While I was at ScienceOnline 2014 last week, I received some great news: the 2013 edition of “The Open Laboratory,” an anthology of the “best science writing online,” was published! It is available as an e-book from The Creativist, and it includes my blog post on “The Barkhausen Effect” as one of the entries!
It really is a great collection, and I feel proud to have made it in once again, especially in light of the company I keep there, which includes Deborah Blum, Jennifer Ouellette, Maggie Koerth-Barker, Christie Wilcox, Melanie Tannenbaum, Jason Goldman, Krystal D’Costa, Blake Stacey and many more! The full list of authors and articles can be read at this blog post, and the collection can be ordered through The Creativist at this link.
The more I research, the more it becomes clear that cats caused all sorts of mischief in the scientific community in the late 1800s! The source of this mischief is the feline ability to turn themselves over in freefall and land on their feet, even when released at rest with no rotational motion. As I have noted in a previous post, this ability is, at a glance, seemingly at odds with the conservation of angular momentum — though in reality it is not! In a rigid body, the angular momentum of the object is directly proportional to its rotational speed. In a flexible body such as a cat, however, different sections can rotate in different ways, producing a net overall rotation even if the cat’s total angular momentum remains zero.
Resident feline fluidity expert Cookie demonstrates the bendy-ness of cats.
The debate, and confusion, was sparked in 1894 when Étienne-Jules Marey presented a sequence of photographs to the Paris Academy showing a cat flipping over at rest. As was later reported in the New York Herald, Marey’s observations were met with hilarious incredulity at the meeting:
When M. Marey laid the results of his investigations before the Academy of Sciences, a lively discussion resulted. The difficulty was to explain how the cat could turn itself round without a fulcrum to assist it in the operation. One member declared that M. Marey had presented them with a scientific paradox in direct contradiction with the most elementary mechanical principles.
Fortunately for the dignity of the scientific community, researchers quickly realized that Marey was correct: non-rigid bodies can flip over, even starting from rest, while conserving angular momentum. This led to a century-long investigation into how, exactly, a cat achieves this feat (you can read about the history in another blog post of mine).
Side view of a falling cat, by Marey. Images chronological from right to left, top to bottom.
Other researchers, however, found immediate inspiration in the cat’s newly-appreciated ability and its implications for physics. Inspired by Marey’s work, mathematician Giuseppe Peano in fact argued that the cat’s flipping talent provided a lesson and a solution for a problem in the most unlikely of places: geophysics!
One of the things I love about using Twitter is the opportunity to connect with people whose work I admire, from writers to scientists to artists to actors to musicians. Those connections can then lead you to new “discoveries” that you would otherwise not have come across.
Case in point: about a month ago, while my wife was out of town, I broke out my DVD copy of The Lost Skeleton of Cadavra (2001), a delightful spoof of low-budget science fiction from the 50s, and The Lost Skeleton Returns Again (2009), its very silly sequel. Both movies, and others, were written, directed, and starred in by the all-around auteur Larry Blamire; on a whim, I checked to see if he was on Twitter, and to my delight, he is, and to my further delight, he graciously acknowledged my existence!
While following him on Twitter, I recently learned that Blamire has also written a compilation of horror stories, Tales of the Callamo Mountains (2008):
Blamire also drew the cover of his book, continuing his efforts to make the rest of humanity look like the lazy talentless slaggards that we are.
Tales of the Callamo Mountains compiles 13 previously unreleased stories of horror, focused in and around the fictional Callamo Mountain Range. Set in the turbulent time following the Civil War, the tales feature settlers, marshals, laborers, soldiers, cowboys and others who, traveling in the remote and untamed West, find themselves up against nature and forces far more diabolical.
These stories are good. I was immediately hooked once I starting reading the first of them, and could hardly put the book down until I had finished it a couple of days later. A couple of the tales are absolutely brilliant, in my opinion.
This post is an exploration of some ideas I put together for a proposed magazine article. Will link to the article if and/or when it becomes available!
Last year, I wrote a blog post about the history of “cat-turning”: the ability of cats to turn themselves over in free-fall and land on their feet. The subject has a long, long history: scientists such as James Clerk Maxwell were investigating how cats do it back in the 1850s, and a complete model of “cat-turning” did not appear until 1969, over a hundred years later!
So what intrigued and, quite frankly, baffled physicists for so long? The surprising observation is that cats can still turn over in free-fall even when they are released at rest, i.e. with no initial rotation! Ironically, this probably freaks out physicists far more than non-physicists, because at first glance it appears to be a violation of the conservation of angular momentum. In fact, when Étienne-Jules Marey first presented his photographic evidence of the phenomenon to the Paris Academy of Sciences in 1894, a number of extremely distinguished researchers argued that his claim was flat-out impossible! The cats must, they argued, push off of the hands of the person holding them at the momento f release. (Others, however, sided with Marey, and at least some of the doubters quickly changed their opinions.)
Side view of a falling cat, by Marey, c. 1894. Images chronological from right to left, top to bottom.
Fortunately, though the “complete” model of cat-turning is quite complicated, it is possible to explain the basic idea in an elegant way — without using any math! How, you may ask, can I accomplish this wizardry?
Ever since reading author Basil Copper’s The Great White Space (1974) and Necropolis (1980), both of which were recently reprinted by Valancourt Books, I’ve been binge-reading the works of Basil Copper. I’ve read two of his short story collections so far, From Evil’s Pillow (1973) and And Afterward, the Dark (1977), and have been ordering other books as I find relatively inexpensive editions.
Last week, I finished reading The Black Death (1991), which was Copper’s final horror/mystery novel (though not his last book, as he continued to write mysteries for over a decade):
At the time of The Black Death’s writing, Copper was in his late 60s. Though it is not a deterministic rule, it is not uncommon to see the quality of an author’s writing decline in his or her later years. With this in mind, I didn’t know what to expect from The Black Death!
I shouldn’t have worried. Copper’s novel is a fascinating mixture of mystery, horror, and period Victorian drama. It is probably my favorite among all the Basil Copper stories I’ve read so far.
Updated with a third footnote clarifying my use of the term “diverge,” thanks to suggestion by Evelyn Lamb, who has also written an excellent discussion of the problem with the video. At the end of this post I list all the critiques I’ve found so far.
I feel like one of those grizzled action heroes who, having given it all up, is dragged reluctantly out of retirement for one more big mission. Over the past month or so (honestly, I forget how long I was working on things), I wrote a series of blog posts on the “weirdness” of infinity in mathematical set theory. Hopefully, there were two things that I got across in those posts: (1) infinity can be very weird, but (2) it can be comprehended, and even reasonable, once one understands the assumptions and limitations built into the mathematics.
Having retired from writing those posts, the other day I came across the following video:
So, using a seemingly simple series of mathematical manipulations, they “prove” the following astounding result: the infinite sum of increasingpositiveintegers equals a finite, fractional, negative number. In short:
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This video was picked up by Phil Plait at Bad Astronomy, who called* it “simply the most astonishing math that you’ll ever see.” It has already spread far and wide across the internet, including making it to the popular site Boing Boing.
But is it true? The video makes it seem so simple, and uncontroversial, almost obvious. But there are some big mathematical assumptions hidden in their argument that, in my opinion, make it very misleading. To put it another way: in a restricted, specialized mathematical sense, one can assign the value -1/12 to the increasing positive sum. But in the usual sense of addition that most human beings would intuitively use, the result is nonsensical.
To me, this is an important distinction: a depressingly large portion of the population automatically assumes that mathematics is some nonintuitive, bizarre wizardry that only the super-intelligent can possibly fathom. Showing such a crazy result without qualification only reinforces that view, and in my opinion does a disservice to mathematics.
I’ve actually discussed this result years ago on this blog, talking about the Riemann zeta function and how -1/12 isn’t really equal to the infinite sum given. But even that discussion is probably a little too abstract, especially since I don’t discuss in any detail how the result -1/12 could be physically accurate. As it has been noted (and I’ve noted myself), the -1/12 result can be used with surprising accuracy in physics problems. But even there, things are much more subtle than they appear.
So let’s take a closer look** at the “proof” that an infinite increasing sum can equal -1/12. We will explain why the answer is not so simple as the video makes it appear, and why it is also not quite so simple to say that physics justifies the answer. We have a lot of ground to cover, so let’s go!
The history of science provides me with a practically never-ending set of delightful surprises! Case in point is a set of articles I found while browsing through volume 17 of Current Literature, “A Magazine of Record and Review,” published in 1895. Current Literature was an eclectic compilation of writings from a variety of other publications, including literature, science, and news magazines. I not only found exactly the bit of physics history that I was looking for (more to be said in a future post) but also a bunch of other weirdness.
The first one that caught my eye was an article with the rather curious title “With a telephone in his hat.” Reprinted from The Electrical Review, it turns out to be a very early, and in retrospect silly, true story of electronic eavesdropping! I reprint it in its entirety below, with only short comments appended.
I must admit that I’ve never been a particularly avid reader of science fiction. I’ve read very few of the works of the classic authors such as Clarke, Asimov, Heinlein, and Bradbury*, and I have many boxes unchecked in my list of “must-read” science fiction novels. I also have an instinctive aversion to “hard” science fiction, which focuses on scientific and technical detail.
Recently, though, my interest was piqued when I learned that actor Morgan Freeman has been trying for years, almost a decade, to make a film adaptation of Arthur C. Clarke’s classic 1972 novel Rendezvous with Rama.
I should note, though, that it wasn’t Freeman’s enthusiasm that intrigued me as much as a variety of related internet comments that suggested that a good film adaptation of Rama was “impossible.” What qualities could make a story a classic book but also make it completely unsuitable (supposedly) for the big screen? I was curious, and reading a synopsis of Rama made me really intrigued.
There probably isn’t much that I can say about the novel that hasn’t been said elsewhere and more eloquently, but it is amazing. It immediately entered my list of favorite books of all time, and I’ve spent lots of time thinking about it for weeks after finishing it.
Harry Bale is a perfectly ordinary fellow. His lives in the suburbs with his wife and two children, works in his attic studio, and indulges in gardening when the season is right. His neighbors are an eclectic but friendly collection, and the Bales often spend time socializing at neighborhood parties.
All of this changes when Harry comes home to find an enigmatic envelope on the mantlepiece. Inside is a typed message of only two words: “Stand by.”
Harry Bale, a sleeper agent for an unknown power, has been activated.
So begins Thomas Hinde’s 1964 novel The Day the Call Came, recently reprinted by Valancourt Books and long unavailable.
What follows is a story of what can only be called suburban paranoia: as the time of Bale’s mission draws near (a mission of which he is still ignorant), his tension increases and he begins to wonder who he can trust around him. Quiet laughter among his neighbors at dinner parties become sinister; every action out of the ordinary becomes suspicious. Additional cryptic messages arrive from Bale’s faceless employers, putting him even further on alert and forcing him to take increasingly drastic action. Eventually, the final call comes and Harry will perform a horrific and irrevocable task.
The Day the Call Came starts somewhat slowly, as Harry’s narration sets the stage of a seemingly peaceful community that he will reassess quickly. Once the background is set, though, the novel moves quickly, as we follow Harry’s activities and his musings on what his cryptic instructions mean.
It is somewhat interesting to note that “suburban paranoia” is almost its own subgenre of horror and thrillers; I have previously talked about Thomas Berger’s (much more recent) novel Neighbors, about a man whose quiet life is turned upside-down by new residents next-door to him. Such tales have appeal because they suggest that idyllic suburban communities are really too quiet, in the same way that a forest becomes absolutely silent just before a predator strikes.
My attention was drawn to Hinde’s novel not only for the strange plot, but because it was a great influence on horror master Ramsey Campbell, who is one of my favorite authors and of whom I have spoken quite often on this blog. Campbell wrote a new introduction for the Valancourt edition, and he brings great insight to Hinde’s work, especially considering that Campbell himself is a true master of stories of madness and paranoia.
I didn’t find that The Day the Call Came held many surprises for me. To some extent, the story played out as I suspected it would. However, the story is almost irrelevant when compared to the remarkable atmosphere of menace that Hinde sets up. Every action, every occurrence, every person in a happy sunlit community become ominous and sinister. For this reason, I found The Day the Call Came to be well worth reading.
The final installment in a series of posts on the size of the infinite, as described in mathematical set theory. The first post can be read here, the second here, and the third here.
We have taken a long, strange journey into the properties of infinity. Over the course of three posts, we have seen that we can characterize the different “sizes” of infinity, though not in the way one might think. We have found, in fact, that there are an infinity of infinities! The smallest one we looked at was the infinite set of counting numbers (labeled ); the next largest we found was the continuum (labeled ): the set of real numbers between 0 and 1. We then found that, for any size infinity, we can construct a larger one.
This leads to an intriguing notion: if we arrange the different size infinities we have found in order, we might have a set of the form
This would seem to suggest a really elegant possibility: if these are all the infinities, then we could imagine that the set of all infinities form a countable infinity themselves, of size , and then we could build up the larger infinities again from this, continuing an endless cycle! For instance, the set of all subsets of the set of all infinities would then be of size , and so on.
For this to be true, however, we need to know whether there are any other infinities between those we have been able to derive so far. We have shown that there are an infinite number of infinities, but we have not shown that these are the only infinities. To condense this into the simplest problem, we can ask:
Are there infinite sets of an intermediate size between and the continuum ?
This is what is known as the continuum problem, and it has vexed mathematicians for well over a hundred years, ever since Georg Cantor first formulated set theory in the 1870s.
But here is where we arrive at what may be the oddest part of the story of infinity! If we look at the history of the continuum problem, the answer to the question has changed over the years:
We don’t know the answer (c. 1870s)
We can’t know the answer (c. 1950s)
The answer is whatever we prefer it to be (today)
Huh? Okay, this is going to take a bit of explanation…
The author of Skulls in the Stars is a professor of physics, specializing in optical science, at UNC Charlotte. The blog covers topics in physics and optics, the history of science, classic pulp fantasy and horror fiction, and the surprising intersections between these areas.
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); the next largest we found was the continuum (labeled 
): the set of real numbers between 0 and 1. We then found that, for any size infinity, we can construct a larger one.
Skulls in the Stars 