Ok, it's not an iPhone, but it is a very old computer from the 1950's. One of the first dozen ever to exist, weighing in at 2.5 tons; and it has been restored back to life by the National Museum of Computing in Buckinghamshire, UK.
Here's a clip:
It's called the Harwell Dekatron (aka 'WITCH' — 'Wolverhampton Instrument for Teaching Computation from Harwell' ). The NMOC website describes its original purpose:
"The Harwell Dekatron computer first ran at Harwell Atomic Energy Research Establishment in 1951 where it automated the tedious calculations performed by talented young people using mechanical hand calculators. Designed for reliability rather than speed, it could carry on relentlessly for days at a time delivering its error-free results. It wasn't even binary, but worked in decimal — a feature that is beautifully displayed by its flashing Dekatron valves."
Storage capacity? It could "store up to 40 8-digit numbers". And was it fast! In around 5 to 10 seconds, it could multiply two numbers. But a machine that could work around the clock, in 1951? That must have been impressive.