Humans and Computers Collaborating on Art

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Occupy Math works with digital evolution on a number of projects including evolving parameters that generate interesting fractals. The advantage to doing this with a computer, assuming you can come up with an automatic function that at least sort of measures “this looks good”, is that you can sort through billions of fractals per hour. One of these is shown at the top of the page. The disadvantage is that people are much better than any of the automatic functions we have found so far at spotting cool fractals. If we use people, though, they burn out way before looking a even a paltry million fractals. This is the phenomenon of user fatigue. This post is about a way to let computers and people collaborate on a project, drawing on the strengths of each. Computers can evaluate huge numbers of fractals to find ones that might look good. Humans have a much better ability to judge which fractals are actually beautiful.

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Why is working at Amazon like an earthquake?

topThis post is about a mathematical notion called self-organized criticality and its relationship to a recent strike by Amazon workers. As we will see, this strike, on Amazon Prime day, was a small “avalanche” (in a sense defined later in the post) that is probably a harbinger of worse problems at Amazon warehouses. Amazon has created a digital work supervision system that tries to maximize productivity by automatically tracking the workers and telling them when they are not working hard enough. The theory of self-organized criticality suggests that, initially, using this system will permit them to find the most productive workers. It will also cause a workplace that is very stressful with high turnover. This is the claim that Amazon workers are now making to explain why they are striking. This situation forces workers to achieve “high productivity”, but also stresses them to breaking point. In the rest of the post we explain self-organized criticality — which actually appears in many systems. Hopefully this will let you recognize it and perhaps avoid doing it to other people.

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Summer Math

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This post is themed “look at the pretty pictures”, with an attempt to make summer appropriate pictures. It is a look at some of the things that math can do. The secret for making Mandelbrot sets look like bouquets of leaves is featured. This is something that Occupy Math discovered by accident, a nice example of when a code bug is really a feature. The Mandelbrot set is an excellent source of complex pictures. The Ghost Mandelbrot set shows how you can switch up the details and get new fractals. In this post we will apply quadrant convergence to the Mandelbrot set and use a green color scheme to get leafy-looking fractals.

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Doing the Space Warp!

topHave you ever tried to enlarge a picture and lost detail? Maybe individual pixels became big single-color squares? The skull to the left is made of circles, ellipses, and rectangles, glued together as a series of tests. For a point in the plane, Occupy Math’s computer checks which of these geometric objects a point is inside of or outside of and, from that, deduces a shade: black or white. This may seem to be a lot of trouble to go to for a sorta-okay picture of a skull. The reason for going to that much trouble is that membership in the black parts of the skull, since we are asking about numerical points (x,y), has a resolution of trillions of pixels by trillions of pixels. This means that if we warp space, we will not get pixelization errors or other distortions. In other words, this skull image is far more malleable than usual images stored as pixels. In this post we are going to apply space-warps to the basic skull image. Having explained about the skulls, it is worth noting that Occupy Math created all this stuff while playing around but the math used to make many different skulls turned out to have applications in statistics. Following the fun parts of your work not only relieves stress, it can have big payoffs.

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Combinatorial Explosions!

topA combinatorial explosion is a situation in which, as you increase the number of things in a situation, the number of possible configurations of those things increases incredibly. Look at the flowers in the picture and consider how they are arranged. The number of arrangements that could have happened is beyond belief and the arrangement in the picture will not occur again before the heat death of the universe, even if flowers sprout in that field again, every spring. Phrased that way, this may sound a little intimidating, but combinatorial explosions can be useful, which is what this post is about. Combinatorial explosions are one of the more interesting outcomes of enumerative combinatorics.

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NEWT: Fractals for everyone!

NEWTwithbkgdThe moment none of you knew you were waiting for is here: Occupy Math is making fractals available to all — not just pictures but an app, Newt, for making your own. Our mascot, Newt, is part of one of the fractals (except for the eyes) and is named after the type of fractal he is — a Newton’s method fractal. One of the perennial topics in Occupy Math is fractals. There are a lot of different types of fractals. One of the less well-explored types is the Newton’s method fractal. Occupy Math Productions is now asking for beta-testers for a new Android app that lets you make your own Newton’s method fractals. If you are interested in beta-testing this app, send a request to occupymathwendy@gmail.com and include your gmail address (they are easy to get if you do not have one already). We are looking for one hundred beta-testers and would really like to hear from you — if you have an android phone or device. Tablets are fine.

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Voronoi Roads

topOne of the things that Occupy Math works on is automatic content generation, using algorithms to generate content for games. Occupy Math’s colleague Julian Togelius posed the following question: “Can we find a space of parameters where all or almost all the ways we fill in the parameters make a good game?” In this case “parameters” are numbers like the board size, number of playing pieces, or numbers that specify rules of a game. This is a very difficult challenge and the other people in the room softened it to finding spaces where there were lots of useful elements for games. In this post we look at a new use for Voronoi tilings in generating game content.

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What do senior research students do all day.

topThis post is the second half of Occupy Math’s report on the last academic year. It focuses on the four senior research projects Occupy Math supervised this year. The “senior research project” is a double-credit course that lets students dip their toes in the pool of research to see if it works for them. One of the students took the course in the fall, three in the winter semester, the semester that just wrapped up. Two of the projects were on very different ways to generate maps, one was on the generation of a new class of mathematical puzzles, and the last was a project in bioinformatics that sought to tune the parameters of an algorithm that generates features for identifying different type of genetic sequences. Three of the students were computer science majors, something that will be happening a lot more as the computer science program at Occupy Math’s home university is expanding. Two of the students are going to start masters degree programs in the fall, one in math, one in computer science.

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Karen Keskulla Uhlenbeck Wins the Abel Prize!

herselfOccupy Math is delighted to report that Professor Karen Uhlenbeck will, on May 21st, 2019, be awarded the Abel Prize for her work in geometric analysis and gauge theory by the King of Norway in a ceremony in Oslo. The prize is awarded at the discretion of the Norwegian Academy of Science and Letters and was established to serve as the “Nobel Prize” of Mathematics. Professor Uhlenbeck is currently at the Institute for Advanced Study in Princeton, New Jersey. She holds a permanent faculty position at the University of Texas at Austin. Dr. Uhlenbeck is the first woman to be awarded the Abel Prize, which Occupy Math takes as evidence that the world is continuing to become a more reasonable place, in some ways.

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Sure Bets are Losing Bets

topA bet is a situation in which you risk something of value which you may lose or, if your bet works out, you may make a gain, possibly a substantial one. Figuring out how gambling works was a massive spur to the development of mathematics. Blaise Pascal, a seventeenth century French mathematician, used mathematical analysis to spot a defect in the national lottery and make money. Pascal’s work is foundational to probability theory, something Occupy Math has talked about before. In this weeks post, Occupy Math will discuss a type of betting: funding research in science, technology, engineering, and mathematics (STEM) disciplines.

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