In human burials, a crematory is a machine for cremation. A crematorium is building that contains a cremator.
A natatory is a network device that burns up customers data into ash through the process of Network Address Translation. A “natatorium” is a building where customer data is burnt in a fire. Also known as a service provider backbone.
IP Network Address Translation (NAT) was developed in the late 1990’s as a way to maximise utilisation of IPv4 address space and simply the deployment of Internet before there was much Internet to be had.
At a technology level, NAT is a serious technical buttache. You must track the state of every unique TCP session in terms of source IP, source TCP port, destination IP, destination TCP port. Load is a function of both the rate of TCP session initiation AND the concurrent sessions. This is worst possible outcome since a NAT gateways must track vast amount of state at very low latencies and without suitable knowledge of the applications which can dynamically and legally change the TCP session state at any time.
And a major security problem as well though low resolution of identifiable sources.
In 2015, service providers have implemented ever bigger devices that implement NAT and device failures, overflows, address exhausation, software bugs cause regular outages.
The correct definition for a natatorium is a an indoor swimming pool or complex. Which is much more boring.