things move around

A wizened old man on the far side of the room extended a claw and beckoned. I approached, and drew myself down to a level three and a half feet off the ground, where the gentleman’s head was suspended on a platter of pipe-smoke. A dull twinkle showed itself in the inkpot of his eye as he began to speak. And this is what he said:

MODULE Sum EXPORTS Main;

IMPORT Math,IO;

VAR n:=0;
sum,last_sum:=0.0;

BEGIN

(* Increasing n. *)

REPEAT

last_sum:=sum;
sum:=sum+1.0/(1000.0*FLOAT(n)+Math.Pi);

(*IO.PutInt(n);IO.Put(”\t”);IO.PutReal(sum);IO.Put(”\n”);*)
n:=n+1;

UNTIL last_sum=sum;

IO.Put(”\nIncreasing n.\n\n”);
IO.Put(”n=”);IO.PutInt(n-1); IO.Put(”\n”);
IO.Put(”sum=”);IO.PutReal(sum); IO.Put(”\n”);

(* Decreasing n. *)

sum:=0.0;
last_sum:=0.0;

 

WITH max_n=n

DO FOR n:=max_n TO 0 BY -1 DO

 

last_sum:=sum;
sum:=sum+1.0/(1000.0*FLOAT(n)+Math.Pi);

 

END;

IO.Put(”\nDecreasing n.\n\n”);
IO.Put(”sum=”);IO.PutReal(sum); IO.Put(”\n”);

END;

END Sum.

There was no doubt that his story had a beginning, a middle and an end. As the exterior world hauled me back in to its lurching deck, like an achor from an uncharted trench, I wondered which bade me the most ill.