On 15 June 2012 21:17, David Leibs <david.le...@oracle.com> wrote: > I have kinda lost track of this thread so forgive me if I wander off in a > perpendicular direction. > > I believe that things do not have to continually get more and more complex. > The way out for me is to go back to the beginning and start over (which is > what this mailing list is all about). > I constantly go back to the beginnings in math and/or physics and try to > re-understand from first principles. Of course every time I do this I get > less and less further along the material continuum because the beginnings > are so darn interesting. >
I think otherwise. According to human's history we tend to create and control more and more complex systems. Just compare today's cars with cars 100 years ago.. Or first microchips and today's microchips. But i agree that going back to beginnings has its own value: since your today's experience is always better than yesterday's one, you can often see solutions which you didn't saw in a first place, which would allow you to understand how to make things simpler. But only to do even more complex things at next iteration. :) > Let me give an example from arithmetic which I learned from Ken Iverson's > writings years ago. > > As children we spend a lot of time practicing adding up numbers. Humans are > very bad at this if you measure making a silly error as bad. Take for > example: > > 365 > + 366 > ------ > > this requires you to add 5 & 6, write down 1 and carry 1 to the next column > then add 6, 6, and that carried 1 and write down 2 and carry a 1 to the next > column > finally add 3, 3 and the carried 1 and write down 7 > this gives you 721, oops, the wrong answer. In step 2 I made a totally > dyslexic mistake and should have written down a 3. > > Ken proposed learning to see things a bit differently and remember the > digits are a vector times another vector of powers. > Ken would have you see this as a two step problem with the digits spread > out. > > 3 6 5 > + 3 6 6 > ------------ > > Then you just add the digits. Don't think about the carries. > > 3 6 5 > + 3 6 6 > ------------ > 6 12 11 > > > Now we normalize the by dealing with the carry part moving from right to > left in fine APL style. You can almost see the implied loop using residue > and n-residue. > 6 12 11 > 6 13 0 > 7 3 0 > > Ken believed that this two stage technique was much easier for people to get > right. But still it won't prevent people from doing mistakes, which you nicely demonstrated by by putting zeroes in right column :) -- Best regards, Igor Stasenko. _______________________________________________ fonc mailing list fonc@vpri.org http://vpri.org/mailman/listinfo/fonc
