iPhone users get free wifi

iPhone users finally get free wifi from AT&T. Basically, you connect to the access point and enter your phone number. AT&T then sends you an SMS message with a 24-hour access key. I haven't tries it yet...

For every thing, there is a season

Every time a colleague asks the question, "What the hell happened to computer science enrollment?" I answer, "These things are cyclical. CS enrollment will come back, and some other field's enrollment will drop." And, indeed, as the dot-com bust has faded in new student memories, enrollment has increased again (new enrollment was up last fall in my department and is up again (over 30%, year over year) this fall.

The title above links to a Computerworld article speculating that the current banking crisis will mean further increases in CS enrollment. That many or may not be true; I'd prefer the steady growth associated with students following their interests than the sudden boom of students chasing the latest fad. The article does at least have some entertainment value, with Carly Fiorina (of HP and now McCain/Palin campaign fame) showing her lack of insight that American workers are also HP (or any company's) customers -- no jobs for Americans mean no customers.

Then again, I understand this, but I'm not getting $42 million for any of my failed efforts.

Math insanity in Washington state

I've taught calculus at the college level and, now that my daughter is taking algebra in middle school, I see why students have so much trouble with college math: they aren't taught math in middle school. Let me clarify this statement by first illustrating what I mean when I say that too many students have trouble with calculus and why you should care about that. Calculus is generally considered to be the first college math course. It's nice if students have taken calculus already, and it's even possible that their high school calculus class was good enough to allow them to skip the first quarter of college calculus, but it's not absolutely necessary. Students generally take calculus from the beginning in college, they get credit for it, and degree curricula are designed with the assumption that they'll take calculus. On the other hand, few pre-calculus or earlier classes count for college credit -- they are offered on a supportive basis to make up for background that students should have already had.

Moreover, calculus has become a gatekeeper course for many degrees in the sciences, engineering, and even business. For many degrees, calculus is an absolute prerequisite for later core classes. In other degree programs, calculus may only be a prerequisite for certain electives, but the faculty have made the decision that they don't want students moving through the program who are unable to take these electives. So, a student unable to succeed in calculus (notice I didn't write "pass"; students need to become facile enough with the subject matter to apply it naturally and without effort in classes that build upon calculus) will not become a science, engineering, or business major. I cannot emphasize this point enough: if a student has not been prepared to succeed in calculus by high school graduation time, it is much less likely that he or she will be able to have some of the most rewarding careers.

So, why are students having trouble in calculus? While there are many reasons, the biggest is a lack of facility with algebra, and by this I mean the ability to solve algebraic equations by symbolic manipulation. A simple example of this might be to solve the equation 3x + 12 = 45. A symbolic approach would be:

3x = 33     (subtract 12 from both sides)
x = 11      (divide both sides by 3)

I'll explain why this is so important for calculus in a moment; let me first describe what children are taught instead.

Basically, they're taught something more like math appreciation than math. Let's use as an example my daughter's textbook, which is Contemporary Mathematics in Context: A Unified Approach, part of the "core-plus mathematics project" from McGraw-Hill. First off, much of this book is statistics, rather than algebra, even though this is supposed to be an algebra I (eighth grade honors, or ninth grade regular) class. The kids spend enormous amounts of time in groups, measuring each other's fingers, counting which thumb is on top, etc., so that they can gather some of their own data. They spend even more time writing paragraphs describing histograms. Then they move on to linear equations, motivated by linear fits to data -- linear regression -- rather than just algebra. Part of the reason for this is that they have yet to see an equation in the book!

Finally, they get to linear equations, though first through a little detour in which the words "NOW" and "NEXT" are used, instead of letters, for variables. Why they do this is mystifying, since all of these kids have seen problems in elementary school in which shapes were used instead of variables. Along the way, they learn about slopes, even of slopes of nonlinear functions, which is a calculus problem. Of course, they don't need to actually do any math in that last case (thought they're given the quadratic equation involved), just write about what the slope of a curved graph might mean, how rate of change relates to slope, etc. By this point, they've note seen more than three equations on any page of the book, and most pages have none at all. No techniques have been presented for solving linear problems; students are asked to solve such problems by inspection of graphs or tables of (x, y) pairs. Finally (precisely 2/3 of the way through the book), a symbolic approach is mentioned (in a chapter entitled "Quick Solutions"). Here's what the book says:

...it is often possible to solve problems that involve linear equations without the use of tables and graphs.

This is absolutely untrue! It is always possible to solve such problems this way (i.e., symbolically). In fact, the fraction of problems that can be solved with tables or graphs -- the only method used so far in the book -- is vanishingly small.

Let me disabuse you of the idea that the book will now introduce methods such as adding/multiplying both sides of the equation by the same value. Instead, what the book does is say that different people might reason about solving such equations different ways. A couple examples are given, and student groups are asked to try to figure out what the reasoning process is in each case. Then, kids are invited to solve equations in whatever way makes sense to them. That's it!

So, to sum up, symbolic manipulation is erroneously introduced as a specialized shortcut that can work in some cases: a sort of mental trick with no fixed methods that you just have to figure out for yourself. This is in a five-page section, after more than 200 pages that are taught with graphs, tables, and calculators in the context of statistics.

So, why is this a problem? Because calculus requires facility with the symbol manipulation approach. Unlike simple algebraic problems, which can (again, in simple cases with integer solutions or the like) be approached graphically, calculus is the mathematics of change. Graphical aids in calculus involve computer programs in which you interactively move things around and watch how solutions change. While solutions are numbers in algebra, they are equations in calculus. If the symbol manipulations of algebra aren't as easy as breathing for a student, he or she will have a tough time in calculus. I cannot see how a student who has used the Core-Plus curriculum can pass calculus, unless his or her math education has been supplemented outside of school. Thus, in Washington state we are preventing most of our children from getting the degrees that lead to the highest-paying, fastest growing career paths that exist: science, technology, and business.

And who is to blame for this mess? Why, the Superintendent of Public Instruction, Terry Bergeson. She's the one who has pressed this kind of instruction for a decade now. She's the one who has instituted a special test for Washington state that prevents our children's performance from being compared to children in other states and countries -- a test that costs much more than commonly-used alternatives.

That's why I'm advocating in this post for Randy Dorn for Superintendent of Public Instruction. If you're a Washington state voter, click on the title of this post to go to his web site. Read about him. Compare what he plans to do to the current abysmal state of education. It's time for a change in this Washington, too.

Actual sexism

I recently received an email for fundraising from a friend's child's school. It includes a link to a web site that's selling magazines. The usual deal is that the school gets some cut of the subscription price and the kids get crappy "prizes" from Oriental Trading. So, I clicked on the "Children" section link and was almost immediately struck by two magazines offered:

• Boys' Life, with a cover on future manned missions to Mars, and
• Discovery Girls, with a cover touting stories like, "Jealousy ruined my friendship" and "Mix & match fashion".

Is it any wonder that so few girls make it through middle school with their natural interest in science and mathematics intact?

Dishonesty

I finished the novel Empire, by Orson Scott Card, a couple months ago and had been meaning to write a review of it, or at least a commentary on it, since then. At this point, enough time has passed by that I'll not be including very much in the way of specific details from the book, though there will be some spoilers.

I think the title above succinctly sums up the book in a variety of ways. Let's start with what would typically be a minor point, since I doubt Card approved it. On the other hand, I generally look to the blurbs to give me some idea of a book's content, and thus a false and misleading blurb is something that will lead me to be less likely to buy other books from the same publisher. In a perverse way, the blurb is representative of the book -- not in terms of factual information, but in terms of being thinly masked propaganda.

So, what does the blurb say? Here it is:

The American Empire is growing too fast, and the fault lines at home are stressed to the breaking point. The war of words between Right and Left has collapsed into a shooting war, though most people just want to be left alone.

The battle rages between the high-technology weapons on one side and militia foot soldiers on the other, devastating the cities and overrunning the countryside. But the vast majority, who only wan tht killing to stop and the nation to return to more peaceful days, have technology, weapons, and strategic geniuses of their own.

When the American dream shatters into violence, who can hold the people and the government together? And which side will you be on?

So, I (naturally, I think) expected a cautionary tale set in the near future, with an imperial America, a civil war between extremists, and presumably a protagonist representing a large middle. Instead, what the reader gets is a political polemic in which all liberals (which, true to ultra-right-wing usage, is equated with extremism) are evil. Even the right wing "side" of the war ends up being (spoilers start here) a head fake by liberals. There's a token "good Democrat"; you know she's good because she sides with the Republicans.

What are we left with? A grand conspiracy to take over the government financed by a thinly-disguised George Soros character. A Bond-like secret headquarters underneath an island in a lake. The liberal conspirators have all sorts of neat, futuristic weapons, but their soldiers are all effete and unskilled (and sneaky backstabbers), eventually bested by virile, right-thinking true Americans (in fact, for some reason I either remember or misremember the liberal soldiers as being foreigners). Card making fun of Armand Hammer's name. A smattering of decent dialog and action. Some mild criticism of Fox News.

And then, to top off my disappointment, there's an angry diatribe written by the author at the end. Apparently, he's pissed off at criticism of his views. He rails against people seeking to rob him of his livelihood, though it's unclear to me that his income has in any major way been affected: he only makes the case for being excluded from SF conventions and the like. He doesn't mention his support for intelligent design as science, which I mention not as a religious comment but as a rather embarrassing lack, in a hard science fiction writer, of basic understanding of what science is.

What is apparent in his essay is that Card is one of those people who for some reason feel that their lives are affected, somewhat like action-at-a-distance, but the unrelated actions of others. Actually, not just their actions, but even their ability to act. In particular, he somehow thinks that the ability for people to marry others of the same sex affects the quality of his own marriage. His protestations aside, I fail to see the difference between this and opposition to interracial marriages. Some people just can't seem to let others live their own lives in peace, if they disagree with them.

And so, Card's closing essay at once clarifies the polemical nature of this "novel" and identifies him as an extremist, like the antagonists in his writing, who seeks control over other Americans' private lives.

New use for old socks

Sock and Keys
Originally uploaded by stiber

No need to fret when one of a pair of socks goes through the interdimensional portal in your clothes dryer. Use the orphan for an iPod case or, as I've done here, to keep your keys from scratching up other things in your bicycle panniers when you commute to work.

truphone: Killer iPhone app for international travel

Two days after the iPhone 2.0 software and the iTunes app store were released, I went on a family trip to Europe. So of course, in the days prior to my trip, I frantically installed, then reinstalled, the 2.0 software. This would make my phone much more useful during my trip, I reasoned. Well, it turns out I was right, and the main reason for that was the truphone application.

Truphone is a VOIP application, with one version running on Nokia phones and one iPhone version. The iPhone version appears as a separate application on the iPhone, providing buttons at the bottom of the display that provide access to your contacts, a keypad, a truphone web page for buying account credit, a list of recent calls, and a list of favorites (which, unfortunately, are specific to truphone and not copied from the Phone app). The application is exceedingly simple in operation:

1. Sign up for an account and buy credit (when I signed up, they gave $8 credit for free; now they give $1 credit).
2. Be someplace that has wifi that you can access.
3. Make a call to one of your contacts, or dial on the keypad. These are calls to regular phones (landlines or mobiles), not to other other iPhones running truphone -- it's like SkypeOut.
4. Pay $0.06/minute (now they've got packages that provide $0.015/minute to the US and Canada).

Perhaps paradoxically, this simplicity has caused some confusion among the commenters on the iTunes store. Part of this is truphone's fault, as they don't distinguish well in their online documentation between the Nokia and iPhone features. The Nokia app includes free truphone-to-truphone calling, SMS, etc. -- much more like a full Skype implementation. It also appears to integrate into the Nokia calling software, so that the phone automatically switches from regular cell to VOIP, depending on circumstances. The iPhone application is simpler, only including calls to regular phones and requiring you to consciously select wifi calling (by running the truphone app, rather than the Phone app).

I actually prefer the iPhone implementation. At this point, truphone doesn't have much market penetration, and besides I don't know that many people I might call who have iPhones or Nokia N95s. So being able to call other truphone users wouldn't have been useful during my trip (with one small exception: you know who you are). More importantly, I wanted to be 100% certain that I was making a VOIP call, and not a $2 or more per minute cell call. I didn't want my phone switching to regular cell calling because of a software glitch or because of some problem connecting to a hotel's wifi network. The fact that I was running the truphone application, not the Phone application, and that truphone only works with wifi, was very reassuring.

I spent at least a couple hours calling various phones here in the Seattle area, Philadelphia, south Florida, and China, from hotels in Prague, Venice, and Rome. Generally, call quality was quite good, equal to the best we've experienced using Skype, with the only issues being a weak signal in one hotel that required me to sit in a particular chair in the lobby that happened to be in a good spot. Also, I tried at one point to add credit to my account using my MacBook, but the truphone web site was abysmally slow; I connected to the mobile version of their add credit page and the transaction went off without a hitch. And it was great to be able to call relatives to let them know we arrived safely and keep them updated on our wanderings without having to deal with phone cards or similar unfamiliar contact methods.

So, is truphone useful for calls within the US? Probably not, unless you've somehow gotten yourself a plan with very few minutes and very high costs for additional minute usage. But, if you need to travel internationally, then calls using truphone are approximately 1/30 the cost of AT&T calls. You could easily pay for the purchase cost of an iPhone 3G with the savings from one international trip.

Getting the right iPhone 2.0 software

For those of you (like me) who followed the information I reference in a previous blog post, note that that unofficial iPhone 2.0 software was for the new iPhone hardware. If you (like me) have the original iPhone hardware, you need to follow the directions at MacRumors linked from the title to get the correct software for your hardware.

Initial iPhone 2.0 app impressions

Here are some of my initial observations about the iPhone 2.0 software:

Settings: Has a "Fetch New Data" item that lets you turn push updates on or off, set data fetch interval (includes the email check intervals for non-push email). Has a new "Mail, Contacts, Calendars" item, which consolidates various items (I think, I don't remember the details of this from the old OS) and includes under calendar "New Invitation Alerts", "Time Zone Support", and "Default Calendar" settings. The latter corresponds to the Calendar app UI now showing the multiple calendars synced from iCal. Played with simplified Chinese international keyboard a bit; neat to be able to draw characters by hand.

Contacts: The iPhone 2.0 software adds a "Contacts" app, which appears to just be a shortcut to the "Contacts" tab in the "Phone" app. We now have search, but it appears to be strangely limited, in that it doesn't search all fields. From playing with it a bit, it appears to search names and company, but not address or notes, for example. At least, this is my tentative conclusion. The on-screen keyboard has a "Search" button, but results update as you type; the "Search" button doesn't seem to do anything.

Calendar: Updated UI includes multiple-calendar awareness.

Maps: UI spiffed up. Circular cross-hairs vibrate as it progressively refines your location.

App Store: It works; looks just like the "iTunes" app.

And some third party apps: BA Flights: Mostly, thought perhaps not entirely, lame. Only lets you search for departures/arrivals within the current month. About what you'd expect: a three-button web app front end.

Talking Italian Phrasebook: Not sure that all of the phrases are correct, but pretty good for free.

Currency: Nothing fancy, just like the Stock app. A nice, simple app.

Exposure: Interface like iPod app. No Flickr upload capability. Not sure I'd pay $3 for Mobile Flickr. Need to compare this to MoPhoTo (which also doesn't seem to support upload).

NearPics: Very slow, and I'm testing via wifi.

Twitterific: Seems fine. Allows "attaching" photos to twitter updates, but I'm not sure this is something I'd like to do often; I think I'd be more likely to photoblog here on Blogger.

So, what do I want?

• Skype! There is an app/service called TruPhone that seems Skype-like. Seems to include the equivalent of SkypeIn for no extra charge. It's in beta, but maybe I'll try it (if it won't insist on calling pay via wifi within the US, given that I have thousands of rollover minutes). I'll report after/during my upcoming trip on my experiences.
• A good photoblogging interface that doesn't force me to switch to another blog platform. In other words, Blogger app.

Neat looking apps that I don't have an immediate need for:

• SignalScope, a spectrum analyzer.
• StageHand, a presentation remote that also displays your talk notes, allows you to highlight/point parts of your slides, etc.
• OmniTuner, which seems, despite the emphasis on guitar, to be a chromatic tuner app. Orfeo is definitely a chromatic tuner, though with less impressive graphics and at twice the price.

And, finally, exactly how many payware tip calculators does the iPhone need? Do people really have trouble calculating tips using a regular calculator (such as the one built into to OS distribution)? Or just ballparking tips in their heads (how difficult it it to figure 10%, then either add in half of that again or double that)?

iPhone 2.0 report

Since I'm in the process of writing my part of a grant proposal before heading off on a trip, I figured, "Hey, why don't I update my iPhone to the 2.0 software?" The software is unofficially available; see this iLounge article for a good summary of how to get it. Here's how things went:

11:55AM: Option-clicked "Check for Update", selected .ipsw file, iTunes extracted update.
11:56AM: iTunes started "Preparing iPhone for software update..."
12:02PM: iTunes started "Updating iPhone software..."
12:04PM: iTunes started "Verifying updated software..."
12:06PM: iTunes started "Updating iPhone firmware..."
12:09PM: iPhone restarting, iTunes sees it, offers to set it up anew or restore from backup. I restored from backup.
12:11PM: iPhone restarting
12:12PM: iPhone reappears in iTunes list. Arrangement of icons same as it was before update. Only immediately apparent differences are "Contacts" and "App Store" icons. Set up synchronization in iTunes to sync all applications. Synced iPhone. 12:30PM: All done, now to see if it works...

More about iPhone apps

Some more-or-less random observations about the available iPhone apps (based purely on their app store descriptions and icons):

• There's a lot of $0.99 apps; I'm not really sure what the rationale is (on the part of the software developer) for not just releasing such apps for free.
• There are many free apps that appear to do the same thing as pay apps. Why would anyone pay for an app that simply produces a white screen to improve the iPhone's ability to act like a weak flashlight?
• Here's my initial list of (free) apps: "BA Flights", "Currency", "Exposure", "Jott for iPhone", "NearPics", "Remote", "Talking Italian Phrasebook". Yes, we're going on a trip.
• Disappointments: no Skype, no official Flickr app (the free version of Exposure is adware).
• A fair number of cute ideas in some of these apps, but I don't think many really take advantage of the synergies available in the full range of iPhone capabilities.

iTunes App Store up and running

Wooo! The iTunes App Store is up! Just use Software Update to download iTunes 7.7, enable "show apps" in iTunes preferences, click on the "Applications" icon, and select "Get More Applications..." (similar interface to podcasts). Can't load the apps yet on the iPhone, since the iPhone 2.0 software hasn't been released, but you can at least browse and make a list (which I will be doing shortly).

Update: You can "purchase" applications and they'll download. This doesn't appear to use the shopping cart, but I've only tried free apps.

Fireworks

The future of video cameras

So, we're getting ready for a trip and really don't feel like lugging our Sony mini-DV camcorder along with our digital camera. Everyone's talking about the Flip Mino, so that would be a possibility. Then again, our still camera has a movie mode, with the same resolution as the Mino (640x480), except that it has a 12X optical zoom, better optics, and a better sensor. It doesn't have much in the way of video compression capability, storing its video as MJPEG (just a sequence of JPEG compressed frames), which means that videos require 1GB per 10 minutes or so. But that's not such a big deal these days. Even though it is discontinued and Konica Minolta is no longer in the camera business, there was a firmware update that allows it to use 2GB SD cards. A quick trip to Costco, and we have enough storage for our trip.

So, it seems that we're on the threshold of major change, not just in laptop computer mass storage, but also in video cameras. For those who need more than a cell phone or Mino -- and who aren't professionals -- what's the motivation behind getting anything other than a good digital camera with video capability? Pretty much every digital camera out there supports at least 640x480, or standard definition. They certainly have the sensors to capture HD. Flash memory prices will be low enough within the next couple years that it will really not make any sense to buy a hard drive camcorder. The only remaining question will be: do you really need to shoot 10 hours of video before the next time you'll be able to dump the video to a computer or DVD burner?

Speaking Respectfully

The title above links to one of the best illustrations I've seen of how to disagree with someone respectfully, even if that respect isn't reciprocated. This is something I should work on.

World RPS Society

Is this for real? Is there really a "World Rock-Paper-Scissors Society"? Is it just an elaborate joke? Would someone really put that much time into such a joke?

Water-fueled car?

Seems there's a company in Japan that says they've built a car that runs on water. Supposedly, they have a "membrane electrode assembly" that breaks water into hydrogen and oxygen; they then use the hydrogen to generate electricity, producing water as the result. Sounds too good to be true? Then it almost certainly is (actually, I would state it more strongly than that). By comparison, cold fusion is very believable. What's really impressive to me about this is the speed of creation of a quality Wikipedia page on the matter. The company had a press release on June 12, 2008, and the Wikipedia page was up on June 14.

Why won't US car manufacturers learn?

Today, we filled up our car's gas tank; it cost $4/gallon for the first time. At Costco. No doubt, in the months and years to come, people may read those last two sentences and wonder briefly if I was bragging about how low the price was.

So, Dodge has release the new Challenger, with an SRT-8 model for 2008 and two down-line models planned for 2009. The car gets 13 miles per gallon (city)! With a 19 gallon gas tank, that means you'll be spending more than $75 every 250 miles to drive this thing. If you drive 12,000 miles per year, that's about $3,700 on gas.

Are US car executive idiots? Yes, I'm not surprised that the 2008 limited edition run of 6,400 cars sold out. But do they really expect this car to sell well over any reasonable model lifespan and production run, given likely future gas prices? And who wants to drive around in a car that looks 30 years old when brand new?

Mac OS X 10.5.3 Update

Apple has released the Mac OS X 10.5.3 update, as of yesterday. This looks like it will be a big win for us Mac users, with stability improvements seemingly throughout the OS and included applications. Notable from my point of view are:

• "Fixes reliability issues with iCal syncing." I use Spanning Sync (click this link to save $5) to sync iCal with Google and back, so I can keep my home and work Mac calendars in sync. This is a topic of conversation on the Spanning Sync blog.
• "Fixes an issue that could occur if two compose windows are open when dragging a file to the Mail icon in the Dock." Actually, I think I ran into this problem with just the main Mail window open.
• "Resolves an issue in which activating an application from the Dock switches to a different space, even if there is a window for that application in the current space." This has been another annoyance for me, such as when I click on the Terminal icon to bring the command line window(s) in the current space to the front, and instead I get switched to another space.
• There's a bunch of Time Machine fixes, which I hope may allow me to get backups over wifi to a disk image on a file server working (finally). I use rsync to mirror my home machine's files, but it would be nice to have incremental backups with rollback, etc.

Hey Bill: why not put your money where your mouth is?

Bill Gates made his annual pilgrimage to DC today to ask the federal government to spare him from raising his employees' wages. He says pay isn't the problem. Bill, if you want us to believe that this isn't just about money, why don't you help out the nearest university campus to you? We desperately want to start science and engineering majors, but the State doesn't have the money to build us a building with labs, buy us equipment, etc. You already employ dozens of our graduates, how about helping us help you with some more? Why not do your part?

IEEE Spectrum: Video Viewer

Here's a very interesting video of the CMU autonomous vehicle they've been developing for the Army. I have mixed feelings about this.

• The chasis is very impressive. This thing would be great at a monster truck rally.
• I don't want to be anywhere near this thing when its gun is loaded. Not based on my assessment of how formidable it will be, but rather how reliably it will function. Shades of ED-209 from "Robocop".
• I wonder how vulnerable this vehicle would be to very primitive countermeasures, like a guy with a can of spray paint.

Math & science: it's good for the economy

An interesting article in that well-known socialist rag, The Wall Street Journal. Math and science do matter, not just for the individuals involved, but for the US economy as a whole. And, despite decades-ago calls to improve science and math education, the US still lags other industrialized nations.

Needing "school math" without using it

I was thinking about my previous posts about the UW College of Education's (CoE's) recent political polemic about so-called reform math. One of their major points is that engineers don't use what they call "school math": they just use computers. Please allow me to outline my own work, which is highly compute intensive and rarely involves what they would call school math, but which nevertheless I could not do without a healthy dose of school math -- not just in my education, but also in my work.

My research is in the area of computational neuroscience, in which I build mathematical models of individual nerve cells (neuron)s and groups of neurons, develop simulation software for single computers and clusters of computers, and analyze data from simulations and also from experiments on actual living tissue. This sort of work is very much like that done by anyone simulating physical systems, be they biological, chemical, mechanical, electrical, etc.

Like the engineers described in the CoE's publication, my work is heavily computational, as it isn't feasible to do this work with pencil and paper, as in "school math". The basics of the mathematical models involve a number of differential equations: equations that describe how some part of the system changes in response to other parts of the system. Now, it turns out that differential equations is covered by a pretty much standard college sophomore mathematics course. So, why isn't the stuff I do "school math"? It's simple:

1. We only cover the mast basic type of differential equations in that class, linear equations. These are actually quite good for describing simple systems: electrical circuits made up of resistors and capacitors, mechanical systems with springs, etc. The advantage of these equations is that we can solve them on paper and they're easy to learn. The disadvantage is that they aren't very good descriptions of complicated systems like neurons (and many other, nonlinear systems). Once we move to nonlinear systems, we almost certainly need to use computers to do numerical simulations.
2. We mostly just solve single equations in that class (there are other classes where we learn to solve groups of differential equations, later on in the curriculum). The systems I'm interested in can have hundreds or thousands of differential equations, and so I have no choice but use computer simulation.

If you were to watch me work, you would see the following (between the long periods of time in meetings, in class, preparing for said things): I decide on a question I'd like to answer, such as how the behavior of a network of neurons changes as some parameter (think: "tuning knob") is changed. I set up the parameters for a simulation or maybe bunch of simulations and, anytime from a few minutes to a few days later, I have some results. I load those results into MATLAB (numerical mathematics software) and plot the results. I then either exclaim, "Wow!", and hurriedly start writing a summary and thinking of what else I need to do to finish telling the story for a publication (rare), or I say, "Nuts!" and think again why the system either displays uninteresting behavior (Who knows; maybe its lack of interest is in itself something noteworthy? Or is that just wishful thinking?) or doesn't behave like the living nervous system. So, the observer sees that I don't "do" "school math". End of story?

Well, not quite. Because the observer doesn't see what's going on "behind the scenes" (i.e., in my mind). First of all, I would have no hope of even being able to start understanding what simulations I need to run without a very firm and extensive "school math" background. For instance, I work with a number of bright undergraduate students in my research. Some of them have math backgrounds that include differential equations and beyond and some don't. This has nothing to do with how smart they are; math beyond calculus isn't required for computer science and so only those students who come to us via a "nonstandard" pathway (e.g., changed major, previous degree/career) will have the more advanced math. Though all of these students can help out in my research, only those with more advanced "school math" are able to understand the underlying mathematical model well enough to mess with that aspect of the project (unless I teach a student some of the required "school math"). After all, unless you want to resort to randomly poking something just to see what it does, you really have to understand what's going on inside it; that's the only way you can intelligently select what kind of "poking" is likely to tell you something interesting. In fact, it's the only way you can begin to ask questions about the system, let alone start formulating experiments to answer those questions.

Even after the simulations are over, I still need to interpret the results, and this requires yet more "school math" running around in my head. What kind of result did I get? What relationship does it have to previous results I've gotten, or for that matter, results others may have gotten? What does this result mean in the overall context of the system in question and the thinks I'd like to know about it/do with it? And so on.

In other words, it is emphatically not the case that the computer has relieved me of the need to know math. All the computer has done is take over the grunt work: it has become an additional tool in my mathematical arsenal. But the computer can't think, and that thinking is where all the "school math" is. It just isn't apparent to the observer because I know it well enough that it happens in my brain automatically. This is no different than the automaticity with grammar that we use in everyday life. Just because we don't carefully label each of our utterances with "subject", "verb", "object" doesn't mean that grammar isn't necessary.

Finally, does this apply to "everyday" engineers, or just people doing research? Of course it applies to engineers (at least those who haven't "moved up" to management)! That's why businesses hire engineers: they need people who can think about solutions to problems and have the depth of background to understand the interrelationships among parts of solutions from "first principles" on up to final product. Some tasks may become routine and thus almost automatic or thoughtless, but its important to have someone who can look at a problem (or a solution proposed by some software) and say, "Wait a minute; something's fishy here." And, in the final analysis, that's the most important contribution of "school math": it is the language of creativity.

A brilliant strategic move

Microsoft is making their software development tools free downloads for all students.

"It's a brilliant strategic move on the part of Microsoft," said Chris Swenson, a software industry analyst with NPD Group. "This is one of the core audiences you have to hit if you really want to make a difference in the rich Internet application market going forward."

Hmm. Aren't there many other software development tools available for free to anyone? Like Apple's XCode and Eclipse? And didn't Microsoft already arrange nearly-free licensing agreements with many schools? What are the qualifications one needs to become a software industry analyst? Enough free time to read a range of trade publications?

More on "modern" math

I'm continuing my reading of the UW College of Education's little treatise on mathematics education. The author(s) are writing about multiple-choice testing on page 25, such as many standardized tests:

Taylor’s research shows that, although males tend to perform well on multiple-choice questions, females do not. The test questions that are most effective for non-Asian minorities and females are conceptual math problems... show how they arrived at their solutions.

These “performance-based” questions offer partial credit for partial understanding...

“The kind of algorithmic math traditionally taught in middle and high school might make sense — with no further explanation — to future theoretical mathematicians, but it seems a fairly elitist thing to push algorithmic math as mathematics instruction for all students.”

“Most kids are not going to become mathematicians, but they are still going to need to use mathematical ideas. What happens is that the largely abstract mathematics instruction becomes a turn-off for many students so they drop out of mathematics. We are one of the very few nations in the world where it’s acceptable to say, ‘I don’t do math.’”

Allow me to deconstruct:

• Again, another false dichotomy. The type of tests that one uses is mostly independent of the way one teaches, and one could use either "show your work" or "choose the correct answer" testing (or even other testing approaches) with either "traditional" or "modern" math.
• Just another straw-man argument meant to equate "traditional" math with what the author(s) consider poor math practices, whether or not such a connection actually exists.
• I'm not sure what to make about the statement that women and minorities don't do as well on multiple-choice tests. Even assuming this is true, this is not necessarily an argument for modifying testing (assuming there are good reasons for such tests). Instead, it would seem to me to be motivation for getting at the underlying reasons and addressing those. And what are these students supposed to do when they hit a point in their education that requires them to take a standardized, multiple-choice test? Bitch and moan about how unfair things are? Well, yes, the world is unfair. Complaining rarely helps. This is a recipe for setting these children up for failure later in life.
• Algorithmic thinking is just for theoretical mathematicians?!? Algorithmic math is elitist?!? What about chefs; they write and follow algorithms all the time. Are they elite mathematicians? The process of computation (which is what we're talking about at the lower grades) is algorithmic; there is no other kind of computation. This is simply incomprehensible, and smacks of someone who doesn't understand what an algorithm is (yes, this is quite a nerve to hit for me as a computer scientist).
• Very few students will become mathematicians? Strictly speaking, this is true; allow me to neglect to discuss what fraction may actually need math beyond those who become mathematicians. The problem is, which ones will go on to need the math? Not so easy to answer. What if the alternative approach to instruction rules out mathematically intensive careers for a good chunk of students? I submit that that's what has been happening: the absolutely brightest students, with parents who have the resources to help them go beyond "modern" math instruction, will do OK, students who will actually never need math may not be harmed one way or another, and a big group in the middle who would struggle under "traditional" math but gain sufficient mastery to continue onward in their studies will be shut out of a wide range of careers.
• The overall tone of the quote implies a mind-set (like much of this document) that "math is hard", "math is irrelevant to everyday life", "math is for mutant theoretical mathematicians", "math is elitist". A wise colleague of mine once said, "Mathematics is a social justice issue." I certainly agree. We need to stop treating math, including algorithms, like something so complex that only Star Trek-like disembodied brains can understand and start treating it as a common human birthright and the only truly international and intercultural language.
• I especially like the last sentence in the quote. After giving a bunch of reasons why algorithms aren't central to mathematics, why certain groups of children need alternative approaches to testing, and why most children won't need "abstract" or "algorithmic" mathematics ("school math" earlier in the brochure), Taylor bemoans the acceptability of people saying that they don't do math! Wait a minute... OK, I've banged my head against the wall, and that still seems like a contradiction of the thesis of the earlier material ("certain types of math are too hard for most children").

I hope that this little brochure isn't indicative of the overall level of scholarship at the UW College of Education...

Even engineers apparently don't need math

From the UW College of Education comes the very attractive publication linked from the title above. It addresses the "math wars" between "traditionalists" and advocates of "modern math education". Of course, like many political debates, they use titles such as those to pre-dispose their readers to see things their way. This is a sign right off the bat that this is not a scholarly work, but a political argument. Other signs are straw-man examples that are supposed to show how "traditional" math is misguided, such as this (p. 9):

A toy is hidden in one of two cakes. One cake is a circle, cut into fourths. The other is a rectangle, cut into sixths. Students must choose the cake that gives them the best chance of finding the toy.

Some choose the rectangle. Why? Because “most toys come in square boxes.”

Of course this is a poor question for students who would answer that way, because it is varying two things at a time (cake shape -- and therefore slice shape -- and fractions of total area). Presumably, this question is trying to get at more abstract thinking; that the shape of the cake and its slices doesn't matter, all that matters is fraction of total area. But the publication doesn't say anything about this, all it does is use this as a straw man to set up the argument that we shouldn't tell students how to do things (like optimal methods for mathematical calculations). All methods are equally valid:

One student may add 28 + 34 with traditional column carryover. Another adds 2 to 28 and subtracts 2 from 34 before adding the two results. A third student adds 8 and 4 to make 12, then 12 and 30 to make 42, and 20 more to make 62. In an effective classroom, all those solutions are studied, the links between them established, and the connection made to larger mathematical concepts (such as place value, the properties of addition, and developing generalized strategies).

This sounds very nice until you consider, "How did these students all arrive at different methods for addition?" The answer is that they weren't taught how to add; they were expected to "discover" it themselves. Go read a history of mathematics book sometime and consider how long humanity has worked to discover what we know about mathematics; how many geniuses have been involved. Does it make sense to systematically (not as an occasional teaching device) expect children to re-create any fraction of this? And is the only way to teach about place value, etc. to compare multiple methods?

Oh, and the implication is that "traditionalists" teach by giving out problems and just marking them right or wrong and "modernists" look at student mistakes and seek to understand why they make them. Nice false dichotomy.

I find this anecdote on page 13 especially interesting. One of the UW Education faculty has spent time observing engineers, scientists, and architects working, and here are his conclusions:

The architects, he discovered, worked problems out with visuals, not textbook algorithms. Engineers use mathematics, but much of that is embedded in their computational tools, and they too use forms of quantitative reasoning that looked very different from the activities of school math. It turned out that school math was a fairly rare species of activity outside of school.

“If you spend a month with architects, you’ll never once see them write an equation,” says Stevens.

The story was the same when he studied roadway engineers. “All the calculations were done on the computer,” says Stevens.

As the brochure continues, the distinction is between "school math" and the math that people actually use in the real world. Well, except for mathematicians, who are like poets, viewing the world in a different way than most people. Apparently, engineers don't need to know math; it's already in the computers (how it got there is unanswered). It's unfortunate that engineering schools and the accreditation folks require math through differential equations, multivariate calculus, etc. They must not know what engineers do as well as UW Education folks.

Get by with a little help from your (non-Windows-using) friends

Seems that a lot of digital picture frames are shipping with a Windows virus pre-installed. This is very convenient; it eliminates all of the hassle of connecting to the net and waiting for infection.

Seriously, and as John Gruber pointed out in Daring Fireball, here is one general approach to avoiding Windows viruses (quoted from the article linked above):

Deborah Hale at SANS suggested that PC users find friends with Macintosh or Linux machines and have them check for malware before plugging any device into a PC.

Tech companies to educators, commuters, the poor: screw you

Washington state is currently ranked 37 in college degree production, though it's in the top 10 in terms of employment of high tech workers. The Seattle area is ranked 3 in traffic congestion. Technology companies in this state complain loudly about the impact of congestion and lack of local college graduates on their companies. Bill Gates started a large foundation dedicated to solving other problems: in public health. But, when you get down to it (as you'll read by following the link above), when push comes to shove, public dollars in these companies pockets is more important to them than anything else. In this case, they're arranging things so they won't have to pay state sales tax on their equipment purchases for their server farms. To put this in perspective, the University of Washington -- a state institution -- pays sales tax on its purchases, even when using money allocated to it from state taxes. It's nice to know for whom this country is really run.

Single point of failure?

Do people really rely on a device that can fail, nationwide, if someone screws up a software upgrade at a single location in the country (apparently the reason for the April 2007 Blackberry outage)? A quick perusal of Google indicates two outages last year and one in 2007. And this is supposed to be a device better suited to corporate use than an iPhone?

This is cool

A first-person shooter for the iPhone, written in JavaScript. It doesn't require jailbreaking, as it runs in Safari. I especially like the pencil-and-paper drawings for the opening scenes; they make the game feel personal, like you're reading someone's diary.