If you haven’t seen this one yet, it’s definitely worth watching.
This juxtaposition of old and new makes me think of a recent post by Andrew McAfee on the flip:
One useful flip test consists of mentally switching the order of appearance of a new technology and an existing one… Let’s say the world has only e-books, then someone introduces this technology called ‘paper.’ It’s cheap, portable, lasts essentially forever, and requires no batteries. You can’t write over it once it’s been written on, but you buy more very cheaply. Wouldn’t that technology come to dominate the market?
In other words, novelty as such has a value all its own in our culture, but since novelty always fades, it pays to discount it. Take away novelty and what have you got? A bad version of the good old scroll, or a truly useful new thing called a book?
Rambles Blog at Star Chamber 
I remember reading something, when I was a teenager, that may have been written by Isaac Asimov but I won’t swear to that. The pilots in some interstellar (navy? air force? why do interstellar military forces always adopt naval traditions rather than air force traditions?) OK I’ll call it an interstellar navy, were shown to be becoming ever more helpless when their on-board computers went down. Someone uncovered arcane literature detailing how one could write numbers in arcane ways to perform arithmetic operations. Skeptics believed it was all an accident or a trick, but the pilots became better able to handle computer failures after that.
–JMike
By a remarkable coincidence, I was thinking of that exact same short story, and nearly included it in my post. I believe the story you’re thinking of is Asimov’s The Feeling of Power.
Five minutes later Shuman said, “Two point zero seven nine six two three.”
Loesser checked it. “Well, now, that’s amazing. Multiplication didn’t impress me too much because it involved integers after all, and I thought trick manipulation might do it. But decimals…”
That’s the one. I guess my version of that story got filtered through a few layers of “Foundation” on its way through my brain :)