Base Number Jokes Explained - Numberphile

There are 10 types of people in the world. Those who understand binary and those who don't. Okay? It doesn't really work when it's said, but written down, uh, the joke kind of holds because if I do a one and then a zero, 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 tw's column. And so, this actually equals two in base 10. And so you expect it to be 10, but it's not. It's two. 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 three. Okay. No, good point. Because I guess you Okay, so it depends on the base. So if you've got one zero, but this time it's in base three, then now you've got a units column and then a threes column and then nines and so on. And so that in normal would numbers would be three and base 10. And so the same one and zero in a different base mean three. Hence the three categories. There are 10 types of people in the world. Those who understand binary, those who don't, and look, you can generalize it to any base. Okay? It's it 1 zero in base B is going to equal B in base 10. Okay. So just I mean you can do you can there's an infinite set of these jokes. Cut it up. There are 10 types of people in the world. Those who understand hexodimal and f the rest. Okay. I give it to you. That one is actually quite funny because now in hexodimal which is base 16 one zero in base 16 still does mean there are 16 uh types of people. And so there's the one category of people who understand uh hexodimal base 16, but then the remaining 15 in hexadeimal 15 is just the letter F. And so when they say f the rest, they're saying 15 are the rest. Uh or I guess the joke is the double meaning where if you just say f in a sentence, it means you're implying fools. You're saying they're very foolish. Uh all the people who don't understand hexodimal. Why do mathematicians confuse Halloween and Christmas? Because oct 31 equals deck 25. Okay, so the joke here is that oct 31 equals deck 25 and uh the surface reading is that this stands for October and this stands for December. But it doesn't. locked can stand for the eighth thing because October is the eighth month in the it was until Julius Caesar messed with it and deck 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 8s column. And so you've now got one unit and 38s. and 3/8 is 25 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. 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/numberfile. I actually sampled the product myself in the last few weeks. I downloaded a couple of mountaineering books while I was holidaying in Nepole. 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, uh, I recommend those two as possible ones when you download your free one. That's audible.com/numberfile. And thanks to them for supporting our videos. [Laughter]