Due 5:00 PM, Wednesday Sept 30, on paper, in class or in the box outside my office (Room 311, 3rd floor, CS building).
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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 -- a brief answer that clearly indicates what you have in mind is fine, 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: it saves paper if you just give the answers. PLEASE submit typed material, not hand-written, if at all possible, and keep a copy for yourself just in case something goes astray.
Relying too much on computers can destroy your ability to make quick quantitative estimates, and to recognize numeric nonsense when you see it. This problem set asks you to do some estimating of your own, and to assess some estimates made by others; both are useful skills. Do not use Google or other search engine for these questions. Your task is to work from what you know and can reason about, not what you can look up.
Webster's 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. If your calculator displays 8 figures, they aren't necessarily significant; do not blindly copy down all the digits. A ballpark or "quick and dirty" estimate is all we want.
(a) How many times a week (total for all undergrads) are prox cards used to enter dorms?
(b) How much disk space 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 characters takes at most one byte of storage.) Write down what might be in one such transaction, just to make it concrete.
(c) 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 this compression. We're not looking for anything sophisticated here, 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.
(a) Google's goal for Street View is to have pictures taken along every street in the USA (and a lot of the rest of the world as well). Estimate how many miles of streets there are in the USA.
(b) How much money would Google spend on gas for all this driving?
(c) How much money would Google spend paying drivers? (This job is probably better paid than flipping burgers, but not much.)
(d) Google takes 9 pictures about every 10 feet. Supposing that Google is just using ordinary consumer-grade cameras (probably not true) and storing JPG images, how much disk space would it take for the images for the whole USA? If you don't know how big a typical image is, look at the sizes of some random pictures.
(e) How much would it cost to buy consumer-grade hard disks to store this data? You can check sites like Amazon to see how much disks cost if you haven't a clue.
For parts (b) through (e), state clearly what value(s) you are assuming from earlier answers, so we can give you credit for sound reasoning even if your starting numbers seem too far off.
The world is full of big numbers, some of which mean something, but most people have no understanding or intuitive grasp of how big such numbers are, nor do they have shortcuts for doing arithmetic on them. The purpose of this problem is to get you to work with some big numbers; the shortcuts will come along soon.
(a) A full page advertisement in the NY Times on Sept 1, 2009 under the heading 'Think America is "Unsinkable?"' notes that the federal debt is projected to grow by more than $9 trillion in the next ten years. It goes on to say that "One million seconds equals 12 days. One trillion seconds is more than 30,000 years!" Are these numbers approximately correct? How long is one billion seconds?
(b) "In late August 2009, WHO (the World Health Organization) predicted a large rise in swine flu cases during the remainder of 2009 and into 2010. WHO advised that there would be a period of further global spread of the virus, and most countries could see swine flu cases double every three to four days for several months until peak transmission was reached." (Wikipedia's version of a widely disseminated news story.) Suppose there are 1000 people with swine flu today. If the doubling period is 4 days and peak transmission is reached after two months, how many people will be infected? (This is the optimistic scenario.)
(c) Now suppose that the doubling period is 3 days and peak transmission is reached only after three months, a pessimistic scenario. How many people will be infected?
There a lot of ways in which we are watched, both literally and figuratively. We have already talked about cell phones and prox cards as gadgets that can report on your location.
(a) Find a surveillance camera somewhere on or near campus. If you want some moral satisfaction, take a picture of it. Report its location precisely enough that others can find it.
(b) Name something else, not already discussed in class, that can quietly report your physical location without any action on your part. How would you defeat its efforts?
