A carrier is the baseline transmission (such as a wave) that is modulated for a signal. Carriers have minimum entropy. Their opposite, noise, has maximum entropy. A signal conveys a message between a sender and a receiver. The entropy of signals is between that of the carrier and noise.

Carriers are the canvas for the artist. The canvas starts out blank. Then paint is added, which is the signal for the viewer. Noise would be like splotches of paint that somehow got put on the canvas. If the canvas were all noise, the signal would be completely covered with random bits of paint. The signal is designed to be between these extremes.

The closer a signal is to looking like the carrier, the lower the entropy and the simpler the message. The closer a signal is to looking like noise, the higher the entropy and the less the complexity of a message that can be transmitted. With the carrier alone or noise alone there is no message.

Design works the same way. A carrier alone or noise alone exhibit no design. A simple design would be similar to a carrier or to noise. A more complex design would be between the extremes of all carrier and all noise.

Entropy is a way to determine the presence of design. The more that entropy is in-between zero and the maximum, the more likely it is a result of design. A simple measure of design may be constructed from entropy as follows:

Define a design index, *Υ* (upsilon) from the entropy, *H*, as

*Υ* := (*H* – *H*_{min}) / (*H*_{max} – *H*_{min}),

which ranges from zero if *H = H*_{min} to one if *H = H*_{max}. If the design index is one-half, then *H* is the mid entropy. The closer the value of *Υ* is to one-half, the more likely the distribution is the result of design.

2015, updated