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Xkcd e a matemática

A revista Math Horizons entrevistou o Randall Munroe – o cara que criou e mantém o Xkcd, “um webcomic de romance, sarcasmo, matemática e linguagem”, como consta na linha fina do site. Além de falar sobre os infográficos de filmes que ele produziu (tendo como fonte principal a Wikipedia), a entrevista também trata dos quadrinhos mais complexos, como o Tic-Tac-Toe.

MH: Another one of your comics that fascinates math people is the self-referential one where each panel describes the amount or location of black ink in itself and other panels. Various people have analyzed this comic by writing code to iterate and get your comic as the fixed point. (Readers can see one example using Mathematica by Jon McLoone here.) Is that how you found it, or did you find it another way?

RM: I found it another way. I didn’t actually write any code for this. I started off thinking about the pie chart in the first panel. I was trying to figure out what other charts there might be that don’t disintegrate to nothing.

That was the problem; there are certain charts or plots whose fixed points are zero. Like a situation where one chart was referring to another, and the other to the first, and you end up with an equilibrium state where both graphs are empty.

And you don’t need a computer program to figure that out. You just sort of think, OK, well, if this graph is right for the one I’ve drawn now, and I make it a little smaller, how does the other one change?

And so just thinking about it, I realized that the three ideas in the panels would work; they’d all have a reasonable amount of black ink in each one, which would make the middle chart work, and so on.

MH: How did you determine how much black ink to put in each of the charts?

RM: I figured out how to measure each of the quantities shown in the charts. I drew up the outlines in Photoshop, added the captions, drew in eyeballed estimates, and then used some utilities to count the number of pixels.

Photoshop will tell you how many pixels are in this area, if you select in a certain way, and I’ve been pixel painting in Photoshop forever. I just wrote down the numbers, used a calculator, and calculated for the first two panels: What should the height of the bar graphs and the angle of the pie chart be?

The third panel I generated by just taking the image and cloning and shrinking it. I had a big sheet of paper to keep track of the math, and I was just doing it all by hand.

O pdf da entrevista tá aqui. O papo com o Munroe rolou logo antes de um encontro dele com estudantes de uma universidade de Newport. Segue o vídeo da palestra:

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