Why is this number everywhere?

expression 1/N times 1, + S over S + 1, plus S over S + 2, and so on, up to S over N - 1. Factoring S, the sum inside the parentheses approximates the function 1/x that goes from S to N. (thoughtful music) Taking that integral, we get the natural log of N over S. So the probability that we select the best option is S over N times the natural log of N over S. To maximize

this

probability, we can find the peak of

this

function by setting its derivative to 0, and this gives that the natural logarithm of S over N is equal to -1.

So S over N is equal to 1 over e, or about 37%. So explore and reject 37% of the options just to get an idea of ​​what's out there, and then choose the first option that comes along that's better than all the ones you've seen so far. And your chances of success with this method are also 37%. (thoughtful music) This math question is known as the secretary problem or the marriage problem, as it also applies to hiring the best employees or even choosing the best life partner. Now, it may be impractical to mark 37% of the options because you don't always know how many candidates there are, but the 37% rule also works over time.

So if you want to get married in, say, 10 years, spend the first 3.7 years seeing what's out there and then pick the next person who's better than anyone you've ever met. (thoughtful music) So 37 is really important to our lives, and people seem to recognize it subconsciously. We gravitate toward

number

everywhere

. (thoughtful music) (movie click) - 37 seconds. - 37 years. - 37 hamburgers? - He was 37 years old. - 37 cubic feet. - Take 37. - 37. - How many enemies do you have? - 37. - 37! - Yeah! - 37%. - 37. - 37. - 37 hours. - Destroyed 37 restaurants. - 37. - I have 37. - 37 interlocking bronze gears. Page 37. 37 years. 37 prototypes. 37%. (uplifting music) This collection of images, everything you see on the screen, has been compiled by one man throughout his life.

And you know who he is. - It's just fun, right? This is all just fun. How many objects are here in the room with us that have a 37? It's probably on the order of four digits, I'd say. It's probably not 10,000, but I'm sure there are more than 1,000 here. Nutri-Grain Granola Bars, 37 grams. It is a criterion of 37 inches. It's just a political cartoon about sports, but there's no reason for that guy to have jersey

number

37. A nail I found somewhere that has 37 on his head. I don't even know what that means. My mom once gave me $37 for my birthday.

They all have 37 in the serial number. - Was your 37th birthday the best birthday ever? - I had a big party and invited everyone I knew. The Texas state lottery was 37 million dollars. So I had two different friends and they both gave me 37 lottery tickets. I didn't win, I won 5 dollars. This is an article from when they found Mersenne number 37. It's just one cut after another. How many hundreds of these do you want me to review? I must have gotten it in Germany, but I don't know... But I don't remember what it was. Was it like a locker number?

I wouldn't steal a locker number. I've never stolen for 37. (speaker 1 laughs) - Look at that. Stolen on the highway when I was on a road trip, I heard you say you never stole anything. - I have committed a crime. - Yes. - There was a bookstore on campus when I was a student at KU, and there were 37 steps on that staircase. Useful facts, these are useful facts. - Do you feel like everyone gets 37 so much in their lives or do you feel like you're just attracting them? - Good question. You know, the reason I started was because it seemed to show up a lot.

I started back in the '80s. There was a Charles Fleischer comedy routine, and he repeated this kind of litany of coincidences about the number 37, as if there were 37 holes in the speaker part of a telephone. (upbeat music) Shakespeare wrote 37 plays. There are 37 movements in Beethoven's Nine Symphonies. There are all these amazing coincidences that he rattled off. He surprised me and I've been collecting them since 1981. Yeah, 43? 43 years, probably. (upbeat music) I first built the 37 website in 1994. I don't know how the website came to be, but somehow it came to be. I started receiving emails from strangers.

I have... Oh, maybe half a dozen people from all over the world, who, every week or month, will post their latest batch of 37 that they've seen out there. - And they've been doing this for how long? - 18 years. - Wow. - We are tireless. The tireless clique of 37 people, yes. - Do you have something to say to someone who might say, "37, that's just a base 10 representation of that number." - I am also interested in the number 37 in all its other forms: Roman numerals; binary numbers 100101, by the way; numbers in any other base. Yes, 25 in hexadecimal. 45 in octal. - And do you think you're going to continue looking for a 37 and collecting 37 all your life? - Yes, yes, I don't see any reason to stop.

Yes, sure. - So maybe there's even something innately universally special about this issue. (thoughtful music) We can argue special coincidences for many numbers, but ultimately we must address the elephant in the room. The vast amount of brain power that 37 secretly occupies in our collective minds. It is the random number that humanity turns to, one of our most prominent prime numbers and, above all, our ideal number for making decisions. Maybe that's why we naturally gravitate toward it. It seems right to us where to settle and what to choose. Although with this video we may have ruined the randomness even more.

I mean, the next time someone asks people to choose a random number between 1 and 100, more people than ever might say "37." (thoughtful music) - It has been the story of my life that I intend to take everything I have here and turn it into individual facts on that website. But the website has been there untouched for 27 years and that hasn't happened. It doesn't seem like it will ever happen. - Maybe on the 37th anniversary we can do it all. - It is a good idea. It is a good idea. Because I have time to do it between now and then, and that would be...

That's a great idea. - Once our video comes out, do you want people to write to you with any instances they see of 37? You may feel overwhelmed for a while. - 37 is out there, it's

everywhere

. I'm trying to collect them all. Bring it. Yes, bring it. (graphic beep) - Our intuition is one of the most powerful tools we have, and the number 37 is just one example of the invisible patterns in our minds. Fortunately, there is a way to boost your intuition, giving you the skills to see beyond the everyday and discover hidden truths about our world.

And you can get started right now for free with this video sponsor, Brilliant. Brilliant lets you practice concepts in everything from math and data science to programming and technology, to help sharpen your thinking and develop your problem-solving skills. At Brilliant, you will learn by doing. So even abstract concepts, just click. Plus, you'll be able to take what you learn and apply it to real-world situations. With each lesson, you'll also develop critical thinking skills and train your brain to use your intuition to draw powerful ideas. There is a lot to learn at Brilliant. They have thousands of interactive lessons to feed your curiosity.

And since each one is bite-sized, it's easy to learn something new, even if you only have a few minutes to spare. The best part is that you can learn from anywhere right on your phone. So wherever you are, you can develop real knowledge and hone your intuition. To try everything Brilliant has to offer free for 30 days, visit shiny.org/veritasium. Scan this QR code or click the link in the description and you will get 20% off Brilliant's annual premium subscription. So I want to thank Brilliant for sponsoring this part of the video and I want to thank you for watching it.