hmm ... i can't say i'm convinced. (unwise as it is for me to say that of Iverson's thinking in this forum! .. but this is purely for the sake of chat, isn't it.)
(the part relevant to L<-R convention from http://www.jsoftware.com/papers/EvalOrder.htm is quoted at the end) 1. is convention that important? we're already shifting gears wrt conventions. Once we're immersed in L->R then: x G F :would naturally be read as: we have x, then G is applied, then F is applied. The situation is constructed as we progress naturally from L->R. If we're discarding conventions, then discard the lot and begin with a clean slate. 2. our L<-R construction is written: +/(X.Y) :.. for L->R it would be written as: Y.X/+ :so no problem as long as we're consistant with our handedness. 3. i'll give you that one. .. on the other hand .. once we're immersed, then we know to read L->R and L<-R according to wether we want to travel from woods to trees or trees to woods. 4. in L->R: x/- :would be the expression for alternating sum of components. In L->R: a-b :would mean the displacement from a to b .. ie starting from a and travelling to b (as in the X axis of a graph). And: d/+|9=0 :would represent divisibility (of n represented by digits d) by 9 in L->R .. and it flows naturally from the keyboard because it types in the direction of the thought process .. no having to invert thought direction or move the insert cursor backwards.. .. on the other hand, the entire question would be irrelevant if i could get my sw to insert text in backwards order when needed. ........................................ quote from http://www.jsoftware.com/papers/EvalOrder.htm " The reasons for choosing a right-to-left instead of a left-to-right convention are: 1. The usual mathematical convention of placing a monadic function to the left of its argument leads to a right-to-left execution for monadic functions; for example, F G x ≡ F (G x) . 2. The notation F/z for reduction (by any dyadic function F) tends to require fewer parentheses with a right-to-left convention. For example, expressions such as +/(x×y) or +/(u/x) tend to occur more frequently than (+/x)×y and (+/u)/x . 3. An expression evaluated from right to left is the easiest to read from left to right. For example, the expression a+x×b+x×c+x×d+x×e+x×f (for the efficient evaluation of a polynomial) is read as a plus the entire expression following, or as a plus x times the following expression, or as a plus x times b plus the following expression, and so on. 4. In the definition F/x ≡ x1 F x2 F x3 F ... F x⍴x the right-to-left convention leads to a more useful definition for nonassociative functions F than does the left-to-right convention. For example, -/x denotes the alternating sum of the components of x , whereas in a left-to-right convention it would denote the first component minus the sum of the remaining components. Thus if d is the vector of decimal digits representing the number n , then the value of the expression 0=9|+/d determines the divisibility of n by 9 ; in the right-to-left convention, the similar expression 0=11|-/d determines divisibility by 11 . " On 2011-08-14 07:57, Roger Hui wrote: > http://www.jsoftware.com/papers/EvalOrder.htm > > K.E. Iverson, > Appendix A, Conventions Governing Order of Evaluation, > Elementary Functions: An Algorithmic Treatment, > Science Research Associates, 1966. > > > > ----- Original Message ----- > From: mijj<[email protected]> > Date: Saturday, August 13, 2011 20:07 > Subject: Re: [Jchat] Fibonacci Sequence > To: Chat forum<[email protected]> > >> interesting that Fibonacci was a significant in spreading the >> arabic >> number system in europe .. but the number order wasn't reversed >> to >> account for our writing in the other direction ... thus the >> reason we >> all write numbers backwards. >> >> .. plus .. while on the subject of direction .. why was APL thus >> J >> direction of evaluation set to be right to left? .. wouldn't >> it'd be >> more natural as left to right? (ie. the same direction as >> writing, or >> the direction which represents the progression of time) >> >> On 2011-08-13 20:25, Joey K Tuttle wrote: >>> A friend pointed me to an NPR audio segment - >>> >>> >> http://www.sciencefriday.com/program/archives/201108124> >>> Which is an author interview, abstract - >>> >>> How Leonardo of Pisa, aka Fibonacci, Introduced The World To Numbers >>> >>> To carry out their calculations, merchants in the early 13th century >>> used an abacus or a system called finger reckoning. Commerce changed >>> when Leonardo of Pisa -- known today as Fibonacci -- published the >>> first arithmetic textbook. Mathematician Keith Devlin talks >> about the >>> history of arithmetic and his new book The Man of Numbers: >>> Fibonacci's Arithmetic Revolution. >>> >>> >>> ~~ >>> >>> An interesting remark in the interview is that the sequence we are >>> fond of was an incidental example among many that Fibonacci >> used to >>> stir up interest. >>> >>> The talk show hawks the Devlin's new book "The Man of Numbers: >>> Fibonacci's Arithmetic Revolution" and a companion ebook "Leonardo >>> and Steve: The Young Genius Who Beat Apple to Market by 800 >> Years" - >>> they look interesting, especially the cheap ($3) Kindle book which >>> purports to be the core content of the longer book. > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
