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Calculating Offset in Mathmagic Land

Posted on April 16, 2011 at 8:28 PM

While I was always a good student, math was never my strong suit. I liked to say that words just made more sense to me and creative writing was just ever-so-much more fun, and, uh, creative. But the truth is, I just never had the stick-to-it-ive-ness needed to master anything beyond geometry. Memorizing formulas and understaning tangents and cosines and TI graphing calculators and and whatnot. And unlike many things that I blurt out in a heat, I’m still not regretting my, “Look! I’m dropping your class. I will NEVER need calculus. NEVER!” speech.


Now, I’m fully competent at the big four (addering, minus-ing, multi-player, and the other one) and I’m even fairly handy with algebra. I actually like solving for X; that is when X is relatively easy to come by and doesn’t try and hide behind his co-conspirators Y and that real SOB, Z. I don’t give two whits when Train A left the station or at what time it is going to cross paths with Train B; that is I don’t care unless there is some story I can work up around it. Say Train A is filled with negotiable bearer bonds and it is heading for a super-mega incineration smelter and Train B is filled with someone you don’t even know and it’s also headed to the fiery cauldron. Using your handy math, you determine you have only time to visit one train; save the paper and spend the rest of your life lavishing yourself in riches trying to forget you let someone you didn’t know burn to a crisp or... See, now THAT’S math!


Now one of the things that I really remember – and actually liked – about math class was that practically every year – usually during that dead week right before Christmas vacation, when you pretty much spent the week of shortened classes drinking red Kool-Aid and eating cakes and cookies and only the totally hateful and douchiest teachers would assign homework – we would watch a Disney cartoon called Donald Duck in Mathmagic Land. I can remember this happening up into my junior year of high school, after which, math and I parted company in the famous Mr. Fee calculus speech. The movie was actually on 8 mm (I think) film reel. They would make a big production of wheeling in a film projector and roll-down screen. (Wow! I just had a total insight! The thing I remember about liking math was watching a movie on a projector and screen! I always kind of thought that getting into the home theater thing just kind of randomly happened, but the signs were clearly there all along!)

 

 

Now, this almost seems like a unique experience to the California education system, because I have talked to many people around my age group and they have no recollection of watching DD in MM Land. Not in school and not in ever. And I know it has nothing to do with an especially good recall on my part because my memory is really a bit of rubbish. (Ask Dana. I’m also absolutely zero value when it comes to finding, well, anything around the house.) So, before we get on with the rest of the story, do me a favor…if you can recall seeing DD in MM Land, leave me a comment. Love to know if this was just a Cali thing...


So, DD in MM Land follows Donald Duck as he discovers bits of math in nature. How math is really an integral part of our daily lives and can be found in music and flowers and architecture and seashells and blah-blah. That part was all so much cake-and-punch-consuming white noise jibber-jabber. The part that I loved, the part I looked forward to each year was when Donald would use math to explain three-cushion billiards. This part was brilliant. This part was fascinating. This part made total and absolute and perfect sense. I would watch this scene each year and be like, “Yes! You’re right, Donald! The diamond system! It’s perfectly simple and obvious! I can know go forth and be the next Minnesota Slim!”


But then a strange phenomena would happen; the movie would end, and with the diamond system dancing in your head, it would all start to get jumbled. And no matter HOW MANY times I watched it, I could never keep the diamond system straight. I felt like the guy from Memento. Minutes after watching it, I would feel the memory unraveling in my mind, and the harder I pulled at trying to retain it, the quicker it fell apart. (Granted, I never fully committed to inking the diamond system onto my body. First, that’s just a tad extreme. And I'm not sure a career in three-cushion billiards was really the future I wanted to pursue. And second like I’m gonna trust some tattoo artist to ink me up with what HE remembers of the diamond system! Yeah, right. Let me see him work the table for a bit and then maybe we can talk.)


And I know this wasn’t unique to me. You would ask other viewers to explain even minutes after it was over and you’d get this immediate flash of, “Duh, stupid! It’s so obvious! You just take the first, uh, position and you… Or is it the object ball subtracted by the cue starting position divided by…? Oh, crap! I can’t remember either!” My friend Dan and I rented it prior to going out and actually playing pool and it still didn't stick. I swear, watching the DD in MM Land billiards scenes is like trying to solve one of the great mysteries of our day. Go on, take a look for yourself. (For some reason, this video has some still images at the beginning and plays some random Bob Marley-style music for the first 25 seconds or so, just hang in there and the video will start.)


 

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Now, wait five minutes and explain the diamond system to me. Go on. I challenge you!


OK, so how this is at all germane to anything? This isn't just some random trip down memory lane to discuss a 50 year old cartoon. Yesterday at our store, Al comes back and he is all excited because he has just gotten the go ahead from a customer to install a video projector, a Runco. So high-fives ensue and then Al goes about trying to make sure that the projector he has specified is going to work in the install. And, since I had just returned from Runco Training Academy – where you could at least assume that I would have picked up something about figuring out how to specify a projector for an install – he asks me to help.


Now, when setting up a projector there’s basically three things you need to worry about. (OK, there's more to it than that, but I’m going to just greatly simplify this...) First you need to know about light output. Basically am I going to have enough light horsepower – lumens – from the projector to adequately fill the screen real estate and material that I’m planning on using. This wasn’t an issue in this case, since we were going with a smallish screen size and had total light control in the room.


Next is throw distance; basically how far back – or how close – can the projector go to fill a given screen size. This is different with every projector because they all use different lenses, and this step requires a bit of math. Now it looks a bit confusing at first, but once you figure it out, it is pretty straight forward. You look at the manual and for the standard lens and it says “1.85 – 2.40 (distance/width)”. So with this you can do...what? Right? It doesn’t exactly scream, "The projector needs to go...RIGHT HERE!" But in reality it does tell you everything. A really common sized screen is 100 inches diagonal, 16 x 9 aspect ratio, measuring 87-inches wide. So you can either multiply any number from 1.85 – 2.40 by 87 and that will tell you how far away – in inches – the projector lens can go. Or you can divide how far away you plan on putting the lens – say you know it needs to go at 15 feet or 180-inches – divided by the screen width. So 180 divided by 87 equals 2.07 which falls between 1.85 and 2.40 so we know we’re golden. See? No problem. Easy breezy.



 


Now, the Mathmagic Land part comes when you need to figure the final part: the vertical offset. This is how high the lens can be above or below the screen area. And it seems that no matter how many times vertical offset calculation is explained, I’m still scratching my head wondering if I’ve got it right and if it is going to work right up until we hang the stupid thing and turn it on and see if it works. Now part of the conundrum is the verbiage and the changing terminology. From the Runco projector spec sheet, it says, “Horizontal and Vertical Offset: -50% to +120% (vertical, ceiling mounted, % of the half height)”. Seriously what the hell does that mean? Then there’s this explanation from the owner’s manual: “Vertical Lens Shift: the LS-3/LS-5 provides up to 25% of upward vertical lens shift and 60% of downward vertical lens shift.” Where’d the 120% go from before?

 

 

We whipped out some markers and a dry erase board and a calculator and we started drawing squares and center lines and trying to work back from the example given in the manual (“a 100 x 56 inch screen, you can shift the image up to 14.00 inches above or 33.60 inches below the screen center") to jive with the -50% to +120% in the spec sheet so we could ultimately figure out if where we wanted to place the projector -- slammed up against the ceiling -- would work. Because working correctly is pretty much the entire reason why people hire us in the first place. I could hear Paul Frees voice softly chastising in the background. “Now, Donald. There’s no guessing with math.”


Ultimately we figured it out, but, like the diamond system, I already can’t totally remember what the rules are for calculating offset, won’t be totally sure that this projector is going to fully fill the screen until we have it hung and mounted and already know that the next time it comes to spec’ing a projector, I’ll still be calling Runco to go over it. I guess you’re never too old for a visit to Mathmagic Land.

Categories: April 2011, CTA, Electronics

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4 Comments

Reply Crume
1:18 AM on April 17, 2011 
Okay, so here goes. I have been keeping up with your blog for some time and up until now have been able to keep from posting, even though I have been tempted to do so many times. The DD in MM Land experience is most definitely a Cali thing, as I have had the same screenings as you. Year after year I have watched for that very same billiards scene and tried to etch the information into my brain over and over again. But unfortunately it just doesn't stick, so I have had to transform it into the much simpler geometric equation thing, thereby kicking my father-in-law's butt at pool.

Please, keep up the posts. My wife and I enjoy them very much and they bring back fond memories of Northern California and friends we haven't seen in a while.
Reply John Sciacca
9:05 AM on April 17, 2011 
Thanks, Crume! To quote Obi-Wan "You have taken your first step into a larger world." Glad you finally decided to throw out a post. Always welcome the comments...even outside of Mathmagic Land! Be interesting to see if any other states chime in with an experience....
Reply T~Law
4:51 PM on May 24, 2011 
Man I remember standing at the pool table many times with cider in hand checking out the angles and listening to you and Dan trying to remember what Donald would have done with the ensuing shot.... Good times!
Reply Michael
10:34 PM on June 30, 2011 
John, I've been trying to remember the name of this show for 30 years. I was at school in Sydney (yes, the "down under" one, in case there are any Sydneys in the US) in 1979, and we too were shown this film in the projection room (a large room at the end of the school with a white rectangle painted on one wall) at the end of term. I too was impressed by the billiards scene, and went home that night to try and explain it to my older and very mathematically gifted brother, and my very gifted pool-playing father - only to find that I couldn't remember what they were going on about. I've just watched it again - with an engineering degree and many years of mathematical gymnastics in various roles under my belt - and I *still* don't think I could explain what's going on!