Department of Electrical Engineering and Computer Science  Department of Mechanical Engineering  6.050J / 2.110J     Information, Entropy and Computation

Frequently Asked Questions

1. Are these questions really frequently asked?

Of course not. Most have never been asked in exactly this form. However, questions and answers are a good way to explain things.

2. What is this course all about?

Information and entropy. Information is a measure of the amount of knowledge; it is not that knowledge itself. Thus information is like energy, in the sense that knowing the amount of energy does not tell you anything about its nature, location, form, etc. The same is true with information. Entropy is one kind of information. It is the information you do not have about a situation.

3. The information I don’t have? Is this different from the information you don’t have?

Certainly. Information is subjective, or observer-dependent. You know things that I don’t. This, after all, is why communication is useful.

4. But is entropy also a subjective quantity?

Strictly speaking, yes. However, in physical situations the difference of entropy as perceived by two observers may be negligibly small.

5. If information is the measure of a quantity, what are its units?

Information is measured in bits. More bits means more information.

6. Is entropy also measured in bits?

Yes. However, in physical situations lots of the information is not known. (Think about how many bits of information are needed to specify the position of all atoms in an object.) It is impractical to work with such large numbers, so another set of units is used: Joules per Kelvin.

7. Wait a minute. Entropy is physical and information is mathematical. How can they be the same?

Historically, information storage and transmission required a physical artifact of some kind (think of newspapers, books, and medieval manuscripts). So traditionally information has also been physical—most of the cost of information processing was due to the physical carrier of the information. Only recently has the cost of storing, moving, or processing information become so low that we think of information apart from its physical form, not even subject to physical laws. But this is only temporary. Eventually, information technology will have to face the limits imposed by quantum mechanics and thermodynamics, and it will again be necessary to understand the fundamental physics of information. This time it will be entropy that is the relevant physical concept.

8. You mentioned cost. What about the economics of information and entropy?

When the physical media carrying information were costly, people could buy and sell information by buying and selling the physical artifact that carried it. Now new economic models and new laws are needed for commerce of intellectual property, the most prominent examples being music and movies. These models and laws will have to be changed again when quantum limitations on information processing become important. If the new laws are consistent with the underlying physics, they will be easier to understand and enforce.

9. Why is information so important?

This is the beginning of the information age. Just as the industrial age was opened up by our ability to manage energy, so the information age is upon us because we are learning how to manage information effectively.

10. Why is entropy so important?

Entropy is one of the most mysterious of all the concepts dealt with by scientists. The Second Law of Thermodynamics states that the entropy of a given situation cannot decrease unless there is a greater increase elsewhere. Thus entropy has the unusual property that it is not conserved, as energy is, but monotonically increases over time. The Second Law of Thermodynamics is often regarded as one of science’s most glorious accomplishments. And also one of the most difficult to understand.

11. If entropy is so difficult, can a freshman really understand it?

Certainly. It’s all in how the topics are approached. It is true that the concepts involved here are not normally taught to freshmen. This is a shame, because freshmen, and even high-school students, have the background to appreciate them if approached from the point of view of information. Traditionally the Second Law of Thermodynamics is taught as part of a course on thermodynamics, and a background in physics or chemistry is needed. Also, the examples used come from thermodynamics. In this course, the Second Law is treated as an example of information processing in natural and man-made systems; the examples come from many domains.

12. I am thinking about taking this course. What do I need to know to start?

You need to understand energy, and how it can exist in one place or another, how it can be transported from here to there, and can be stored for later use. You need to know how to deal with a conserved quantity like energy mathematically, and to appreciate that if energy increases in one region, it must decrease elsewhere. More specifically, the prerequisite for this course is the first semester freshman physics subject 8.01 (or 8.012, 8.01L, or 8.01T).

13. Is entropy useful outside of thermodynamics?

All physical systems obey the laws of thermodynamics. The challenge is to express these laws in simple but general forms so that their significance in, for example, a biological system gives insight. Besides, laws similar to the Second Law of Thermodynamics are found in abstract systems governed more by mathematics than physics—two examples discussed in the course are computers and communications systems. In these contexts the “information” part of “Information, Entropy and Computation” is important.

14. Why aren’t information and entropy normally thought of together?

Most scientists now recognize that information can be exchanged for entropy and vice versa. but they don’t consider that fact important. The reason is that in typical physical situations the number of bits of entropy is far larger than the number of bits of information that even the largest information processing systems can deal with. In other words, the scales involved are vastly different. This is because there are a large number of atoms in physical systems.

15. But then why treat them together now?

For two reasons. First, the underlying principles are the same so you only have to learn them once, and once learned they can be appreciated in a broader context. And second, modern technology is continuously increasing the amount of information that computers and communication systems can deal with. Another way of saying this is to observe that modern microelectronic systems control more bits with fewer atoms. As the number of atoms per bit comes down, the difference in scale between information in computers and communications systems and entropy in the corresponding physical systems shrinks. Eventually it will be possible to make devices that cannot be understood without considering the interplay between the information stored in the device and the entropy of its physical configuration. A growing technical field, known as Quantum Information Processing or Quantum Computing, deals with this situation.

16. If I take this course, can I get a summer job?

Certainly, but probably not because of anything you learn here.