But when I do, it usually because of some deeply nerdy, cutting snark. Like this:
As someone who has read thousands of academic papers, I’ll answer those questions as calmly as possible.
NO.
~ “dynomight“, from Please show lots of digits
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…and then it goes on, CAPSLOCKed, for several paragraphs. The only thing better than math-nerds, is when a math-nerd who is also a reason-nerd stomps on the vanilla-variety math-nerds. This stuff? This stuff makes the world a better place.
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What’s a system for fairly dividing— actually… What does “fair” even mean? If we’re dividing up cake, is fair equal size shares? …or shares proportional to each person’s daily caloric requirements? …or their average recent caloric deficit (so starving people get the cake)? And that’s just cake. What if you want to divide up something important, like say, geographically divide a State into voting districts?
In the first step, one party draws districts on the map. However, unlike regular redistricting, in which they draw the exact number of districts needed, our process requires the first party to draw twice that number of half- or sub-districts. Like full electoral districts, these half-districts must have equal populations and be physically contiguous. Many states also have requirements for district compactness, which would apply to this first stage of map drawing too. We also don’t allow “doughnut” districts – where one district is entirely surrounded by another district.
In the second step, the other party chooses how to pair neighboring half-districts into full-size districts.
Even if each party acts entirely in its own interest, attempting to maximize its own chances of winning the most districts, the fact that the process is split into these two stages holds each party’s ambitions somewhat in check.
~ Benjamin Schneer, Kevin DeLuca and Maxwell Palmer from, How politicians can draw fairer election districts
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Like my examples for possible meanings of “fair” for dividing cake, there are many possibilities for what would be “fair” for voting district maps. To date, every solution has been to have some third party (a commission whose composition itself is contentious) draw the maps and then have judicial review (with the judges themselves also being contentious). The system laid out above is brilliant. One side draws up a map, and the other side chooses how to assemble the map into voting districts.
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I love metaphors about hills and valleys. If it’s an uphill struggle, imagine the view. Hills and valleys is a great metaphor for the concept of a local maximum: It’s visually clear (standing atop a hill) and mathematically clear (at a local maximum) that it is “down” in every direction. But only a special sort of hilltop is actually interesting. A hilltop that is really large becomes a flat tabletop. And a hilltop socked in with fog is easily mistaken for not a hilltop. Only hilltops which are pointy enough, and from which we can see other things, are interesting.
[…] our economy—resource allocation based on employment […]—is a local maximum and we cannot expect to arrive at a good outcome without activism.
[…]
But, unless we automate a lot more, we the species will never have enough wealth to offer a decent basic income, and everyone will continue to waste half their lives at work.
~ Gavin Leech from, Automatic for the people
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Is it clear that every direction is “down”? Can we see anything else; if we can’t see anything else we can’t be sure this is a local maximum. How can we explore “down” in some of the directions… when we’re talking about global scale culture and human lives?
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In high school I had a class where your final grade was based on a total number of points earned through the semester. The final exam was worth a large portion of the total semester points—let’s say it was 500 of your semester’s possible points. Your percent-score on the exam determined how many of those points you received. (Ace the exam, and you get all 500 points.)
The exam was many hundreds of multiple-choice questions; The exam was so long that no one could ever finish it. The questions had to be shuffled to mix the material taught in the course. Every year the questions were identical, but each year the teacher made a copy of the master list, cut up (yes, with a scissors) the questions, shuffled the strips, and then taped the questions onto a sheet with question numbering, to create a unique Frankenstein-exam every year. This Franken-xam was then photocopied (via a Volkswagen Beetle sized behemoth in the main office) to produce the actual exams.
In the days before the exam, we were told to work at our own pace, to answer each question (skips counted as wrong answers) and to simply stop when time was called. Afterwards, the teacher would calculate the average number of questions attempted by the class. That average was then used as the possible number of questions for calculating our exam scores. (Thus the shuffling to create an exam that is however-long we made it as we took it!) If you went farther than the class’s average attempted number, then you could score some extra points (if you get the answers right, of course) to offset any wrong answers you had along the way. A lot of work to shuffle it every year, but it was a neat idea.
I think it had always worked because kids just didn’t care enough to think it through. We weren’t told the total number of questions, nor what previous classes had attempted. But, for discussion here, let’s say the class’s average-attempted is 200. And let’s say I were to answer 227 questions, but I get 24 wrong. That feels like an 89%, right? No, actually I end up with 203 correct answers, which is more than the class’s average-attempted of 200. I actually score 101.5% and I would get all of the exam’s 500 points towards my semester total. Wait, there’s more: As extra credit, my 3 extra correct answers (my 203 against the 200 attempted average) become extra credit points just added right to my semester total. I’d get 503 points towards my semester!
After the exam was announced, two of my friends and I, realized…
For example, if we could get just 60% right—normally a really poor performance on an exam—while attempting twice as many as the class average, we win big. Say, 200 average-attempted, against our 400 attempted, at 60% correct (240 correct answers of 400)… we’d score 120% on the exam, plus 40 extra points (our 240 correct above the 200 needed) That’s 540 points towards the semester. And, if we could get 75% correct, while attempting 3 times as many questions, then our exam score is 225% (that’s our 450 correct answers, while needing only 200) plus an extra 250 points (that’s our 450, minus the 200 to ace the exam) That’s 750 points towards the semester! Now do you see the attack? :)
I never understood why no one else ever tried that.
I know this is a minor thing in the universe of problems with secondary education and grading, but I found the hack interesting.
~ Bruce Schneier from, Hacking the High School Grading System – Schneier on Security
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…and I’m actually not sure if what we tried even worked. You thought I was going to have a clear take-away about my actual scores, or the test never being given again?! No the take-away is: Oh, I’ve been thinking like a hacker for a Long. Long. Time.
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Inside this box is a thing of beauty—and absurdity. It’s a one-of-a-kind puzzle created just for me by one of the greatest puzzle makers in the world. It is, almost surely, the hardest puzzle ever to exist. But before I open the box, let me tell you how the puzzle came to be, and why I think it’s not a trivial pursuit.
~ A. J. Jacobs from, The Puzzle That Will Outlast the World – The Atlantic
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There was a time… who am I kidding? The time is now. Must. Resist. The urge. To buy…
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But in our Physics Project we’ve developed a fundamentally different view of space—in which space is not just a background, but has its own elaborate composition and structure. And in fact, we posit that space is in a sense everything that exists, and that all “things” are ultimately just features of the structure of space. We imagine that at the lowest level, space consists of large numbers of abstract “atoms of space” connected in a hypergraph that’s continually getting updated according to definite rules and that’s a huge version of something like this…
~ Stephen Wolfram from, On the Concept of Motion—Stephen Wolfram Writings
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I’m not sure what to say about this. I am certain that Wolfram is not crazy and that he is brilliant, but he’s pretty far beyond what I can understand. (Picture me doing that slightly askew, squinting thing.) On the other hand, if they really are making the progress they seem to be… it’s going to be a neat time to be alive, in another decade when they get things sorted out.
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However—fourth—over the last century there’s a huge relationship between how rich a country is and the variance in growth. The richest countries have low variance: They all stubbornly keep growing at around the same 1 or 2%. However, middle-income countries vary enormously.
~ “Dynomight” from, Do economies tend to converge or diverge?
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There’s several different interesting threads in this article. But this point about variance leapt out at me. I’m reminded of how just the other day, a piece about statistics that I mentioned was talking about variance (if you clicked through and read the article.) Variance feels like a sort of second-order thinking that I probably should be doing more often.
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For five years as a data analyst, I forecasted and analyzed Google’s revenue. For six years as a data visualization specialist, I’ve helped clients and colleagues discover new features of the data they know best. Time and time again, I’ve found that by being more specific about what’s important to us and embracing the complexity in our data, we can discover new features in that data. These features can lead us to ask better data-driven questions that change how we analyze our data, the parameters we choose for our models, our scientific processes, or our business strategies.
~ Zan Armstrong from, Stop aggregating away the signal in your data – Stack Overflow
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This one just has neat graphs in it. And it has some interesting insights about what data analysts do. The phrase “big data” has been tossed around a lot in recent years—the way “quantum mechanics” gets tossed around by people who have no idea about that either. This article isn’t about truly big data sets, but it’s a neat dive into energy usage as an example of some spiffy data analysis.
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It’s broadly agreed these days that consciousness poses a very serious challenge for contemporary science. What I’m trying to work out at the moment is why science has such difficulty with consciousness. We can trace this problem back to its root, at the start of the scientific revolution.
~ Philip Goff from, A Post-Galilean Paradigm | Edge.org
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I once had a mathematics professor make a comment that it’s fascinating that mathematics is able to explain reality. I double-clutched at the time. And every single time I think about the point he was making, I still pause and my mind reels. If one is looking at—for example—classical mechanics, and one studies the ballistic equations, one can go along nicely using forces and trigonometry, and understand golf balls and baseballs in flight. Soon you realize your mathematics is only an approximation. So you dive into fluid mechanics, which requires serious calculus, and you then understand why golf balls have dimples and why the stitching on baseballs is strictly specified in the rules. All along the way, mathematics models reality perfectly!
But why? So you keep peeling. The math and physics gets more and more complicated—stochastic processes, randomness, quantum mechanics, wave-particle theory, etc.—as each layer answers another “why”… but it’s … is “cyclical” the right word? No matter how far you go, you can always ask “why” again, for the most complex and most accurate system you model and explain.
Down there at the bottom, that’s where Galileo declared there was a distinction between physical reality, and consciousness and the soul. We’ve had hundreds of years of progress via science on what Galileo divided off as “physical reality.” (And that progress is a Very Good Thing.) But as this article explores, is there actually a distinction? What if making that distinction is a mistake?
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So in a nutshell, Gömböc is cool, Hungarians are proud of it greatly. So naturally, they made a 4.5-ton statue replica of the shape.
~ Atlas Obscura from, Gömböc – Atlas Obscura
I could probably write a blog post about other interesting math-related puzzles and shapes that come from Hungary… or about the number of Hungarian mathematicians… but instead, I’ll just point you towards this particularly interesting thing.
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