Human DNA contains almost twice as much information as is needed to code for all the substances produced in the body. Likewise, the digital data sent from Voyager II contained one redundant bit out of every two bits of information. The Hubble space telescope transmits three redundant bits for every bit of information. How is entropy related to the transmission of information? What do you think is accomplished by having so many redundant bits of information in both DNA and the space probes?

Entropy is a concept in information theory that represents the uncertainty or randomness in a set of data. It's a measure of the amount of information needed to specify an outcome from a set of possibilities. In the context of information transmission, lower entropy implies less uncertainty and therefore more predictable outcomes, while higher entropy implies high uncertainty and more unpredictability.

The reason behind having redundant bits of information in both DNA and space probes lies in the concept of error detection and correction. In real-world applications, both biological processes and digital transmissions may experience various forms of noise, such as errors during replication (in the case of DNA) or disturbances in the transmission medium (in the case of space probes). Redundant information helps in detecting and correcting these errors by providing additional context that can be used to infer the original intended message even if some part of the message was corrupted or lost due to the noise. This process improves the reliability of the information transmission and reduces the impact of uncertainties.

In the case of DNA, having nearly twice as much information as needed for coding plays an essential role in ensuring the accurate replication of genetic information. Errors in the DNA replication process could lead to mutations and potentially cause diseases or other health issues. Thus, the presence of redundant information allows for error detection, and it helps to maintain a stable and accurate genetic structure in living organisms.

When communicating with space probes, such as Voyager II and the Hubble Space Telescope, the chances of the digital data being corrupted or lost are significant due to the vast distances, energy fluctuations in space, and potential interference from cosmic phenomena. The use of redundant bits for every bit of information increases the probability of correctly transmitting the data to Earth, despite any errors. To summarize, the transmission of information is related to entropy: redundant bits of information are essential for maintaining reliable and accurate data transmission. Redundancy in both DNA and space probes exemplifies how living organisms and human-engineered systems overcome uncertainties and improve the stability of information transmission.