
Title:
0705 Puzzles and Algorithms

Description:

What is it about math and these kind of tricky puzzles that just intrigues people so much?

Have you spent time thinking about that?

I have a little bit,

and I don't take it for granted that it intrigues everyone.

Meaning it doesn't actually intrigue everyone, but it intrigues a lot of people.

Even mathematicians and computer scientists

many of them run when they hear a puzzle.

Oh, no. They'll say, "I'm no good at puzzles. I'm leaving the room."

It is certainly true that you can goodin fact, you can do great mathematics

without being a puzzlesolver kind of a person, and great computer scientist,

great computer science as well.

There are some kinds of math and computer science where you create structures of things,

and you don't try to solve puzzles.

You try to create structures.

You try to define things.

You can do all kinds of great stuff this way.

Not all mathematicians or computer scientists like this kind of puzzle

or like puzzles of any kind.

On the other hand, lots of people who are not mathematicians and computer scientists

love mathematical puzzles.

There are loads and loads of amateurs out there who adore this kind of puzzle.

There are lots of people with mathematical talent, logical talent,

people just with good creative minds who are not doing mathematics

or computer science or any thing like that who are really good at this sort of thing.

If you like puzzles, obviously, they're good for mental exercise, keeping the mind sharp,

but mathematical puzzles really do introduce you to techniques

that you can actually use in solving problems that you run across,

and I gave examples of this as you just saw.

These problems arose and the techniques used to solve them

can be used to solve other problems.

They give you new ideas.

They help you think creatively.

On the negative side, solving puzzles could distract you from doing something more important.

But I like to think that you can't do important stuff 24hours a day.

You need to spend some time doing stuff that's just fun,

and if there's a blurry line between what's fun and what's hard work,

so much the better.

But there's also something very satisfying at the end when all the pieces fall into place

and you didn't know why it had to be 15 prisoners or whatever it had to be,

but everything kind of makes sense at the end,

and I think some of us find that extremely gratifying.

I think I agree.

It's just a little bit likemany puzzles are like riddles.

Once you see the solution, once you can really grasp the solution,

you've "ahha!" It's that kind of thing.

I have to say that there are also other kinds of puzzles,

not sort of the riddletype puzzles,

but puzzles which challenge your intuition, and I like those a lot too.

Those have a different function, which is to keep your mathematical intuition

from running off the rails,

to get you to distrust certain notions of, for example, probability.

Probability, which we humans invented to try to deal with all the uncertainty

that's in the world from our perspective,

is something that we don't always know how to deal with.

Puzzles involving probability, especially ones with very counterintuitive results

that you try to prove or disprove, can really help you keep sharp.