Information Theory and Projections

I am an amateur aficionado of information theory from a purely conceptual standpoint. For instance, for many years I’ve had an interest in both data encryption and data compression, which as it turns out go together like peas and carrots.

Prior to plaintext data being encrypted, applying a compression algorithm to reduce the amount of redundancy can make the ciphertext more difficult to crack by increasing the unicity distance. Early on, an easy way to remove redundancy was to remove vowels from the plaintext prior to encryption. The plaintext was still readable and its meaning was conveyed, and therefore no information was lost. In other words, the vowels were redundant, and removing redundancy strengthened the encryption.

Periodically on Reddit I stumble upon stunning art pieces that the community found interesting enough to vote up. Tonight one of them was a collection of shadow art. Clearly the artists are wonderfully talented, and yet I cannot help but see beyond the art itself to be intrigued by the underlying mechanism in which the original message (plaintext) was hidden and revealed.

Every piece appears to be random bends in wire, trash haphazardly clumped together, or blocks or boxes strewn about. At first glance we would attempt to visually decode – to discover the pattern within those objects and comprehend the artist’s message. In fact, we might lead ourselves down an entirely different path of interpretation (e.g. assuming the heaped trash is conveying a statement about our society). However, only until a source of light illuminates the piece from precisely the correct X,Y,Z coordinate do we discover the plaintext is deciphered before our eyes as a two-dimensional projection from three-dimensional space.

Redundancy helps

In many of these art pieces, there is a high degree of redundant information that actually works to strengthen the encryption. For example, in art piece where trash was heaped together, the labels and wording on the trash items obfuscate the artist’s message by leading you down a path of inspecting the trash itself.

Another art piece with letters and numbers glued to the wall might cause the viewer to try to assemble words to understand the message. In fact, if the letters actually assembled words, they could lead the viewer to conclude she successfully deciphered the message when in fact she has not.

Decoding through a dimensional projection

Arguably the ultimate redundancy is the dimensionality of the art piece. The fact that each piece is created in three dimensions entices the viewer to inspect the piece (or individual components thereof) for meaning without considering the plaintext message exists outside of the piece itself. The key that will decipher the art piece to yield the plaintext is the X,Y,Z coordinate of light source with respect to the art piece’s location.

What I find interesting is that general mechanisms of conveying secret information tend to:

  1. Encrypt the plaintext message into something generally unreadable by anyone but the intended recipient (via some key), and/or

  2. Hide the unencrypted message in plain sight, relying on surrounding noise to distract everyone but the intended recipient who understands where to find the message and meaning amongst the noise.

For shadow art, I cannot easily lump it into either category because the piece does not contain the message as plaintext nor ciphertext. Only by projecting it down a dimension with a unique key (x,y,z) can it be deciphered. It’s more closely related to an encryption, but without an algorithm required to decode. Just shine the light from the right spot, and there’s your message. It’s as if the art piece itself has the encryption and decryption algorithm built-in, so applying the key yields the message immediatly.

So what now?

Like many people, I think in analogies. I see how this art obfuscates a message that can only be revealed in a dimension below its own. I feel like there’s an analogous type of encryption that could be applied to textual messages. As I said, I’m an amateur, but I’ll continue to contemplate it.