Great story Marv. I am starting to look at some of the YouTube videos on Friden calculator repairs. These are interesting mechanical devices but I never used one. In the late 70's I was in an R&D lab where the 1950s vintage old Fridens were removed from storage as surplus equipment and to be thrown into the dumpsters. They let me take one home and that is why I still have it. The oldest calculator I remember using in the late 60's was a Wang electronic calculator with those cool looking nixie tube displays.
I used to program in FORTRAN approximations based Newton's Method in grad school and after going to work in oil and later in gas exploration developing software. My PhD is in Geophysics but minored in Mathematics with a specialty in numerical methods. The nice thing about Newton's Methods is it converges pretty quickly using a computer but it would drive me nuts to have to do this manually. In fact with the use of computers some of the old numerical methods were discovered to be unstable if calculating high precision with hundred to thousands of iterations but the instabilities were never discovered when done by hand. Once you were aware of the situations you could mathematically prove the existence of an unsuitability. This very important to know in automated controls.

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