QuickTake Brain-breaking Challenge Results

I'm impressed guys. Seriously. Yesterday, I laid out a mind-bending challenge – given the limits of 1994 Apple QuickTake 100, how many different photographs is it possible to record?

And we got the answer – in two different forms of notation – in less than four hours. Given the results, the QuickTake might be all the camera any of us ever need. And the implications of this problem are apparent in Mac UI history.

Technorati Tags: apple, icon, Quicktake mindbender

For those who never got to discrete math, I'll talk you through the formula. Reader Guillermo was the first to point out that a camera with a resolution of 640x480 in 8-bit color can take 256^307,200 pictures. In other words, each of the 307,200 pixels can be any of 256 colors in any given moment.

So how much is 256^307,200, anyway? Well, that's where Dustin stepped in. It works out to 2.0765567298666158102085281115549e+739811. Put in simpler terms, that's 2 followed by 739,811 zeroes. It's no Googolplex, but it's tremendously large. For example, it's assumed that there are no more than 10^85 particles in the entire universe. You would need to first double that number and then raise it to the power of 17,000.

Because Dustin is smarter than I am, he decided to apply the math a bit further, first discovering that the 24-bit equivalent is way larger, 8.954295049582472660707590425663e+2219433, or roughly a 9 followed by more than two million zeroes. In order to view all of these 640x480 photos, if you were to view six of them at a time at 24 frames per second, it would take 1.9704478322492646296656287113931e+2219424 years to view every possible image the QuickTake is capable of capturing.

So what's this all about? Why have we spent 24 hours mulling a problem that concludes that very large finite quantities exist but are wholly impractical from the standpoint of time actually elapsing? For a few very simple reasons:

1. To have some fun imagining very large numbers and remember that even the massive is not infinite (to really freak yourself out, consider that there are an infinite number of irrational numbers between every rational number of the number line. Yow)

2. To look for practical applications of this problem, and point to its peculiar place in Mac history.

Bill Coleman really inaugurated part two of the discussion, noting the application of such thought to image compression:

While the number of possible photos is exceedingly large, as others have pointed out, the number of "interesting" photos is much, much smaller.

Consider that many of the photos in the domain would show lots of high-frequency energy. (Think of what an old television looks like when it is tuned to a channel with no station) These photos would look like, well, static. Boring.

And consider the huge number of images that differ from each other by just one value in one pixel. These would be indistinguishable from each other. In fact, a whole host of pixels could have slightly different values without perceptably changing the photo.

Considering these two factors, the number of "interesting" photos drops by several orders of magnitude.

It's precisely this phenomenon that allows image compression to work. Once you've eliminated all the "uninteresting" data, there's much less information to send.

A very "interesting" point, Bill. For consider how you might apply this kind of thinking to an 16x16 black-and-white grid. Remember, that was the canvas Susan Kare had to paint on when creating the first icons for the Macintosh. This is a much simpler, much smaller number of possibilities, just 2^(16x16) or 2^256. This is why with a great artist like Kare, it's possible to create a huge number of visually distinct and information-rich graphics on a canvas with "only" 256 possible switches on and off.

And that, I would argue, is the founding principle of the Macintosh Way. A small, deceptively simple box that can produce the highest possible art for a given medium. Be simple but not shallow.

Two other points to raise, because I don't have good answers for them.

Moretti questions the fundamental principle of a picture:

I think we're forgetting a central principle here... what is a "picture"? A grid of pixels does not a picture make. A picture as a representation of something natural in our universe, I would imagine that there would not be a complete one to one correlation. The number of possible combinations of pixels in the given scenario would far exceed the natural subjects actually available.

Devilsadvocate goes further: Can two pictures that are identical in data but different in subject be considered the same? Does the dimension of time fundamentally alter the number of possible photographs in the world?

Yes, there may (I say may, it depends on whether you think the universe is finite) be a finite number of subjects available at any given moment, but time marches on, theoretically, you would only have to wait long enough to take every conceivable picture. That said, if I wait long enough that another earth develops and goes about it's lifecycle and I stand in the same place I am today (but on the new earth) and take a picture of the same scene such that every pixel is identical, is it really the same picture?

even easier, if I walk into two perfectly dark, but distinct rooms and take a picture of the blackness such that every pixel on the resulting images are identical, is it the same picture?

Phew. Mind-bending metaphysics and Mac history in one post. You guys are the hardest-working readers in show business!