NetDoc:I could still divide and multiply with a sliderule today. Calculators had just come out; the TI10 and the next year we had the TI11. WHOA! But, Mr's Hymes was convinced that these calculators were just a passing fancy and WHAT IF the batteries ran out? You had better get this slide rule down pat! Bwahahahahahaha!
I'm not sure why you keep going back to talking about sliderules. Since I'm not an engineer any longer the math I need to do these days is a little simpler but it's there. While shoeing horses on the road it's mostly just in billing. In the shop it's figuring length and weight of stock...a little simple trig, some algebra, geometry and plain old arithmetic. I have lots of calculators laying around but I usually can't find one when I need it and I'm in a hurry. In most cases a piece or soapstone on the face of my anvil gets me by (the paper and pencil equivilant for a blacksmith). It would be a real pain if I had never learned to do that. For more complex problems I just go in the house and use a calculator or sit down at the computer but those things are usually done in early planning stages of a project.
The same with diving. What I have to calculate in the water, I can do in my head. The more complex stuff is all done before hand on the surface.