I was screwing around on this site this afternoon and my random scrolling happened to stop on the number 17. Apparently, that’s the number of wallpaper groups.
What’s a wallpaper group?
That’s what I wanted to know.
So I checked it out. Apparently, the wallpaper groups are the 17 possible symmetry groups in the plane. The groups classify patterns based on certain characteristics of symmetry. The Wikipedia page has a bunch of pretty pictures that help show the different symmetries as well as several patterns that fall into each group.
The groups themselves are named with Crystallographic notation. They start with either a p or a c (for primitive cell or face-centered cell, respectively) and then contain several letters or other letters to describe specific components of symmetry (read here!).
The shorthand name of one of the groups happens to be cmm (my initials!). Patterns with this type of symmetry can be turned upside down (e.g., be rotated 180 degrees) and still look the same. Its lattice is rhombus-shaped. It’s a pretty frequently-encountered pattern, as bricks (like in brick buildings) are often arranged utilizing this group of symmetry.
Here’s a pattern of cmm-type symmetry that I particularly like:
WOAH, I’m pretty sure I’ve heard of this before but didn’t know what it was.
This is a Weierstrass function. Pretty, isn’t it?
Know what else is cool about it? While it’s continuous everywhere, it’s differentiable nowhere.
This challenged the notion that every continuous function was differentiable except on a small set of isolated points when it was discovered and published by Karl Weierstrass in 1872 (though some suggest that Riemann had made this discovery in 1871).
Haha, and I didn’t know this, but examples like this (functions that are continuous but not differentiable except only on a set of points of measure zero) are called monsters of real analysis.
That would be a FANTASTIC thrash metal band name. They could tour with Step Reckoner (the other fictional metal band I came up with, named after Leibniz’ calculating machine).
Ever wonder what the shiniest living material in the world is?
(Me neither, but aren’t you curious now?)
Well, apparently it’s this type of fruit that grows in the forests of central Africa. The plant, Pollia condensate, produces these iridescent berry-sized fruits in little clusters. And while iridescence is not too hard to find in the animal kingdom (jewel beetles, butterfly wings, the wings of some birds), its much rarer in the world of plants.
Investigation of the fruit at a microscopic level reveals that the outer part of it contains layers of thick-walled cells, each of which contains even more layers of cells and fibers. It is the distance between these layers combined with the angles of the fibers that amplify beams of light and create super strong colors. The technical term for this is “multilayer interface.”
But the coolest part of this whole thing is WHY scientists think these plants have such ostentatious fruit.
The fruit of the Pollia is of practically no nourishment—they’re dry, seed-filled husks. Thus, animals don’t naturally want to eat them. But Pollia tend to grow in the same region as the Psychotria peduncularis—a plant that also produces blue berries but whose berries ARE edible and ARE desirable by animals. So scientists who study the plants think that the Pollia evolved fruit that would imitate the look of the more desirable plant, thus tricking animals into eating them and thus spreading their seed around.
How freaking cool is that?
Matt, I think you’ll dig this (if you ever get a break from babies, haha).
BoxCar2D is a program that learns to build a little boxcar using a genetic algorithm. Starting off with a population of 20 cars in generation 0, the 20 cars all run (or don’t, some of them are pretty pathetic, haha) and those that run the longest “reproduce.” If you let it run long enough, you really see pretty dramatic improvement from the 0th to the nth generation. There is also a mutation rate in play that you can set on a sliding scale from no mutations to “100% mutations”, where all components of the car are changeable.
I’ve got a run going in the background as I type this. It’s on generation 6 and some of the cars are running for a whole minute.
Read about the algorithm here.
Check it out, it’s really cool! You can also design your own.
HORRENDOUS JOKE HAS NOTHING TO DO WITH ACTUAL EXPLODING LAKES!
So up until this point, I think the scariest thing I’ve posted involving lakes was this drilling accident that happened in 1980 on Lake Peigneur.
But I just stumbled upon the Wikipedia article for a phenomenon called a limnic eruption. A limnic eruption occurs when a large amount of CO2 gas “erupts” out of a lake that is nearly saturated with it. The eruption of CO2 kills pretty much every oxygen-dependent thing in the near vicinity and also may trigger a tsunami from the rapid displacement of the gas.
Limnic eruptions are said to be triggered by such things as landslides and volcanic activity. Luckily, though, they’re rare; only two have been observed in recent history. The first occurred in 1984 at Lake Monoun in Cameroon and killed 37 people. Two years later, a much deadlier eruption occurred in Lake Nyos, a neighboring lake to Monoun, which killed between 1.700 and 1,800 people.
The consequences are fairly immediate. The CO2, denser than air, displaces the breathable atmosphere close to the ground. People either suffocate from lack of oxygen or die by CO2 poisoning. The erupting gas is also supposedly cold enough to cause frostbite, as the survivors of these two historical eruptions had frostbite-like blisters on their skin. Also, according to Wiki, “the survivors also reported a smell of rotten eggs and feeling warm before passing out; this is explained by the fact that at high concentrations, carbon dioxide acts as a sensory hallucinogenic.”
Even though this type of natural disaster is rare, scientists are keeping a close eye on Lake Kivu, a lake between Rwanda and the Republic of Congo. A much larger lake than Nyos and situated in a much more densely populated area, Kivu’s CO2 and methane saturation levels have been increasing over the years, making it a potential candidate for an eruption sometime in the future. It is also near Mount Nyiragongo, an active volcano that last erupited in 2000. As of now, scientists are trying to figure out if scrubbing the lake of CO2 could have any real impact in reducing the danger of a limnic eruption.
Freaky stuff, nature, freaky stuff.
Happy birthday to one of the greatest statisticians ever: Sir Ronald Fisher!
Fisher (1890 – 1962) was an English statistician/biologist/geneticist who did a few cool things…you know…like CREATING FREAKING ANALYSIS OF VARIANCE.
Yes, that’s right kids. Fisher’s the guy that came up with ANOVA. In fact, he’s known as the father of modern statistics. Apart from ANOVA, he’s also responsible for coining the term “null hypothesis”, the F-distribution (F for “Fisher!”), and maximum likelihood.
Seriously. This guy was like a bundle of statistical genius. What would it be like to be the dude who popularized maximum likelihood? “Oh hey guys, I’ve got this idea for parameter estimation in a statistical model. All you do is select the values of the parameters in the model such that the likelihood function is maximized. No big deal or anything, it just maximizes the probability of the observed data under the distribution.”
I dealt with ML quite a bit for my thesis and I’m still kinda shaky with it.
I would love to get into the heads of these incredibly smart individuals who come up with this stuff. Very, very cool.
New giant prime! New giant prime!
(It’s still really hard for me not to automatically capitalize “prime” after NaNo.)
Curtis Cooper at the University of Central Missouri came across the prime as part of the GIMPS computing project.
GIMPS, the Great Internet Mersenne Prime Search, is a distributed project designed to hunt for the rare Mersenne Primes, of which there have only been 47 found. Mersenne primes have the special form of 2p – 1, where p is itself a prime number.
The new colossal number has been confirmed as the 48th instance of a Mersenne Prime, which makes it super special. To prove the primality of the incredibly huge number, one of Cooper’s computers ran for 39 straight days. Other researchers then had to verify the primality.
I can’t wait to see the spazzing everyone falls into when we find the next DOUBLE Mersenne Prime. There are only four of them thus far discovered, you know.
Here’s some beautiful stuff, people.
This Galton board (or “bean machine” or “quincunx”) demonstration of the Central Limit Theorem is one of the most beautiful things in the world to me.
While the data and trends are fascinating themselves in this demonstration, it’s really Rosling’s enthusiasm about how freaking cool this stuff is that makes me love this video. Yes, I know I’ve posted this one before. Watch it again, it’s badass.
I apologize for how sparse my TWSB posts have been lately; school exploded last week and that’s basically all I’ve had time for. Expect a lot more calculus-related blogs, though, so if you’re into that…
GUYS IT LISTENS TO US NOW!
Alpha Dog, Boston Dynamics’ creepiest freaking dog creature to date, has been updated and now is able to follow vocal commands. He’s quieter than his predecessors and is still able to carry 400-pound loads, navigate uneven terrain, right himself when he bites it, and creep people out.
Haha, 2:16: “LS3, do a barrel roll!”
2:22: “Nailed it! Let’s go.”
Happy Birthday, Stephen Hawking!
Woah, I had no idea he was in his 70′s. He’s like 40 years old in my mind for some reason.
I’m not going to BS my way through this and attempt to describe in any significant detail some of Hawking’s major discoveries and theories, so instead I’ll just post something that’s sciency but pretty much totally unrelated to Hawking. ‘Cause I’m dumb.
Anyway. The KILOGRAM!
The kilogram intrigues me. It’s my favorite SI unit. Of the seven basic SI units, it’s the only one still based on a physical object. The blog post actually started my This Week’s Science Blog series was, in fact, about the kilogram. At that time I’d read an article detailing how several of the actual “copies” of the kilogram—that is, the various chunks of metal that all once weighed exactly the same—have been damaged/broken over the decades, resulting in different countries’ kilograms all being defined as slightly different weights.
But now, scientists have discovered that several copies of the kilo have gotten heavier due to surface contamination in the form of carbon and mercury. The actual gain is no more than tens of micrograms, but that’s a big deal considering that things like radioactive materials are often restricted by weight. A few more micrograms of radioactive substance could mean a lot in some situations.
Scientists hope to “clean” the kilo using ozone and ultraviolet light, which would, according to research, not harm the actual metal. But a better solution according to many would be to actually redefine the kilogram based on some law of nature rather than a physical object—something that has been accomplished for the other six major SI units.
Hang in there, kilogram…your day of reckoning is coming!