Bielefeld May In Fact Not Exist – Empirical Evidence From Official Population Data

1 Introduction

For more than 25 years now, rumors have persisted that the ostensible city of Bielefeld in the west of Germany does not really exist, not at all or at least not as an actual city (see Butkus et al. 2010 for background). Some of these rumors seem rather “far-fetched”, and also easily refutable by anecdotal evidence like “but I already have been there twice” on first glance. Although the latter is even known to be false – interested readers are referred to Halle (2013) for explanations and convincing counter arguments, as those are not in the focus of this paper – these two may be primary reasons why researchers have so far dismissed the theories altogether as one great “Bielefeld conspiracy” and in advance. Almost no actual research has thus been carried out on the true nature of Bielefeld, not even on those theory variants that do have a valid line of argumentation (e.g., that Bielefeld may be the cover for a secret governmental project) and therefore deserve some respectful attention.

It is not straightforward though to investigate claims such as these. Two theoretical considerations will be helpful. For one thing, the supposed existence of Bielefeld does not differ from those of genuine cities in any obvious way; approaching it at a logical, deductive level should therefore hardly be possible. Instead, it should be regarded an empirical hypothesis and approached with corresponding methods. For another thing, however, a hypothesis of non-existence can empirically only be falsified but never be verified with complete certainty under the paradigm of falsificationism. One consequentially can approximate a proof of the Bielefeld conspiracy only indirectly, namely by showing that its opposite – that is, the existence of Bielefeld as an actual city – were very unlikely given the empirical evidence.

Which data would allow to derive such a conclusion? Necessarily, they need to differ between existence and non-existence of Bielefeld, but they should also be as unbiased by other determinants as possible, which generally means not too specific. Data therefore seem most suited that directly relate to Bielefeld as a city; their mere existence would already proof its genuineness, but only if they can be regarded as genuine themselves. Vice versa, it were unlikely that a genuine city would fake such data (this point will be discussed in more detail later). Thus, in order to prove the Bielefeld conspiracy, it should be sufficient to find satisfactory evidence that the data officially published about Bielefeld are fake.

In this paper, such a proof will be approached with regard to data that arguably present the most constitutive data about a city at all, namely the population numbers of Bielefeld. More concretely, it will be tested whether these numbers respect a general law – the Benford law (introduced in Section 2) – that such data should follow if they are genuine (Section 3). The result will then be substantiated by additional supporting analyses and robustness checks (Section 4), from which finally a conclusion can be derived on the validity of the Bielefeld conspiracy (Section 5).

2 The Benford Law

When observing the respective first digit of a given set of numbers, one would intuitively not expect that these digits follow a special distribution. Benford (1938) (re)discovered,^[1] however, that for most sets of numbers which have originated “naturally”, in particular have neither been forged nor manipulated, a common distribution exists, and a surprisingly skewed one at that: following this Benford distribution, almost each third such number begins with digit 1 (30.1%), while only roughly each twenty-second begins with digit 9 (4.6%); in general, digit d occurs with a probability P(d) of

The reasons for the appearance of this statistical pattern, called the Benford law, are complex, varying in dependence on the numbers’ origin, and correspondingly diverse (see, e.g., Fewster 2009 for a plausible explanation). Nevertheless, it has been found and confirmed by Benford himself as well as in many subsequent studies for a multitude of applications, amongst them river courses, physical constants, numbers printed in newspapers, address data, molecular weights, and mortality rates. The website https://testingbenfordslaw.com presents graphically visualized results for several further areas.

Of special relevance for this paper are results in the context of population numbers. In fact, these exhibit a particularly strong tendency to follow the Benford law (Sandron 2002): The growing or shrinking of an area can be described as an exponential process, and from that follows under weak additional assumptions (1) (Ross 2011). This holds true regardless of the granularity at which areas are considered (e.g., countries vs. regions vs. cities, etc.). Empirical results confirm the theoretical prediction: The pattern has been found to be applicable for, amongst others, the worldwide nations (Olofsson 2015), the US counties (Nigrini 1999), and the cities of Indiana (Ross 2011). Further examples in the context of population numbers can be found at the above-mentioned website.

When data are manipulated, on the other hand, the fragile “balance” on which the Benford law is based is disturbed, and for (naively) forged data it usually does not exist from the beginning (Gauvrit et al. 2017; Hill 1999). This can be used for testing whether suited data are genuine: if they violate the Benford law, they are probably not (the converse argument would, of course, not be true in general; see Durtschi et al. 2004 for a discussion). Although rather simple, this idea is of great practical relevance, since it is the basis of many fraud detection methods in business, taxation, and other sensitive areas (e.g., Nigrini 2012). It has enabled researchers to uncover manipulations even of highest political order, such as in the balance sheets of Greece (Rauch et al. 2011).

In the following, the same approach will now be applied to the population numbers of Bielefeld, in order to test whether they are genuine or also manipulated.

3 Inspecting the Population Numbers of Bielefeld

According to its professed statistics authority (https://www.bielefeld.de/statistik), Bielefeld has 339,367 inhabitants (as of 31 December 2018), who live distributed among 10 city districts or 72 quarters (statistical divisions). Since the Benford law does not depend on area granularity, as mentioned above, in principle both structurings could be evaluated by it. The number of city districts is too small to present reliable evidence, however, so the breakdown by quarters is used in the following.

From this breakdown, the frequency distribution of the first digits was derived; it is given in Table 1 and visualized in Figure 1, both times in comparison to the expected Benford distribution P(d).

Figure 1:

Expected versus actual distribution of the leading digits in the population numbers of Bielefeld.

The two distributions apparently strongly diverge; especially striking is – besides the large frequency differences from 18% (digit 8) to 72% (digit 4) – that the actual distribution does not monotonously decrease but increase again at two places (digits 2 and 8). This is not only in contrast to the structure of the expected distribution, it also contradicts the above-mentioned mathematical reason for the presence of the Benford law in (genuine) population numbers (Ross 2011).

But of course, one should not rely on a mere visual inspection of the data; a statistical test is necessary of whether the actual frequency distribution really differs significantly from the expected one or whether the deviations can be explained by statistical variation. The most popular procedure for such a test is the χ² test; however, it exhibits some severe weaknesses for Benford-type applications (Cerasa 2022; Morrow 2014), which is why nowadays more specific procedures are used for this case. Here, the m test by Leemis et al. (2000) is employed, which is sometimes regarded as particularly suited (Morrow 2014). It will be shown later that this choice is not critical, since other procedures would lead to similar results.

For carrying out the test, the reported population numbers of Bielefeld were imported in the data analysis program R (R Core Team 2022) and evaluated therein by the package BenfordTests (Joenssen 2015). α=0.01 was chosen as level of significance, since the other common one, α=0.05, is sometimes considered too conservative with regard to Benford-type analyses (Kruger and Yadavalli 2017). So, put explicitly, the test may reject the assumption that the population numbers follow the Benford law only if the probability to observe them under this condition is below 1%.

The test result shows that this probability is actually even lower by far, namely at a level of p=0.0007 (0.07%). This confirms the visual impression at highest statistical significance. It can therefore be concluded (within the usual bounds of empirical evidence validity) that the population numbers of Bielefeld violate the Benford law and thus are very probably non-genuine.

4 Supporting Analyses

Some objections still could be raised against the obtained result. These are addressed in the following sections to further corroborate the findings.

5 Conclusion

In this paper, it has been shown the reported population numbers of Bielefeld – and only these, in contrast to those of all other cities in the same state and of similar size, as well as those of further cities – violate a statistical law that almost all genuine data, and population numbers in particular, should follow. This result has been confirmed by five different statistical tests at highest significance. It thus provides strong evidence for the population numbers of Bielefeld being manipulated or even made-up.

But why should a city do that? Possible explanations that are based on incentives or mistakes of the people in charge were found to be very unlikely given that the same data anomaly has occurred – at least – since the year 2005 and continuously from then on. If Bielefeld does not exist, on the other hand, as it has long been argued by the (so-called) Bielefeld conspiracy, no one can live there, and the reported population numbers need to be made-up. Similarly, if Bielefeld does exist as an entity but just mimics the semblance of a city as a cover for its real nature (e.g., a secret governmental project), as other conspiracy variants argue, the numbers need to be manipulated.

The Bielefeld conspiracy can therefore be regarded the most plausible explanation for the found anomaly, if not the only remaining plausible explanation.