Reconstructability of population history, from genetic information of extant individuals, is studied under a simulation setting. We do not address the issue of accuracy of the reconstruction algorithms: we assume the availability of the theoretical best algorithm. On the other hand, we focus on the fraction (1 - f) of the common genetic history that is irreconstructible or impenetrable. Thus the fraction, f, gives an upper bound on the extent of estimability. In other words, there exists no method that can reconstruct a fraction larger than f of the entire common genetic history. For the realization of such a study, we first define a natural measure of the amount of genetic history. Next, we use a population simulator (from literature) that has at least two features. Firstly, it has the capability of providing samples from different demographies, to effectively reflect reality. Secondly, it also provides the underlying relevant genetic history, captured in its entirety, where such a measure is applicable. Finally, to compute f, we use an information content measure of the relevant genetic history. The simulator of choice provided the following demographies: Africans, Europeans, Asians and Afro-Americans. We observe that higher the rate of recombination, lower the value of f, while f is invariant over varying mutation rates, in each of the demographies. The value of f increases with the number of samples, reaching a plateau and suggesting that in all the demographies at least about one-third of the relevant genetic history is impenetrable. The most surprising observation is that the the sum of the reconstructible history of the subsegments is indeed larger than the reconstructible history of the whole segment. In particular, longer the chromosomal segment, smaller the value of f, in all the demographies. We present the very first framework for measuring the fraction of the relevant genetic history of a population that is mathematically elusive. Our observed results on the tested demographies suggest that it may be better to aggregate the analysis of smaller chunks of chromosomal segments than fewer large chunks. Also, no matter the richness of samples in a population, at least one-third of the population genetic history is impenetrable. The framework also opens up possible new lines of investigation along the following. Given the characteristics of a population, possibly derived from observed extant individuals, to estimate the (1) optimal sample size and (2) optimal sequence length for the most informative analysis.