Test




Term Duration may refer to the historic models of collapse of empires.
Here, Duration \(X\) is time between the two events:
A. Some empire at the level of Federal Law abolishes, nullifies the separation of powers
B. The empire collapses
Historic cases of nulling of separation of powers are related with historic personages shown in pictures at right.
Dates of these cases and dates of the following collapse by documents
[7][8][9][10][11][12][13][14][15][16][17]
are collected in the table below:
\(i\) | country | nulling | collapse | days | \(~ X_i\) , y. | refs |
1 | England of Cromwell | 1653.12.16 | 1661.04.23 | 2685 | 07.3513 | [7][8] |
2 | France de Napoléon | 1802.08.04 | 1815.11.20 | 4856 | 13.2953 | [9][10] |
3 | Italia di Mussolini | 1928.05.17 | 1947.12.27 | 7163 | 19.6116 | [11][12] |
4 | Germany of Hitler | 1933.03.24 | 1945.05.08 | 4428 | 12.1235 | [13][14] |
5 | Soviet Union | 1977.10.07 | 1991.08.20 | 5065 | 13.8675 | [15][16] |
6 | RF of putin | 2020.03.11 | 2028-2042 | 3k-7k | 8 - 22 | [17][not yet] |
The first 5 rows of this table are used to estimate parameters of three historic models described below.
The 6th row allows the forecast for century 21 and testing the models.
Introduction
This article deals with forecasts. We try to interpret them in a scientific way.
The first documented historic forecasts appear in the Bible[18]. The Great Flood, the destruction of Sodom and Gomorrah, and other divine predictions also appear in the early scripture. These stories represent not only moral or theological lessons but some of the earliest narrative models of large-scale societal collapse initiated by the corruption, lawlessness.
Historically, forecasts like these are presented without revealing any reasoning behind them. The tradition is to hide the method of generation from the readers. Even when one listens carefully to a forecast by a political analyst, one cannot reconstruct the basic assumptions used to build the model, nor can one reproduce the deduction by which the prediction is derived.
The most serious forecasts of the 20th and 21st centuries (from the point of view of the Editor) include:
- Will the Soviet Union Survive until 1984 (Просуществует ли Советский Союз до 1984 года) by Andrei Amalrik
[19] (1969)
- Moscow2042 («Москва2042») by Vladimir Voinovich
[20] (1986, Войнович Владимир Николаевич. Москва2042)
- Russia2028 by Semen Skrepetski ( Россия2028 by Скрепецкий Семён)[21] (2019).
Even in these notable examples, the deduction is hidden from the reader.
More historic predictions are listed in article «предсказания революций» (in Russian). Most of them turned out to be wrong.
Generally, forecasts in historical or political contexts are not treated as scientific concepts by academic historians, because they do not offer historic models that could be verified or refuted.
On the other hand, Editor considers History to be a science. Any science must present concepts that can be verified or rejected by future observation. This follows from the Third of the TORI axioms.
This version of the article presents two such models. Both are based on published historical documents whose authenticity is not in doubt. The data and calculation methods are fully transparent, allowing any colleague to independently reproduce the results.
Both the models below relate the separation of powers (that seems to be important achievement of the Human civilization) and collapse of those empires that exclude this achievement at the level of the Federal Law. Namely with time (Duration) between these two events in each case.
Historically, the principle of separation of powers has often led to the establishment of stable, prosperous democratic states.
Conversely, many empires have collapsed due to war, internal coups, or revolutions. Some revolutions give rise to long-lasting dictatorships - often under the facade of democracy.
There are also examples of relatively stable honest monarchies that do not pretend to be republic, but persist for centuries.
But cases in which a formally democratic state, by Federal Law, explicitly nullifies the separation of powers are rare. Only six such cases are noted (see Table near the top of this article). So far, there is no known case where the state, "republic" continued more than 20 years after such a nulling.
In this article, we use the term «nulling» («nullification»).
The term is borrowed from Russian word «обнуление»[22][23][24] that appears mainly during the 2020 constitutional amendments.
No other appropriate English equivalent to refer this phenomenon is found;
so, we apply this term retroactively to earlier historical events where similar legal mechanisms were used to consolidate the authority.
Here, term «nulling» denotes a formal or quasi-legal process
by which a governing regime deliberately
disables or cancels key institutional constraints - typically those related to the separation of powers and/or democratic oversight, providing the lifetime ruling of the current dictator.
Unlike a military coup,
nulling often occurs via legislative acts,
constitutional amendments, or official decrees -
preserving an appearance of legality
while consolidating authoritarian control.
It is frequently a
symptom of administrative weakness,
where the regime seeks to stabilize itself by eliminating internal checks.
This article attempts to generalize the observation mentioned (the nulling is followed by the collapse of the country) into a scientific model. Two such models are constructed to describe the observed values of Duration. Thery deal with the first 5 examples in the table above. This predetermines the title of the article: Duration, analyzed with 5 historic examples. The sixth example is still ongoing and may serve as a test: it may confirm or refute the model(s).
Model First (linear time scale)
The first model is based I the following postulate:
Durations for all human civilizations, societies are distributed independently and have the same Gassian (normal) distribution with some mean value \(X_0\) and some width \(\sigma_0\).
We have no ab initio model for the collapses of an empire the pretends to be democratic; so, we do not know values \(X_0\) nor that of \(\sigma_0\). I try go get as much as possible from the empyrics.
We nave \(N\!=\!5\) completed cases in the Table 1. From the first 5 rows of the Table, I estimate the following quantities:
the sample mean \[ t=\tilde X = \frac{1}{N} \sum_{i=1}^N X_i \approx 13.249838 ~ ~\rm [years] \]
The sample spread \[ s = \sqrt{ \frac{1}{N\!-\!1} \sum_{i=1}^N \left(X_i-\tilde X\right)^2 } \approx 4.385140 ~ ~ \rm [years] \]
Scale for the Student distribution as the likelihood density for the sample mean \[ c = \frac{s}{\sqrt{N}} =\sqrt{ \frac{1}{N(N\!-\!1)} \sum_{i=1}^N \left(X_i-\tilde X\right)^2 } \approx 1.961094 ~ ~ \rm [years] \]
I keep 6 decimal figures after a decimal point in order to simplify the tracing of my calculus; everyone performing the same calculus is supposed to get the same values. However, only first two digits in these estimates may have some predictive meaning.
Here I measure time in years. As a reminder, these units are indicated in rectangular parenthesis at each formula when the value suggested have sense of time.
For the sample with \(N\) cases, the likelihood density \(f(t)\) for \(X_0\) to have value \(t\) is expressed through the Student Distribution with \(N\!-\!1\) degree of freedom:
\[ f(x)= \frac{1}{c} \mathrm{Student}_{N-1}\!\left( \frac{x-\tilde X}{c} \right) \]
This function is shown in figure below with red curve.
The five blue bars show the 5 observed values \(X\) of the Duration.
The two yellow bars show the values for the RF (Moscovia of century 21)
taken from the sci-fi
[20][21].
These "yellow" values are not taken into account at the calculus; but they shows what would the artists expect for the 6ht row of the table above - as soon as the case will be completed.
The blue curve refers to the similar distribution \(g\) for the next measurement \(X_{N+1}\)
under condition that the first \(N\) values are already observed;
\[
\displaystyle
g(x)= \frac{1}{c_1} \mathrm{Student}_{N-1}\!\left(
\frac{x-\tilde X}{c_1}
\right)
\]
Here parameter \[ c_1 = s \sqrt{ 1+1/N} \approx 4.8037 ~ \rm[years] \] determines the scale of the distribution.
Under condition, that the first \(N\) quantities \(X\) have given values, the probability \(p_{\rm mean}(A,B)\) that the interval \((A,B)\) includes value \(X_0\) is expressed through the likelihood density \(f\); the similar relation refers to the probability \(p_{\rm next}(A,B)\) that the interval \((A,B)\) includes value \(X_{N+1}\) that is not yet measured: \[ p_{\rm mean}(A,B)=\int_A^B f(x) \ \mathrm d x ~ ~ , ~ ~ ~ p_{\rm next}(A,B)=\int_A^B g(x) \ \mathrm d x \]
For distribution densities \(f\) and \(g\), the spread, ("standard error") appear as
\[ v=\sqrt{\int_{-\infty}^{\infty} f(x) \ (x-\tilde X)^2 \ \mathrm d x } ~ ~, ~ ~ w=\sqrt{\int_{-\infty}^{\infty} g(x) \ (x-\tilde X)^2 \ \mathrm d x } \]
Usually it is denoted with letter \(\sigma\), but we deal with several spreads; so, we need a specific letter for each of the spreads.
Case of \(N\) observations refers to function \(\mathrm{Student}_{N-1}\). For this function, the spread is
\( \displaystyle \mathrm{Spread}_N=\sqrt{\int_{-\infty}^{\infty} \mathrm{Student}_{N-1}(x)\ x^2 \ \mathrm d x } = \sqrt{\frac{N-1}{N-3}} \)
The mean-square deviation \(v\) of estimate \(\tilde X\) from the "true" historic constant \(X_0\) appears as follows:
\[ v=c \sqrt{\mathrm{Dispersion}_N} = c \sqrt{\frac{N-1}{N-3}} = \sqrt{ \frac{1}{N(N\!-\!3)} \sum_{i=1}^N \left(X_i-\tilde X\right)^2 ~} \approx 2.773406 ~ \rm [years] \]
\[ w=c_1 \sqrt{\mathrm{Dispersion}_N} = c_1 \sqrt{\frac{N-1}{N-3}} = \sqrt{ \frac{N+1}{N(N\!-\!3)} \sum_{i=1}^N \left(X_i-\tilde X\right)^2 ~} \approx 6.793429 ~ \rm [years] \]
The formulas shows why the deal with only 3 historic cases would not be sufficient to estimate the standard error of sample mean \(\tilde X\), id est, the deviation from the "true value" \(X_0\).
In our case, roughly, the estimate \(\tilde X\) may deviate from the "true value" \(X_0\) for a quantity of order of 3 years. The nest measirement \(\tilde X_{N+1}\) is expected to deviate from the estimate \(\tilde X\) for a quantity of order of 7 years.
The likelihood densities distributions \(f\) and \(g\) for these quantities is expressed through the Student Distribution with \(N\!-\!1\) degrees of freedom.
Note, that the estimate \(w\) for the uncertainty of the next measurement happens to be significantly bigger, that naive estimate \[ \sqrt{c^2+s^2} \approx 4.803680 ~ ~ \rm [years] \] for the uncertainty of sum of two independent normally distributed quantities with uncertainties \(s\) and \(c\). This estimate seems to be not correct.
Various naive estimates similar to that above are wifely used by the specialists. The common confusion with mistaken estimates of the uncertainties is mentioned by several authors [25][26][27][28][29][30].
Model Second
Model Second is based on the following postulate:
Binary logarithms of Durations measured in years for all human civilizations, societies are distributed independently and have the same Gassian (normal) distribution with some mean value \(L_0\) and some width \(\ell_0\).
Whitin this model, we have \(N\) measurements \(L_i=\log_2(X_i)\) and these logarithms are independent random quantities distributed with the same parameters \(L_0\) and \(\ell_0\).
From these values, I try to estimate \(L_0\), \(\ell_0\) and plot
the likelihood distribution density \(F\) for the estimate \(T=\tilde L\) and
the likelihood distribution density \(G\) for next measurement \(L_{N+1}=\log_2(X_{N+1})\) and
the likelihood distribution density \(h(x)=\frac{G(\log_2(x))}{x \ \ln(2)}\) for the next measurement \(X_{N+1}=\exp_2(L_{N+1})\).
For this model, denoting various estimates, I use capital Latin letters, to avoid confusion with analogous parameters of Model First denoted with the lowercase letters.
I calculate the sample mean value \[ T=\tilde L=\frac{1}{N} \sum_{i=1}^N L_i \approx 3.659569 \] This mean value corresponds to duration \[ \exp_2(T)≈12.636885 \approx 12.636885 ~ \rm[years] \] This quantity appears as mean geometric value of \(N\) observed values of Duration. As expected, the mean geometric happens to slightly less than the mean arithmetic, id est, the sample mean.
Continue the similar calculations, as in Model First, I evaluate the sample variance \[ S=\sqrt{\frac{1}{N-1} \sum_{i=1}^N (L_i-T)^2\ } \approx 0.509859 \] and the scale \(C\) for the Student distribution of the sample mean \[ C=\frac{S}{\sqrt{N}}=\sqrt{\frac{1}{(N\!-\!1)N} \sum_{i=1}^N (L_i-T)^2\ } \approx 0.228016 \]
Now I express the likelihood distribution density \(F(L)\) for the mean value \(L_0\) to have value \(L\):
\[
F(L)=\frac{1}{C}\ \mathrm{Student}_{N-1}\!\left(\frac{L-T}{C}\right)
\]
This function is shown with red curve in the figure:
The blue bars show the 5 observed values of the logarithm, id est, \(L_i=\log_2(X_i)\).
The yellow bars show the two values from sci-fi (that are not taken into account at the computation).
The blue curve shows the likelihood density function \(G(L)\) for the logarithm \(L_{N+1}\) of the next measurement to gets value \(L\), under condition that previous \(N\) measurements gave values \(L_i\)): \[ G(L)=\frac{1}{C_1}\ \mathrm{Student}_{N-1}\!\left(\frac{L-T}{C_1}\right) \]
In analogy with Model First, the parameter \(C_1\) is estimated as follows: \[ C_1=S\ \sqrt{1+1/N} \approx 0.558522 \]
In the similar way I evaluate the spread for the sample mean and the spread \(V\) the sample mean \[ V=\sqrt{\int_{-\infty}^{\infty} F(L) \ (L-T)^2 \ \mathrm d L\ } =\sqrt{ \frac{N\!-\!1}{N\!-\!3}\ } \ C \approx 0.322463 \] and the spread for the estimate \(T\!=\!\tilde L\) for the next value: \[ W=\sqrt{\int_{-\infty}^{\infty} G(L) \ (L-T)^2 \ \mathrm d L\ } =\sqrt{ \frac{N\!-\!1}{N\!-\!3}\ } \ C_1 \approx 0.789870 \]
As in the Model First, this spread is bigger than the naive estimate \[ \sqrt{C^2+S^2} \approx 0.558522 \]
Finally, I evaluate the sigma interval for the next value of L: \[ T \pm W \approx 10.105761,15.801964 \] and for the next value \(X_{N+1}\) in this model: \[ \exp_2(T \pm W) \approx 7.309128 , 21.848142 ~ \rm [years] \]
These are values that are supposed to be compared with the next measurement - perhaps, as soon as the row 6 in the First Table be completed.
Model Third
The two models above show that the mean value of Duration is similar to its spread. This provokes the seduction to suggest even simpler model with single adjusting parameter (mean value) instead of two (mean value and the spread). Such a model is considered in this section.
Assume, that in our era, any prosper and/or powerful country has 5 relatively independent branches of power,
5 basic institurions:
1. Legislative (making and modifying the the Laws, parliament)
2. Executive (government, President, prefectures, police, army)
3. Judical (Courts, judges)
4. Informative (TV, internet, radio, newspapers)
5. Religious (religious communities, Churches, Synagogues, Mosques, etc.)
Assume, the usurper and his accomplices dismount the institutions mentioned, replace them with the imitations, one by one; and fall of each of them appears as the exponential decay. This leads to the model with the cascade of exponential decays.
Assume that all the decay rates per each institution mentioned are equal. (Anyway, we have no way to estimate decay rate of each institution having only 5 mrasurements.)
The assumptions above lead to the model with single parameter. The probability distribution density appears as Gamma Distribution with \(\alpha=5\) degrees of freedom. Hope, the number of degrees of freedom \(\alpha=5\) in this model will not be confused with number \(N=5\) of values of duration, available at the moment of preparation of this article.
The resulting probability density function \[\psi(x)=\mathrm{Gamma}(\alpha, \theta, x)= \frac{1}{\Gamma(\alpha) \ \theta^\alpha} \ x^{\alpha-1} \exp(-x/\theta) \]
Here, character \(\Gamma\) denotes the Gamma function; \(\Gamma(z)= \ \)Factorial\((z\!+\!1)= (z\!+\!1)!\)
For this distribution, the mean value \[ \int_0^{\infty} \psi(x) \ x \ \mathrm dx = \theta\alpha \]
As \(\alpha\) is already fixed, the native estimate for the second parameter is just \[ \theta=\tilde X/\alpha= t / 5 \approx 2.649968 ~ \rm[years] \] At least, such a choice reproduces the sample mean value.
The spread is estimated as follows: \[ \sqrt{ \int_0^{\infty} \psi(x) \ (x-t)^2 \ \mathrm dx } = \sqrt{\alpha}\theta = \frac{\tilde X}{\sqrt{\alpha}} = \frac{t}{\sqrt{\alpha}} \approx \frac{13.249838}{\sqrt{5}} \approx 5.925507 ~ \rm[years] \]
In this model, each branch of power lasts of order of 3 years before to fall allowing the next one also to fall, to collapse, to decay with the similar rate; each crime in the chain appears as a trigger of the next crime, until the collapse of the country. Similar mechanism scaled down to only few participants makes the plot of movie The Domino Principle 1977 [31].
While we do not know exact mean value \(X_0\), we have to interpret function \(\psi\) as an approximation, even within this model; so \(\psi\) appears as a likelihood density distribution. This function is compared to similar functions for the other two models (Model First and Model Second) in the next section.
Comparison
It may have sense to compare predictions of the 3 models above.
For this comparison, I express the likelihood density function \(h(x)\) for the next value \(X_{N+1}\) to get value \(x\) in Model Second: \[ h(x)=\frac{G\big(\log_2(x)\big)}{x \ \ln(2)} ~ \rm [years^{-1}] \]
This function is shown with the black curve in the figure below:
For comparison, the likelihood density \(g(x)\) for the next
value \(X_{N+1}\)
to have value \(x\) in the Model First is shown with blue line; it is the same curve as the blue curve in section about Model First; the only scale in the ordinate axis is a little bit stetted to show better curves.
The dark green curve represents likelihood density distribution for the next measurement in Model Third; it is scaled Gamma Distribution with 5 degrees of freedom; the scale is chosen to reproduce the sample mean \(\tilde X\).
The blue and yellow bars are repeated from the picture of section «Model First»;
so, I do not describe them again.
Finally, the estimates for the two models above are compared in the table below:
Quantity | Normal distribution of durations) | Normal distribution of the binary logarithms |
---|---|---|
Distribution | \( X \sim \mathcal{N}(X_0, \sigma_0^2) \) | \( L = \log_2 X \sim \mathcal{N}(L_0, \ell_0^2) \) |
mean; \(N\!=\!5\) | \(t=\frac{1}{N} \sum_{n=1}^N X_n\approx 13.249838\) [y.] | \(T=\frac{1}{N} \sum_{n=1}^N L_n\approx 3.659569\) \(\exp_2(T)\approx12.636885\) [y.] |
samle spread | \(s=\sqrt{\frac{1}{N-1} \sum_{n=1}^N (X_n-t)^2}\approx 4.385140\) [y.] | \(S=\sqrt{\frac{1}{N-1} \sum_{n=1}^N (L_n-T)^2}\approx 0.509859\) |
scale for Student | \(c=\sqrt{\frac{1}{(N-1)N} \sum_{n=1}^N (X_n\!-\!t)^2}\approx 1.961094\) [y.] | \(C=\sqrt{\frac{1}{(N-1)N} \sum_{n=1}^N (L_n\!-\!T)^2}\approx 0.228016\) |
Density for mean | \(f(x)=\frac{1}{c} \mathrm{Student}_{N-1}\!\left( \frac{x-t}{c}\right) \ ~ \) [y.\(^{-1}\)] | \(F(L)=\frac{1}{C} \mathrm{Student}_{N-1}\!\left( \frac{L-T}{C}\right)\) |
Spread for mean | \(v= \sqrt{ \int_{-\infty}^{\infty} f(x) ~ (x\!-\!t)^2 \ \mathrm d x \ }\) \( = \sqrt{\frac{N-1}{N-3}}\ c \approx 2.773406\ \) [y.] |
\(V= \sqrt{ \int_{-\infty}^{\infty} F(L) ~ (L\!-\!T)^2 \ \mathrm d L \ }\) \( = \sqrt{\frac{N-1}{N-3}}\ C \approx 0.322463\) |
scale for Next | \(c_1 = s \sqrt{1+1/N}\approx 4.803680\) [y.] | \(C_1 = S \sqrt{1+1/N}\approx 0.558522\) |
density for Next | \(g(x)=\frac{1}{c_1} \mathrm{Student}_{N-1}\!\left( \frac{x-t}{c_1}\right) \ ~ \) [y.\(^{-1}\)] | \(G(L)=\frac{1}{C_1} \mathrm{Student}_{N-1}\!\left( \frac{L-T}{C_1}\right)\) |
Spread for Next | \(w= \sqrt{ \int_{-\infty}^{\infty} g(x) ~ (x\!-\!t)^2 \ \mathrm d x \ }\) \( = \sqrt{\frac{N-1}{N-3}}\ c_1 \approx 6.793429\ \) [y.] |
\(W= \sqrt{ \int_{-\infty}^{\infty} G(L) ~ (L\!-\!T)^2 \ \mathrm d L \ }\) \( = \sqrt{\frac{N-1}{N-3}}\ C_1 \approx 0.789870\) |
Naive for next | \(\sqrt{s^2+c^2}\approx 4.803680 ~ \) [y.] | \(\sqrt{S^2+C^2}\approx 0.558522 \) |
sigma interval for mean | \(t\pm v\approx 10.476432, 16.023244 ~ \) [y.] | \(T\pm V\approx 3.337106, 3.982032 ~ \) \( \exp_2( T\pm V) \approx 10.105761, 15.801964 ~ \) [y.] |
sigma interval for next | \(t\pm w\approx 6.456409, 20.043267 ~ \) [y.] | \(T\pm W\approx 2.869699, 4.449439 ~ \) \( \exp_2( T\pm W) \approx 7.309128, 21.848142 ~ \) [y.] |
Model Third is not presented in the table. In model Third, the mean for the next value is the same as model First. The estimate of the spread (approx 5.925507) for the next value is also similar.
The table above is loaded also separately as Duraton5table2big; there it is supplied with the C++ generator. The same code generates also the three explicit plots above.
Discussion
The 3 models above suggest that after approximately 13 years since the Federal Law breaks the principle of separation of powers, the republic, the empire collapses and the administrative system has to be reinstalled. All the 3 models suggest, that duration of any country after such a nulling is of order of 13 years plus-minus 6 yers.
Several decimal digits are kept in the estimates above in order to simplify the tracing of calculations. Colleagues may repeat the calculus and get the same values. However, only the first two digits have some predictive sense.
The precision of the predictions is not too good. The error of the estimate of the duration for a next case happens to be comparable to its value.
Adding of new cases can enrich the statistics; improving the precision of the estimate \(\tilde X\) of some "true mean value" \(X_0\) within each of the models.
However, the precision of prediction of Duration for any new case is expected to remain of order of few years.
In such a way, we seem to reach the limit of the models.
The improvement of the precision of the forecast seem to require taking into account other parameters of an empire, that pretending to be a republic eliminates the Separation of powers. The phenomenological modeling could be performed if more cases are added to Table 1.
The prediction of Duration in the models suggested is not so high. Several digit are kept in the estimates in order to simplify the tracing of the calculus described.
Practically, the results of all the 3 models are similar. Since the elimination of Separation of powers, the state lasts from few years to a couple of tens of years.
The low precision is typical for primitive models.
The estimate for collapse of USSR by Andrei Alalrik [19] also happened to be not so precise; the relative error of the prediction happens to be or order its half. In 1969, Amalrik expected the USSR to collapse to year 1984 (1984-1969=15 [years]) while it collapsed, roughly, in 1991, id est, lasted 22 years (1991-1969=22 [years]) instead of 15 yeas.
Attempts of usurpation of power are observed in various epochs and in various countries. Stable democracies can resist it.
The attempt of American President to break the American Constitution and to serve the third Presidential term (see «CivilWar2024» and «TrumpForever») can be considered
[32][33]. Such a destruction of the Constitution can be interpreted as elimination of Separation of powers (cutting the three with at least 3 branches of power: Executive, Legislative, Judicial) as it is shown in the cartoon at right.
At the moment of preparation of this article,
no document is found to confirm the successful passing of such a project through the legislative system of the USA.
In sigh a way, yet, within the models considered, no certain prediction about the collapse of USA can be formulated.
However, if success of the project «TrumpForever» in the USA Congress and the USA Senate, the American case falls into the area of applicability of the models suggested and also can be used for the testing.
The same may refer to any other country. Up to my knowledge no such a model had been published preciously. The models above give a hint for construction and testing of other refutable historic models, based on various (and perhaps completely different from the above) observations. Upon the verification(s) with a posteriori observations, such a model(s) can be useful in the practical activity.
Conclusions
The ideology of construction of historical models is suggested.
The example is considered for Duration of the state since the federal law abandons the separation of powers, justifying the life-time dictatorship juridically.
Duration is defined as time between the two events:
1. The federal law of an empire eliminates the previously declared separation of powers.
2. The empire collapses, its political and administrative system is reinstalled.
For Duration, the 6 examples are mentioned in Table 1.
At the moment of loading of the article, the last, 6th case is not yet completed,
but it can be used for the future testing the models suggested.
The two models are considered
with the normal distribution of Duration and
with the normal distribution of logarithm of Duration.
Both the model give similar prediction for Duration; it is expected to be of order of 13 years.
The likelihood distribution density \(f(t)\) for the mean Duration \(X_0\) to have value \(x\) and
the likelihood distribution density \(F(L)\) for the mean binary logarithm of Duration \(L_0\) to have value \(L\)
are shown in the figures for these two models.
The likelihood density for the next valie \(X_{N+1}\) to have value \(x\) is plotted in the last figure for all the 3 models above.
In Model First, it is expressed with function \(g(x) ~ \rm [years^{-1}]\) through the Student Distribution.
In Model Second, it is expressed with function \(h(x)=\frac{G(\log_2(x))}{x\ \log(2)} ~ \rm [years^{-1}]\)
In Model Third, it is expressed with function \(\psi(x)=\mathrm{Gamma}(\alpha, \theta, x)= \frac{1}{\Gamma(\alpha) \ \theta^\alpha} \ x^{\alpha-1} \exp(-x/\theta)\) through the Gamma Distribution.
These functions allow the comparison with the future measurement(s).
All the 3 models give similar predictions about any country that at the level of the Federal Law abandons the principle of Separation of powers: the administrative system of such a country is expected to last approximately 11-13 years (roughly, from 6 to 22 years). According to these models, the putin's RF is expected to collapse between years 2026 and 2042. These estimates shows qualitative agreement with independent forecasts from the sci-fi (years 2028 and 2042).
Warning
Article Duration5 is loaded at TORI with scientific goals.
Politics and affection of decisions of powerful offees of any country is not element of the set of these goals.
The analysis above is not an attempt to influence policy of any country.
In the case of RF, after the nulling of the Constitution in 2020, perhaps, already nothing can be done to save the country; since 2020, the big (and lousy for RF) war was unavoidable.
As for the USA, this case does not yet fall into the range of applicability of the models above, while even first date for the table in the Preamble is not yet fixed.
If Americans are not interested in True [34] and decide to convert the peaceful democratic USA to an aggressive monarchy, to destroy the USA
[35][36][37],
then no scientific analysis can help them.
However, even in this case, Editor keeps his right (and even duty) to call things with their proper names, to suggest definitions for euphemisms and other ambiguous terms, to construct historic models and to compare their predictions to a posteriori observations.
References
- ↑ https://commons.wikimedia.org/wiki/File:Oliver_Cromwell_by_Samuel_Cooper.jpg Oliver Cromwell (1599-1658) After Samuel Cooper (1609–1672)
- ↑ https://commons.wikimedia.org/wiki/File:Buonaparte_closing_the_farce_of_Egalité.jpg Buonaparte closing the farce of Egalitè, at St. Cloud near Paris Novr. 10th. 1799
- ↑ https://ja.m.wikipedia.org/wiki/File:Benito_Mussolini_portrait_as_dictator_(retouched).jpg Portrait of Benito Mussolini as dictator of Italy (between 1922 and 1943), published in 1943 for conmemorate his 60th birthday.
- ↑ https://www.marketwatch.com/story/putin-defends-molotov-ribbentrop-pact-says-it-was-the-west-not-russia-that-appeased-hitler-2019-12-20 Putin defends Molotov-Ribbentrop pact, says it was the West, not Russia, that appeased Hitler// Associated Press Published: Dec. 20, 2019 at 1:56 p.m. ET
- ↑ https://nickmix01.livejournal.com/276909.html Записки работающего тунеядца. November 9th, 2014, 09:42 am. Свободу советским евреям! 1978. Три снимка 1978 года с митинга Greater New York Conference on Soviet Jewry перед офисом "Аэрофлота" Сбор подписей в поддержку петиции о свободном выезде. .. А какие у них были плакаты! Просто шик! Ручная работа. Original filename: https: //i.imgur.com/ZCnZMGj.jpg
- ↑ https://www.bbc.com/news/world-europe-64992727 Putin arrest warrant issued over war crime allegations. 2023.03.18.
- ↑ Jump up to: 7.0 7.1 https://www.staff.ncl.ac.uk/j.p.boulton/his211instrument1653.htm Modern History Sourcebook: Commonwealth Instrument of Government, 1653 .. The Instrument of Government is important in the history of written constitutions. It was adopted by Cromwell and his Council of Officers on December 16, 1653, and under it Cromwell assumed the office of Lord Protector. When the Parliament for which it provides met in September, 1654, it passed a constitution of which the Instrument was the basis. .. XXXIII. That Oliver Cromwell, Captain - General of the forces of England, Scotland and Ireland, shall be, and is hereby declared to be, Lord Protector of the Commonwealth of England, Scotland and Ireland, and the dominions thereto belonging, for his life. ..
- ↑ Jump up to: 8.0 8.1 https://www.nationalarchives.gov.uk/coronations/historical-coronations-highlights/coronation-expenses-part-1/ Record of plans for Charles II’s state procession through London, and the expenses arising from the procession and coronation [23 April 1661] (AO 1/2022/5A).
- ↑ Jump up to: 9.0 9.1 https://fr.wikisource.org/wiki/Constitution_du_13_décembre_1799 CONSTITUTION DE LA RÉPUBLIQUE FRANÇAISE Du 22 FRIMAIRE AN VIII ( 13 décembre 1799) .. Article 39.// Le gouvernement est confié à trois consuls nommés pour dix ans, et indéfiniment rééligibles.// Chacun d'eux est élu individuellement, avec la qualité distincte ou de premier, ou de second, ou de troisième consul.// La Constitution nomme Premier consul le citoyen Bonaparte, ex-consul provisoire ; second consul, le citoyen Cambacérès, ex-ministre de la Justice ; et troisième consul, le citoyen Lebrun, ex-membre de la commission du Conseil des Anciens. ..
- ↑ Jump up to: 10.0 10.1 https://fr.wikisource.org/wiki/Traité_de_Paris_(1815) Traité de paix signé à Paris le 20 novembre 1815 entre la France d’une part, l’Autriche, la Grande-Bretagne, la Prusse et la Russie de l’autre. Amyot, éditeur des archives diplomatiques, 1864 (2, p. 664-670).
- ↑ Jump up to: 11.0 11.1 https://it.wikisource.org/wiki/L._17_maggio_1928,_n._1094_-_Istituzione_dell%27Azienda_autonoma_statale_della_strada L. 17 maggio 1928, n. 1094 Istituzione dell'Azienda autonoma statale della strada Regno d'Italia
- ↑ Jump up to: 12.0 12.1 https://olympus.uniurb.it/index.php?option=com_content&view=article&id=10322:1947costituzione&catid=5&Itemid=137 COSTITUZIONE DELLA REPUBBLICA ITALIANA. G.U. 27 dicembre 1947, n. 298
- ↑ Jump up to: 13.0 13.1 https://www.1000dokumente.de/index.html?c=dokument_de&dokument=0006_erm Gesetz zur Behebung der Not von Volk und Reich [«Ermächtigungsgesetz»], 24. März 1933 Zusammenfassung// Das Gesetz zur Behebung der Not von Volk und Reich vom 24. März 1933, mit dem der deutsche Reichstag der Regierung Adolf Hitlers eine pauschale Befugnis zur Gesetzgebung übertrug, bildete neben der «Reichstagsbrandverordnung» vom 28. Februar 1933 das grundlegende verfassungsrechtliche Instrument des NS-Staates. «Das Ermächtigungsgesetz», das zunächst auf vier Jahre begrenzt war und dann mehrfach verlängert wurde, griff formal auf die bereits in der Weimarer Republik entwickelte Praxis weitgefaßter Ermächtigungen zurück. Im Unterschied hierzu besaß es freilich einen konsequent antiparlamentarischen Charakter und diente so zur Zerstörung des Weimarer Verfassungsgefüges. Das Ermächtigungsgesetz von 1933 gilt daher als Symbol für die Selbstausschaltung des deutschen Parlamentarismus gegenüber dem Machtanspruch der Nationalsozialisten.
- ↑ Jump up to: 14.0 14.1 https://www.lpb-bw.de/kriegsende Landeszentrale für politische Bildung BW8. Mai 1945: Kriegsende Zweiter Weltkrieg: Kriegsende am 8. Mai 1945. Am 8. Mai 1945 endet der zweite Weltkrieg. Als die Waffen endlich schwiegen, waren mehr als 60 Millionen Menschen tot.
- ↑ Jump up to: 15.0 15.1 http://www.hist.msu.ru/ER/Etext/cnst1977.htm КОНСТИТУЦИЯ (Основной Закон) СОЮЗА СОВЕТСКИХ СОЦИАЛИСТИЧЕСКИХ РЕСПУБЛИК// Принята на внеочередной седьмой сессии Верховного Совета СССР девятого созыва 7 октября 1977 г. .. Статья 6. Руководящей и направляющей силой советского общества, ядром его политической системы, государственных и общественных организаций является Коммунистическая партия Советского Союза. .. Статья 39. .. Использование гражданами прав и свобод не должно наносить ущерб интересам общества и государства,..
- ↑ Jump up to: 16.0 16.1 https://estonianworld.com/life/estonia-celebrates-the-day-of-restoration-of-independence Einar Vära. Estonia celebrates the 30th anniversary of the restoration of independence. Estonian World, August 20, 2021. .. On 20 August 1991, Estonia declared formal independence during the Soviet military coup attempt in Moscow, reconstituting the pre-1940 state; ..
- ↑ Jump up to: 17.0 17.1 http://duma.gov.ru/en/news/48039/ What changes will be in the Constitution of the Russian Federation? March 12, 2020, 15:04. On 11 March the State Duma adopted the third and final reading of the amendments to the Constitution of the Russian Federation. On the same day these amendments were approved by the Federation Council. On 22 April the national vote on proposed amendments is scheduled in Russia. In our material you will find out the most noticeable and important amendments to the current Constitution of the Russian Federation {\it.. The Federal Assembly also supported the amendment to nullify the presidential term. ..}
- ↑ https://biblehub.com/genesis/15-13.htm — Genesis 15:13 (Lamsa Bible): .. And the LORD said to Abram, Know of a surety that your descendants shall be strangers in a land that is not theirs, and shall be in servitude: and they shall afflict them for four hundred years. ..
- ↑ Jump up to: 19.0 19.1 https://www2.stetson.edu/~psteeves/classes/amalrik1.html WILL THE SOVIET UNION SURVIVE UNTIL 1984 by Andrei Amalrik (1969)
- ↑ Jump up to: 20.0 20.1 https://oceanofpdf.com/Fetching_Resource.php Full Book Name: Moscow 2042 Author Name: Vladimir Voinovich Book Genre: Cultural, Dystopia, Fiction, Literature, Russia, Russian Literature, Science Fiction ISBN # 9780156621656 Date of Publication: 1987– PDF / EPUB File Name: Moscow_2042_-_Vladimir_Voinovich.pdf, Moscow_2042_-_Vladimir_Voinovich.epub PDF File Size: 1.8 MB EPUB File Size: 424 KB .. 1986 ..
- ↑ Jump up to: 21.0 21.1 https://boo.zone/russia-2028.html Аудиокнига «Россия 2028» автора Семёна Скрепецкого. Книга повествует о приключениях порядочного земелекопа в постапокалиптической России. Кстати да, в книге много философии, нотки Борхеса. Внимание : в книге присутствует ненормативная лексика. Автор: Семён Скрепецкий Чтец: Семён Скрепецкий Композитор: Семён Скрепецкий Год выпуска: 2019 Жанр: Фантастика, постапокалипсис, сатира Продолжительность: 03:17:51 (Only the Russian version (Россия2028) is found in the free access.)
- ↑ https://meduza.io/news/2020/03/10/deputat-valentina-tereshkova-predlozhila-vnesti-popravku-ob-obnulenii-prezidentskih-srokov Депутат Валентина Терешкова предложила внести поправку об обнулении президентских сроков. «Единая Россия» согласилась ее поддержать. 19:48, 10 марта 2020. Депутат от «Единой России» Валентина Терешкова предложила внести в законопроект об изменениях в Конституцию поправку об обнулении президентских сроков. ..».
- ↑ https://novayagazeta.ru/articles/2020/03/11/84262-nesmenyaemost-putina-uzurpatsiya-vlasti Несменяемость Путина — узурпация власти. Заявление Общественного конституционного совета. 21:11 11 марта 2020. Решение о несменяемости Путина на должности Президента РФ, принятое по его предложению сегодня Госдумой, является узурпацией власти. Это решение антиконституционно.// Обнуление президентских сроков Владимира Путина — то есть предоставление возможности Путину находиться в должности Президента ещё то ли 12, то ли 16 лет под предлогом внесения его поправок в Конституцию — есть не что иное, как грубое нарушение действующего Основного закона и циничное пренебрежение российскими законами.// Сама процедура «вброса» этой инициативы — предложение «обнулить срок» президентских полномочий, озвученное депутатом Терешковой, как и немедленное согласие на это Владимира Путина являются трагикомической постановкой. ..
- ↑ https://rusmonitor.com/zhurnalisty-vyyasnili-chem-zaplatili-tereshkovoj-za-obnulenie.html Журналисты выяснили, чем заплатили Терешковой за «обнуление». Четверг, 12 марта 2020 17:20. Как известно, 10 марта, в Госдуме депутат от «Единой России» Валентина Терешкова якобы спонтанно, и по просьбе неких таинственных «простых людей» предложила коллегам поправку к Конституции согласно которой можно будет «обнулить» количество президентских сроков, фактически открывая кремлевскому мошеннику заход на пятый круг. ..
- ↑ https://pmc.ncbi.nlm.nih.gov/articles/PMC4742505/ Richard D Morey, Rink Hoekstra, Jeffrey N Rouder, Michael D Lee, Eric-Jan Wagenmakers. The fallacy of placing confidence in confidence intervals. Psychon Bull Rev. 2015 Oct 8;23:103–123. doi: 10.3758/s13423-015-0947-8 .. Interval estimates – estimates of parameters that include an allowance for sampling uncertainty – have long been touted as a key component of statistical analyses. There are several kinds of interval estimates, but the most popular are confidence intervals (CIs): intervals that contain the true parameter value in some known proportion of repeated samples, on average. The width of confidence intervals is thought to index the precision of an estimate; CIs are thought to be a guide to which parameter values are plausible or reasonable; and the confidence coefficient of the interval (e.g., 95 %) is thought to index the plausibility that the true parameter is included in the interval. We show in a number of examples that CIs do not necessarily have any of these properties, and can lead to unjustified or arbitrary inferences. ..
- ↑ https://pmc.ncbi.nlm.nih.gov/articles/PMC4877414/ Sander Greenland, Stephen J Senn, Kenneth J Rothman, John B Carlin, Charles Poole, Steven N Goodman, Douglas G Altman. Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations. Eur J Epidemiol. 2016 May 21;31:337–350. doi: 10.1007/s10654-016-0149-3 // Misinterpretation and abuse of statistical tests, confidence intervals, and statistical power have been decried for decades, yet remain rampant. A key problem is that there are no interpretations of these concepts that are at once simple, intuitive, correct, and foolproof. Instead, correct use and interpretation of these statistics requires an attention to detail which seems to tax the patience of working scientists. This high cognitive demand has led to an epidemic of shortcut definitions and interpretations that are simply wrong, sometimes disastrously so—and yet these misinterpretations dominate much of the scientific literature. In light of this problem, we provide definitions and a discussion of basic statistics that are more general and critical than typically found in traditional introductory expositions. Our goal is to provide a resource for instructors, researchers, and consumers of statistics whose knowledge of statistical theory and technique may be limited but who wish to avoid and spot misinterpretations. We emphasize how violation of often unstated analysis protocols (such as selecting analyses for presentation based on the P values they produce) can lead to small P values even if the declared test hypothesis is correct, and can lead to large P values even if that hypothesis is incorrect. We then provide an explanatory list of 25 misinterpretations of P values, confidence intervals, and power. We conclude with guidelines for improving statistical interpretation and reporting.
- ↑ https://link.springer.com/article/10.3758/s13423-015-0947-8 — *Psychonomic Bulletin & Review*, Oct 2015 “Confidence intervals are thought to index the precision of an estimate… CIs do not necessarily have any of these properties and thus cannot be used uncritically in this way.” Why it’s relevant: highlights the error of treating CIs as direct measures of probability about parameters.
- ↑ https://www.frontiersin.org/articles/10.3389/fpsyg.2022.948423/full — *Frontiers in Psychology*, 2022 “It is given as interpretation … that any value within the 95% confidence interval could reasonably be the true value … This is a very common problem and results in ‘confusion intervals.’” Why it’s relevant: shows the widespread nature of this misunderstanding.
- ↑ https://pubmed.ncbi.nlm.nih.gov/27256121 — *Eur J Epidemiol*, Apr 2016 “There are no interpretations … that are at once simple, intuitive, correct, and foolproof … users routinely misinterpret them (e.g. interpreting 95% CI as ‘there is a 0.95 probability that the parameter is contained in the CI’).” Why it’s relevant: authoritative critique on core misinterpretations.
- ↑ https://arxiv.org/abs/1807.06217 — *arXiv*, Jul 2018 “The so‑called ‘confidence curve’ … may assign arbitrarily low non‑zero probability to the true parameter; thus it is a misleading representation of uncertainty.” Why it’s relevant: supplies theoretical foundation for careful formulation of \(f_N(x)\).
- ↑ https://www.youtube.com/watch?v=VII1FGBHfJg The Domino Principle - 1977. Carnaby Street, Jan 2, 2021
- ↑ https://stanfordreview.org/civil-war-review/ 'Civil War' Review: Is This America's Future? Minor spoilers ahead! JACK KOMAROFF April 24, 2024 . 7:55 PM // America is on fire. Or, at least it is in A24’s latest feature film, Civil War (2024). In the Alex Garland war flick, set in the near-present, we see a vision of the nation where a violent civil war has broken out between the Loyalist States, the Western Forces (an unlikely pairing of Texas and California), and the Florida Alliance. // The film does not give the viewer much information about the catalyst for this catastrophic war, only hinting that the film’s fictitious President (Nick Offerman) broke with precedent by taking a third term. Instead, it drops us directly into the middle of a country that bears only a passing resemblance to the USA that we currently call home. In Garland’s world, paramilitary units enforce their own laws, journalists are shot on sight in the capitol, and cellular service is suppressed. To quote Charles Dickens, “it [i]s the worst of times.”
- ↑ https://ogles.house.gov/media/press-releases/rep-ogles-proposes-amending-22nd-amendment-allow-trump-serve-third-term Rep. Ogles Proposes Amending the 22nd Amendment to Allow Trump to Serve a Third Term Image January 23, 2025
- ↑ https://www.youtube.com/watch?v=Zh3Yz3PiXZw Alternative Math | Short Film// Ideaman Sep 19, 2017 // A well meaning math teacher finds herself trumped by a post-fact America.
- ↑ https://www.youtube.com/watch?v=ZjfgHZdZuVI Почему Америка должна спасать СЕБЯ Mark Solonin Jul 23, 2024
- ↑ https://www.youtube.com/watch?v=qHYbhlHltRw Америка собралась самоубиться? Беседа с профессором Знаменским. Mark Solonin. Aug 21, 2024.
- ↑ https://theconversation.com/why-annexing-canada-would-destroy-the-united-states-249561 Why annexing Canada would destroy the United States Published: February 11, 2025 5.07pm GMT As United States President Donald Trump relentlessly threatens to annex Canada, some Canadians are worried that an American invasion could one day become a reality. // How would that scenario play out? Looking at the sheer size of the American military, many people might believe that Trump would enjoy an easy victory. // That analysis is wrong. If Trump ever decides to use military force to annex Canada, the result would not be determined by a conventional military confrontation between the Canadian and American armies. Rather, a military invasion of Canada would trigger a decades-long violent resistance, which would ultimately destroy the United States.
Keywords
«[[]]», «Annexation of Crimea», «Après moi le déluge», «Brezhnev Constitution», «Bridging Probability Theory and Statistical Estimation», «Budapest memorandum», «Collapse of RF», «Collapse of USA», «Collapse of USSR», «Duration», «Duration5», «Fascism», «Likelihood density distribution», «Likelihood density function», «Mechanisms of history», «Moscow2042», «Moscovia», «Nulling», «Orwell1984», «Russia2028», «Separation of powers», «Student Distribution», «Terror», «Test01», «USSR», «Usurpation», «Will the Soviet Union Survive until 1984»,
«Брежневская конституция», «Вертикаль власти», «Войнович Владимир Николаевич», «Всех убьём, всех ограбим», «Гаага», «Гитлер Адольф Алоизиевич», «Диктатура», «Машины истории», «Москва2042», «Московия», «Мы попадём в рай а они сдохнут», «[[]]», «Новый Мировой Порядок»,
«Обнуление», «Орвелл1984», «Паханат», «Просуществует ли Советский Союз до 1984 года», «Путинская мировая война», «Распад РФ», «Распад СССР», «Россия2028», «Самодержавие», «Фашизм»,
- Adolf Hitler
- Autocracy
- Breznev Constitution
- Brezhnev Leonid Iliich
- Benito Mussolini
- Collapse of RF
- Collapse of the USSR
- Designate Russia as state sponsor of terrorism
- Designate Russia as terrorist state
- England
- Fascism
- France
- Germany
- Historic model
- History
- Italy
- Likelihood density distribution
- Likelihood density function
- Mechanisms of history
- Moscovia
- Nulling
- Oliver Cromwell
- Putin
- Separation of powers
- Student Distribution
- UK
- USA
- Will the Soviet Union Survive until 1984