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Movie Cliche of the Day

I bring you the Movie Cliche of the Day site. Go check it out.

As a teaser, here are numbers 12, 79, and 318:

When you cut the wire to the detonater, the timer will stop.

People in movies have lots of candles, and they're always new.

Movie scientists never have a Southern accent.

More from Capitalism and Arithmetic

An interesting multiplication algorithm from Capitalism and Arithmetic is known as gelosia or graticola.

It got that name from the diagonally latticed windows in Venice, from which cloistered women watched the world. Those windows are also the root word for jealousy, and in contemporary America are called jalousy windows. The alternative name, graticola, is Italian for grill.

I'm not sure why they don't still teach this technique in elementary schools - it's pretty cool once you get the hang of it. However, it does not lend itself to HTML, but I'll do my best.

Suppose you want to multiply 934 by 314 [pp. 208-9]. You would write out the 934 in a row, and the 4 and then the 1 and then the 3 (of the 314) going down the right hand side. Like this:

I intentionally left a little space at the left of each row. (I found a somewhat different layout on the internet in this photo).

With imagination, you can envision this is as a window; add diagonals and you have the Venetian gelosia.

OK. Now, multiply the top term in the right hand column times the right term in the top row:4 times 4 is 16.

The trick is to write the answer in a position that corresponds to those two numbers, but with the units digit to the "northeast", and the tens digit to the "southwest".

Now, continue doing that for all the other numbers along the right and top.

When you're done it should look like this:

I put the zeroes in as placeholders, but they are not necessary. If you look carefully, you can can see that there are some diagonals - envision them running from "northwest" to "southeast".

Anyway, the technique is easy now. Just add up the numbers along the diagonals.

Starting at the "northeast" the first diagonal only contains a 6. Write this where you want your answer. The second diagonal contains 2, 1, and 4, and sums to 7. I marked this diagonal in red. Write the 7 to the left of the 6, and continue to the third diagonal. This contains a 6, 1, 3, 0, and 2. I marked these in green on the figure.

Now we have to carry (which is a problem in all methods of multiplication).

These green values sum to 12. Write the 2 to the left of the 7. Carry the 1 from the tens digit of 12 to the top left of the next diagonal (marked in blue), which now sums to 23. Write the 3 next to the 7 in the answer, carry the 2 and add up the next (cyan) diagonal to get 9. Write that next to the 3 in the answer, and do the last diagonal (in magenta). This sums to 2 which is the leftmost term in the answer. You should have 293,276.

Even though this method isn't taught any more, it has a huge advantage, and two smaller ones. The huge advantage is that in doing multiplication the conventional way, it is very easy to make mistakes when carrying: most of us make a tick mark, and we have to remember not to count it more than once. This method does not have that problem, since the carries don't get lined up on top of each other. One smaller advantage is that the method we learn in school requires us to multiply at each step and then remember to add anything we carried, whereas this method completely separates the multiplication and addition. The other smaller advantage is that when we get a result that requires carrying in the conventional method, we have to write part of it below "the line" and part of it above the terms being multiplied, instead of close by each other. This makes checking more difficult.

This is difficult to see because you are used to it. Here's the conventional method:

First multiply the 4 times the 4 to get 16. Write it like this:

That shows the third advantage: the ones and tens digit have to be separated in this method.

Note that I've included all the space and lines we'll need; one reason that gelosia seems intimidating is that we don't realize how much advance planning is required to lay out conventional multiplication. In gelosia, I did it first because I had to, but we are more cavalier with the conventional method we know so well.
 

Continuing on, multiply the 4 times the 3 and add the tick mark, which is written like this:

That step shows the third advantage once again. However, it also shows the second and first advantages as well. The second advantage is that you have to multiply and add at this step, something that never comes up in the gelosia method. The first advantage is more subtle: I had to remember to strikethrough the first tick mark after I used it, and then put a new one in a different place.

When all is said and done, this method doesn't look that easy either.

It turns out the gelosia method is also more efficient. Both techniques require you to do 9 multiplications. Gelosia requires you to do more additions: 14 of them, as opposed to 10 in the conventional method. However, to save those 4 addition operations, the conventional method requires you to do 6 carries, 3 strikethroughs, and you have to remember to shift two rows to the left (and the top row of carries too) to get your columns in the right spots. Gelosia only requires 2 carries. In sum, gelosia requires 25 operations of 3 different types, while the conventional method requires 31 operations drawn from 5 different types. The conventional method requires you to write 17 digits in the intermediate stage before you get an answer (and that is not counting superfluous zeroes). The gelosia only requires you to write 16 intermediate numbers.

It's also easier to check gelosia: all of your products are written out in obvious spots with the tens and units digits close by each other, whereas the conventional method sometimes combines multiplication and addition to yield a single answer which is then split into parts that are no longer contiguous.

As a final check on this, I timed myself doing some multiplication of 2 random 3 digit numbers. I made a point of doing them the formal way for both methods. After 35 years of experience, I can do the traditional method in 27 seconds, and having only done the gelosia about a dozen times, it took me 39. However, 14 of those 39 seconds were spent drawing the gelosia matrix. The actual calculation time was smaller. I didn't realize until I was done that I am used to doing the conventional method without vertical rules to line everything up, but if I'd had to draw them the time saved would probably be dissipated.

I wonder if computer programmers know about this algorithm? How much money could be saved worldwide if multiplication operations were done in this more elegant manner?

N.B. This is the post that crashed Typepad on Thursday morning, and made most of my blog disappear. It was very easy to write this the first time around using HTML tables instead of images, but apparently it was more than Typepad could handle.

UPDATE: Craig Depken of Heavy Lifting and UT-Arlington pointed me to this video showing a different technique, and from there I found this video of gelosia:

From Capitalism and Arithmetic

From Capitalism and Arithmetic

It is with these money lenders and their benches, banco, ... When a money lender was found to be cheating he ws publicly disgraced and put out of buiness by having his bench broken, banco ruptus. [pg. 277]

Savage Reign Wants a Photo

I got an e-mail from the bass player of Savage Reign - a classic rock cover band from Jonesboro - the other day (the guitar solo on Layla is original and pretty sweet).

They'd seen this picture on vX and wanted to use it for the cover of their forthcoming CD.

This came from a book my neighbor gave me about World War I.

I posted it the first time because I thought it was so odd: what exactly is this guy going to do - usually cavalry and lances aren't much good against the sort of people who have access to poison gas.

For the curious, I suspect the horseman is French (because of the helmet), and that the picture was taken in 1916-8, since the gas mask wasn't invented until late in 1915.

Technical Difficulties

Sorry for the site being down this morning - Typepad was choking on some of the HTML coding in a post. I'll rewrite it and try again.

36% Chance Housing Sales Are Up

The legacy media has been crowing about the 3.9% decline in new house sales. You know ... the sky is falling.

However, Social Sciences Statistics Blog points out that, hidden in the footnotes, is the fact that the 90% confidence interval around this point estimate is plus or minus 17.4%.

The problem with the 3.9% decline is that it is a point estimate based on survey data. No one actually went out and counted new house sales. They estimated them - so an interval estimate is really critical.

In this case, just about the only thing we can be certain of is that the decline in new house sales was almost certainly not precisely -3.9%.

What we can be fairly certain of is that new house sales fell into the broad range of -20% to +15%. That's a big range.

I won't bother you with the statistics or assumptions, but it works out to a 36% chance that new home sales actually went up in February  (see below the fold for details).

That isn't great news. But, it's worse news that there is a lot of negativity about the economy generated on the basis of a statistic that amounts to a claim that the split on whether sales went up or down is basically 60/40. Those just aren't betting odds for serious people.

But, there's the rub: the media who crow about this haven't been asked to commit anything serious to back up their worries. Their cheap talk is just that.

Hat tip to Drexel's Bruce McCullough.

N.B. I'm not just being pedantic here. In an earlier draft, I made a fairly serious (undergraduate level) error in my statistics. But, the difference between me and the legacy media is that I posted this with a time delay long enough to reconsider what I wrote. It was 11 PM and I was lying in bed, but I mentally caught the error and came downstairs to fix it. Problem solved, and no one need have been the wiser. But you're aware of it now because it is important to understand the statistics and get the right answers. I wonder if that occurred to the dim bulbs in the newsroom. If not, why do we listen to them?

The Coming Dog Food Warning

You can expect there to be a new warning on dog food that it isn't fit for human consumption (hat tip to JH).

It seems that a woman in Ottawa ate some of the tainted dog food going around in order to entice her (already sick) dog to eat.

It takes all kinds ... although I know someone who gave mouth-to-mouth to a puppy once.

The Saturnians Are Sending Us a Message

Here's one for the annals of "bizarre stuff that people will claim is a sign from little green men".

Yep ... that's a hexagon in the clouds at Saturn's north pole.

Now, will the earthoids and humanlings just get the message to broadcast more Blossom reruns.

Via SpaceWeather and the Cassini-Huygens mission.

EconLit Is Now Free for AEA Members

EconLit is now freely accessible for members of the American Economics Association.

This is a great service for those of us who no longer work at research universities.

For those not in the know, EconLit is a bibliographic service that links to abstracts of published research in economics. It doesn't cover all journals, but, as a test, it did find most of the papers I've published in journals (although no working papers or proceedings).

A blanket e-mail has gone out, but here's the link if you need it.

From "Capitalism and Arithmetic"

  Capitalism and Arithmetic points out that one of the reasons for the slow adoption of the Hindu/Arabic numbering system (that we still use) was that:

... the old [Roman] figures alone are used because they cannot be falsified as easily [pg. 182]