## Tricky Math

I just came across the following elementary math question:

Pablo buys a horse for $10,000, sells it again for $12,000, buys it again for $14,000, and finally sells it again for $16,000. Did Pablo make a profit or a loss, and if so, how much of one?

Got an answer? Now, stop reading and think over it again, just to be sure :D.

…

Done? Good! The thing is, Tim Gowers in his blog told a story about an experiment on Math teachers in Latin America in which those teachers were asked the above question. Guess what, only a small percentage of their answers are correct :D. Two common wrong answers are as follows.

1. Pablo bought the horse for $10,000 and sold it for $12,000, making a profit of $2,000. But then he bought it again for $14,000, so he made a

lossof $2,000. Finally, he sold it for $16,000, making a profit of $2,000. Adding up the profits and loss you get $2,000.2. Pablo started off buying the horse for $10,000 and ended up selling it for $16,000 so at the end of the whole process he had made a profit of $6,000.

The correct answer is $4000 [Hint: Think of how much he paid totally, and how much he got totally]. Amusingly, even given a very clear explanation, those Math teachers still didn’t get the answer (see Gower’s post for more details).

So, the bottom line is, be very careful with Mathematics :P.

## Wind of change

A couple of weeks ago, Prof. Constantine Caramanis (UT-Austin) visited Stanford and gave a talk in our group meeting about robust optimization. During the talk, he had a comment (which I’m rephrasing here): “previously (ten years ago, maybe?) linear optimization is easy, and non-linear is hard; now, actually convex optimization is easy, and non-convex is hard…”

That made me again thinking about how fast the science and technology change over the last ten years, and how hard it is to keep up with current advances if you are working in an engineering/science field. In 2002-2003, I did my undergrad final research project on 3G cellular wireless networks, which was one of the hottest research topics in Vietnam at that time. However, I couldn’t imagine that just 5 years later I would be able to watch a YouTube streaming video on my 3G cell phone while driving at 70mph on highway. It’s just amazing!

On the other hand, some of the current advances will possibly die in the next few years. There are quite a lot of such examples in the past, e.g., ISDN (Integrated Services Digital Network), or ATM (Asynchronous Transfer Mode). There were times (not too long ago) that they received much attention, but now, well, you probably can only find them in a dead-tree textbook.

Of course, I really hope that these cutting-edge researches I’m seeing now won’t disappear and will be realized in the next 10 years or so. Let’s see…

## Aloha!

I’ve decided to create another blog, apart from my personal one, just for technical stuffs. So, viewer discretion is advised :D.