Three August Ones and the Five Emperors

470 Xia Dynasty

554 Shang Dynasty

275 Western Zhou Dynasty

514 Eastern Zhou Dynasty

246 Spring and Autumn Period*

254 Warring States Period*

15 Qin Dynasty

215 Western Han Dynasty

16 Xin Dynasty

195 Eastern Han Dynasty

45 Three Kingdoms

52 Western Jin Dynasty

103 Eastern Jin Dynasty

161 Southern and Northern Dynasties

37 Sui Dynasty

289 Tang Dynasty

53 Five Dynasties and Ten Kingdoms

167 Northern Song Dynasty

152 Southern Song Dynasty

209 Liao Dynasty

119 Jin Dynasty

97 Yuan Dynasty

276 Ming Dynasty

1 Shun Dynasty

267 Qing Dynasty

4 Empire of China

First of all, you include on the one hand the Liao and the Jin dynasties and on the other the two Song dynasties, even though they coexisted. (The Liao was a state ruling the north China plain and vast stretches of the steppes founded by the Khitans, an early Mongolic people; the Jin was founded by the ancestors of the Manchus after they revolted against the Liao. The two Song dynasties were their native rivals in the south.)

Second, there's no cause to include the Shun or the supposed "empire of China," and in any case the period given for the latter is dubious. The first was founded after the death of the last Ming emperor by a rebel peasant leader who captured Beijing (amid other powerful figures in the rest of China) in April 1644; his forces were defeated a month later by the Manchus, and his supposed dynasty was just a claim to the throne and a name. The duration of a year given in that list refers to his lifespan after April 1644, not to any period of effective rule. The second was founded by the first president of the Republic of China, Yuan Shikai, who served an elected term of 4 years, 1912-1916. In December 1915 he decided to reestablish the monarchy and declared himself emperor; the empire was abolished three months later and far from ruling any part of China effectively, it greatly sped the collapse of the republic into a congeries of domains of competing warlords (a period that lasted until Chiang Kai-Shek's Northern Campaign of 1926). So that figure you have of 4 years confounds his republican term of office and his three months of failed empire-building. In both cases they are historical curiosities that for whatever reason (they do have some slight historical importance, but not of the same degree as the Tang and Song) Wikipedia included out of a whole constellation of earlier futile and abortive bids for power that they ignored.

Third, you include several periods of disorder and disunity as single units: The Three Kingdoms period after the end of the Later Han (the terms Former Han and Later Han are probably more mainstream than the geographical designations, but both are common enough currency, both in Chinese and Western scholarship), the Jin dynasty (which ruled only the northern part of China; the rest of China was divided among the so-called "16 Kingdoms," a period lasting from 304-439, and thus overlapping with the following period), the period of the Southern and Northern dynasties, when again China was divided into more than one state, and the period of the Five Dynasties and Ten Kingdoms after the collapse of the Tang. By lumping these all together, you follow a native tradition common in Confucian historiography (which means pretty much any Chinese history written in the imperial period, but identifies the intellectual source of the tendency) to disregard from consideration all dynasties that were not decided on whatever grounds (usually sheer success) to have received the Mandate of Heaven. Those periods were ones in which no agreement was reached on whether the Mandate had been passed down at all or simply withheld by Heaven, and thus much complexity is written off by using a simple canonical list. (Though even here the list is not canonical: The Shun certainly was not canonical, and by no means was Yuan Shikai's empire.)

On the other hand, when the Mongols established the Yuan dynasty, their political program, such as it was, put them forward as successors to both the Chinese native dynasties and the empires of the steppes, and as a result the Confucians who wrote history for the Yuan wrote dynastic histories of both Song dynasties as well as the Liao and the Jin; had the Mongols not conquered the south of China, it is doubtful the successor of the Southern Song would have commissioned histories of the Liao and Jin. More generally, the choice of whether a dynasty was canonical or not was determined partly by the political circumstances of its successor, for the successor would in imperial Chinese political tradition have the obligation to compile a history (actually more of an encyclopedia of governance and administrators with lots of added almanacs) of its predecessor; after a period of disunion, the state that unified China (or at least part of China) could pick and choose favorites in the past with some freedom.

Similarly, your figures are based on the view of the Former Han dynasty starting in 206 BC, but in fact the Qin dynasty was overthrown by a number of local rulers, and the one who declared himself supreme, Xiang Yu, ruled from 206-202 BC, before he was finally killed by the ruler of the Former Han, his former vassal. Since this was before the full-fledged intellectual dominance of Confucianism (which pretty much established its dominance in governance and political thought with the eclectic syncretism of Dong Zhongshu around the middle of the Former Han), it was the historical writings and schema of Sima Qian that set the date of 206 BC as the founding of the Former Han and the end of the Qin. (His biography of Xiang Yu is well worth reading, by the way, well-written, well-drawn, and wonderfully dramatic.)

Fourth, while you include the Xin dynasty that overthrew the Former Han, your list leaves out many other cases of effective usurpation that simply weren't treated as canonical by later scholars. For example, Wu Zetian (Empress Wu) established what she called the Zhou dynasty (same character as the Zhou dynasty beloved of the Confucians) from 690 to 705; it ruled China effectively and was not ended by strife--Empress Wu abdicated due to illness and handed the govrnment over to a son, who reestablished the Tang dynasty. In essentials her dynasty was almost the same as the Xin dynasty, except that the founder of that dynasty (a son of a Former Han empress) was killed by an army of peasant rebels and the Han reestablished by the descendants of the emperors of the Former Han; whether you view the Hans and the Tang in either case as one long dynasty or two small dynasties separated by a short usurping dynasty is a matter of debate and in the list you use is something that was decided purely and simply by the political needs of the victor over the usurper.

Fifth, the actual dates of each dynasty used by Wikipedia are somewhat arbitrary. Their article on Chinese dynasties includes one example: The Qing unified much of Manchuria by 1599 and took all the measures necessary to make a successful bid for traditional dynastic power by 1616; they established the Qing dynasty as such in 1636 when they gained rule over the Inner Mongolian tribes and received the imperial seal of Chinggis Khan; they captured Beijing in 1644; they defeated the last Ming pretender in 1662; but they also had to fend off a massive revolt in the period 1674-81 (the Revolt of the Three Feudatories). Which date do you choose? Similarly, the Mongols defeated the Jin and declared war on the Southern Song in 1234; they effectively (well, effectively by their lights, but they had quite different views of governance than the Chinese, so a Chinese view would be "effectively and cruelly") ruled much of north China from 1215, but it was only because Khubilai Khan had been trained by Confucian scholars as a young man that he saw the need to declare himself emperor in the Chinese tradition in 1271, and only in 1279 defeated the Southern Song and took control of all of historical China. So why 1271 in his case (the year he declared the dynasty) but 1644 for the Qing (the year they captured the rival capital)?

Sixth, this list of dynasties covers a long period in which there was massive systematic change in the very character of Chinese society and political thought, as well as extensive geographical expansion; it's not geography or social structure or political structure but ethnic continuity that determines what you have chosen to compare as like to like. (For example, historically China was situated on the North China Plain around the Yellow River, and the Chinese still revere this as the cradle of Chinese civilization; when that area was ruled by non-Chinese dynasties after about 300 AD, Chinese literati in the south mourned themselves as exiles in their own homeland--they lived under native dynasties but what they saw as their true homeland was under alien rule. A similar situation held in the Southern Song.) Similarly with the social structure: The Shang and Zhou were feudal states; the emperor enfeoffed each local ruler in a ceremony in which (at least under the Zhou) he handed his vassal a handful of earth from the territory in which he established him. As a result, the emperor had an important political role as the figurehead who legitimized the power of the local ruler, regardless of his degree of political power in the imperial realm--this is why the end of real imperial power by the end of the Spring and Autumn period didn't lead to the end of the dynasty. Had it been expedient to do so, the Zhou would have been deposed. In terms of real political power rather than polite fictions, the Warring States period was a period of competition and disorder like the Three Kingdoms and other such periods, and note that while the Zhou dynasty was recognized, actual political power was vested in the title of Hegemon (ba in Chinese), which was the title that all rulers until towards the end of the Warring States period strove for--it's quite analogous to the Japanese case, in which effective imperial power ended in 1092 with the establishment of the Kamakura Shogunate, but because of Japanese political ideals the emperors could not be deposed even if they were purely ornamental throughout much of Japanese history.

The Qin on the other hand represented the culmination of the bureaucratizing trends in all of the individual states of the Warring States period, during which the aristocracy exterminated itself en masse as a group or class and power and administration turned increasingly from the personal to the bureaucratic (whenever a state fell, its victor enslaved much of the leading nobility and made the rest commoners; at the same time, Confucianism was spreading as the ideology of the commoners who staffed the administration, and their political views were for a fully bureaucratic, rigidly moral administration in the service of a legitimate ruler); however, the mixed feudal system of the later Warring States period did not die out immediately; significantly, Xiang Yu took the title of "Hegemon-King" (bawang) and the other rulers as kings (wang), such as the founder of the Han dynasty as King of Han (a state around the Han River, hence the name of his dynasty), precisely the political system of the Warring States and thus a repudiation of the Qin system; and while the Han kept the less objectionable features of Qin bureaucratism, they still found it necessary to enfeoff a number of powerful local figures as princes who revolted throughout the Former Han dynasty. (It was that process that finally killed off the remnants of the Warring States political tendencies.) Of course, bureaucrtization continued to develop throughout Chinese history (selection of officials by examination rather than personal recommendation by a patron and birth into an aristocratic family was not established for much of the administration until the Tang dynasty, and selection by examination as the sole source of officials until some time in the Northern Song, I believe, and it was only after that time that an ideology of personal advancement purely by merit and scholarship regardless of the circumstances of birth spread throughout society and showed up strongly in literature), but there was a sea change between the Zhou and the Tang that makes treating them as part of one long history but the dynasties of France or Italy as distinct from the Roman Empire essentially arbitrary. There is a great difference between a feudal monarchy and an absolute monarchy heading a bureaucratic administration--at least as great as the difference between the latter and a modern republic. To focus on monarchy to the exclusion of all other political factors is a drastic oversimplification that by its very nature lumps together many dissimilar regimes that should be treated separately.

Finally, very little is known about the actual history of the Shang dynasty; the Confucians revered the Shang and in lieu of actual detailed information about it treated it with a simple schema of dynastic establishment and decline. It is unclear that it was actually one unified dynasty with effective rule throughout that period, nor do we know the details of whatever political fictions might have been erected to give a gloss to the machinations of political actors behind the scenes or to give legitimacy to fundamentally new institutions, actors, or families. If we restricted ourselves to the same level of detail for the rest of Chinese history, the Eastern and Western Zhou would have to be treated as one single dynasty, as would the Former and Later Han and the Northern and Southern Song; the Jin and Liao would have to be excluded entirely, and the Three Kingdoms period and the following period of disorder probably lumped in with the Han and the Tang, respectively; the Sui and Qin would probably disappear (they were usurpers whose innovations, which were pretty extensive, were picked and chosen among by their successors), and the Yuan would as well, most likely. So no, I don't think it valid to include the Shang; it's simply incomparable in the amount of actual hard facts to the rest of Chinese history. (And I've already stated my objections to including the first two that you ilist above--tell me, do you include Adam and Methuselah in your king lists somewhaere? If not, then you should exclude those two periods as well without the slightest qualms.)

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I wrote a lengthier reply earlier that I tried to post just as the power went out, so it's lost. While not as fleshed out with examples, at least I hope this version gains in clarity from concision.

I agree with these concerns, broadly speaking, but I don't regard them as a conclusive argument against including the data. On the level of analyzing individual rulers, I won't use semi-legendary figures who live 400 years; but given some circumstantial evidence I will accept a dynasty whose precise sequence of rulers is unclear or disputed as nonetheless having governed for X years in total. I see your concern about pre-literate societies but then we have to ask, if they had no records and could not themselves determine who had ruled in the past, does the concept of a "dynasty" even apply? Part of the basic idea of a dynasty is that it establishes the legitimacy of successive rulers by demonstrating their connection to the past. At the point where records do not exist, any argument about the stability of multi-generation rule starts to become moot.

No, institutions of headship or chieftainship involving lineages over several generations are well-nigh universal whenever we look at non-literate societies. The Samoans, for example, had well-developed kingships and aristocratic societies with well-defied lineages despite not being able to write, as did the Hawaiians, the Bedouins of Arabia, the Salishan peoples of the Pacific Northwest, and on and on and on. It is clear that such societies kept track of their history through oral transmission, and while the details were unclear and fluid, the very fact that their rules had lineages was apparently universal. And when the great powers have had dealings with any part of the world peopled by other societies, we know from their records that they encountered states with ruling lineages, if only in the fact that those rulers paid them tribute in submission recorded in their monuments; these states could be quite large and powerful, as with the various steppe empires neighboring China. And remember: The Iliad and Odyssey themselves were preserved for centuries by oral transmission; oral transmission is not as reliable as writing, but it’s hardly just to conclude, as you do, that without writing these people had no sense of the past or of their neighbors and thus their states cannot be counted as dynasties.

In any case, we again run into a basic methodological problem with your entire approach: What do you mean by “dynasty” anyway? We know these dynasties you do recognize were surrounded by states with lineages of rulers; we can also be fairly sure that these latter were shorter-lived than your dynasties on average. You exclude them for reasons you haven’t fleshed out, but until you support such a distinction, all you have done is sidestepped the fact that your methodology quite clearly introduces systematic biases towards longer average durations in the earliest periods (before 500 BC), biases that moreover are very great because so few dynasties of medium or short length would be expected to be recorded.

I agree the early record may indeed be biased toward longer-lived dynasties, and that short-lived dynasties that did keep written records might have been overlooked. But to use this argument to exclude data items kind of begs the question. We're trying to discover what gives a society stability. If stability goes down as the size and complexity of a social system goes up, for example, then small kingdoms not in the historical record might actually have supported longer-lived dynasties. Obviously, we don't know, and I won't rule data in or out based on speculation.

First of all, you’ve made a basic assumption, bolded above, that needs a great deal of argument: That what gives a society stability is one and the same thing for all societies at all times and places with any social structure, political institutions, technical achievements, or economic systems, as if exactly the same factors make a skyscraper and a tent stable in the same degree. However, feudal monarchies and bureaucratic monarchies are very different, as are sedentary and nomadic societies, agricultural and herding societies, and industrial and pre-industrial societies, and it is a dubious enterprise to lump them all together in periods when one or another form of social, political, or economic organization is spreading at the expense of others.

Yes and no. I considered throwing out everything after the start of the Industrial Revolution, for example, but I found it again begs the question. New dynasties formed after 1800 had lifespans averaging only a few decades. Existing dynasties made it through the century intact only to die in the Great War, or World War II. So under the pressure of republicanism, expanding literacy, steam power, capitalism, what have you, the early dynasties still behave differently from the late ones within that span of time. That's what we're testing for, so no data gets thrown out.

So instead of throwing out data from fundamentally dissimilar cases you practice the equally egregious error in the other direction of lumping them all in together.

Well, at this point you've thrown out roughly a third of my data, focusing on the extremes on either end, and yet there's still a downward trend. I agree that even after 1000 AD the list isn't complete, but again I'm reluctant to speculate about the statistical character of dynasties we know nothing about, and that may not even have existed. (Just for example, we now know that New Guinea supported a large population over the past several thousand years. There were enormous numbers of people living in the interior of the island that early 20th century explorers simply missed. But when first contacted, these previously unknown peoples didn't have large-scale political systems, or dynastic rule, or even written language. It seems unlikely that they had these things in the past, and lost them.)

Ah, but we know that other states did exist, and some were quite large and powerful without leaving records of their own. We also know of others by name that did have contemporary records, but these have been lost--the Greek kingdom of Bactria, for example, from which only coins, archeological remains, and brief, ever so brief mentions by later Greek historians survive. Similarly, the Toba Wei (who established the Jin states in north China) might have possessed writing, but no trace of it has survived. And there are many other examples, such as the Hephthalites of Central Asia, the southern Arabian kingdoms before Islam (much of what we know about them is due to their importance to the struggle between Rome and Persia).

I agree that apart from the Old and New Worlds prior to 1492, dynasties were never absolutely independent of one another, but I think the idea that the trend can be explained by them competing for territory is kind of vague. I wouldn't say China was seriously competing with Spain at any point in their histories, for example. The Silk Road trade no doubt allowed East to influence West and vice versa, but it hardly seems like a determining factor in regime stability.

So what? That entirely misses the point. Spain and France competed bitterly in that period against each other and against Britain, Austria, and their neighbors, and in so doing they gobbled up many shorter-lived neighboring states and put ends to their dynasties. You lump this process of consolidation in with the co-existence with little mutual influence of Spain and China on opposite ends of the same landmass, which is dump oranges in the apple bin and sell them all as Granny Smiths.

And anyway, merely being able to come up with an alternative hypothesis for why there is a decline trend doesn't show mine is unsound.

Ah, but "merely being able to come up with an alternative hypothesis" is an uncharitable description of what I've done. I'm pointing out alternative factors we know existed and pretty clearly were in play but that you ignore, and whose exclusion introduces systematic extensive bias towards your conclusion. It doesn't deal your case a fatal blow, but it does constitute a major body blow against the reliability and completeness of your data.

I'm aware of the complexity of the story, and the problems with the quality of the data. However, the whole point of a maximum entropy curve is that it allows estimates to be made of the trend or the range of outcomes without knowing the details of how the system works. The data are sufficiently good to perceive that kind of simple trend (and sadly, as I observed, if kingship lists aren't good enough as data, then almost nothing from ancient history is).

You have to ask, good enough data for what? For the dynasties for which they survive, yes, but as representative of the experience of the rest of human societies at the time, hardly. They introduce systematic biases that you rely on as model cases of the processes you claim to detect.

Toynbee makes a good point of comparison, as does Spengler. I don't think it's fair to say either man "cherry-picked" his data, just as I don't think that that complaint is true of me. If you want to accuse them of something, or me, I think a better charge would be overly broad generalization -- a theory that is excessively inclusive rather than exclusive.

Which entails something akin to unconscious cherry-picking. If a historical schema is over-inclusive, then to support it in argument you have to disregard lots of contradictory data, which Toynbee and Spengler most certainly did--and what would their criteria have been? That the contradictory data was unimpressive. Unimpressive why? Because it didn’t fit the program. You can call it something besides cherry-picking if you like; in any case, it’s the sort of error that historians are trained from their earliest years of study to recognize and avoid, and thus strikes historian critics of Toynbee and Spengler as basic errors of the crudest sort.

They intended to cover all the relevant cases and made a good-faith effort, but their arguments were too simple to explain all the facts. Mine starts with an apologia for why a very, very simple model might actually be sufficient. (And not to be snarky, but I think Toynbee and Spengler both stand up quite well as scholars and historians in comparison with Rand's "Attila and the Witch Doctor" essay.)

“John has more moral failings than Bill” is hardly a shining encomium, and “John has more moral failings than Bill, so Bill deserves respect” is fallacious. In any case, I think Ayn Rand’s emphasis on basic philosophical positions much more convincing than Toynbee’s Christian apologetics or Spengler’s etatist pessimism.

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First, let me say I'm excited to be talking with a serious historian (or history buff) about this, and thank you for commenting. If my thesis seems naive and presumptuous and annoying, well, perhaps it is all of those things. I started by saying it was preposterous, and I'm not going to flinch if people are skeptical.

I'm not a professional historian, I'm a linguist. You don't need historical training to treat such issues, just determination, curiosity, and time.

To get a positive curve I have to start with the Qin, which basically throws out everything in Chinese history prior to 221 BC.

So starting with the Qin you start getting positive trends even with your method: Hardly ringing evidence for a universal trend towards decay!

Again, I'm not averse to doing the analysis independently of Wikipedia or some neutral source, assembling a custom data set. But coming from someone who is not a professional historian, I think the cries of "cherry picking" if I did it that way would be all the louder.

It's a question of how reliable you yourself to know your data to be. Otherwise you're just picking cherries some boss has laid out a path for you to pick along.

Now, in regard to your first question, I use rank number versus cumulative years to get average duration, and plot the decline in average duration. Why do the calculation based on the cumulative curve? Because the theory says that the pattern depends on increasing set size, or rank. We can certainly do it other ways and still get a decline -- as you did when you fitted a linear estimate to my table and got the downward trend of about 1.5 years lost per additional dynasty. But if you think the cause is entropy, then you want above all to see what the pattern looks like in a cumulative plot. That allows me to compare apples to apples when I look at disparate data types.

But the question is how to prove this to someone like me skeptical of your claim about entropy. (And technically, I fitted a power law to your data, though by the quickest method I could, so the details doubtless differ.) The very first step of using cumulative data introduces a bias towards the earlier data that I pointed out renders your method nugatory since it gaves negative trends for reversed time series as well in certain circumstances.

However, that also creates a strong auto-correlation effect. The scores for a cumulative plot are always good if the slope is even slightly downward. So if I were to cite correlation scores for the graphs the reader actually sees, it would be meaningless and misleading.

If used for comparison of alternate methods, no, they're useful.

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