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Gadgets can get confused

Photographs in a newspaper are composed of tiny dots. Images on a computer screen are similar: they’re composed of pixels (“picture elements”).

Counting with your fingers (digits), there’s nothing between ‘one’ and ‘two.’ In a digital image, there’s nothing between two pixels.

When pixels are small, our eyes blend them together, and edges look smooth. But make the picture (and its pixels) large enough, and edges get jagged – there’s a jump from one pixel to the next.



Such “stair-stepped” or “pixilated” images are suffering from “aliasing.”

Aliasing also occurs in time.




The lights go down and the screen fills with images of the old west. The stagecoach is pullin’ into town, each wheel a blur. As the stage slows down, the blur begins to clear. And then something strange happens.

The wheels, just for a moment, seem to stop … and then – even as the stage continues to move forward – the wheels begin to turn backwards.

Take a pad of paper (or a book you don’t mind marking up a little). Starting on one page, draw a dot in one of the corners. On the next page, draw another dot, slightly closer to the edge. Do this again and again on a dozen or so pages, putting each dot a bit closer to the edge of the page.

Now quickly flip the pages with your thumb so you can see each page in quick succession. The result is a “movie”: the adventures of a dot moving toward (or away from) the edge of the book.

Watching a movie, we see one snapshot after another: 24 snapshots – 24 frames – every second.

Let’s make a movie of the cheerleaders for our local ball team, the Pluggers. We don’t have a movie camera, so we’ll take a series of snapshots, then assemble them into a flip book.

The cheerleaders exhort the fans to spell out a cheer. As a visual aid, they hold up cue cards, one after another:

“Gimme a P!” (They hold up a “P”)

“Gimme an L!” (They hold up an “L”)

“Gimme a U!” (They hold up a “U”)

“Gimme a G!” (They hold up a “G”)

And again:

“Gimme a P!”

“Gimme an L!”

“Gimme a U!”

“Gimme a G!”

And again and again and again.

We shoot snapshots, but our timing’s a bit off. The first letter we capture is “G.”

Next time, we’re a bit faster, if not quite fast enough. We get a picture of a “U.”

Another shot. Now we’re getting better, getting closer to the beginning of the sequence. We shoot an “L.”

Fourth shot. Finally, we catch a “P.”

Now we assemble our flip book. Using the snapshots in the order in which we shot them, we see our cheerleaders spell out … “G … U … L … P.”

Suppose we were filming a clock. When we begin, the second hand is pointing straight up, to 12 o’clock. We then shoot the next frame before the second hand can make a full rotation; we catch it at 11 o’clock.

The next frames catch the hand at 9 o’clock; 8 o’clock; 7 o’clock; and so on.

When we watch our movie, the frames screen in the order in which we shot them, with the second hand pointing first at 12, then 11, 10, 9, 8, 7… the clock seems to move backwards.

Same with the wheels of the stagecoach.

Designing the technology for compact disks, engineers first and foremost had to choose a sampling rate fast enough to ensure that the vibrations making up the music not be recorded backward.

ooo

Alan Stahler trained as a biologist and is an amateur astronomer. He teaches private enrichment classes for students of all ages. His science programs can be heard at noon on alternate Tuesdays on KVMR-FM (89.5).


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