whence the sun rises

admin — Fri, 27 May 2011 02:15:23 +0000

Somebody was commenting here that they thought the sun would rise from the Boston (south) side of the river in the morning, but in fact it rises from the Cambridge (north) side these days. A little more than ten years ago, sitting in my northern-latitude abode watching the sun set into the northwest, I wondered the same confused thing: why does the sun appear to venture into the northern part of the sky? (For reference, the sun’s direct projection on the earth never crosses north of the tropic of cancer, and that is south of here.)

The answer is recognized with the aid of this map, which shows the interesting effect due to the earth’s tilt and its spherical geometry. At every point along the day-night boundary curve, the sun’s rays are orthogonal to the curve and on the plane tangent to the earth’s surface at that point. In other words, the sun appears to rise (set) from (into) the direction orthogonal to the day-night boundary. This means between the spring and autumn equinoxes, the sun rises out of the northeast and sets into the northwest, and between the autumn and spring equinoxes, the sun rises out of the southeast and sets into the southwest.

This reminds me of a rather surprising method for direction-finding without a compass. It goes like this: point a stick in the direction of the sun, at any time during the day, and wait a short moment, then the direction of the new (very short, infinitesimal) shadow from the base of the stick points to the east. Here’s a short “proof”: Let the sun’s original location be called Q, let the base of the stick be called A and let the tip of stick be called B. So the vectors AB and AQ are collinear. At any given moment, the earth’s surface instantaneously rotates into the eastern direction at A, so in the earth’s local reference frame (the one we’re interested in) the sun’s apparent location moves slightly to the west to a new point Q’. Now, the shadow cast by the stick has a tip at a new point C (on the ground). Since A, B, C, Q, Q’ all must be coplanar, and the vector AC has no elevation component (same as QQ’), then the vector AC must be parallel to QQ’, and BQQ’ and BAC being similar triangles, AC must point to the east.

The trick is, you can’t wait too long, or else all the linear approximations and Euclidean geometry break down and you won’t get the right direction.

stuff on internet tv

admin — Fri, 05 Dec 2008 10:52:21 +0000

NBC hosts flash versions of all of its TV series on its site. The interface is generally good but there are some quirks about when ads must be viewed. The ads are forcibly inserted between chapters of an episode. Whenever the chapter boundary is crossed in the forward direction, the overlay ad is played and the underlying video is paused. (As an aside, this kludgy architecture actually makes me believe it is possible to disable the ads…) So for example, if you’ve already watched to certain chapter, then backtrack, then return to it, the boundary is crossed again in the forward direction and the ad must play again. This shouldn’t happen. Also, suppose you want to start playing a late chapter. The ad immediately before that chapter plays, but if the video was freshly loaded, the ad at the beginning of the video is also forcibly played before a chapter can even be selected. This also seems like incorrect behavior.

But I understand… playing ads too many times in error is of no concern to NBC, of course.

So what’s on NBC’s site? Most shows have only the latest episodes on a time delay (to not preempt live broadcast and DVD sales, I suppose), but a few have all past episodes available. One of these I’ve been watching is Friday Night Lights. Actually never saw any ads for this, but all of Season 1 was surprisingly good. Unfortunately, Season 2 was crap and total BS. Sadly, there is only so much good material for writers to crank out.

Some stuff » direction

whence the sun rises

stuff on internet tv