To state that the modern day Jews were descended from just 4 females is ludicrous in the extreme.
No, it is hard science, bottle neck effects were common in human history.
The mentioned 4 females are not only the founding mothers of Ashkenazi communities, but also the ancestors of many, many different European ethnic groups.
Sorry, but it seems to me that you have no idea about human evolution and the science, called genetics.
Find one mention of khazaria prior to the second world war in any history books.
Are you kidding, aren't you?
Any historian knew about Khazaria, even ancient historians, there is a big amount of historical documents, Khazaria is not a controversial topic any more.
ALL historians agree that the first Jewish communities in Poland were created by Khazars, it is accepted by ALL historians that the ruling elite of Khazaria converted to Judaism.
There are different opinions about the scope of conversion of the common population in Khazaria (some of Khazars converted to Islam) and about the number of Khazars and "German Jews" who moved to Poland.
Some historians believe that the number of "German Jews" was bigger, which is ridiculous, because only a tiny number of "German Jews" migrated to Poland, and scientists do not believe in "demographic miracles".
You have to explain the sky rocketing fertility rate of "German Jews" (that had a very low fertility in Germany) with a demographic "miracle", but "miracles" is something that works in fairy tales, hard science does not accept miracles.
The most simple explanation is that there was a big number of Khazars in Poland/Lithuania/Ukraine that could not have been counted, because they were semi-nomads.
After the Russian Tsars ordered the "pale of settlement", they could count all nomads and semi-nomads, and that explains the sudden demographic miracle of Ashkenazi Jews.
Solzhenitsyn writes about this phenomenon in his books "200 years together" and supports his claims with documents.
But, unfortunately, these very important books were never translated into English.
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