Midterm Solution Sheet

CS599: New Perspective/Directions for Computing

October 18, 2007

This midterm is open book (i.e., readings) and notes (lecture notes, etc.). The answers on this test must be your own work though. Point assignments roughly correspond to time allocations. There is a total of 60 points, although you have the full class period should you need it.

1. For each of the following topics, specify one appropriate expression to represent it (in terms of P, L, S, and C) and give a short explanation. There may be more than one appropriate expression, but just give one.
• Babbage’s Analytic Engine {3}

C/P: It is a physical (mechanical) implementation of computing.

• Fredkin’s Digital Physics {3}

P/C: It is the implementation of the physical world by computing.

• Biochemistry {3}

L/P: It is the physical (chemical) implementation of life.

• A RAP team (a group of collaborating Robots, Agents, and People) {5}

((L/P)[S/C])ⁱ«(S/C)^j«S^k: Robots are physically implemented life with embedded computationally implemented mind (although it is okay to think of them otherwise as well, such as without the life aspect: P[S/C]) and agents are computationally implemented mind (although they also could be embedded in computing: C[S/C]). There are multiple of each type of entity interacting in general.

2. For each of the following expressions, specify one appropriate topic to which it corresponds, and give a short explanation. There may be more than one appropriate topic, but just give one.
• C/Cⁿ {3}

This is a layer of computing implemented by multiple interacting computers, and so could be grid computing, a distributed operating system or other such things.

• S«(L/P) {3}

This is a human interacting with a physical implementation of (at least some part) of life, and so, for example, could be a human controlling a prosthetic arm via a brain computer interface.

• (L/P)[S/C] {5}

This is a lifelike intelligent robot, and so could be an android or other such entity.

3. Energy usage is an issue in a number of the topics we have examined. List the two in which you think that energy usage is the most challenging, and explain why it is particularly challenging in those two topics. There is no single right answer, but some topics are clearly more challenging than others. {15}

Two obvious ones are brain prostheses and sensor networks (or, more broadly, ubiquitous computing). In the former, you have two major problems: (1) heat dissipation can damage the delicate brain tissues within which the prosthesis is embedded, so either very low power or some other means of dissipating the energy is required; and (2) it must be autonomously powered without requiring frequent surgeries to change batteries or a permanent external connection that would risk infection. In the latter, you have anything from tens to millions of devices, many of them inexpensive and wireless, but which must operate for years without human intervention.

4. Mathematics (M) might be thought of as a fifth great domain that could be related to the other four we have examined. Is it useful to look at it in this way? Please justify your answer. {20}

One possible view is that, while mathematics clearly interacts with the other four domains – e.g., providing tools for modeling aspects of those domains – because it is passive (just a language for description), it doesn’t actually behave and thus can’t implement, interact or be embedded in the others, and thus is not a domain of the same kind as the others.

A second possible view is that mathematics can actually behave, when combined with appropriate equation solving and theorem proving methods, and so is a legitimate candidate as a fifth domain. In this sense, logic plus theorem proving (M) may be able to implement intelligent behavior (S), as pursued by the logicist paradigm in AI; and C can implement M as is done with everything from calculators to Mathematica to automated theorem provers. Where it would fit in a hierarchy of domains, if there really is a hierarchy, is as ambiguous as with C though.

A third possible view is that when equation solving and theorem proving methods are included as part of mathematics, M just becomes a subdomain of computing (C) instead of being an autonomous fifth domain. The rationale for this is that mathematics is just one special instance of the algorithmic manipulation of symbols – where certain formal properties govern the process – whereas computing is about investigating this in all of its aspects.

The point of this question was not that any one of these perspectives is necessarily right, but to get you to think about the relationship and to articulate your thoughts and arguments in a coherent fashion. My current intuition is that the second approach won’t hold up ultimately, but either the first or third could, depending on whether the processes are included in M.