I got an email from an organization asking me to take action, and tell the MPAA to stop marketing violent PG-13 movies to preschool children.  Since the MPAA wouldn’t listen to me (it doesn’t have ears), I skimmed one of the articles it referenced referenced in the footnotes. You can read it if you want.

I guess I’m glad someone’s doing this kind of research, but at the same time, it seems like when something’s this obvious, you shouldn’t have to do research about it and publish it in academic journals — it seems more like fodder for proverbs, folk music, or, perhaps, a violent movie?

Maybe they are so many jerks because so few of them are thoroughly happy… or vice-versa.

http://www.gallup.com/poll/159254/latin-americans-positive-world.aspx#1

bigredben:

“Singapore is slowly losing its nationality.” Does that mean you won’t shove past me during rush hour to get on the MRT before me? Does that mean you won’t chope a 4-person table in a crowded hawker centre when you’re eating alone? Will you actually look after your kids in a busy mall and give up your seat on the bus to frail old ladies? No? You won’t? Then don’t worry, your identity is probably quite secure, lah.

I found this page of notes that jehk left me 9 years ago (for reasons I can’t recall) while cleaning my office today. 

Interestingly, the green background of the engineering paper weren’t captured by the scanner.  It’d be cool if one of these formulas described why that is, since I gather there’s some sort of connection between photons and electrons (the electrophotic effect, right?), but I’m guessing the paper and the dye aren’t made of any of the compounds or isotopes listed on the page.

When I got home I was still hyped on caffeine, and thinking about how some of my students apparently need to develop some muscles in their hands to be able to control them well enough to draw and shade spheres and cylinders for art.  So I wrote a Logo program to randomly generate circles with radii in a given range, located within a bounded area, so I could print them out and have them used them as warm-ups.

Bonus points if you can tell which parentheses are optional due to precedence rules.

to distance.to.frame :x.y.frame :point.p
 localmake “a (last first :x.y.frame) - (first :point.p)
 localmake “b (first :point.p) - (first first :x.y.frame)
 localmake “c (last :point.p) - (first last :x.y.frame)
 localmake “d (last last :x.y.frame) - (last :point.p)
 if :b < :a [ make “a :b ]
 if :c < :a [ make “a :c ]
 if :d < :a [ make “a :d ]
 op :a
end

to draw.frame :x.y.frame

pu setxy first first :x.y.frame first last :x.y.frame
pd
 setxy first first :x.y.frame last last :x.y.frame
 setxy last first :x.y.frame last last :x.y.frame
 setxy last first :x.y.frame first last :x.y.frame
 setxy first first :x.y.frame first last :x.y.frame

end

to narrow.frame :x.y.frame :margin
 localmake “new.x1 (first first :x.y.frame) + :margin
 localmake “new.x2 (last first :x.y.frame) - :margin
 localmake “new.y1 (first last :x.y.frame) + :margin
 localmake “new.y2 (last last :x.y.frame) - :margin
 op (list (list :new.x1 :new.x2) (list :new.y1 :new.y2))
end

to rand.between :a :b
 op :a + random (1+ :b - :a)
end

to random.circle.within.frame [:n 10] [:x.y.frame [[-200 200] [-100 400]]] [:radii.range [50 200]]
 draw.frame narrow.frame :x.y.frame -50
 repeat :n [
  (print “Circle repcount)

  localmake “test.point (random.pt.within.frame narrow.frame :x.y.frame first :radii.range)
  (print “Center: :test.point)
  (print “Distance “to “frame: distance.to.frame :x.y.frame :test.point)

  localmake “a last :radii.range
  if (distance.to.frame :x.y.frame :test.point) < :a [
   make “a distance.to.frame :x.y.frame :test.point
  ]

  localmake “test.radius rand.between first :radii.range :a
  (print “Radius: :test.radius)
  print []

  pu setpos :test.point pd arc 360 :test.radius ; should be test.radius, right?

 ]
end

to random.pt.within.frame [:x.y.frame [[-200 200] [-100 400]]]
 localmake “x (rand.between (first first :x.y.frame)  (last first :x.y.frame))
 localmake “y (rand.between (first last :x.y.frame)  (last last :x.y.frame))
 op (list :x :y)
end

“So, Friday night, any big plans?”

“Uh…”

Some asshole talks about word choice.

The solution to all of my problems was rectangles.

inking

Occurred to me while walking the dog this morning:

AVERAGE VALUE * NUMBER OF TERMS

so, for 1 + 2 + … + n this is (n+1)/2 * n

A lot of times, these are cast in terms of the constant difference, the starting term, and the number of terms, as in

s + (s+d) + (s+2d) + … + (s+(n-1)d)

For deriving, it may be easier to think of it as (FIRST + LAST)/2 * n

(s + (n-1)d/2)*n

Since this is essentially a discrete “integral” of a linear function, it may be easier to formulate it as a quadratic, since you have a category for quadratics, and probably recognize that a quadratic is appropriate, leaving less “bits” of information to memorize:

(d/2)n^2 + (s-d/2)n

This formula seems reasonable, since if n=0, the sum is 0, and for n > 1 and d > 1, larger d or n results in a larger sum.

Now, if you take the derivative with respect to n, you get

dn + s - d/2 = s + (n-1/2)d

This struck me as odd at first: it seems that that increasing the number of terms by 1 adds the number halfway between the last term and the next term, whereas what actually gets added is

s + nd

But the derivative can’t be applied that way to a discrete function.  What you’re really getting with s + (n-1/2)d is the slope of the line between one value and the next.

Honestly, what puzzles me the most about this is that you said you use it so often you wish you could memorize it.  I’m having trouble thinking of when this comes up, as opposed to an integral.  But maybe that’s because I haven’t had a remotely technical or scientific job for the past 9 years.

Cue dramatic music… yes, cranes really do build themselves.  I’m going to use a video like this as a big metaphor for constructivism, to help teachers remember, although the analogy is imperfect (eg, the steel used to make the frame is out there, in the world, whereas the source of logical knowledge is inside the learner’s mind).