-There are 10 types of people in the world.
Those who understand binary, and those who don't.
MATT PARKER: OK, it doesn't really work when it's said.
But written down, the joke kind of holds.
Because if I do a 1 and then a 0, that looks
like the number 10.
Because you expect it to be a normal base 10 number.
However, if this is in binary, then this is our units column.
That's our twos column.
And so this actually equals 2 in base 10.
And so you expect it to be 10, but it's not.
It's 2, and that's the joke.
There are actually two types of people.
Those who knew this was binary, and those who didn't.
-There are 10 types of people in the world.
Those who understand binary, those who don't, and those who
didn't expect this joke to be in base 3.
MATT PARKER: OK, good point, because I guess you--
OK, so it depends on the base.
So if you've got 10, but this time it's in base 3, then now
you've got a units column, and then a threes column, and then
nines, and so on.
And so that in normal numbers would be 3 in base 10.
And so the same 1 and 0 in a different base mean 3.
Hence the three categories.
-There are 10 types of people in the world.
Those who understand binary, those who don't, and--
MATT PARKER: Look, you can generalize it to any base, OK?
10 in base b is going to equal b in base 10, OK?
There's an infinite set of these jokes.
Cut it out.
-There are 10 types of people in the world.
Those who understand hexadecimal, and F the rest.
MATT PARKER: OK, I give it to you, that one is actually
quite funny.
Because now in hexadecimal, which is base 16--
10 in base 16 still does mean there are 16 types of people.
And so there's the one category of people who
understand hexadecimal, base 16.
But then the remaining 15 in hexadecimal--
15 is just the letter F. And so when they say F the rest,
they're saying 15 are the rest.
Or I guess the joke is the double meaning, where if you
just say F in a sentence, it means you're implying--
uh, fools.
You're saying they're very foolish, all the people who
don't understand hexadecimal.
-Why do mathematicians confuse Halloween and Christmas?
Because Oct 31 equals Dec 25.
MATT PARKER: OK, so the joke here is that Oct
31 equals Dec 25.
And the surface reading is that this stands for October,
and this stands for December.
But it doesn't.
Oct can stand for the eighth thing, because October is the
eighth month in the--
it was until Julius Caesar messed with it.
And Dec used to be the 10th month, blah, blah, blah.
So anyway, instead of using these as months, you can use
Oct to mean base 8.
So instead of 31 being in our normal base 10 setup, if we
put it into base 8, you have a units column.
You have an eights column.
And so you've now got one unit and three 8's.
And three 8's is 24, plus a single unit equals 25.
And so 31 in base 8 equals 25 in base 10, which is why one
equals the other, and why a mathematician
would confuse them.
BRADY HARAN: This video was supported by audible.com.
And if you'd like to download one of their 100,000 titles
for free, go to audible.com/numberphile.
I actually sampled the product myself in the last few weeks.
I downloaded a couple of mountaineering books while I
was holidaying in Nepal.
I love books about mountains.
These are the two I chose.
They were both excellent.
And it was actually really good fun to be walking through
the mountains while listening to the book, having it sort of
inside my head.
So I recommend those two as possible ones when you
download your free one.
That's audible.com/numberphile, and
thanks to them for supporting our videos.
[LAUGHTER]