Here’s a neat little video, which holds the Milky Way (galactic-centric) steady as the Earth rotates relative to it.
For comparison, here’s the original video by Stephane Guisard and Jose Francisco Salgado, showing the geocentric view of the sky moving:
It is always revelatory to see things from unexpected perspectives. Brian Swimme was amazed by the immensity of it when he first truly recognized that he was standing on a planet that was rotating through space orbiting the Sun.
I’ve always been struck by the opposite point of view. To think that if you hold still enough, and think about it a bit, from one point of view you could be the central reference point for the entire universe, with everything else moving relative to you: the Earth still beneath your feet; the Sun (almost) orbiting around you; and the planets arcing through their epicycles.
Orbits of the inner planets viewed from the Earth (a geocentric perspective). Paths plotted using Gerd Breitenbach's neat little applet.
The epistemological approach to education suggests that the best way to learn a subject is to learn how to think like the experts in the field: how to think like a scientist; how to think like an historian; how to think like an engineer; etc.
If you want to understand mathematics and to think clearly, then the discipline of writing in sentences forces you to think very carefully about your arguments.
It’s an interesting introduction to how mathematicians see the world, and its a useful reminder that many of the ways of thought that apply to any field can be useful in other places, or even in life in general.
The mascot Kergolus superimposed on the islands of Kerguelen. Mascot by Mathieu Valleton and posted on Frank Jacobs' blog Strange Maps.
In response to the submission from a reader, Frank Jacobs has a wonderfully detailed post on the Southern Ocean island of Kerguelen. The island has a French scientific outpost but no permanent population.
Looking at the satellite image, with the marked contrast between the glacial snowfields and the green lowlands, the mascot fairly jumps out at you.
This one’s for the nerds. It’s hard to argue against the elegance of using tau instead of pi. Natalie Wolchover explains, while Kevin Houston makes the argument in video:
This is the first of an excellent series covering the history of English from The Open University. They make for a great spark-the-imagination lesson for etymology.
There’s lots more interesting videos at The Open University’s YouTube channel.
“Malthusian” is often used as a derogatory term to refer to alarmist predictions that we’re going to run out of some natural resource. I’m afraid I’ve used the term this way myself, however, according to Lauren Landsburg at the Concise Encyclopedia of Economics, Malthus is being unfairly maligned. He wasn’t actually predicting catastrophe but wondering why the catastrophes don’t usually happen.
What Thomas Malthus did, in 1798, was point out that while populations grow at a geometric rate – the U.S. population, he noticed, doubled every 25 years – but resources, like food, only increase at an arithmetic rate. As a result, any naturally growing population will eventually run out of resources.
The red line shows geometric growth. No matter how much you start off with, the red line will always end up crossing the blue line.
The linear equation has the form:
where y is the quantity produced, t is time (the independent variable), and m and b are constants. This should not look to unfamiliar to students who’ve had algebra.
The geometric equation is a little more complicated:
here a, g and c are constants. g is the most important, because it’s the growth rate – the higher g is the faster the curve will rise. You can play around with the coefficients and graph in this Excel spreadsheet .
At any rate, after the curves intersect, the needs of the population exceeds how much it can produce; this is the point of Malthusian catastrophe.
The intersection point is where the needs of the population exceeds the production.
The observation is, indeed, so stark that it is still easy to lose sight of Malthus’s actual conclusion: that because humans have not all starved, economic choices must be at work, and it is the job of an economist to study those choices.
— Landsburg (2008): Thomas Robert Malthus from The Concise Encyclopedia of Economics.
Iceland’s drafting a new constitution. To make it more transparent and involve the citizenry, they made the draft available online and used social media, like Facebook, to get comments. The Constitutional Council even broadcast their weekly meetings on YouTube.
Suggestions from the public that have been added thus far include livestock protection and a clause that specifies who owns the country’s natural resources (the nation), …
I’ve been having my students write their classroom constitution on our Wiki. It’s great for transparency and collaborative writing, but usually very few students are interested in looking beyond the section they write. The Iceland experiment is apparently running into a slightly different problem; well-wishers are clogging up the social media sites.
Cynical, but, if you consider the current “kinetic military action” in Libya, way to close to reality. Indeed, this highlights the question: When does it become too easy to go to war?
American planes are taking off, they are entering Libyan air space, they are locating targets, they are dropping bombs, and the bombs are killing and injuring people and destroying things. It is war. Some say it is a good war and some say it is a bad war, but surely it is a war.
Nonetheless, the Obama administration insists it is not a war. Why?
…, the balance of forces is so lopsided in favour of the United States that no Americans are dying or are threatened with dying. War is only war, it seems, when Americans are dying, when we die. When only they, the Libyans, die, it is something else …
