I apologize up front for the insane nerdiness of this post.

So the other night I was lying in bed, unable to sleep, and I started to think about numbers. It’s actually not something I do a lot, but every once in awhile, especially when my brain wont shut up long enough for me to go to sleep, I’ll try to bore it to sleep with math. On this particular night, I started thinking about number systems and units of measure.

People are quick to deride the Imperial system of measurement we use here in the US as “archaic” and “illogical.” Most of the time people point to the ease of converting between units in the decimal based metric system as evidence of its superiority. And no doubt about it, the metric system shines if what you want to do is convert between units. However, if what you mainly want is the ability to divide things into equal pieces easily, that’s where the Imperial system has the metric system beat hands down. The entire reason a foot has 12 inches and a yard has 3 feet is because 12 is evenly divisible by 2, 3, 4, and 6. So if you have a piece of cloth 4 yards long and you want to divide it into thirds, the math comes out even–each piece should be 48 inches (4 feet) long. Good luck doing the same with the corresponding metric units. A piece of cloth 4 meters long cut in thirds would have each piece be 133.33~ centimeters long. Have fun finding a ruler that can handle that easily.

Now, this isn’t meant as a defense of the Imperial system. It’s all just my usual roundabout way of getting to the point. As I lay there thinking about this stuff, I started thinking how useful (for a very specific and narrow definition of “useful”) it would be to find a number that would be evenly divisible by all the integers up through 10. The Babylonians used a base 60 system, specifically because it has so many useful small factors (2, 3, 4, 5, 6, 10, and 12.) They’re also the ones who first divided the circle into 360 equal parts for exactly the same reason (the factors of 360 include 2, 3, 4, 5, 6, 8, 9, 10, and 12.) 360 is really very close to what I was looking for.  It lacks only the number 7 as a factor, in fact!

Wow, so close, and yet, so far away! I lay there in my sleep deprived state, and turned the problem over and over in my mind. The only answer I came up with before finally falling asleep was that there was at least one number that was evenly divisible by 2, 3, 4, 5, 6, 7, 8, 9, and 10, and that’s 10 factorial, which is 3,628,800.  The factorial operation means to multiply together all integers that are less than or equal to the number being operated on.  So 10 factorial is the same as 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800.

That answer satisfied me enough to finally let me sleep. However, I kept being bugged by the issue in days to come. 3,628,800 is a pretty big number. It sure seems like there must be a smaller number that works, but I couldn’t for the life of me puzzle out what it could be. I would occasionally think of a number that might work, and whip out a calculator to test it, and inevitably it wouldn’t work out. The problem baffled me.

Until today. Today I realized with a sudden flash of the blindingly obvious that the answer I was looking for was 2520. How did I come up with that number? Simple. 360 x 7 = 2520. I already knew that 360 was divisible by all the other numbers I cared about, so what I was really looking for all this time without even realizing it was a number that was evenly divisible by both 360 and 7. The easiest way to find a common multiple between any two numbers is to simply multiply them together.

Ah, but is this the smallest number that works? I puzzled for a bit longer. It was clear to me that just multiplying two numbers does not automatically give you the smallest number that is evenly divisible by both. 6 x 4 = 24, and yet 12 is also evenly divisible by both 6 and 4. If only there was some way to discover the smallest possible number that is evenly divisible by two or more given numbers. Some kind of… I don’t know, some kind of least common multiple.

…

Yes, ladies and gentlemen. It took me weeks to realize the answer to my conundrum was to apply a little grade school math. Hell, they probably teach this shit on Blue’s Clues now. It’s easy enough to find an LCM with a bit of tedious calculating, but the interwebs makes it trivial. Just go over to Wolfram Alpha and punch in “lcm 2,3,4,5,6,7,8,9,10″ and in like half a second it spits out 2520. A second’s further thought had me slapping my head, since of course the least common multiple of 7 and 360 was simply 7 x 360, because 7 is fucking prime. So the only real question I should have had this whole time is whether 360 is the LCM of 2, 3, 4, 5, 6, 8, 9 and 10. And of course it turns out it is. Those Babylonians knew their shit.

Unlike me.

So a few weeks ago it was brought to my attention that science has proven that piracy is a good thing. I mean, you can’t get more official than a blog relating an anecdote, right? All I know is, if it’s on ScientificAmerican.com, it must be true.

Well, as it turns out, I have something I’m trying to sell.  It’s a book.  A really bad book! Now, don’t everybody run for the hills, hear me out. I wrote this truly epic fantasy novel when I was a teenager, and for years I thought it was awesome. Well, it aint. It’s actually pretty hilariously bad. So a few years ago, I went through it and decided to do a sort of MST3K job on it by adding over two hundred snarky, self-deprecating footnotes to the text. I packaged that up with the help of my wife, who knows a thing or two about editing and graphic design, and started offering it for sale. Because hey, I like money. Don’t you? Well, as it turned out, most people liked their money more than they liked the idea of owning my book. I sold mumbldy-mumble copies, but failed to rake in the pile of filthy lucre that I was hoping for.

So now I’m going to try a different tactic. Since according to the crazy moon logic of Scientific American, giving shit away makes you money somehow, I’ve started giving away the electronic version of my book.  You can click right here for the PDF version,  which is probably the best version to read it in since it preserves the page formatting and keeps the footnotes in their proper place.  However, I have not forgotten my legion of Kindle followers either–you folks (and anybody else who has an e-reader that can read the MOBI format) can click right here for the .mobi version. If you’re reading this on your Kindle now, you should be able to just click that link and the book will be downloaded to your device automatically. The Kindle version of the book contains the footnotes, but it transforms them into endnotes, and you have to click on the superscript to be taken to the footnote text, and use your “back” button to go back. It’s a little bit more of a hassle, but hey, you paid none moneys for it, so don’t complain!

Of course, those of you who enjoy paying for free shit, you can always go to the Amazon.com page for the Kindle version, where you’ll be given the privilege of paying $2.99 for the same file I’m giving away for free here. Hey, don’t blame me, Amazon won’t let me give it away on their site. They won’t even let me give it away at cost for some reason. Fucking capitalists!

And since science has proven that once you’ve read the free electronic version, you’ll simply NEED to buy the paperback or, better yet, the hardcover edition, here are the handy links you’ll need to do that:

Trade Paperback:

Hardcover:

So, have fun! If you have any questions/issues/comments you can comment below, or send me an email.

I’m told that once upon a time, Hewlett-Packard was a great company. Founded and run by engineers it made solid, well designed products and treated their employees well. I haven’t any idea how they treat their employees these days, but I can tell you that the days of making well-designed products are over.

The other day, one of the executives of the company I work for decided he needed a new printer. He was tired of switching paper around or using manual feed whenever he wanted to print on legal sized paper, so he requested a printer with two paper trays–one for letter, and one for legal. This is not an unusual request, and when it comes from an executive, the answer is always “Yes sir, right away sir.” So a dual-tray printer was ordered and arrived in short order.

Now, I don’t actually deal directly with desktops and printers in my day job, so I was only aware of this whole scenario when the giant box showed up in my team’s area the other day. It was quickly unpacked and set up in our test area, which happens to be right behind my cubicle. It didn’t take long for the banging to begin. Thumps, crashes, and muttering very quickly disrupted my concentration (believe it or not, I was actually working at the time) and I turned around to see what the fuss was all about.

“It must be caught on something,” says one teammate. “There’s probably a catch somewhere you have to press to make it go all the way in,” says another. I turn around and see them struggling to get the legal sized paper tray into the new printer. It goes in smoothly most of the way then stops, leaving about two inches of the tray sticking out. It looks a little something like this:

Clearly something isn’t right. They pull the tray out again, and examine it more closely. “It’s catching on these two plastic clips,” says teammate one. “Do they come off?” says the other. “…no, they look pretty solid.”

At this point I get up to take a closer look. Sure enough, there are two plastic “ears” sticking out from the side of the paper tray, preventing it from being inserted any farther into the printer. I put the tray back in the printer myself and bang it around a bit. It’s not going anywhere, it’s just stubbornly stuck in that seemingly wrong position.

“Let me try printing something from that tray,” says teammate one.  He punches the menu buttons a few times, and the printer whirs to life. Fairly quickly, a test page printed on legal paper comes out the top. We stand there in stunned silence. “No way,” says teammate one finally. “There’s no way it’s designed to be that way.”

Finally, somebody suggests reading the manual. We’re men, and IT guys besides that, so of course it has taken a long time for us to actually think to look at the setup instructions. Sure enough, we find this gem in the manual: “The extended paper tray will extend beyond the edge of the printer.”

Wow.

“I’m taking this up with me when I take the printer to his office,” teammate one says. “He’ll never believe it’s supposed to be this way otherwise.”

So I say to you, HP, if you actually put out a printer that looks like this by design:

Then you fail at engineering, and no longer get to hype up your “founded by engineers” background.