Daily Archives: October 29, 2011

Math… amazing

Every so often someone will forward me one of these “amazing!” math tricks, and I will of course feel compelled to explain just how outrageously simple the math in them actually is. The latest one going around is even simpler and more obvious than most, and yet people still seem impressed by it:

Take the last two digits of the year you were born, add your age this year, and it will add up to 111. Amazing!

I have to say, I’m kind of amazed that it’s not gobsmackingly obvious to absolutely everyone who can add and subtract two digits. But so many people will do anything to avoid arithmetic, so it seems to have that “magic wand” quality pretty readily.

So OK. Say someone were to send you an email that said “The year you were born plus your age this year equals 2011 – but only this year! Amazing, huh?” Wouldn’t you find that obvious? Now, 2000–1900=100, and you were born in the 1900s (we assume no one under 12 years old got the email), and it’s 2011 now…

Put it another way: if you subtract 1900 from everything, as though 1900 were the year 0, this year would be the year 111; and if you start with the last two digits of your birth year, you’re subtracting 1900, so…

There are some really cool number tricks out there. But you don’t too often see them being passed around in emails, because different people have different definitions of “cool”.

At the very least, they could try tricks that use more than just disguised simple addition and subtraction. For instance, there are fun facts such as that your age (or any two-digit number) plus the reverse of your age (e.g., 49+94) will always be divisible by 11 (in fact, it will be 11 times the sum of the digits in your age); your age minus the reverse of your age, or the reverse of your age minus your age (e.g., 94–49) will always be divisible by 9; your age minus the sum of its digits (e.g., 49–13) will also always be divisible by 9… And the digits of any number divisible by 9 will always add up to a number divisible by 9, which means if you have any two-digit number divisible by 9 and add its digits, you will get 9 or (in the case of 99) a number the digits of which add to 9.

All of this is explainable with simple algebra on the basis that a two-digit number cen be represented as ten times a one-digit number plus another one-digit number, e.g., 49=(4×10)+9.

So for any number 10x+y (e.g., 40+9, where x=4 and y=9), the reverse will be 10y+x (e.g., 90+4), meaning if you add 10x+y (the original number) to it you get 11x+11y (e.g., 40+9+90+4=44+99), and if you subtract the reverse you get 9x–9y (e.g., (40+9)–(90+4)=40+9–90–4), and if you subtract the sum of the digits (x+y, e.g., 4+9) you get 9x (because 10x+y–(x+y)=9x, e.g., 40+9–(4+9)=36). And of course 10x+y+10y+x=11x+11y=(x+y)×11.

So assuming a person of a normal adult age, you can say

1. Take your age (e.g., 49).
2. Add the digits together (e.g., 4+9=13).
3. Subtract that from your age (e.g., 49–13=36).
4. Add the numbers of the resulting number together (e.g., 3+6).
5. The answer is 9.

Of course, you want to gussy this up with something fancy. Add in some other calculations to distract. Instead of step 5, maybe say

5. Multiply by the last two digits of the year.
6. The answer is 99. This always works!! But it will only work this year!!! And not again for a hundred years!!!! OMG it’s amazing tell all your friends!!!!11

or, if you think they can handle the math (!), say

5. Now add your age to the reverse of your age (e.g., 49+94).
6. Divide the result by the sum of the numbers in your age (the number in step 2).
7. Multiply this by the number from step 4.
8. The result is the answer to the question “Who’s the greatest hockey player of all time?”!!! OMG Gretzky rules!!! Number 99 forever!!!!

Even this is pretty straightforward for people who like to think about numbers. But there aren’t that many of us. Anyone who graduated from high school is officially able to figure this sort of thing out easily. But as long as people think math is hard and mystifying…

I suppose you could argue that the general “Numbers! Oh noooooes!” attitude people tend to have in our culture allows them actually to have fun with simple things like this, but it deprives them of the much greater fun they can have with more complex number problems, and it makes them easy marks for misleading advertising, misleading politicians, and so on. And generally vulnerable to making dumb mistakes. There’s a classic Dilbert cartoon (two of them, in fact) illustrating this – see http://search.dilbert.com/comic/40%25%20Sick.

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philtrum

If you’ve read my note on aglet, you know already that this is a word for something that needs a name but doesn’t have it, but actually does. It’s something you see every day and might just occasionally wonder what to call. Don’t you just love those? Ha. As in they get up your nose.

Looking at this word, you can see classical origins – or perhaps pseudo-classical, in the mode of the Victorian/Edwardian era fads for inventions and fancies such as phlogiston and names such as Phineas. That ph bespeaks a Greek origin, probably brought down to us by way of Latin. And, come to think of it, that whole phil looks phamiliar – excuse me, familiar. Perhaps related to the Greek philos “love”, as in philosophy “love of wisdom”, Philadelphia “place of brotherly love”, and Philip “person with a lip shaped like the letter phi (φ)” – sorry, no, it’s from Philippos “horse lover”.

On the other hand, it also makes me think of plectrum, which is a fancy word for pick as in guitar pick – that triangular thing you use to provoke strings to vibrate. If music be the food, of love, pick on! And if it’s really groovy, take your pick.

Take your pick and do what? Or take your pick of what? How about taking your pick of people with upper lips with grooves in them? Well, that’s kind of everybody, isn’t it… though some people’s grooves are more pronounced than others. I tend to think of Roland Orzabal of Tears for Fears (see www.youtube.com/watch?v=w0TYun-Nq1Q for a version of the “Head Over Heels” video with lyrics describing the action – a digression but really funny), though his isn’t really abnormally pronounced; I did know a few other guitar pickers around that time who looked as though they had vertical equal signs under their noses. It always seemed kind of self-important to me, which is in some sense the opposite of groovy.

Anyway, yes, where I’m going with this is that the groove in your upper lip – anyone’s upper lip (except some with fetal alcohol syndrome) – coming down from the nose is called the philtrum. Some legends say it’s where an angel touches a baby’s lip before birth. But others relate it to Aphrodite (you will see the ph balance going up here, and that’s not baseless). Philtrum is a Latin word meaning not only “groove in the upper lip” but also “love potion” – taken from the Greek philtron, which has the same two meanings. The “love potion” meaning is now normally spelled philtre – although, frankly, love potions are more likely to bear the legend unfiltered these days. And then you can nose them, wafting the scent up past your philtrum. And feel groovy (see www.youtube.com/watch?v=TBQxG0Z72qM for that musical reference – though neither Simon nor Garfunkel has a pronounced philtrum).