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Volume 23, No.1

In Session

The Ruler’s Edge

Stephen Taylor
sjt@5jt.com

This article begins the In Session columns, in which working programmers share from their session logs fragments that are useful or instructive (or just plain showing-off, like this piece) but don’t warrant an entire article. Please send your contributions to editor@vector.org.uk. Ed.

A Zen master famously began each day with the following conversation with himself.

— Master! Master!
— Yes? Yes?
— Wake up! Wake up!

It’s morning. Time to work. But are you awake enough? It’s not a silly question. To write well you want to be not just eyes-open awake, but razor-sharp awake. Coffee and wild dance music can do only so much.

To work, you need your duty sleep.

Sadly, our subjective sense of sleepiness is entirely unreliable. Hans van Dongen has shown [1] that as sleep deficit accumulates, cognitive impairment rises steadily; but the subjective sense of sleepiness plateaus after an initial rise. We know we’re short of sleep; we feel a touch sleepy; but it seems manageable. And then we find it hard to finish sentences…

Are you ready to cut code? Or should you grab a nap—at worst fill in time with less demanding work? Here’s my Morning Rule to decide it. If I can write the Ruler’s Edge in the session, I’m sharp enough to work.

Dyalog installs with the session log configured to an 80Kb limit. I reset this to 8Mb; I need a log longer than my memory. Searching a long log is easier when it’s divided into sections, so I like to rule a line under each day’s work; and sometimes between different tasks during the day.

A good ruler shows units of measure. Character widths are less useful since laser printers and proportional fonts replaced line printers; but they’re still helpful for visually parsing displayed arrays. So I want a function rule. Its right argument will give the length of the line it draws; its left, the intervals at which numbers are displayed. Let’s say the left argument defaults to 10, and that these periods are marked on the line by inverted carets, somewhat like notches on a physical ruler.

We’ll write the numbers above the line. So the gross structure of the function is clear:

      rule←{⍺←10 ⋄ ↑(exp1)(exp2)}

where exp1 returns the superscribed numbers, and exp2 the notched line.

Cutting the notches

Let’s start with the notched line. This is a pattern characters long, reshaped to length :

      ⍵⍴'¯∨'/⍨ {something} ⍺

For an of 10, we need something to return 9 1; in the general case, (⍺-1)(1). So

      10 {⍵⍴'¯∨'/⍨(⍺-1),1} 55
¯¯¯¯¯¯¯¯¯∨¯¯¯¯¯¯¯¯¯∨¯¯¯¯¯¯¯¯¯∨¯¯¯¯¯¯¯¯¯∨¯¯¯¯¯¯¯¯¯∨¯¯¯¯¯

does it. But the truly awakened mind sees unity in the two 1s. They could both be, say, 2 or 3 (if one wanted double or triple notches) but they must be the same number. So we factor out the repetition:

      10 {⍵⍴'¯∨'/⍨(,⍨∘(⍺∘-)⍨)1} 55
¯¯¯¯¯¯¯¯¯∨¯¯¯¯¯¯¯¯¯∨¯¯¯¯¯¯¯¯¯∨¯¯¯¯¯¯¯¯¯∨¯¯¯¯¯¯¯¯¯∨¯¯¯¯¯

Numbering the notches

Now for the numbers.

We want to select from the numbers up to , so exp1 will be something like

      {(-⍺)↑¨⍕¨⍺ select ⍳⍵}

where select selects only the elements of its right argument that are multiples of its left; i.e.

      {⍵/⍨0=⍺|⍵}

or:

      {⍵/⍨~×⍺|⍵}

or, avoiding nesting D functions:

      /⍨∘~∘×∘(⍺∘|)⍨

Putting that together:

      10 {⊃,/(-⍺)↑¨⍕¨(/⍨∘~∘×∘(⍺∘|))⍨⍳⍵} 55
	        10        20        30        40        50

and substituting for exp1 and exp2:

      rule←{⍺←10 ⋄ ↑(⊃,/(-⍺)↑¨⍕¨(/⍨∘~∘×∘(⍺∘|))⍨⍳⍵)(⍵⍴'¯∨'/⍨(,⍨∘(⍺∘-)⍨)1)}
      rule 55
        10        20        30        40        50     
¯¯¯¯¯¯¯¯¯∨¯¯¯¯¯¯¯¯¯∨¯¯¯¯¯¯¯¯¯∨¯¯¯¯¯¯¯¯¯∨¯¯¯¯¯¯¯¯¯∨¯¯¯¯¯
      15 rule 55
             15             30             45          
¯¯¯¯¯¯¯¯¯¯¯¯¯¯∨¯¯¯¯¯¯¯¯¯¯¯¯¯¯∨¯¯¯¯¯¯¯¯¯¯¯¯¯¯∨¯¯¯¯¯¯¯¯¯¯

OK: we’re awake—time to get to work!

Reference

  1. Hans P.A. Van Dongen, PhD; Greg Maislin, MS, MA; Janet M. Mullington, PhD; David F. Dinges, PhD “The Cumulative Cost of Additional Wakefulness: Dose-Response Effects on Neurobehavioral Functions and Sleep Physiology From Chronic Sleep Restriction and Total Sleep Deprivation” Sleep 26.2 pp117-126 http://www.journalsleep.org/citation/sleepdata.asp?citationid=2198

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