5. Diluting the Distribution of All Persons to Adults

As noted above, we believe that the correct comparison between stellar multiples and humans should be to number of adults in household rather to all people. Thus, we attempt deriving this distribution by subtracting children and elderly from the total population. The ratios between American adults (18 - 65 years) to all people in family household in the cells 1, 2 ··· 5 are: 1.398, 1.441, 0.628, 0.232 and 0.131. For bins 6 and 7, no data are available. To be consistent with the decreasing trend from cell 2 to 5, we assumed factors of 0.5 and 0.25 between these cells and bin 5. Note that the values in the last two cells are relatively small and have a minor effect on the distribution. The distribution of adults was then calculated, normalized to one, and tabulated at the bottom of Table 3. The dilution impact was some shift towards lower num-

bers. Figure 3 displays this effect for both the sums and means of the six countries. The distribution of all persons in the sum of the six countries, which was displayed in Figure 2 as well, is shown in red, while the green curve presents the synthetic distribution of adults (18 - 65 years) in this sample. The distribution of the mean of the six countries is shown in blue together with the one standard deviation (1σ) errors. The diluted distribution of the means (in black) is very like the diluted distribution of the sums. The diluted distribution of the sum of the six countries is also plotted in Figure 1. A remarkable similarity between this distribution and that of stellar multiples is seen. It was deduced from Monte Carlo simulations that the two distributions are consistent with each other with a probability level higher than 99% (Appendix).

6. Discussion

The results presented in this paper are quite strange, extraordinary and difficult to believe and to understand. This work presents a fantastic numeric resemblance between the distributions of stellar multiples observed in the night skies and humans. From extensive numerical simulations it was concluded that the similarity between number of American adults in household and stars multiplicity is significant at a confidence level higher than 98%. Furthermore, the distribution of stellar multiples is also consistent with the synthetic distribution of adults in the six countries at a confidence level higher than 99% (Appendix).

There is still a little chance that the similarity between human adults and stars is only a coincidence. The data used in this work were taken from partial samples. The distribution of star multiples was built using observational data of the 4559 brightest nearby stars and a theoretical analysis of the observational biases, which may suffer from some uncertainties. The collection of data on persons in household suffers from a bias of English speaking countries. In addition, the distribution of adults in household in USA and in the sum of the six countries was estimated using simplified coefficients taken from USA data. All these facts naturally lead to some uncertainties. Yet, to date, these samples are the best available.

The sum of adults in the six countries is strongly influenced by a single country—USA, whose data constitutes about a half of the total population. Note, however, that if all countries are given the same weight, the results and significance level are hardly affected as the distribution of the mean values of the six countries is almost identical to the distribution of the sum of all data (Table 3, last 4 entries, Figure 3, see also Appendix and Table 4).

The distributions of stellar multiples and adults in household are not simple Gaussians so they are not common. It can neither be argued that there is a general Nature rule that states that individuals tend to couple in a certain way with a peak at two because it is clear that the multiplicity distributions of certain animal species (e.g. fish or bees) are clearly different. It seems that the surprising resemblance between the distributions of stellar multiples and human adults requires some explanation.

The perception that led to this research is similar to one interesting interpretation of Quantum Mechanics that seems absurd—that the observer influences the experiment. The educated reader may ask: “Why comparing the current distribution of humans with that of stars, which is older by the time interval, it took light to reach Earth?”

According to this perception, the results depend on the time of the observations. Thus, we expect that people with a different distribution, who observe the universe in the future with better equipment, would reach different conclusions! This is the reason for trying to collect data around the same time (Sections 2-4, Tables 1 and 3).

Finally, this paper actually presents only a glimpse of our ideas, which we admit sounds completely absurd. Some similarity between the distributions of American children and planets was found as well, although for a small sample of planets [4,5]. Combining this result with the significance value of 98% estimated for the resemblance between stellar multiples and American adults in household (Appendix), the significance level is even higher and cannot be regarded as an anecdote. These results should be re-examined in the future when larger data samples are available, but the picture that arises from them [see also 24] is quite strange. It is noted that two predictions of the Astro-Sociology model [4,5] for orphan and adopted planets have already been verified by observations [25] and simulations [26,27]. This fact adds some support to this unusual perception. It is also anticipated that many more predictions of the theory, in example for twin planets, will be confirmed within the next few years.

7. Acknowledgements

It is a pleasure to thank Shlomo Heller (Kartar) for many stimulating discussions, the anonymous referee and Ram Krips for valuable comments and Doron Retter for some help preparing the tables.

REFERENCES

Appendix—Significance Estimates

The distributions of people and stars multiplicity were discussed above and it was concluded that they are alike (Figure 1). The purpose of this appendix is to check whether these results are significant. One may try to use the Kolmogorov-Smirnov (KS) probability test [28] to check whether two different distributions are consistent with each other. This test is, however, adequate for a large number of points that can get continuous values, while the relevant distributions of stars and adults only have a few discrete points. Therefore, it was decided to test the statistical significance of the results by extensive Monte Carlo simulations.

Given a distribution, for bins that complies for , we posed the question: “what is the chance probability to obtain by random a second vector distribution, with?” We defined a difference parameter

between the corresponding cumulative distributions:

For the cumulative distributions of the pair—American adults ([0.378, 0.860, 0.960, 0.992, 1]) and stars ([0.321, 0.800, 0.914, 0.958, 1]), n = 5 and δ = 0.101. Note that the stars data were re-arranged into 5 bins in order to fit the first data set. For the synthetic cumulative distribution of adults in the sum of the six countries ([0.398, 0.850, 0.954, 0.987, 0.995, 0.998, 1]), and stars ([0.321, 0.800, 0.914, 0.958, 0.980, 0.990, 1]), n = 7 and δ = 0.106. The third pair was the cumulative distribution of adults in the mean of the six countries ([0.398, 0.841, 0.950, 0.986, 0.996, 0.999, 1]), and stars. For this couple δ = 0.100.

For the test we built one million random distribution samples with noise taken from the data using a few different methods. First, the mean and standard error of the Pa data were found, and then for every simulation we raffled Gaussian distributed noise and obtained n random numbers around the data mean. Negative numbers were shifted upwards and given a random number around 0.01, and the total simulation vector was normalized to 1, so. From this initial simulated vector, , the cumulative distribution was calculated to obtain the final probability vector

The difference parameter between this simulated distribution and the second given distribution, δ (Ps_cum, Pb_cum), was calculated. For one million simulations, one million values of this parameter were obtained. The significance level was defined as the ratio between the number of values higher than the observed difference parameter, δ (Pa_cum, Pb_cum), calculated above, to the total simulations number. This test suggested that there is 99.5% chance probability that the first pair (American adults, stars) is significant and 99.9% for the second (adults in the sum of the six countries, stars) and third couple (adults in the mean of the six countries, stars).

The strongest peak in the distributions is at the second cell (2) and the second highest is at bin 1. We repeated the simulations, giving a preference for the largest probability value in each simulation to be either at bin 1 or 2, while all other n-1 figures were randomly shuffled in the remaining bins. The results of these simulations were that there is 98.8% chance probability that the two distributions of stars and American adults are consistent with each other. For the second and third pairs: stars— adults in the sum or mean of six countries values of 99.0% and 99.1% were found. These figures were adopted in the paper and they mean that the couples are highly significant. This is a conservative approach, because a priori given the distribution of adults, the distribution of stars could be completely different, say with all multiples above n = 5, and there is no reason why the strongest peak in the astronomical distribution would be either at 1 or 2.

We performed another test that clearly underestimated the significance level of the results. We imposed the highest probability value in the simulated vector exactly as observed—in the second bin. The other values were randomly placed in the other bins. In this test the resulting significance level was 97.9% for the first couple, 99.4% for the second and 99.6% for the third. These simulations confirmed that once the distribution of adults is given, there is a very low chance probability to randomly obtain the observed distribution of stars. Table 4 summarizes the results of the significance tests.

The data and errors were also modeled in a different way. We either fitted a 2D or 3D polynomial to the data. The standard errors were calculated from the difference between the fit and the data. Then we raffled random numbers according to the standard error and added them to the fit to obtain n random numbers. Negative values were given random numbers around 0.01, and the total simulation vector was normalized to 1. The data bins were either randomly shuffled or given some preference in the first two bins or only in the second cell as discussed above. The cumulative distribution was then calculated to obtain the final simulation vector, and the difference parameters, δ (Ps_cum, Pb_cum), was calculated. The outcome of these simulations was very similar to the results obtained above with differences of up to tenths percent between the two methods.