tag:blogger.com,1999:blog-69185394403984699122018-03-06T01:37:02.490-08:00SyzygyYes, syzygy is a real word. (Knowing it gave me a perfect score on a bonus spelling quiz during high school optics.) Syzygy refers to the alignment of celestial objects (such as during an eclipse). Besides being a cool word (three y's and one z!), I thought it would be a fitting title for a blog that covers *all* of my interests.Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.comBlogger122125tag:blogger.com,1999:blog-6918539440398469912.post-29703751079705883952012-02-07T14:27:00.000-08:002012-05-25T14:15:41.777-07:00Why I hate programming (part 4 of n)back to <a href="http://www.r-project.org/">R</a>:<br /><br />1. Writing some code, seemed a bit slow, looked to <a href="http://stackoverflow.com/">stack overflow</a> for help:<br /><blockquote>"First of all, for anyone who hasn't seen this yet, I strongly recommend <a href="http://wiki.r-project.org/rwiki/doku.php?id=tips:programming:code_optim2">reading this article on the r-wiki</a> about code optimization."</blockquote><br /><span style="font-style:italic;">status of link:</span> dead<br /><span style="font-style:italic;">reason:</span> R's <a href="http://wiki.r-project.org/">wiki page</a> is dead<br /><br />2. Populating a matrix from a vector. (In R, a <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/matrix.html">matrix</a> is different from an <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/array.html">array</a> is different from a <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/vector.html">vector</a>.)<br /><pre><code><br />vec <- 1:9<br />mat <- as.matrix(vec, nrow = 3, ncol = 3)<br /># mat is 9x1 (silent fail on invalid arguments nrow and ncol)<br />mat2 <- matrix(vec, nrow = 3, ncol = 3)<br /># mat2 is 3x3<br /></code></pre><br />3. How big is my vector?<br /><pre><code><br />vec <- 1:9<br />mat2 <- as.matrix(vec, nrow = 3, ncol = 3)<br />nrow(vec) # NULL<br />nrow(mat2) # 3<br />NROW(vec) # 3<br />NROW(mat2) # 3<br /></code></pre>Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0tag:blogger.com,1999:blog-6918539440398469912.post-84245177246154097312011-08-27T20:51:00.000-07:002011-08-29T21:39:31.740-07:00USPC 2011Well, it just wouldn't be a <a href="http://wpc.puzzles.com/uspc11/">USPC</a> without a roundup. (see also <a href="http://collinear.blogspot.com/2010/08/uspc-2010.html">USPC 2010</a>, <a href="http://collinear.blogspot.com/2009/06/uspc-2009.html">USPC 2009</a>, <a href="http://collinear.blogspot.com/2008/06/uspc-2008-wrapup.html">USPC 2008</a>, <a href="http://collinear.blogspot.com/2007/06/uspc-2007.html">USPC 2007</a>)
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<br />1. Battleships
<br />Ugh, I spent too much time running around in circles, trying to figure out where to place the cruisers. Somehow I got it into my head that I needed one in the leftmost column, because they couldn't fit in the rightmost two columns. I ended up printing out this page three times, making the same deductions before finally solving it.
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<br />2. Sudoku
<br />Ok going at first, but then I got stuck, so I did a little bit of guessing and worked it out. Slower than I like, but not as bad as Battleships.
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<br />3. Crossied Countries
<br />No problems here.
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<br />4. Barn Storm
<br />For some reason, I thought had one less difference than I had found and wasted a few minutes trying to find an 11th!
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<br />5. Easy as ABCD
<br />More information than I was used to (compared to the Mensa Blue Book), but also larger than the ones I had practiced on. After a few initial deductions, I did a little bit of guessing and got it completed.
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<br />6. Times Like These
<br />Tried fiddling with the first row for a bit, and then looked at the third row. The 7 there needs to be either the tens digit in the product or the ones digit of one of the multiplicands. Some quick checking yielded 2x6x7=84. Cross-referencing the columns, I got the placements, filled in the first column, and then the rest.
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<br />7. Masyu
<br />Did as much logic stuff as I could, most notably the top-left and bottom-left corners, then did some pencilwork for filling in the rest.
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<br />8. Square Count
<br />More or less ok, but missed 2 of the A=2 diagonal squares, so only partial credit.
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<br />9. Crack It On
<br />Worked on breaking the right side first, since it required at least three words beginning with the same letter. Some trial and error with the remaining words got the left side.
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<br />10. Flash Cards 1
<br />Mostly trial and error, working with different digits for the single in the product.
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<br />11. Flash Cards 2
<br />Quickly realized that the denominator needed to factor into two single digits for the flip, and only a few possibilities existed among the digits (32, 36, 27, 63, no right side up 8 or 9 for 72 to work).
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<br />12. Takeout
<br />Pretty straightforward.
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<br />13. Corral
<br />Not bad, but slower than usual, esp. trying to figure out whether the central mass in the 7th row needed to break out right or left.
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<br />14. Blocks (solved after time)
<br />Easy deduction of the square and 4-long piece. Then a dead-end in the bottom-right yielded one more. Worked out a <a href="http://en.wikipedia.org/wiki/Hamiltonian_path">Hamiltonian path</a> in the middle-left that seemed likely, and made placements from there.
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<br />15. Hex Words
<br />Still working on it.
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<br />16. Word Connection (solved after time)
<br />The two "P"s and two "T"s were good for fixing September/April and October/August, respectively, and then just needed to fit the rest in.
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<br />17. Hopper (solved after time)
<br />Not as bad as <a href="http://motris.livejournal.com/149835.html">Tom Snyder's practice</a>. The second 1 didn't leave a lot of choices, and I stopped trying to make it too compact, since it needed to be a unique fit for 8x8.
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<br />18. Corral Crates
<br />Still working on it. Doesn't seem too bad, if larger than <a href="mellowmelon.wordpress.com/corral/crate-corral/">Palmer's</a>.
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<br />19. Kaku Rogue
<br />Got everything but the top-left and lower-right corners. Not sure of a good way to go about it except to try different numbers until one works. The first time for me that checking column and row sums worked: in this case, for the singleton connecting squares.
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<br />20. Jumping Crossword
<br />Still working on it.
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<br />21. Hungarian Tapa
<br />Still working on it.
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<br />22. Dynasty Sudoku (solved after time)
<br />A long time making deductions, then guessing, only to get a solution that is only slightly wrong with two transpositions and violating the single-connected-space constraint.
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<br />Potential points: 170
<br />Expected points: 160 (partial credit on 5.)
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<br />Fingers crossed for a good ranking this year.
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<br />EDIT: Hex Words isn't bad, once you realize that intersecting words on a hex grid need to have valid words along all three axes. This forces JUDO into the upper-left, and using an efficient packing heuristic for the rest works pretty well.
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<br />Corral Crates also wasn't too bad, though I messed up early and had a contradiction. Much of the strategy is the same as for Corral: since each crate cannot touch empty space diagonally, the really useful anti-checkerboard constraint still holds.
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<br />Kaku Rogue worked out with more guessing, but I need to check my answer -- Oops, didn't even see the second constraint on exactly one negative number per row and column. Good thing I didn't do this one, I guess!
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<br />EDIT 2: Looks like I did miss a 10th difference on Barn Storm, so my total score this year is 154.Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0tag:blogger.com,1999:blog-6918539440398469912.post-68250226667270973262011-03-23T17:44:00.000-07:002011-03-23T18:11:30.878-07:00On FuzzinessI have debated (with myself) on whether to blog about my (mis-)adventures in tutoring at the City Heights Farmer's Market/Library as part of <a href="http://gdawgsio.org/">SIO GDAWG</a>'s outreach efforts. I figure it will be ok to simply remark about both the (1) gaps in knowledge (conceptual or otherwise) of the kids and (2) weirdness of homework that these kids bring.<br /><br />One girl (who came twice, but whom I haven't seen in a month or two) had trouble in her math class. She was taking Algebra I, and somehow had made it through most of the first semester (I'm guessing they started algebra in the Fall) without anyone noticing that she was having basic trouble with arithmetic. For the most part, she could do basic numerical operations, but had a very flaky grasp of <a href="http://en.wikipedia.org/wiki/Order_of_operations">order of operations</a>, <a href="http://en.wikipedia.org/wiki/Distributive_property">distributive properties</a>, and <a href="http://en.wikipedia.org/wiki/Negative_number">negative numbers</a>. (from what I could tell) Needless to say, it was a bit much to ask her to do operations involving linear equations.<br /><br />One boy (4th grade?) hadn't yet memorized his multiplication tables. Irregardless of this (which isn't uncommon for his age), he didn't understand that multiplication represented repeated addition. The problem with not knowing this concept is that treating multiplication as a black box operation is going to be very bad news for this kid when he starts algebra (see above).<br /><br />Last week I also helped a kid with some worksheets dealing with St. Patrick's Day (SPD). The first page was basically a crossword with a single clue running vertically that spelled out "leprechaun". Problem is, there were some really vague (and obscure) clues that depended on both awareness that it was SPD-themed as well as the cultural aspects associated with SPD. (Really, how many people will know of the top of their heads that "Emerald Isle" refers to Ireland?)<br /><br />In the same packet, there was a word association page where one item would be given and two blanks needed to be filled with items from a word box. Unfortunately, some of the examples were synonyms ("wee" -> "little", "small") and some were same-category-membership ("Japan" -> "Mexico", "Japan"). What this demonstrates and what you were supposed to do if you didn't know some of the words (e.g. the kid didn't know what "wee" meant) is beyond me.<br /><br />On a later page, there were a series of analogies. Besides the fact that analogies were not explained, a lot of the problems violated the standard guidelines for analogies (as they are used in the SAT and other "important" tests). For example, in A:B::C:D, the relationship between A and B should be the same as that between C and D. The analogy should NOT rely on any association between A and C or B and D. (which is what SAT writers like to do to trip people up)<br /><br />On another page, there were some weird set exclusion problems (e.g. "What are the numbers that are in the square, but not in the triangle and circle?") in reference to a figure. Problematically, the use of language was imprecise: the questions sometimes used "and" and sometimes used "or", when in both cases, the desired <a href="http://www.youtube.com/watch?v=mkO87mkgcNo">conjunction</a> was "nor"!<br /><br />The busywork nature of the worksheets also seemed weird to me. I guess the standard purpose of homework these days is to occupy time rather than practice what you learned or apply those skills in reasonable useful example situations. I am reminded of Feynman's <a href="http://www.textbookleague.org/103feyn.htm">remarks</a> on science textbooks:<br /><blockquote>Finally I come to a book that says, "Mathematics is used in science in many ways. We will give you an example from astronomy, which is the science of stars." I turn the page, and it says, "Red stars have a temperature of four thousand degrees, yellow stars have a temperature of five thousand degrees . . ." -- so far, so good. It continues: "Green stars have a temperature of seven thousand degrees, blue stars have a temperature of ten thousand degrees, and violet stars have a temperature of . . . (some big number)." There are no green or violet stars, but the figures for the others are roughly correct. It's vaguely right -- but already, trouble! That's the way everything was: Everything was written by somebody who didn't know what the hell he was talking about, so it was a little bit wrong, always! And how we are going to teach well by using books written by people who don't quite understand what they're talking about, I cannot understand. I don't know why, but the books are lousy; UNIVERSALLY LOUSY!<br /><br />Anyway, I'm happy with this book, because it's the first example of applying arithmetic to science. I'm a bit unhappy when I read about the stars' temperatures, but I'm not very unhappy because it's more or less right -- it's just an example of error. Then comes the list of problems. It says, "John and his father go out to look at the stars. John sees two blue stars and a red star. His father sees a green star, a violet star, and two yellow stars. What is the total temperature of the stars seen by John and his father?" -- and I would explode in horror.<br /><br />My wife would talk about the volcano downstairs. That's only an example: it was perpetually like that. Perpetual absurdity! There's no purpose whatsoever in adding the temperature of two stars. Nobody ever does that except, maybe, to then take the average temperature of the stars, but not to find out the total temperature of all the stars! It was awful! All it was was a game to get you to add, and they didn't understand what they were talking about. It was like reading sentences with a few typographical errors, and then suddenly a whole sentence is written backwards. The mathematics was like that. Just hopeless!</blockquote>Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0tag:blogger.com,1999:blog-6918539440398469912.post-43692333555300548312011-03-02T11:08:00.000-08:002011-03-02T11:13:01.281-08:00bibtex & capitalizationIt seems that most of the default bibtex styles convert all non-first letters in titles to lowercase. This is problematic, since of course many papers have proper nouns (e.g. locations, species, named concepts) in their titles! Rather than go through and attach braces "{}" around all letters that need capitalization preserved, it makes more sense to edit the bibtex style file (*.bst) to preserve the title:<br /><blockquote>If you prefer to edit the bibtex style (.bst) rather than the bibliography (.bib), you can search for occurences of change.case$ in it. This is the function that capitalizes or title-izes fields that are not people names.<br /><br />Typically, for the title field, you should find something like title "t" change.case$. Since you want the title unmodified, replace that by just title.</blockquote><br />All I needed to do was copy the bibtex style file into the local folder with my tex document, edit it, and re-compile. Voila!<br /><br />From <a href="http://stackoverflow.com/questions/2800527/preserving-all-capitalization-in-bibtex">here</a>.Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0tag:blogger.com,1999:blog-6918539440398469912.post-3300261849561568932011-02-22T13:47:00.001-08:002011-02-22T13:56:07.464-08:00Streamlining the workflowYes, <a href="http://pages.uoregon.edu/koch/texshop/">TexShop</a>'s keyboard-command typesetting is nice, but I couldn't figure out a way to get it to run through the whole 4-step process (latex/bibtex/latex/latex) for making a file with cited references with one keystroke.<br /><br /><a href="http://www.lyx.org/">Lyx</a> will do the whole compilation in one command, but its interface doesn't allow me to edit just the latex code, instead forcing me to use some weird WYSIWYM viewing mode.<br /><br />Luckily, I found some <a href="http://www.xs4all.nl/~msneep/latex/">scripts</a> that will integrate <a href="http://www.tug.org/mactex/">MacTex</a> and <a href="http://www.barebones.com/products/textwrangler/">TextWrangler</a>.<br /><br />I still needed a single keystroke full-compile-and-view command though, so I glued the "Full document compilation" and "Show result" scripts together and assigned it a keyboard shortcut (Window->Palettes->Scripts->Set Key...).<br /><br />I also needed to edit the shell script to use Preview instead of <a href="http://skim-app.sourceforge.net/">Skim</a>. Maybe this means I should play around with Skim a bit?<br /><br />Anyway, this now allows me to select a bunch (or all) of references in <a href="http://mekentosj.com/papers/">Papers</a>, export to bibtex, and cite them easily (assuming that the metadata in Papers is correct).Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0tag:blogger.com,1999:blog-6918539440398469912.post-75077561337921279742011-01-30T17:20:00.000-08:002011-01-30T17:23:54.056-08:00JJ Abrams and his love of nicknames(or maybe just his writers?)<br /><br />NOTE: SPOILERS AHEAD!<br /><br />Examples:<br />Alias (season 4): "Arvin Clone" (imposter of Arvin Sloane)<br />Lost (all seasons): anything Sawyer says<br />Fringe (season 2): "Walternate" (<a href="http://en.wikipedia.org/wiki/Portmanteau">portmanteau</a> of Walter and alternate)<br />Fringe (season 3): "Faulivia" (portmanteau of Faux and Olivia)Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0tag:blogger.com,1999:blog-6918539440398469912.post-18650560177117993732011-01-27T11:53:00.000-08:002011-01-27T11:58:35.988-08:00Why I hate programming (part 3 of n)1. Matlab's inability to remember the current folder. Sure, you can set it so that the default location is a different location, but would it be so hard to remember the current folder when quitting and to automatically open that location when started again. Seems like a no-brainer to have some sort of checkbox for this in the preferences...<br /><br />2. Matlab's default renderer's inability to handle transparency. Yes, that's right, I want to plot two histograms on top of each other, but the only way it can do transparency is to enable the OpenGL renderer. This would be fine if the OpenGL renderer could do fonts properly, but it can't, and moreover is unable to save images in vector format. (Don't even get me started on trying to draw patterned bars...)<br /><br />more to come...Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0tag:blogger.com,1999:blog-6918539440398469912.post-8885465258152588082011-01-17T17:47:00.000-08:002011-01-17T17:51:26.145-08:00Verbification<object width="512" height="288"><param name="movie" value="http://www.hulu.com/embed/EJqYrjId0L20fJwhVxV01g/768/790"></param><param name="allowFullScreen" value="true"></param><embed src="http://www.hulu.com/embed/EJqYrjId0L20fJwhVxV01g/768/790" type="application/x-shockwave-flash" width="512" height="288" allowFullScreen="true"></embed></object><br /><br />Yes, <a href="http://en.wikipedia.org/wiki/Moe_Szyslak">Moe</a> just used <a href="http://en.wikipedia.org/wiki/Trompe-l'%C5%93il">trompe l'oeil</a> as a verb.Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0tag:blogger.com,1999:blog-6918539440398469912.post-19099376722452600212010-12-06T09:12:00.000-08:002010-12-06T09:18:05.647-08:00Dear Puerto RicoI humbly ask that you consider declaring independence. I realize that you may enjoy your position as an unincorporated territory of the United States, but the fact is, our federal government is, to put it nicely, insane. In this day and age, who still lives without representation at all levels of government? (dictatorships don't count!) I think it is only fair for Puerto Rico to take the reins of governing its own country and have the ability to assess and collect taxes and tariffs for its own well-being. Think of all that EEZ that you control and can make money off of. Or how about getting rid of the tariff for Roquefort cheese that Bush II passed out of spite? Such wonders (and more!) await a people that throw off the shackles of Western Imperialism!<br /><br />(Note that that is not in any way related to my trying to get NSF to give me international travel money to visit your fine state in February for a conference.)Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0tag:blogger.com,1999:blog-6918539440398469912.post-62971919589794944252010-11-19T03:11:00.001-08:002010-11-29T12:14:00.911-08:00CHMMC Tiebreaker 1Since they've put up the <a href="http://chmmc.caltech.edu/problems.html">problems</a> for the Fall 2010 competition, I figure it should be ok to discuss them publicly here.<br /><br />AFAIK, Henry Maltby was the only one (of 12 students) to solve Tiebreaker 1 correctly in the allotted time (10 minutes). I've reproduced the problem below:<br /><p class = "math">The numbers \(25\) and \(76\) have the property that when squared in base \(10\), their squares also end in the same two digits. A positive integer is called amazing if it has at most \(3\) digits when expressed in base \(21\) and also has the property that its square expressed in base \(21\) ends in the same \(3\) digits. (For this problem, the last three digits of a one-digit number \(b\) are \(00b\), and the last three digits of a two-digit number \(ab\) are \(0ab\).) Compute the sum of all amazing numbers. Express your answer in base \(21\).</p>One straightforward way to solve the problem is to find all the amazing numbers (in base \(21\)): Let the number be \(xyz\). Then \(xyz^2 = \left(x \cdot 441 + y \cdot 21 + z\right)^2\). We only need to consider the last three digits of this result, which is given by \((2 \cdot x \cdot z + y^2) \cdot 441 + 2 \cdot y \cdot z \cdot 21 + z^2\). This gives us the following equations:<br />\[\begin{align}<br />z^2 & \equiv z \, (\bmod{21}) \\<br />2 \cdot y \cdot z + \left\lfloor\frac{z^2}{21}\right\rfloor & \equiv y \, (\bmod{21}) \\<br />2 \cdot x \cdot z + y^2 + \left\lfloor\frac{2 \cdot y \cdot z + \left\lfloor\frac{z^2}{21}\right\rfloor}{21}\right\rfloor & \equiv x \, (\bmod{21})<br />\end{align}\]<br />We find that there are 4 solutions to the first equation: \(z = 0, 1, 7, 15\) with the corresponding \(\left\lfloor\frac{z^2}{21}\right\rfloor = 0, 1, 2, 10\). Solving for \(x\) and \(y\) yields the ordered triplets \((x, y, z) = (0, 0, 0), (0, 0, 1), (7, 16, 7), (13, 4, 15)\). Adding these together yields the base \(21\) number \(\boxed{1002_{21}}\).<br /><br />Of course we can generalize the problem by considering different bases, \(b\), as well as a different number of "digits", \(d\). Define \(A(b, d)\) to be the set of integers with at most \(d\) "digits" in its base \(b\) representation that, when squared, has the same last \(d\) "digits". Then define \(S(b, d)\) to be the sum of all the elements in \(A(b, d)\). The above problem is the special case, \(S(21, 3)\).<br /><br />First, we note that having the same last \(d\) "digits" in its base \(b\) representation is equivalent to having the same residue \(\bmod{b^d}\). So \(A(b, d)\) is the set of all solutions for \(x^2 \equiv x \, (\bmod{b^d})\) where \(x < b^d\). Simplifying, we get \(x(x-1) \equiv 0 \, (\bmod{b^d})\).<br /><br />Representing the prime factorization of \(b\) as \(b = p_1^{\alpha_1} p_2^{\alpha_2} ... p_k^{\alpha_k}\), this yields the following system of equations:<br />\[\begin{align}<br />x(x-1) & \equiv 0 \, (\bmod{p_1^{d \alpha_1 }}) \\<br />x(x-1) & \equiv 0 \, (\bmod{p_2^{d \alpha_2 }}) \\<br />\vdots \\<br />x(x-1) & \equiv 0 \, (\bmod{p_k^{d \alpha_k }})<br />\end{align}\]<br />For each equation, \(x\) must be either \(0\) or \(1\) \(\bmod{p_i^{d \alpha_i }}\). The <a href="http://mathworld.wolfram.com/ChineseRemainderTheorem.html">Chinese Remainder Theorem</a> tells us that each binary ordered \(k\)-tuplet (the \(i\)th bit being the solution to the \(i\)th equation above) corresponds to a unique residue (or value of \(x\)) \(\bmod{b^d}\).<br /><br />To find \(S(b, d)\), we observe that each ordered \(k\)-tuplet (corresponding to a solution, \(x\)) has a binary "inverse" (corresponding to a different solution, \(x^\star\)). The \(2^k\) ordered \(k\)-tuplets divide up perfectly into these pairs. Furthermore, we note that \(x + x^\star \equiv 1 \, (\bmod{p_i^{d \alpha_i }}) \, \forall \, i\) which means that \(x + x^\star \equiv 1 \, (\bmod{b^d})\). Because \(0 \le x, x^\star \le b^d-1\), \(x + x^\star\) is either \(1\) or \(1 + b^d\).<br /><br />However, \(x + x^\star = 1\) only for one \((x, x^\star)\) pair: \((0, 1)\). Therefore all other \((x, x^\star)\) pairs must sum up to \(1 + b^d\). Then \(S(b, d) = \boxed{(2^{k-1}-1)(1 + b^d) + 1}\). For the case where \(d = 3\) and \(k = 2\) such as when \(b = 21\), the answer will be \(\boxed{1002_b}\) as above.Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0tag:blogger.com,1999:blog-6918539440398469912.post-90351853427062196582010-11-18T22:01:00.000-08:002010-11-29T12:12:55.766-08:00MathJax TestIt works!<br />\[1+e^{i \pi} = 0\]<br />I basically followed this:<br /><a href="http://highly-distractable.blogspot.com/2010/07/math-math-everywhere.html">http://highly-distractable.blogspot.com/2010/07/math-math-everywhere.html</a><br />but used svn for easier updating and tweaked the access file to only outside access from my blog per the very last bit here:<br /><a href="http://www.mathjax.org/resources/docs/?installation.html">http://www.mathjax.org/resources/docs/?installation.html</a>Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0tag:blogger.com,1999:blog-6918539440398469912.post-85059976597438194312010-10-30T10:57:00.000-07:002010-10-30T11:05:39.146-07:00The ongoing search for the "Perfect Black Pen"Partially inspired by <a href="http://alteredartists.blogspot.com/2010/10/ode-to-pens-redux.html">this post</a>, I've decided to blog my continuing search for the "Perfect Black Pen".<br /><br />My own personal ideal has 3 main points:<br />(1) fine-point smooth dark ink (0.38mm Uniball Signo)<br />(2) retractable<br />(3) nicely weighted slim metal body (like a nice drafting pencil)<br /><br />The ability to write smoothly in a dark ink is the biggest priority and is also the biggest restriction on the latter two, because gel pens have the nasty property of being quite wide, which means they don't fit very well in slim metal bodies (not that many of those even exist for pens).<br /><br />Right now I use a silver-body G2 Limited with a black 0.38mm Uniball Signo cartridge. The pen looks nice and writes very well, but the body is still quite cheap (in comparison to nice drafting pencils). In particular, the metal body feels like an alloy of some sort (instead of brushed aluminum or stainless steel), and there is a preponderance of plastic parts that feel cheap (namely, the clip, tip, and clicker). The body is also not slim enough to fit in my organizer, which is a bit problematic, since I would really like to replace the Pentel ballpoint I have in there right now.Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0tag:blogger.com,1999:blog-6918539440398469912.post-22176183581747819782010-10-12T13:37:00.000-07:002010-10-12T13:49:17.230-07:00Why I hate programming (part 2 of n)The difference between using "=" and "<-" for assignment in R:<br /><br />It seems that, historically, "=" was not allowed for variable assignment. My understanding is that in modern R, using "=" for assignment is (mostly) equivalent to using "<-", so that:<br /><pre><code><br />x = 2 % This line is the same as<br />x <- 2 % this line.<br /></code></pre><br />However, one should be aware that when using "=" to give parameters for functions, assignments do not occur (in the global workspace):<br /><pre><code><br />x <- rep(2, times=5) % "times" does not have value 5<br />times % gives an error<br />x <- rep(2, times<-5) % "times" IS set to have value 5<br />times % this will have value 5<br /></code></pre><br /><br />There's also some weird differences with how "<-" and "=" get interpreted (maybe has to do with order of operations / syntactic sugar?):<pre><code><br />x = y = 5 % both "x" and "y" will have value 5<br />x <- y <- 5 % both "x" and "y" will have value 5<br />x = y <- 5 % both "x" and "y" will have value 5<br />x <- y = 5 % gives an error<br /></code></pre><br /><br />This is what R's documentation has to say about this nonsense:<br />"The operators <- and = assign into the environment in which they are evaluated. The operator <- can be used anywhere, whereas the operator = is only allowed at the top level (e.g., in the complete expression typed at the command prompt) or as one of the subexpressions in a braced list of expressions."Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0tag:blogger.com,1999:blog-6918539440398469912.post-60982963589356596982010-09-24T22:45:00.000-07:002010-09-24T22:55:26.299-07:00pageviewsGuess how many pageviews I have:<br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://2.bp.blogspot.com/_sbw5AHJSsYQ/TJ2Owi4UJqI/AAAAAAAAD1w/jmGZ4UILyPA/s1600/l33t_pageviews.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 400px; height: 170px;" src="http://2.bp.blogspot.com/_sbw5AHJSsYQ/TJ2Owi4UJqI/AAAAAAAAD1w/jmGZ4UILyPA/s400/l33t_pageviews.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5520725682873968290" /></a><br /><br />That's right, 1337!<br /><br />The most popular page is still my post on <a href="http://collinear.blogspot.com/2009/06/histograms-in-excel-for-mac-2008.html">histograms in Excel without the Analysis Toolpak</a>. I'm not sure if that makes me happy or sad.Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0tag:blogger.com,1999:blog-6918539440398469912.post-5405972771424378412010-08-21T12:43:00.000-07:002010-08-21T13:00:28.318-07:00USPC 2010The contest only just ended, but given that the penalty for submitting solutions this late outweighs any possible points that might be derived from reading this post, I figure it's ok for me to just go ahead and discuss the puzzles.<br /><br />1. Battleships - straightforward, but I got caught up a bit trying to use some pens that utterly failed. Went to my 2nd copy of the puzzles to complete.<br /><br />2. Sudoku - got stuck for a bit and moved on. Returned after a few more puzzles, and did some guesswork in the upper left to unravel.<br /><br />3. Count Me In - interesting puzzle, since all of the pentagons were concave. There's probably a rigorous way to do the counting, but I simply labeled the smallest regions and used that to record the pentagons I found, making sure to indicate where mirror matches were possible.<br /><br />4. Islands - It wasn't clear to me at first that all the given letters had to be in one of the words, but I assumed so and was able to figure this out. I got stuck on fitting in Earth and Saturn on the right, but resolved it pretty quickly.<br /><br />5. Groundhog Day - straightforward, but I eliminated almost all possible choices before getting to the three pairs.<br /><br />6. Hex Equation - skipped<br /><br />7. Mirror Mirror - skipped (dealing with the diagonal reflection seemed like a pain)<br /><br />8. Masyu - filled in some and then skipped. I think I just don't like Masyu that much.<br /><br />9. Rectangle Maze - burned a lot of time on this puzzle, before finally working it out. Going through F twice threw me off, I think as I had trouble getting both B and I on the path.<br /><br />10. Digitile - skipped.<br /><br />11. Route - skipped at first, then returned with 10 (or so) minutes left. Figuring out the 34->46 segment was a bit tricky at first, but once I more or less got that part, it was fairly straightforward to massage the other segments (46->57 and 57->69 were the trickiest) into a solution.<br /><br />12. Takeout - straightforward. I started with Basketball on the far right side, which filled in a few other clues. Then it was just a matter of searching for the words minus a particular letter.<br /><br />13. Corral - skipped. I really suck at these puzzles.<br /><br />14. Sukoro - once I thought about it some, I was able to get most of the bottom half, but made an error towards the end that burned a lot of time. Returning to this later and realizing it wasn't going to work, I started again from first principles, found my mistake and got it pretty easily.<br /><br />15. Constant Sum - skipped.<br /><br />16. Criss Cross Sums - skipped. About 1 minute before the end, I realized the pattern (each binary number has exactly 3 1's), so any square with a 5 in the corner had to be a 1 (no duplicate counting of that square) and any square with a 6 in the cornet had to be a 0. It solved fairly quickly at that point, but I didn't get it till 10 or so minutes over time, so I didn't submit. This puzzle was my one shoulda for this year.<br /><br />17. PentaPath - skipped.<br /><br />18. Sukazu - skipped. Though I may try this one now that I have some idea on how to solve it.<br /><br />19. Hex Masyu - skipped.<br /><br />20. X-Agony - skipped.<br /><br />21. Four Square - skipped.Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0tag:blogger.com,1999:blog-6918539440398469912.post-64845760557904328932010-06-21T14:31:00.000-07:002010-06-21T14:42:34.515-07:00US Customs Language FAILWhen I was returning from the US yesterday, I had to pass through customs and fill out a form. Question 15 threw me for a loop, however:<br /><br />"15. Residents -- the total value of all goods, including commercial merchandise I/we have purchased or acquired abroad, (including gifts for someone else, but not items mailed to the U.S.) and am/are bringing to the U.S. is:"<br /><br />and then a blank for the monetary value.<br /><br />The obvious intended meaning is for you to give the monetary value of all goods being brought back that have not been subject to US taxes. As written, the wording on the actual form is, at best, ambiguous. The problematic portion is "including commercial merchandise", which SHOULD be a parenthetical statement. However, some IDIOT dropped a comma, such that the parenthetical statement is now "including commercial merchandise I/we have purchased or acquired abroad", which now renders 15. as "the total value of all goods", instead of "the total value of all goods I/we have purchased or acquired abroad"<br /><br />The instructions on the US Customs webpage says this more clearly, perhaps because whoever was writing it knows HOW TO USE PUNCTUATION: "15. If you are a U.S. resident, print the total value of all goods (including commercial merchandise) you or any family members traveling with you have purchased or acquired abroad (including gifts for someone else, but not items mailed to the United States) and are bringing into the United States." The instructions on back of the actual form are much less detailed and are essentially useless.<br /><br />When I asked the guy at Customs about it, he admitted it was confusing, but said it made sense after more readings. I did not want to press the issue at the time, cuz they can confiscate your laptop without due process. I think it's pretty clear that I was doing an accurate job of interpreting the syntax AS WRITTEN when I asked if I had to report the value of all the objects I brought with me to Finland as well.Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0tag:blogger.com,1999:blog-6918539440398469912.post-11734509692189323002010-05-20T20:50:00.000-07:002010-05-20T21:00:20.682-07:00I used to like wall-jumpinguntil I started playing the <a href="http://drewseph.zophar.net/">Super Metroid Redesign rom hack</a>.<br /><br />On the one hand, I admire people who make rom hacks. Different maps, different items, different controls and interface, and increased challenge all sound like a really great idea.<br /><br />However, I must say that the people who come up with these have taking the challenge bit so far to the extreme that it is no longer fun. Harder bosses = yes. Spending the first half-hour of the first dungeon without a sword = crap.<br /><br />I figured I'd at least give the Super Metroid rom hack the same amount of time I gave to the Zelda: A Link to the Past <a href="http://sites.google.com/site/zeldaparallelworlds/">one</a>, given that I quit last time because I didn't know where to go.<br /><br />This time, I actually stumbled across the fake wall that was necessary to go through to progress. The one fake wall I remember from Super Metroid (the original) at least had an enemy on the other side so that you would notice it...<br /><br />So I fight the boss, fall down the pit and finally get the wall-jump boots that will allow to me to climb back to the surface. Then, after 10 minutes of trying to wall-jump, I decided to quit. If wall-jumping is such a critical component of the game, it should not have to be this hard. (unless you don't want people to play your hack)<br /><br />I am, however, amused that other people have wasted similar copious amounts of time on wall jumping in this game.Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0tag:blogger.com,1999:blog-6918539440398469912.post-71022814909754930352010-04-30T13:51:00.000-07:002010-04-30T14:06:09.029-07:00Why I won't be buying new desktop partsBased on my normal computer cycle, I should have upgraded my desktop in late 2008, early 2009, but haven't. As a computer approaching 5 years old, my desktop is aged, if not obsolete. There are some things that it chokes on, mainly any computer game released after 2005, and playing back certain poorly-compressed HD video. Looking at the parts I would buy to make it new and fancy again, they are relatively cheap (in computer terms): ~ $600 for new motherboard, processor, and RAM. I could probably make do with spending half as much if I were planning to replace it sooner (i.e. in 3 years instead of another 5).<br /><br />Still, my computer is fine as-is (i.e. until something breaks), I don't need a slightly shinier and fancier new monitor, and $600 (or even $300) goes a long way towards buying more Legos. :)Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0tag:blogger.com,1999:blog-6918539440398469912.post-45471898770423992922010-04-29T12:06:00.000-07:002010-04-29T12:14:25.793-07:00Rating investment productsAlthough not the sole factor (by far) that led to the financial crisis, a failure of ratings agencies to provide accurate estimates of the risk associated with various investment products definitely played a big role. (i.e. investments were rated as being safer than they actually turned out to be -- at least this is what is commonly believed)<br /><br />I'm wondering whether ratings agencies should take notes from places that continually calculate risk, like authorized bookies in Vegas who produce odds for various bets. If the odds of an outcome are set properly, one would expect roughly even numbers of bettors for both outcomes. If an overly large number of bettors choose to bet on one outcome instead, then that may be taken as a signal that the odds are not set correctly and a bookie (or whomever is handling the bets) can adjust the odds based on the behavior of the crowd.<br /><br />As has been reported recently, many firms and organizations bet that certain CDOs would fail. A ratings system based on crowd-sourced information would consider these bets as an indication that these produces actually have more risk than previously assessed. In other words, treat all players in the system as more or less rational actors and use their betting behavior as economic indicators to set risk rather than relying solely on independent estimates that may be biased/incorrect. This type of rating system would, of course, depend heavily upon a databased of what bets people are taking, but that's what the SEC is for, right? (i.e. don't allow firms to make bets hidden to the SEC)Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0tag:blogger.com,1999:blog-6918539440398469912.post-61955531557828547802010-04-12T23:34:00.000-07:002010-04-13T00:16:13.813-07:00Dynamic Range CompressionTaken at face value, Maaya Sakamoto's <a href="http://www.cdjapan.co.jp/aff/click.cgi/e86NDzbdSLQ/378/A014492/detailview.html?KEY=VTZL-15" target="_blank">Everywhere</a> is a pretty good value: 30 pretty famous songs spanning her career for just 700 yen more than a regular CD, and it includes a DVD with some promotional videos on it.<br /><br />Here's the problem. At some point in the past, I stumbled across <a href="http://catsspat.dyndns.org:2080/anime/">Richard's website</a>, which really is just an index to his vast collection. (You should be aware that searching for "Animephile" now returns some rather sketchy results in Google -- this wasn't always the case...) Anyway, as Richard points out, <a href="http://en.wikipedia.org/wiki/Dynamic_range_compression">dynamic range compression</a> has now <a href="http://catsspat.dyndns.org:2080/anime/00ARTICLE/DRC/index.html">infected </a>our beloved Jpop imports!<br /><br />Compare, for instance, the waveform from the Nikopachi* version of <a href="http://www.cdjapan.co.jp/aff/click.cgi/e86NDzbdSLQ/378/A014492/detailview.html?KEY=VTCL-60216">Hemisphere</a> looks like this:<br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://2.bp.blogspot.com/_sbw5AHJSsYQ/S8QVCvbRG-I/AAAAAAAADsc/-p8nHH7Sx4Y/s1600/hemisphere_nikopachi_waveform.png"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 400px; height: 131px;" src="http://2.bp.blogspot.com/_sbw5AHJSsYQ/S8QVCvbRG-I/AAAAAAAADsc/-p8nHH7Sx4Y/s400/hemisphere_nikopachi_waveform.png" border="0" alt=""id="BLOGGER_PHOTO_ID_5459511785114639330" /></a><br />The version on <a href="http://www.cdjapan.co.jp/aff/click.cgi/e86NDzbdSLQ/378/A014492/detailview.html?KEY=VTZL-15">Everywhere</a>, whioh I believe to be a remaster of the Nikopachi version (based on length and waveform) looks like this:<br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://1.bp.blogspot.com/_sbw5AHJSsYQ/S8QVUCTmMwI/AAAAAAAADsk/bzepw63tNjE/s1600/hemisphere_everywhere_waveform.png"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 400px; height: 132px;" src="http://1.bp.blogspot.com/_sbw5AHJSsYQ/S8QVUCTmMwI/AAAAAAAADsk/bzepw63tNjE/s400/hemisphere_everywhere_waveform.png" border="0" alt=""id="BLOGGER_PHOTO_ID_5459512082240516866" /></a><br />On first playing the two, the most noticeable difference is the increased volume in the "Everywhere" version. The obvious reason for this is simple psychology: people generally prefer louder music, hence increasing the volume on a song makes people like it more. With a hard limitation on the maximum amplitude in a given format, this naturally results in a reduction in dynamic range. In essence, the softer sounds become louder while the louder sounds get clipped. For a song like Hemisphere with both loud sections and soft sections, this makes a pretty big difference.<br /><br />A good analogy is going to a rock concert vs. going to a classical music concert. In a rock concert, the music is blared at near pain-inducing levels to a point where it can be hard to make out subtleties in music. Contrast this with classical music concerts, where the venues are (usually) designed for acoustics, everyone tries to be super-silent (you'll notice a distinct increase in the number of coughs in-between movements). There's a ton more dynamic range between the softest solo portions and the bits where the orchestra is going full blast. Because of these differences, I avoid rock concerts even for artists I really like, but will go to any classical music concert if it's in my budget or if I really like the pieces.<br /><br />* For those of you who are curious, the Nikopachi version looks noticeably different from the single version beyond the addition of some silence at the end. It looks like at least some parts may have been rerecorded or remastered. Here's the waveform for the single version:<br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://3.bp.blogspot.com/_sbw5AHJSsYQ/S8QZSWFTK8I/AAAAAAAADss/00QQ76r4l6o/s1600/hemisphere_single_waveform.png"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 400px; height: 132px;" src="http://3.bp.blogspot.com/_sbw5AHJSsYQ/S8QZSWFTK8I/AAAAAAAADss/00QQ76r4l6o/s400/hemisphere_single_waveform.png" border="0" alt=""id="BLOGGER_PHOTO_ID_5459516451236031426" /></a>Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0tag:blogger.com,1999:blog-6918539440398469912.post-36101276578990399162010-04-08T21:48:00.001-07:002010-04-08T21:57:51.293-07:00The return of touchscreen?Remember back in 2002, when Microsoft had these big plans for tablet PCs, with a whole separate <a href="http://en.wikipedia.org/wiki/Windows_XP_editions#Tablet_PC_Edition">version </a>of XP?<br /><br />Yeah, you probably don't, but back then I had this wonderful pipe dream for a slick note-taking application. First, it would obviously need to be able to open and write a variety of file formats, including plaintext, richtext, MS word, PDF, and PPT. Being able to annotate the last two formats would be especially wonderful for marking up papers and lecture slides. Couple this software with handwriting recognition, a computer-algebraic system, and graphing capabilities, and math nerds would eat it up. Imagine being able to note down equations, converting them into symbolic entities, manipulating and solving them in software. As a tool for doing math homework, it could be invaluable.<br /><br />Separate pieces of software would probably be likely to simplify things, but if they were all made by the same company and shared UI structure...Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0tag:blogger.com,1999:blog-6918539440398469912.post-60584157404606328082010-03-29T15:46:00.001-07:002010-03-29T15:50:45.207-07:00This blog has moved<br /> This blog is now located at http://collinear.blogspot.com/.<br /> You will be automatically redirected in 30 seconds, or you may click <a href='http://collinear.blogspot.com/'>here</a>.<br /><br /> For feed subscribers, please update your feed subscriptions to<br /> http://collinear.blogspot.com/feeds/posts/default.<br /> Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0tag:blogger.com,1999:blog-6918539440398469912.post-60206849070049153402010-02-18T18:44:00.000-08:002010-02-18T19:09:45.700-08:00Aw, spicy cashews, how I have missed you soBack in the day (ok, maybe 6 years ago), a group of us went to a South Indian place in the LA area, where Akils ordered us a bunch of different foods. One, in particular, was some kind of rice/bread cup that we were supposed to eat along with a spicy broth-like liquid. When asked how much we should use, he said something along the lines of "it more you use, the tastier it gets". In response to this, and because I do stupid things, I filled it nearly to capacity and then tried to consume it. As a result, some of the spicy broth went down the wrong tube, which ended up with me convulsing it into my nostrils, where it burned a steady fire for the next ten minutes as I tried to clear my air passages in the bathroom.<br /><br />The good news is, I managed to score some spicy cashews to go from the snack counter, after which we browsed the Indian video rental? store next door. That's all I remember about this place.<br /><br />Fast-forward to yesterday, when I went to <a href="http://www.suratifarsan.com/">Surati Farsan Mart</a> (on Black Mountain Road), had a delicious and cheap meal, and bought ... more spicy cashews! Remembering that <a href="http://mmm-yoso.typepad.com/mmmyoso/2009/04/comc-surati-farsan-mart-.html">Kirk</a> had mentioned a second location in Artesia, I looked up the address and confirmed, via Google streetview, that yes, it was next door to a video place. In some miracle of coincidence, I had gotten spicy cashews again after six long years.<br /><br />And yes, they are delicious, with a wonderful spiciness that builds over time, until you realize that you just a whole bag of cashews. Luckily, I am pacing myself so that I have some to bring up with me for the <a href="http://chmmc.caltech.edu/">CHMMC</a> on Saturday.Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0tag:blogger.com,1999:blog-6918539440398469912.post-20753308339385622282010-01-31T03:21:00.000-08:002010-01-31T03:27:06.638-08:00New Album from Maaya!Apparently, Maaya is coming out with a new album for her 15th anniversary (of debuting with Yoko Kanno on Escaflowne). Of course, <a href="http://www.cdjapan.co.jp/aff/click.cgi/PytJTGW7Lok/378/A014492/detailview.html?KEY=VTZL-15" target="_blank"><br />here</a> is the requisite link to purchase it on CDJapan, so that I can get a few percentage worth of kickback. (which is quickly becoming necessary with the current dollar's weakness against the Yen) Yes, Nintendo, you're not the only one suffering.<br /><br />In other news, they are using some fancy material/method called SHM-CD, which is supposed to "sound better". It may have been a factor in the past when CD quality was poor, but my understanding these days is that you really don't get bit errors anymore when reading CDs, so having a "cleaner" signal really doesn't mean much when it's all processed digitally anyway.Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0tag:blogger.com,1999:blog-6918539440398469912.post-20525508821141296502010-01-13T00:41:00.000-08:002010-01-13T03:08:01.185-08:00Thoughts on departmental examsDisclaimer: I'm not familiar with the format of departmental exams given in other curricular groups, at other departments, at other universities, or even in different years, so these thoughts really only apply to that of the BO departmental given at SIO in 2009. However, I suspect, given the strong "tradition-esque" property of departmentals, that it is conducted in a similar manner to single-session oral exams elsewhere (and elsewhen).<br /><br />My main issue with the process of departmental exams is the opaque process in which they are conducted. First, the issue of which members comprise the departmental committee varies from year to year. I believe it typically includes five members, one physical, one chemical, and three biological. At least one of each is one of the professors who taught the corresponding introductory course that year. However, replacements occasionally occur when certain members are unavailable. The remaining two biological members are drawn from the faculty, though it is unclear to me how they are chosen.<br /><br />Once the committee members and time for the exam are decided, first-years are simply told to show up. No information is given about what will be asked, what the committee is looking for, etc. Yes, individuals can contact the committee members and ask questions about what they are likely to be asked about, and the committee members will likely respond truthfully, but it's still a very mysterious process.<br /><br />Aside from the fact that the committee expects you to know *something* about oceanography, it's unclear what the expectations are. It seems that they take into account things like what classes you took, how large your courseload was, what research you did, your background, etc. I suspect the departmental exam is thought of as a test of your ability/qualifications to be a Ph.D student. My personal opinion is that this is an extremely subjective decision and that each committee member probably has different views on what qualities are most important.<br /><br />I also think that a departmental exam isn't necessarily the best (i.e. accurate and/or fast) way to determine success of a Ph.D. student. It's not like you can track the students that don't pass the departmental exam to see how well they do in graduate school. There's probably an overly strong emphasis on academia success, which doesn't seem like a good idea, either. Given current numbers of graduating students and the number of positions available, it's clear that not all students will end up in (or even want to be in) academia. Success in academia depends on somewhat different factors than success in other fields for which a degree would be useful.<br /><br />I think what really irks me is that the subjective/opaqueness of the committee's decision means that it's really hard to practice for. Practice committees with students probably does a close job of approximating the situation, but it's hard to say how useful any feedback will be. The feedback you get from passing (or not passing) the exam is usually along the lines of 1. take class x, 2. study more on subject y, which focuses just on the knowledge portion of the exam.<br /><br />Finally, there's a huge element of luck. 90 minutes seems like a long time, but there are five committee members, who usually take 15-18 minutes each to ask questions, with some slack for follow-up questions and for the committee to take a break between examinees. Because the committee can ask virtually anything, it's likely that you won't know the answer to every question. (One aspect of the exam is probably to see how you respond when you don't know the answer and try to bootstrap from what you do know, make connections from related knowledge, etc.) However, it's also possible that the committee stumbles upon your area(s) of expertise. I'm not sure what they do in such a situation, but obviously you're at an advantage for passing if you know the answers to all the questions.Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com0