The costs of 51% attacks on Proof of Work cryptocurrencies

While trying to find an effective solution for the Byzantine Generals problem in order to prevent double spends for Bitcoin, Satoshi Nakamoto has invented a rather brilliant system of incentives. In layman terms, the protocol has historians who agree on the correct version of the timeline (nodes) and researchers who constantly require electricity in order to make new discoveries (miners). Between them there is an interesting system of check and balances which demands for parties who value their asset holdings to further invest in securing the system.