MoMath, more problems —

Here's an awesome activity for anybody who happens to be in New York City. Next week, on December 15th, The National Museum of Mathematics (MoMath) will open at a location near the Flatiron Building. Opening weekend festivities (and the museum, itself) look really cool. — Maggie •

At his Psychology Today blog, Michael Chorost delves into a question about exoplanets that I've not really thought much about before — how easy they would be to leave.

Many of the potentially habitable exoplanets that we've found — the ones we call "Earth-like" — are actually a lot bigger than Earth. That fact has an effect — both on how actually habitable those planets would be for us humans and how easily any native civilizations that developed could slip the surly bonds of gravity and make it to outer space.

The good news, says Chorost is that the change in surface gravity wouldn't be as large as you might guess, even for planets much bigger than Earth. The bad news: Even a relatively small increase in surface gravity can mean a big increase in how fast a rocket would have to be going in order to leave the planet. It starts with one equation — SG=M/R^2.

Let’s try it with [exoplanet] HD 40307g, using data from the Habitable Exoplanet Catalog. Mass, 8.2 Earths. Radius, 2.4 times that of Earth. That gets you a surface gravity of 1.42 times Earth.

... it’s amazingly easy to imagine a super-Earth with a comfortable gravity. If a planet had eight Earth masses and 2.83 times the radius, its surface gravity would be exactly 1g. This is the “Fictional Planet” at the bottom of the table. Fictional Planet would be huge by Earth standards, with a circumference of 70,400 miles and an area eight times larger.

Does that mean we could land and take off with exactly the same technology we use here, assuming the atmosphere is similar? Actually, no. Another blogger, who who goes by the moniker SpaceColonizer, pointed out that Fictional Planet has a higher escape velocity than Earth. Put simply, escape velocity is how fast you have to go away from a planet to ensure that gravity can never bring you back. For Earth, escape velocity is about 25,000 miles per hour. Fictional Planet has an escape velocity 68% higher. That’s 42,000 miles per hour.

Read the full story at Psychology Today blogs

Thanks to Apollo 18, who also helped with the math for Chorost's post.

Image: Vintage ad via Christian Montone

Gifts for the space fans in your life —

If yesterday's BoingBoing Gift Guide didn't give you enough holiday ideas, Popular Science has a collection of gifts for aspiring rocket scientists. Includes meteorite jewelry, a scarf printed with a pattern inspired by measurement systems, and some natty blazers designed by NASA. — Maggie •

Vi Hart is Khan Academy's professional mathemusician. (Yeah, I KNOW, right?) And, this year, she's making the most delightfully nerdy Thanksgiving dinner ever.

It begins with green bean matherole, topped with fried Borromean onion rings. But, besides the fact that it's finished with crispy, delicious hyperbolic geometry, what makes the matherole a matherole?

Vectors. Like the rings, vectors are part of geometry. They've got a magnitude (think: size of the green bean) and they've got a direction (think: which way the green bean is pointing). Most importantly, a single vector can be part of a field of vectors. And that, my friends, is an excellent starting point for a 9 x 13 pan full of beans.

Yes, it's $72. But this 3-D printed metal sculpture/bottle opener is fantastic. And so is its marketing copy.

The problem of beer That it is within a 'bottle', i.e. a boundaryless compact 2-manifold homeomorphic to the sphere. Since beer bottles are not (usually) pathological or "wild" spheres, but smooth manifolds, they separate 3-space into two non-communicating regions: inside, containing beer, and outside, containing you. This state must not remain.

Read the rest of the product description and, you know, maybe buy the bottle opener, too. If you're feeling spendy.

Via Cliff Pickover

Chad Orzel's post, "Financiers Still Aren’t Rocket Scientists" is a timely reminder that Mitt Romney and other Wall Street Types are not, by and large, superhero math geniuses with their fingers on the arcane numeric truths underpinning all reality. Some quants are genuinely impressive mathematicians, but the industry's reputation for "numbers guys," is just wrong-o.

You would think that the 2008 economic meltdown, in which the financial industry broke the entire world when they were blindsided by the fact that housing prices can go down as well as up, might have cut into the idea of Wall Street bankers as geniuses, but evidently not. The weird idea that the titans of investment banking are the smartest people on the planet continues to persist, even among people who ought to know better– another thing that bugged me about Chris Hayes’s Twilight of the Elites was the way he uncritically accepted the line that Wall Street was the very peak of the meritocracy. It’s not hard to see where it originates– Wall Street types can’t go twenty minutes without telling everybody how smart they are– but it’s hard to see why so many people accept such blatant propaganda without question.

Look, Romney was an investment banker and corporate raider at Bain Capital. This is admittedly vastly more quantitative work than, say, being a journalist, but it doesn’t make him a “numbers guy.” The work that they do relies almost as much on luck and personal connections as it does on math– they’re closer to being professional gamblers than mathematical scientists. This is especially true of Bain and Romney, as was documented earlier this year– Bain made some bad bets before Romney got there, and was deep in the hole, and he got them out in large part by exploiting government connections and a sort of hostage-taking brinksmanship, creating a situation in which their well-deserved bankruptcy would’ve created a nightmare for the people they owed money, which bought them enough time for some other bets to pay off.

Romney has no shortage of nerve, and while he creeps me out, he has the sort of faux charm that works well in the finance community. But he’s not a “numbers guy” in any sense that looks meaningful from over here in the land of science. He can do the math needed to add up his personal fortune, but the game that he made his money playing isn’t a rigorously mathematical one– people get rich in finance as much by playing hunches and cutting sharp deals as by crunching numbers. There are people who make their way in that business by taking a rigorously data-driven approach to investing– one of the many things I need to write up for the blog at some point is a review of a forthcoming book called The Physics of Wall Street– but they’re nowhere near a majority of the industry, and Romney’s not one of them.

Financiers Still Aren’t Rocket Scientists (via Making Light)

Math + Too Much Free Time = —

Here is a detailed analysis of the amount of time it would take to ride a hypothetical elevator down through the Earth's core and back out the other side of the planet. Apparently, this has something to do with the remake of Total Recall. But it's interesting even if (like me) you have no intention of seeing that movie. (Via Rhett Allain) — Maggie •

The election is next week. And, with that in mind, Salon's Paul Campos has posted a helpful reminder explaining what the statistics at the fivethirtyeight blog actually mean (and what they don't).

In particular, you have to remember that, while Nate Silver gives President Obama a 77.4 percent chance of winning the presidential election, that's not the same thing as saying that Obama is going to win.

Suppose a weather forecasting model predicts that the chance of rain in Chicago tomorrow is 75 percent. How do we determine if the model produces accurate assessments of probabilities? After all, the weather in Chicago tomorrow, just like next week’s presidential election, is a “one-off event,” and after the event the probability that it rained will be either 100 percent or 0 percent. (Indeed, all events that feature any degree of uncertainty are one-off events – or to put it another way, if an event has no unique characteristics it also features no uncertainties).

The answer is, the model’s accuracy can be assessed retrospectively over a statistically significant range of cases, by noting how accurate its probabilistic estimates are. If, for example, this particular weather forecasting model predicted a 75 percent chance of rain on 100 separate days over the previous decade, and it rained on 75 of those days, then we can estimate the model’s accuracy in this regard as 100 percent. This does not mean the model was “wrong” on those days when it didn’t rain, any more than it will mean Silver’s model is “wrong” if Romney were to win next week.

What Silver is predicting, in effect, is that as of today an election between a candidate with Obama’s level of support in the polls and one with Mitt Romney’s level of support in those polls would result in a victory for the former candidate in slightly more than three out of every four such elections.

Read the full story at Salon.com

Guangzhou's Utopia Design created this Fibonacci Cabinet, whose drawers are scaled according to ratios from the Fibonacci sequence.

Fibonacci Cabint - 乌托邦建筑设计 - UTOPIA ARCHITECTURE & DESIGN: (via Neatorama)

The peer-reviewed journal Advances in Pure Mathematics was tricked into accepting a nonsense math paper that was generated by a program called Mathgen.

To be fair, the journal did note several flaws in the paper, such as "In this paper, we may find that there are so many mathematical expressions and notations. But the author doesn’t give any introduction for them. I consider that for these new expressions and notations, the author can indicate the factual meanings of them," and requested that they be corrected prior to publication.

However, the "author" of the paper replied with a set of pat rebuttals ("The author believes the proofs given for the referenced propositions are entirely sufficient [they read, respectively, 'This is obvious' and 'This is clear']" and these were seemingly sufficient for the editors.

Sadly, the paper wasn't published, as the "author" wasn't willing to pay the $500 peer-review fee.

On August 3, 2012, a certain Professor Marcie Rathke of the University of Southern North Dakota at Hoople submitted a very interesting article to Advances in Pure Mathematics, one of the many fine journals put out by Scientific Research Publishing. (Your inbox and/or spam trap very likely contains useful information about their publications at this very moment!) This mathematical tour de force was entitled “Independent, Negative, Canonically Turing Arrows of Equations and Problems in Applied Formal PDE”, and I quote here its intriguing abstract:

Let ρ=A. Is it possible to extend isomorphisms? We show that D′ is stochastically orthogonal and trivially affine. In [10], the main result was the construction of p-Cardano, compactly Erdős, Weyl functions. This could shed important light on a conjecture of Conway-d’Alembert.

This is a nice follow-on from the Sokal hoax, wherein a humanities journal was tricked into accepting a nonsense paper on postmodernism. Goes to show that an inability to distinguish nonsense from scholarship exists in both of the two cultures.

Mathgen paper accepted! (via Neatorama)

Little-scale offers music procedurally-generated from prime numbers. A "full version", available for download, is 26 hours long. [Little-Scale]