Non-linear is a good description for many things. This topic is a can of worms so I apologize if this does not flow linearly. (ha!) Okay, first the running stuff. Renato Canova posted the July and August training of some runners who ran at the world championships including Abel Kirui who won the marathon.
The point is I have been on a linear (nearly identical weeks) running schedule most of my life, but it is not the best for development. In fact, many of my best workouts leading into the marathon were out of my ordinary routine (30 miles on Good Friday). Furthermore, many of the best marathoners of the 70s thrived off of one major workout/long run per week and smaller workouts during the week. In other words, a week between hard workouts. Say it takes five days for a body to recover over the course of seven weeks implies ten workouts versus the 70s era seven workouts. I won't even address the 90s era three workouts a week because it complicates thing. But since you are curious, the idea was more workouts would be better, but without enough days to over compensate and respond to the workouts the workouts will not be as effective. In other words, after hard workout X in three days you can run 12 miles at marathon pace but if you wait five days you can run 16 miles at marathon pace, even though you feel the same on the warmup or five miles into the workout.
Changing subjects, life seems to happen in leaps and bounds and plateaus instead of a little progression every minute. After 400 job applications why did I get hired here in Dubuque after only a one hour interview?
In the material deformation world non-linear is where it gets interesting. I had the chance a few months ago to do a finite element simulation using viscoelastic material properties and it was exciting. Plastic deforms permanently even at very small strain levels where as a piece of metal or ceramic will elastically rebound to it's former shape after small strains. When there is any plastic deformation all sorts of crazy things happen. Vacancies dislocate, interstitial atoms resist vacancy dislocations, crystals deform and work harden, and there is some heat released typically. Hundreds of Ph.D.s are granted based on non-linear material properties. All metal forming (machining, casting, and extruding) and joining (welding) involves non-linear material properties.
There you have it, non-linear, it's not a line.
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