Stupid math tricks on social media

Recently as documented by this New York Times article, this rather ambiguous math problem (middle-school pre-algebra level) has been making the rounds. The article references the Yanny/Laurel controversy as well as the dress that people saw as different colors. I didn’t really take a side in either of those, but this one highlights some of the potentially ambiguous nature of mathematical notation.

The math problem in question:

x = 8 ÷ 2(2+2)

First, let me state the obvious: this is poorly written, and normally when using algebraic multiplication notation, i.e. putting the terms right next to each other, one would also use the fraction bar or vinculum instead of the obelus (“÷”) symbol. So instead, one would write either the equivalent of:

x = (8÷2)(2+2)


x = 8 ÷ (2(2+2))

Indeed, in the computer programming language Forth, which I have spent a bit of time dabbling in (still need to package up some of the code I’ve written into a proper release), there is no need to memorize the time-honored mnemonic of Please Excuse My Dear Aunt Sally for the order of operations (parentheses, then exponentiation, then multiplication and division, then addition and subtraction). One would code either of the following:

8 2 / 2 2 + *


8 2 2 + 2 * /

The first one gives you 16 as in the first example above (with the 8÷2 grouped together), the second one gives you 1 as in in the second example above (with the 8 being a term by itself).

The article’s author seems to imply the “correct” answer is 16. The fact that there’s any debate on the correct answer, and that I apparently arrived at the “wrong” answer despite my stellar math background (I aced every high school math class except geometry and that one only because I blew off all the major projects), says to me there’s something wrong with how the question is written. Nobody, and I mean nobody, uses this half-baked obelus symbol notation for division at any serious level of mathematics unless they are printing calculator buttons. This type of problem is one reason. The other is that a sloppily written (or blurry-printed!) obelus can look way too much like an addition symbol. Indeed, the author of the article goes on to state:

No professional mathematician would ever write something so obviously ambiguous. We would insert parentheses to indicate our meaning and to signal whether the division should be carried out first, or the multiplication.

The lessons to be learned here are:

  1. Be careful how you write math problems; and
  2. Apparently anything is fair game to debate on social media.

Take off? Take a leak first

Apologies in advance to the easily offended… but this story was just begging for a few really bad jokes to be made.

The London newspaper Metro reports on a Japanese airline’s very strange new policy, which may already have some passengers a bit pissed off.

All Nippon Airways is desparate to reduce their carbon emissions, and is thus requiring passengers to urinate prior to boarding. This policy was put in place for a trial period of four weeks beginning on October 1.

Personally, I think ANA’s management is just peeing into the wind here. This is probably going to lose them quite a few customers, and probably for longer than a month. Customers tend to remember bad experiences longer than good ones. Put another way, ill will lingers longer than goodwill. Case in point: anyone remember ValuJet? (They are still around, but shed the old name with near-zero or possibly even negative goodwill when buying up a smaller carrier named AirTran.)

Astroturf a la Redmond: Windows 7 Parties

While cleaning out the draft posts queue, I found this. The original article is a bit old, but the parties haven’t happened yet.

A recent TechFlash article discusses a Microsoft initiative for the upcoming Windows 7 release, describing it as a “Tupperware-style twist.” The idea is to encourage users, partners, and of course Microsoft employees to throw parties to show off Windows 7.

I see, as the title implies, what is essentially astroturfing at its worst. If Windows 7 were that great of an operating system, Microsoft would have people volunteering, or even paying Microsoft, to have these launch parties.

As far as my personal PCs go, I haven’t really looked back since the spring of 2002 (I didn’t write down the exact date, unfortunately) when I reformatted two different Windows 98 PCs and installed, at the time, the GNU/Linux distribution maintained by Red Hat on one (today’s equivalent would be the community-supported Fedora Project), and FreeBSD on the other. (Both of those PCs eventually wound up running Debian GNU/Linux years later.)

I do use a Windows XP laptop PC, which still has what I deem to be an unacceptable crash rate. By unacceptable, I mean it crashes at least five to ten times as often as the Debian GNU/Linux PC next to it which is at least most of a decade old. No, that’s not a mistake. Simply put, even with less than half the CPU and a fourth of the RAM, I get much better stability, even with the obvious reduction in performance. Put simply, Centerpoint Energy (our local electric utility) and the forces of nature responsible for thunderstorms force reboots of the Debian PC more often than any technical problems with Debian itself.

(Why haven’t I bought Apple’s products instead? Regular readers should know this, but I’ll provide a starting point for the new readers.)

Microsoft has still done next to zilch with regard to helping ensure the freedom of its customers. In fact, Microsoft has pretty much made itself the sworn enemy of the free software movement, with apparently no shame or regret. While Microsoft has made token efforts to contribute to the open source movement, it is very important to note that the ideals of the open source movement only encourage access to the source code for convenience and open source licenses do not always protect all the essential freedoms of users and programmers of the software released under them. It is also important to note that without the work of Richard Stallman and the FSF on the free software movement, there would be no free software movement for the open source movement to have splintered from.

Those readers unfamiliar with what I discuss above are encouraged to read some of Stallman’s essays, most notably these two: “Why Open Source misses the point of Free Software” and an earlier version “Why ‘Free Software’ is better than ‘Open Source'”.

Several of Microsoft’s licenses appear to have been intentionally worded to provide the illusion of freedom while in reality providing just the opposite. Most notably, these are the Limited Public License (Ms-LPL) and Limited Reciprocal License (Ms-LRL). Both of these licenses require that any modified versions of the original code must run on Microsoft’s Windows operating system. To those who value freedom on their own terms, not those of a large corporation with no particular incentive to be nice, this type of restriction is abhorrent.

In summary, my view is rather simple. Windows 7: same song, seventh verse, even bigger and even worse.

Games book publishers still play

Josh Catone writing for Mashable reports on the not-too-surprising pitfalls of digital textbooks and why they are not ready for prime-time for many students. The primary focus of the article appears to be college students where textbooks are purchased. (If I have any readers still in high school out there, yes, it’s true, senior year of high school is the last time you’ll get to borrow your textbooks for free.)

Indeed, very predictable it is that the third reason (of three) is “questions of ownership.” Cited are DRM (digital restrictions management) limiting time of use to 180 days in one example, after which the books are automatically deleted. The example cited is a biology textbook available via both hard copy and electronic textbook distributor CourseSmart. (The article refers to CourseSmart as a publisher, but it appears this is technically incorrect.) The hard copy version is available for US$50 used, US$80 new; CourseSmart charges US$70 for what is in effect a 180 day rental. Given the cost, and that this is never a concern with printed textbooks, this is simply unacceptable. US$70 for a non-DRM copy is more in line with what I’d consider fair. If Pearson (the publishing) company insisted upon a silly, odious, and obnoxious 180-day time limit, I honestly think US$20 is more realistic. Yes, one-fourth the cost of the print version.

The lack of standardization doesn’t help either, which in turn highlights just how bad of an idea DRM really is, as that is a large part of the reason for lack of standardization. It’s similar to the reason Microsoft’s “PlaysForSure” campaign looked pretty dumb when Microsoft then came out with the Zune, in essence saying “Thanks, hardware manufacturers, for supporting our patented Windows Media format and making it easy for PCs running Windows to use your players, we like you so much that we’re going to say, here’s our Zune, and here’s our middle finger.”

Most digital audio players prior to Apple’s iPod, Microsoft’s Zune, etc. used a standard, if patent-encumbered, format called MPEG Layer III Audio or MP3. Most understood Windows Media (WMA/WMV) files alongside MP3, but MP3 was still a fairly reliable “lowest common denominator” format.

In the world of digital print publishing, despite the clear winner being Adobe’s PDF format (which is as far as I know not patent encumbered, or the patents thus covering it have been made available under a royalty free license), many e-book readers do not support plain PDF, or do so in a manner that’s obnoxious and clumsy compared to grabbing the DRM-infested version.

It seems like print’s slow transition to digital may be the last frontier for DRM elimination. College textbooks are just the tip of the iceberg, though I think students not being able to sell their books at the end of a semester anymore will be quite annoyed. Or, they may just shell out the money again for what’s in reality an expensive rental. Hopefully, the kids smart enough to get into college will be smart enough to see the shell game being played before them.