What colour is 27? - Numberphile

BRADY HARAN: A little while back, we spoke to Alex from Bite Sci-zed about her number/color synesthesia, basically how she sees numbers as colors. The video created a lot of interest and a lot of comments from you guys as viewers. One of the things you did was you all sent in what color you think numbers are. We've taken that information and done a bit of work with it to create a few graphs and other things. But I'll have more about that at the end of the video. The other thing was you had loads of questions for Alex herself. Now, a little while ago, I caught up with her at an event. And I had all of your questions. So I sat her down and asked some of them. Now, one of the things a lot of you said was you thought she was making it up. So I asked Alex that. ALEX DAINIS: No. Why? BRADY HARAN: How do we know you're not making it up? ALEX DAINIS: I guess it's hard. I mean, as a scientist, I encourage skepticism. And I want to be able to show you in my head and show you data points. But I can't. You're just going to have to take my word for it. BRADY HARAN: Have you been to a doctor? Has it been diagnosed? ALEX DAINIS: I haven't, actually. That's a good point. I know that I make these associations between numbers and colors very strongly. And synesthesia is the best word that I have found to describe that. BRADY HARAN: Do the numbers give you the colors or do the colors give you the numbers? ALEX DAINIS: The numbers give me the colors. So if I see a color, it doesn't back translate into a number. But if I see a number, then I can see the color. It helps me to memorize things. It's really good for memorizing phone numbers. BRADY HARAN: So another thing that came up in the previous video was that sometimes the color of a number was created by its factors. So some of you asked, could Alex take a number, look at its color, and then reverse engineer the factors just by using the color? So I asked. ALEX DAINIS: No, unfortunately. The factors influence the color of the number if I already know them. So for something like 14, 7 is such a huge part of 14 to me that that yellow is really prominent in there. But if I see a giant number, I unfortunately cannot see a color with it and pull it back. BRADY HARAN: How do you see prime numbers? ALEX DAINIS: So it depends really on what the prime number is. So something like 13, it's really a 1 and a 3. It has a lot more to do with their digits. Only the things, really, from zero to nine have their own specific colors if they're prime numbers. One on its own is just white, if it's just a single digit. But when it can be combined with other things-- so in 10 and 100 and 1,000-- then it takes on that sort of black flicker, almost. BRADY HARAN: If you see numbers written down on a piece of paper in black print, which is the most common thing, do they become colorful for you? ALEX DAINIS: No. So when they're still on that page, they just exist in whatever color they are, whatever color that print is. But when I think about that number, when it moves into my head, then it takes on the color. But the ink on the page stays the same color. I, unfortunately, do not think about numbers and bases very often. And so I think because my brain really works on a base 10 system, it's just the digits zero to nine that have their own colors. If I were to think in base six, I would still just see the digit one, five, and not translate it. BRADY HARAN: Is mathematics a sort of colorful, psychedelic experience? ALEX DAINIS: I don't think I would consider to be psychedelic. It is colorful. I mean, I am seeing these colors in my mind. But because that's just the way I've always experienced the numbers, it's not weird to me. It's not distracting to me. Just, they are numbers. BRADY HARAN: A lot of other people who responded to this video said that for them, numbers have personalities or genders. Do you associate personalities or genders with any numbers? ALEX DAINIS: I do. So that's actually how I sort of realized that I was seeing these colors is that I had had that gut reaction in class that numbers have personalities, not colors. And so I think the example I gave before is that nine is a very dark red. And so it seems like sort of an angry number to me. Whereas the two, four, and eights are sort of cooler numbers. And they seem a little bit more chill. And they seem a little bit more friendly. But that's really sort of the realm of things are. Seven is not intrinsically jealous because it's yellow, but sort of basic personalities of nice or mean. BRADY HARAN: Gender? ALEX DAINIS: No gender, no. BRADY HARAN: Can you give me a color for these numbers, because these are just numbers people asked for? ALEX DAINIS: Sure. BRADY HARAN: 79. ALEX DAINIS: 79 is yellow, and that nine, maroon at the same time. BRADY HARAN: So it's not like you've mixed paints. It's two things? ALEX DAINIS: It is for a much of the larger digit numbers, yeah. So things that are, I would say, probably below 40, is a lot more mixing, I think, because I do know those factors and I've thought about those numbers a lot more. But the higher ones is really just the digits. It's as if you had two colored sheets of cling film, one that was yellow and one that was that maroon, and sort of laid them over each other. So it's not really like you're mixing paints. I understand that they're two separate things. But they're existing in the same space. BRADY HARAN: 854,685,254. ALEX DAINIS: As you're saying them, I can see the blue, black, blue. But it does not exist as one whole number in my head. BRADY HARAN: And now I'll show it to you. There you go. I'm showing it to you now. ALEX DAINIS: Oh yeah, still. So the digits all have their own thing. But I think because I'm not processing the quantity that is that large number, just the digits have their own identities. BRADY HARAN: Fractions? ALEX DAINIS: Fractions just look like a digit over a digit. Negative numbers, the negative doesn't have any impact on the colors. BRADY HARAN: Irrational numbers. So how do you deal with pi? ALEX DAINIS: With pi. So pi as a symbol doesn't have anything. It's just a symbol. But if I think of 3.14, then it does take on the red, white, and blue. I can do pi to 22 digits. BRADY HARAN: Go. ALEX DAINIS: I hope I still can. 3.141592653589793238462. BRADY HARAN: Was anything colorful happening in your head then? ALEX DAINIS: I mean, as I say the digit, I can see the color. But it's not cramming itself all into one big color. BRADY HARAN: i, and complex numbers, and imaginary numbers. ALEX DAINIS: Again, they don't have digits to me. And so if I think of i as a number, I guess, then it does. But i itself is just i. BRADY HARAN: The final thing is a lot of people responded to what you had to say in the last video, and understood what you were saying, but completely disagreed about the colors, said Alex is wrong. That's not that color. It's this color. And they even gave whole sets of what they think the colors are. What do you say to that? ALEX DAINIS: I completely understand that, because I've seen people give me those sets as well. And I have that same reaction of no, that's wrong. It's such an intrinsic link to me that I don't get that people can-- I mean, I understand logically that people can see other colors. But no, three is red. I don't know what-- green is three, people are saying. Three is red. BRADY HARAN: What is five again? ALEX DAINIS: Five is black. BRADY HARAN: So look at those five chairs there. ALEX DAINIS: Yes. BRADY HARAN: What do you feel about that? ALEX DAINIS: It's funny because if I don't-- I mean, it's fine. This does not impede my life, but it is wrong. I think it's more with things under 10, because you can see the quantity and understand at the same time. If I had to count every chair in here, I wouldn't be very upset that all the white chairs, if there were 20 white chairs and they were all white, that would be fine. But now that you've brought it up, it's not right. BRADY HARAN: So thanks so much to Alex for talking to us more about this subject which so many of you find interesting. Now also, all of those comments from last time and all of the colors that you guys attributed to numbers have been analyzed by Dave Wiley, our resident graph number expert who helps us out. And he's come up with this. This is a graph showing the most popular colors for each number. This is going to be on my blog. So have a look at the link under the video description if you want to pore over this in more detail. But also, Dave has put this together. Based on the HSV Color Space, this is the average color of each number. So here we go. Zero, one, two, three, four, five-- a lot of greens you can see-- six, seven, eight. Again, more green. But then we go 9, 10, 11, 12, 13, 14, 15. And this is where Dave stopped for now, because the data started getting a bit thin after that. 19 of you said that numbers to you seem to have genders. 13 people said the days of the week have colors. And the area of most agreement amongst all of you as viewers was that the number 27 is green. So there you have it. This video has been brought you by Squarespace, which is an all-in-one platform for designing your own websites, blogs, portfolios, online stores. They've got a whole range of templates you can use to get your site looking just how you want. But then you can customize it. You can choose your own colors. Maybe you're going to choose green after this video. But you can get it just how you like. 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