Chapter IX PEAKS OF PRINTED STATISTICS 1
We see that the pattern of distribution of various epidemic diseases over 11-year cycles is quite complex. While some epidemics fall in years of solar activity maxima, others predominantly occur in years adjacent to the maxima, and a certain portion of epidemics falls in years of minima. However, amidst this complexity, one general and most stable characteristic of most epidemics clearly emerges—grouping within that half of the 11-year cycle which lies under the sign of intense solar activity. Therefore, it is interesting to examine the relationship between the pattern of general mortality—that is, the number of all recorded deaths from all diseases over a large territory and over a long period of time—and the solar cycle.
Based on the temporal distribution of epidemics, one should assume that the curve of general mortality must show significant deviations from the curve of solar activity. This is all the more probable since general mortality includes deaths from many other causes: famine, suicides, cases of sudden death, etc. This circumstance should introduce extremely sharp deviations into the course of the general mortality curve from any theoretically possible curve. Nevertheless, there are some grounds even a priori to suppose that within the complex and tangled picture of general mortality, certain moments should stand out, indicating the predominant role of environmental factors compared to all other random local and temporary phenomena*.
* In this work, I do not address the question of which socio-economic factors might have played a role in fluctuations of general mortality. Undoubtedly, these factors could in some cases entirely determine certain changes in the curve. This question has been thoroughly analyzed by many authors in a number of statistical studies in political economy. Therefore, taking numerical values of general mortality for our investigation, we should not expect, based on all said above, to discover a complete or perfect parallelism between the curves of general mortality and solar activity. Our ultimate goal is to determine the relationship between certain points on these curves (specifically, mortality maxima) and the maxima and minima of solar activity.
Of great interest is the statistics of general mortality in Russia over the period from 1876 to 1917. First of all, this statistics covers a 40-year time span, and secondly, it is expressed in relative critical values rather than absolute ones. Examining the empirical mortality series for Russia, one can easily notice that its movement consists of various oscillations—namely periodic rises and falls—apparent throughout the entire curve, if we disregard the general decline in mortality. On the contrary, periodic declines and increases in relative mortality figures are most vividly expressed, although at first glance appearing rather chaotic. If we attempt to compare the curve of mortality in Russia with the curve of relative Wolf-Wolfer numbers, we will see that although our lines are not very similar to each other, still some common tendencies emerge. Thus, the sunspot curve shows clear 11-year periods, albeit possibly somewhat imprecise; the mortality curve tends to follow the sunspot curve, yet still exhibits significant irregularities in its movement. Thus, despite the diversity of our curves, a certain parallelism between them is noticeable, indicating some connection between them (cf. Fig. 92).
Let us attempt to determine the strength of the connection between our curves (Table 30). First, we perform preliminary processing of the data. In order to eliminate random minor fluctuations and highlight the average level of our mortality series, we perform mechanical smoothing over three points using the simple moving average formula, resulting in a smoothed series. To identify the trend level, we perform mechanical smoothing over 11 points: bt = ⅟₁₁ Σai.
* It should be noted that mortality statistics for 1916 and 1917 are inaccurate, and from 1918 to 1920 it is entirely absent. Therefore, the divergence between the mortality and solar activity curves for 1916–1917 is entirely understandable. Starting from 1920 to 1926, we again observe a fully consistent course of our curves (see chart).
Fig. 91. Top: Mortality in Russia from 1867 to 1925—empirical series, smoothed series over three points, parabola of 2nd order. Bottom: Curve of periodic solar activity.
Table 30
Correlation between solar activity and mortality
| No. | Year | Wolf-Wolfer Numbers | Mortality in Russia per 1000 persons | Average over 11 points | Solar activity | Mortality calculated by 2nd order parabola | Deviation of mortality from 2nd order parabola | Deviation x–X̄ | ||
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1867 | 36.8 | 36.379 | +0.421 | –33.1 | |||||
| 2 | 1868 | 37.3 | 39.7 | 38.3 | 36.489 | +3.211 | –3.1 | |||
| 3 | 1869 | 73.9 | 38.3 | 37.7 | 37.5 | +4 | ||||
| 4 | 1870 | 139.1 | 35.0 | 37.1 | 36.666 | –1.666 | +98.7 | |||
| 5 | 1871 | 111.2 | 37.6 | 38.0 | 36.733 | +1.167 | +70.8 | |||
| 6 | 1872 | 36.8 | 56.6 | 36.686 | +4.414 | +61.3 | ||||
| 7 | 1873 | 66.1 | 36.5 | 37.6 | 16.9 | 46.2 | 36.5 | 36.848 | –1.648 | +4.3 |
| 9 | 1875 | 17.1 | 34.6 | 34.9 | 36.3 | 49.6 | 36.857 | –2.257 | –23.3 | |
| 10 | 1876 | 11.3 | 34.9 | 34 | 2.096 | –29.1 | ||||
| 11 | 1877 | 12.3 | 34.4 | 35.8 | 36.4 | 37.2 | 36.833 | –2.433 | –28.1 | |
| 12 | 1878 | 3.4 | 38.2 | 35.8 | 36.1 | 33.8 | ||||
| 13 | 1879 | 6.0 | 34.8 | 36.4 | 35.9 | 33.5 | 35.5 | 36.751 | +1.951 | –34.4 |
| 14 | 1880 | 32.3 | 36.1 | 35.0 | 35.9 | 34.2 | 36.688 | –54.3 | ||
| 15 | 1881 | 34.1 | 36.9 | 35.8 | 34.9 | 36.611 | –2.511 | +13.9 | ||
| 16 | 1882 | 59.7 | 40.4 | 37.3 | 15.7 | 15.1 | 36.520 | +3.883 | +3.8 | |
| 17 | 1883 | 63.5 | 34.4 | 35.9 | 35.4 | 34.9 | 36.3 | 36.294 | +1.894 | +23.2 |
| 18 | 1884 | 35.5 | 35.0 | 36.159 | –0.359 | +11.8 | ||||
| 19 | 1885 | 25.4 | 33.2 | 34.3 | 33.5 | 35.3 | 36.010 | –2.810 | –15.0 | |
| 20 | 1886 | 13.3 | 35.847 | –2.047 | –27.3 | |||||
| 21 | 1887 | 6.8 | 33.4 | 34.2 | 35.6 | 39.3 | 35.669 | –2.269 | –33.6 | |
| 22 | 1888 | 6.3 | 35.5 | 35.2 | 35.5 | 0.023 | –34.1 | |||
| 23 | 1889 | 7.1 | 36.7 | 36.0 | 35.4 | 40.6 | 35.270 | +1.430 | –33.3 | |
| 24 | 1890 | 35.6 | 35.8 | 37.8 | 35.2 | 39.5 | ||||
| 25 | 1891 | 73.0 | 41.0 | 37.1 | 35.0 | 39.7 | 34.814 | +6.186 | +32.6 | |
| 26 | 1892 | 84.9 | 34.4 | 36.6 | 35.0 | 41.0 | 34.569 | |||
| 27 | 1893 | 78.0 | 34.3 | 34.7 | 34.8 | 41.4 | 35.7 | 34.300 | –0.000 | +37.6 |
| 28 | 1894 | 64.0 | 35.5 | 34.4 | 34.4 | 41.7 | 34.021 | +1.489 | +0 | |
| 29 | 1895 | 33.3 | 33.5 | 34.0 | 41.3 | 33.728 | –0.428 | +1.4 | ||
| 30 | 1896 | 26.2 | 31.7 | 32.7 | 33.6 | 38.5 | 33.421 | –1.721 | –14.7 | |
| 31 | 1897 | 32.6 | 34.1 | 33.099 | +0.101 | –13.7 | ||||
| 32 | 1898 | 12.1 | 31.2 | 31.8 | 32.1 | 30.2 | 31.9 | 32.763 | +1.563 | –28.3 |
| 33 | 1899 | 1.2 | 28.9 | 32.412 | –1.312 | –30.9 | ||||
| 34 | 1900 | 2.7 | 32.1 | 31.5 | 31.9 | 28.0 | 32.047 | +0.053 | –37.7 | |
| 35 | 1901 | 5.0 | 31.3 | 8.0 | 0.368 | –35.4 | ||||
| 36 | 1902 | 24.4 | 30.0 | 30.4 | 31.1 | 31.9 | 31.274 | –1.274 | –16.0 | |
| 37 | 1903 | 42.0 | 29.9 | 32.3 | 30.8 | 36.3 | 6.1 | 6 | ||
| 38 | 1904 | 63.5 | 36.9 | 32.2 | 30.8 | 34.0 | 30.443 | +6.457 | +23 | |
| 39 | 1905 | 62.0 | 28.4 | 28.9 | 30.0 | 33.7 | 29.555 | –1.155 | +21.6 | |
| 40 | 1906 | 48.5 | 28.3 | 28.7 | 29.6 | 33.4 | 29.089 | +3.9 | ||
| 41 | 1907 | 29.5 | 29.8 | 29.3 | 32.1 | 29.0 | 28.609 | +0.891 | +3.5 | |
| 42 | 1908 | 18.6 | 31.5 | 29.5 | 28.7 | 32.6 | 28.114 | +3.386 | –21.7 | |
| 43 | 1909 | 28.5 | 27.3 | 32.0 | 20.605 | –0.205 | –34.7 | |||
| 44 | 1910 | 3.6 | 26.5 | 27.1 | 26.6 | 36.5 | 27.082 | –0.582 | –36.8 | |
| 45 | 1911 | 4 | 0.856 | –39.0 | ||||||
| 46 | 1912 | 9.6 | 26.7 | 25.7 | 25.1 | 25.992 | +0.708 | –30.8 | ||
| 47 | 1913 | 47.4 | 23.0 | 23.8 | 25.425 | –2.4 | ||||
| 48 | 1914 | 21.7 | 22.1 | 24.844 | –3.144 | +16.7 | ||||
| 49 | 1915 | 103.9 | 21.7 | 24.249 | –2.549 | +63.5 |
As a result of smoothing, we obtain a new series in which the 11-year periodicity is eliminated and the “age trend” of the series is revealed, which in this case has a form very close to that of a second-order parabola. Guided by this, we accept the second-order parabola as the analytical trend. We perform analytical smoothing of the obtained series using the method of least squares. Then we find the equation of the second-order parabola, which represents the trend of the general mortality curve in Russia:
Y = 35.962 + 0.803X – 0.181X²
Assuming X = 1, 2, 3, …, 50, we obtain corresponding Y values and construct the graph.
Before proceeding to calculate the correlation coefficient between mortality and solar activity, we can use the obtained series of deviations in mortality to preliminarily clarify the sought relationship. For this purpose, we determine the average deviations of mortality from the obtained trend (second-order parabola) in the years of sunspot maxima and minima, as well as in the preceding and following years. We obtain the following table (31) for years of maximum solar activity.
Table 31
Deviations of mortality in Russia from the trend
| Years of solar activity maxima | In the year of maximum | In the preceding year | In the following year | Average deviation |
|---|---|---|---|---|
| 1870 | –1.666 | +1.085 | –2 | 1.715 |
| 1883 | +3.880 | +6.186 | –0.966 | –3.144 |
| 1893 | +1.176 | –1.894 | –1.106 | +0.405 |
| 1905 | +1.024 | +2.007 | +1.795 | –2.846 |
| 1917 | Average +0.63 |
From the table, we see that mortality higher than the average level most frequently occurs in the year preceding the solar activity maximum, both in terms of number of cases and magnitude of average deviation. A similar direct relationship, though weaker, is also observed in the years of solar activity maxima. In the years following the maximum, mortality generally appears lower than the average level. Thus, from our table we can draw the following conclusion: in the year preceding the solar activity maximum, mortality reaches its maximum value. In the year of the maximum, general mortality begins to slightly decrease, yet remains higher than average.
Let us compile a similar table for solar activity minima (Table 32).
Fig. 92. Mortality in Russia from 1867 to 1924—dashed line: deviation of mortality from the parabola. In the years of minima—peaks of sad statistics.
Table 32
Deviations of mortality in Russia from the trend
| Years of solar activity maxima | In the year of minimum | In the preceding year | In the following year | Average deviation |
|---|---|---|---|---|
| 1867 | 0.023 | +0.053 | +0.856 | –2.433 |
| 1878 | –2.269 | –1.312 | –0.582 | +3.211 |
| 1889 | –1.951 | +1.430 | –0.068 | +0.708 |
| 1901 | +1.816 | –0.42 | 0 | |
| Average +0.551 –1.649 +0.606 +0.112 |
In the years following minima, mortality is above average—the relationship is inverse. Comparing both our tables—31 and 32—we can draw the following conclusion: despite the inconsistency of the relationship, it is most clearly manifested in the years preceding both the maximum and minimum of solar activity. Such is our preliminary conclusion.
Now let us attempt to apply the correlation method for quantitative determination of the strength of the relationship between mortality and solar activity. We take our two series: the series of deviations from the second-order parabola and the series of deviations of relative sunspot numbers from their annual mean. We find the correlation coefficient between our series assuming a two-year forward shift of the mortality curve. We obtain: r = +0.363 and e = 0.089,
where r is the correlation coefficient and e is its probable error. From this we can say that r = +0.36 with a probable error e = 0.09, which is four times smaller than the correlation coefficient.
Summarizing all the above, we can say that when comparing our curves simultaneously, the connection is weak, but when shifting the mortality curve two years forward, it becomes stronger and more robust. The sunspot-radiative activity of the Sun undoubtedly influences general mortality. The fact that we obtained a relatively low correlation coefficient is well explained by the observation that even in years of solar activity minima, we observe small rises in the general mortality curve.
When we arrived at the above conclusion regarding the relationship between general mortality in Russia and periodic solar activity, it seemed interesting to investigate whether a similar phenomenon is observed in extensive statistical data on mortality in Simbirsk Province (now Ulyanovsk Province), where medical statistics had been well established since the end of the first half of the last century.
In the most comprehensive work by Ya. Shostak (1928), we found statistical data on mortality covering the period from 1844 to 1921, i.e., 78 years, also expressed in relative numbers.
Let us now attempt to narrow the territory under study with respect to general mortality. Let us now use statistical data on mortality in Moscow and St. Petersburg (Leningrad). General mortality data for Moscow are found in the work of P. I. Kurkin and Chortov from 1862 to 1926. These data are expressed in relative numbers per thousand inhabitants. The empirical series, presented graphically (Fig. 94) and compared with the solar activity curve, already indicates a certain undeniable connection with the latter. Smoothing this series over three points (see Table 35), performed twice for the purpose of eliminating random fluctuations, results in a clear picture of the dependence of the Moscow mortality curve on fluctuations in solar activity intensity, revealing double mortality waves within one period.
Data for St. Petersburg (Leningrad) are especially rich. We have data from 1764, expressed in relative values per thousand inhabitants. From comparing the two series—the mortality series for St. Petersburg and the series of relative solar activity numbers—we see that although some simultaneity of peaks and troughs is apparent, the connection between them is quite weak. Therefore, let us first eliminate the age-related fluctuations in both series and then examine whether there is a dependence between their “age” oscillations and solar activity.
Thanks to the kindness of G. I. Pokrovsky, I have received already prepared, processed according to known formulas, and published material on mortality in St. Petersburg and the Russian Empire for the specified time intervals. I present this material in Table 36 and as a graph in Fig. 95. As seen from this graph, the age-related course of mortality curves for St. Petersburg and Russia forms very consonant oscillations with the age-related course of solar activity.
Let us touch upon one more question.
