Technologically Improved (But Mathematically Flawed)


I know it’s time to post when less than 5 people are visiting the site.  This one isn’t particularly interesting, but it’s something to fill the space.

My family’s home in New Jersey has received quite a technology upgrade over the last three months, culminating with the iMac replacing the five and a half year old eMac as my mom’s main computer.

The initial process began in October when I moved to NYC.  I needed a wireless hub and the one I got for free by a fortunate mistake on Apple’s part eight years ago not surprisingly did not function.  I thought about getting the Airport Express but when I went to the Apple Store, it occurred to me that Time Capsule, which doubles as a wireless hub and a backup hard drive, made sense in light of Apple’s ingeniously easy to use Time Machine application and three Macs around the house .  So I bought Time Capsule and took the Airport Express at home to my apartment.  Now all computers in New Jersey are automatically and wirelessly backed up.  This also turns out to eliminate a lot of hassle when replacing a computer because I no longer have to physically move data from the old computer to the new.  I just have to hook up the new machine to wireless connection and recover the data from Time Capsule.

The next round of upgrade was a massive one impacting every important room in the home.  In October, the family’s VCR broke and it made little sense to buy a new one; in fact, I don’t think they sold a stand alone VCR at Best Buy.  We couldn’t just get a DVD burner, though, because there were (I kid you not) hundreds of VCR tapes still floating around the house.  The goal, then, became to buy a combo DVD burner / VCR player with an eye towards eliminating all VCR tapes by the time next upgrade is necessary.

This was easier said than done.  The guy I first spoke with at Best Buy wasn’t too helpful and I bought a machine that was a crap from Samsung.  When I went to return it, the guy who assisted me was quite helpful in explaining that I have to be careful with the DVD-VCR combo I picked because it may not be digital.  Thus began the whole discussion about how by February, all transmissions would become digital and non-digital TVs would no longer receive a signal without a converter.

What happened next is predictable, although mathematically and financially illogical.  I thought, well if we’re going to get a converter (which is free), we might as well replace all three, non-digital, tube  TVs around the home.

Alas, we waited until black Friday in November to take advantage of the whatever little discount being offered.  One main advantage of digital TVs, besides its graphics quality, is its weight.  The TV in the basement was 22 inches, but it weighed like an elephant.  We replaced it with a lighter 40 inch flat-screen Sony Bravia, which I thought would be too big only to discover that there is no such thing with television.

In the upstairs living room was a 17inch Sony Trinitron we bought as our first second TV back in 1994.  It was far too small for a living room.  The 32 inch flat-screen from LG that’s replacing it has nearly 70% more viewing space (do people understand why a 50% increase in dimensions leads to 75% increase in area?  If not, you are living proof American education system needs vast improvement) [see below for why I have also become the victim of American educational system, as this claim about 70% increase in area is simply false]*, thus finally permitting the family to view the TV from the distance of the sofa.

Then there’s the small TV in the kitchen that we got for free when my parents bought my sister our one and only PC.  The PC (not surprisingly) did not last long, but the TV sure did.  The manufacturing date on it was 1998.  That TV was replaced with a 14  inch flat-screen from Westinghouse (a company long gone, although apparently not the brand) which provides a crisp picture unworthy of the kitchen.

And that DVD-R/VCR combo?  We got that too, a nice one with a TV tuner.  I gave it a ride this weekend, and it seemed to record and dub well enough.  I was surprised to learn that a normal DVD only records 2 hours.  That’s a little short, so I made sure we got a recorder that supported dual layer.

The highlight of the new gadgets, though, is the new iMac.  It is a machine of exquisite beauty and compelling features.  Its thickness, or lack thereof, is a technological marvel, but what impresses me most about Apple is its attention to detail, including packaging, that makes buying their product a  pleasure from the moment you walk into one of their stores until you set it up in your home.  For the first time that I can remember, every computer at our home is less than a year old–except my original PowerMac 6100/60 from 1994.

The total cost of all these upgrades?  Don’t ask.  Let’s just say our family is putting in our share of trying to rescue the economy out of a recession.

*  As pointed out by Tony, the change in aspect ratio from my old TV to the flatscreen likely meant a 50% increase in diagonal did not increase the area by 70% plus.

The statement is true in the case of a square, where the length of the diagonal is enough to calculate the area.  Hence, a 1.5 times increase in the diagonal will lead to a 1.75 times increase in the area of the square.

In the case of the rectangle, though, length of the diagonal alone is insufficient to calculate the area since the area is dependent on the length of two unparallel sides, with the area maxed when the two sides are as close in length as possible (i.e. a square).  It’s easy enough to see this mathematically as well:  Assume the diagonal of a rectangle is 6 and lengths of the sides are x and y.  The area of the rectangle is xy.  From the Pythagorean Theorem, x^2+y^2=6^2, since the rectangle’s length, width and the diagonal create a right triangle.  Now, (x+y)^2=x^2 + 2xy + y^2.  Solving for 2xy, 2xy=(x+y)^2-(x^2+y^2).  We know x^2+y^2=36, so 2xy=(x+y)^2-36.  But we get stuck here.  It’s impossible to calculate xy without knowing what (x+y) is.

The flaw in my calculation was my assumption that the TV is a square, which it clearly is not.

Well done, Tony.

Advertisements

4 Responses to “Technologically Improved (But Mathematically Flawed)”


  1. 1 Tony February 10, 2009 at 6:06 pm

    Haha, glad to see some contributing to the economy :-)! Although I must mention that you likely didn’t experience a 75% gain… more likely than not, the aspect ratio of your new TV is different from that of your old TV… the shift from 4:3 to this widescreen standard unfortunately reduces screen real estate :-(…

  2. 2 joesas February 11, 2009 at 9:18 am

    Tony,

    I stand corrected. You are correct. In the case of a square, the length of the diagonal is enough to calculate the area, so a 1.5 times increase in the diagonal will lead to a 1.75 times increase in the area.

    In the case of the rectangle, though, length of the diagonal alone is insufficient to calculate the area since the area is dependent on the length of two unparallel sides, with the area maxed when the two sides are as close in length as possible (i.e. a square). It’s easy enough to see mathematically too: Assume the diagonal of a rectangle is 6 and lengths of the sides are x and y. The area of the rectangle is xy. From the Pythagorean Theorem, x^2+y^2=6^2, since the rectangle’s length, width and the diagonal create a right triangle. Now, (x+y)^2=x^2 + 2xy + y^2. Solving for 2xy, 2xy=(x+y)^2-(x^2+y^2). We know x^2+y^2=36, so 2xy=(x+y)^2-36. But we get stuck here. It’s impossible to calculate xy without knowing what (x+y) is.

    The flaw in my calculation was my assumption that the TV is a square, which it clearly is not (whether flat screen or not), or that the aspect ratio is the same, also clearly not true.

    Well done, Tony.

  3. 3 Chris Schroeck February 11, 2009 at 2:18 pm

    Yes, obviously since you would need a digital converter you should buy three new TVs.

    By the way, don’t you have cable? I thought if you had cable you didn’t need digital conversion.

    And if you don’t have cable, you can’t watch the most trusted and objective name in news, MSNBC.

  4. 4 joesas February 11, 2009 at 5:35 pm

    Chris,

    Oh yeah, right. I think all cable boxes do have digital conversion. Only one TV in the house had that, though, so they’d’ve gone blank, so there! We needed a new TV!

    It’s funny you mentioned MSNBC, ’cause I was watching Fox News over the weekend and I love how the channel has gone from being all supportive of the White House to being critical. I bet it’s the complete opposite at MSNBC, but quite frankly, I don’t care to find out.


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s




Enter your email address to follow this blog and receive notifications of new posts by email.

Top Rated

Categories

Archives

February 2009
M T W T F S S
« Jan   Mar »
 1
2345678
9101112131415
16171819202122
232425262728  

%d bloggers like this: