Satoshi's discovery is often thought of as simply money over IP but the scope of his discovery is much wider than this - his legacy much greater. Sometimes, it is important in a network to be able to achieve consensus. Other times, it is important in a network to be able to avoid centralized points of weakness. Individually these problems are solved relatively easily. However computer scientists found it more challenging to describe a method for allowing both of these qualities to be achieved simultaneously. This is Satoshi's true legacy, not money over IP specifically, but how to achieve a consensus in a decentralized network. The difficulty of the problem results from the fact that in a decentralized network no two distinct perspectives can ever be expected to witness the same picture of the state of the network. It's not even a question of right verses wrong, they are both correct, but different. Satoshi's solution was to use something called a block-chain to house a consensus record, and proof of work as a fair means of determining whose perspective the official record should be a reflection of.
Nxt offers a slightly different solution to this same problem. It, too, uses a blockchain to house the consensus record. However, it solves the problem of determining whose perspective the consensus record should be a reflection of differently. NXT uses proof of stake rather than proof of work. In a proof of stake scheme, one demonstrates their administrative capacity over a particular quantity of a digital asset in-order to gain the right to author a block. However unlike its predecessor Peercoin, NXT introduces the idea of randomness in the selection of which stake holder has the right to author a block. Think of it like the number of coins you administer being analogous to the MHash/second that you would have in a proof of work crypto. Or, another way to think of it, as each unit of currency being an entry into a lottery where the winning lottery ticket is selected at random
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