Backwards Thinking


Image source: - Backwards Edition Dude Perfect


You might find it strange, it but I have a habit of reading a calculus textbook before bed.  Rather than do the problems to understand math, I read math to understand the problems.  One of my barriers to understanding recently vanished when I discovered how proofs are written.


If you’re a math-phobe or have just forgotten, I’ll explain proofs.  When a math textbook tells you something is true  — “The square root of 2 can’t be written out as a number because it keeps going forever,” — they don’t expect you to take their word for it.  They prove it without a shadow of a doubt so that they can use it in later proofs.


I realized that these proofs, often quite magical in their design, might have been written backwards.  It often appears that the writer figured out what they wanted the end result to look like first, then they worked back until they reached a starting place they could claim was already true.  It reminds me of when I was a kid and I figured out that it’s easier to do mazes by starting at the end!


In fact, thinking backwards seems to be a hugely beneficial skill.  Feldenkrais, whose Method I use with myself and my students, believed that “reversibility” was a core necessary ability for a living being to be able to learn.  In other words, whatever movement you want to be able to do, playing an instrument, shooting a ball, walking without pain, you ought to be able to completely reverse at any moment.


This may be one of the reasons why, when I’m having trouble playing a passage on the piano, it’s incredibly helpful, magically helpful, to play it backwards.  As long as I am stuck playing it forwards, it is dependent on time, linked movement by movement to the idea behind it and the idea in front of it.  Make one mistake and my whole conception of the sequence breaks down.


If I can play it backwards, though, I transcend time and causality.  The movement can be started or stopped at any moment and reversed, just the same way I could tell you a fairy tale and stop at any point and go backwards.  The complete, timeless apprehension of the passage makes for  a superior execution.


In writing this blog, I actually started with the last thing I discovered.  Want to know what stirred me to write it first?  Drawing trees.


I’ve always had a terrible time understanding how to draw trees.  The other day it occurred to me that, when I draw them, I always go from the roots to the branches.  But how do I actually see trees?


I see the branches first, because they are in the way of the trunk.  Therefore, if I’m drawing a tree, it makes sense to start at the tips of the branches and then conceive of the drawing, including the part I can’t see, going backwards towards the roots sticking into the ground.


I began with the idea that you would find this interesting.  Then I wrote it.  I won’t really know if my backwards process was correct until I get your comments!

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