Due 5:00 PM, Wednesday Sept 18, on paper, in the box outside my office (Room 311, 3rd floor, CS building) or in class.
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Collaboration policy for COS 109:
Working together to really understand the material in problem sets and
labs is encouraged, but once you have things figured out, you must part
company and compose your written answers independently. That helps
you to be sure that you understand the material, and it obviates questions
of whether the collaboration was too close.
You must list any other class members with whom you collaborated. |
Problem set answers need not be long, merely clear enough that we can understand what you have done, though for computational problems, show enough of your work that we can see where your answer came from. There is no need to repeat the question, and it saves paper if you just give the answers. PLEASE submit typed material, not hand-written, and keep a copy for yourself just in case something goes astray. Thanks.
Do not use Google or other search engines for these questions. Your task is to work from what you know and can reason about, not what you can look up.
"Any sufficiently advanced technology is indistinguishable from magic."
(Arthur Clarke, "Report on Planet 3", Technology and the Future, 1972)
We are surrounded by technology that does many things for us, but most of the time we hardly even notice. Everyone on campus carries an example: the prox card. The purpose of this problem is to encourage you to think about how prox cards work and why they are as they are.
The external manifestation of the prox card is simple: you wave your card near the little black box and the door unlocks. Clearly the card and the black box hook up, at least briefly. But how? How does the card know there's a black box nearby? How does the black box know there's a card nearby, and which card it is? How does it know whether to unlock the door? What is the black box connected to? What information is transferred from where to where? What happens when you lose your prox? What can go wrong, and what are the consequences? What other systems are similar?
How does this relate to the course? In microcosm, the prox card system involves much of the kinds of material we'll be talking about. There is hardware, software to make it work, and communication among components. There are tradeoffs in how information is represented, processed, transferred, and stored. And there are non-technical concerns like privacy, security, and economics.
Answer the following questions. There's no need for long essays or even full sentences -- a brief phrase that clearly indicates what you have in mind is fine. For numeric answers, keep in mind issues like measurement accuracy and significant figures.
(a) "Prox" is short for "proximity." How close is that? Measure the distance from the sensor at which your prox card unlocks the door. Do the experiment 5 times under constant conditions and report all 5 distances. Be careful, but don't fudge: there's no reason to expect that the result will be exactly the same each time, and one of the purposes of the experiment is to see how variable the sensitivity is.
(b) Normally the prox works even if it's in a pocket or a purse. Find a (non-destructive!) way to prevent the sensor from noticing your card even if you hold it quite close.
(c) Distance sensitivity is only one of a variety of experiments that one might perform to determine properties of the prox card system. Describe two similarly simple and plausible experiments that you could perform that would not arouse the interest of Public Safety and that would not damage your card. A single clear phrase or sentence that states what you would be trying to determine and what you would do is enough for each. For example, "Test whether the sensitivity varies during the day by measuring the distance at 4-hour intervals." You don't have to actually perform the experiments, though you're welcome to do so.
(d) Your prox has a number of visible things that identify you specifically. List them all.
(e) You open doors by waving the prox, you get food by swiping it, and the library uses yet another mechanism when you check out a book. Why does the library neither wave nor swipe? Suggest a plausible explanation.
One of the problems with the pervasive use of computers is that they can destroy your ability to make quick quantitative estimates, and to recognize numeric nonsense when you see it. This problem asks you to do some estimating of your own; later assignments will also ask you to assess estimates made by others. Both are useful quantitative reasoning skills.
My Webster's dictionary defines estimate as "to judge or determine generally but carefully; calculate approximately." Note the words generally and approximately. If the data you start with is approximate, the results cannot be precise; your calculator displays 8 figures, but they aren't necessarily significant, so for the following questions, a ballpark or "quick and dirty" estimate is enough. Brief answers are best, but show enough of your work that we can see how you got your answer.
(a) How many times a week (total for all undergrads) are prox cards used to enter dorms?
(b) How many bytes might it take to store a record of a typical single transaction: a particular student opens a specific entry/door at a specific time on a specific date? (Think of the number of characters you would have to write down if you were doing this by hand; each of those takes at most one byte on a computer.) Write down what might be in one such transaction, just to make your numeric answer concrete.
(c) Roughly how many megabytes would be required to hold the records for all students for one week?
(d) If you had records for a bunch of transactions, say an entire semester, you might be able to compress the information so it takes less space. Briefly describe a way that you might be able to do some compression. We're not looking for anything sophisticated, just an idea that might work. It may help to think about what's repetitive and thus redundant and thus only needs to be stored once for a large group of related transactions.
(e) Suppose a surveillance system takes a picture of each student each time he or she uses their prox. How many gigabytes (very roughly) would be required to store these pictures over the course of one academic year? Be as quantitative as necessary to support your position, but not excessively so -- this is a question about ballpark figures. The "right" answer will depend on your assumptions, so state them clearly.
(a) What is the capacity of the hard drive in your computer, in gigabytes? On a Mac, push the Apple logo button at the top left of the screen, and look at "About this Mac". On a Windows PC, try Start > Control Panel > System and Security > System.
(b) How much RAM does your computer have, in gigabytes?
(c) How many pixels does the screen of your computer have horizontally and vertically? How many total pixels is that?
(d) The "aspect ratio" is the ratio of width to height, and is usually given as something like "5:3", where the values are the width and height reduced to lowest common denominator. What is the aspect ratio of your laptop screen?
(e) Assuming that the pixels on the screen of your cell phone are the same size as the pixels on your laptop, approximately how many pixels are there on your cell phone screen? (Hint: how many pixels are there per square inch or cm on your laptop screen?)
