Here are some pendulums:
I didn’t want the video to end!
According to the site, one complete cycle lasts 60 seconds. In that period, the longest pendulum oscillates 51 times and each successively shorter pendulum makes one additional oscillation more than the last—thus, the shortest oscillates 65 times.
I really like how when they’re all out of sync it looks like they’re slowing down and coming to a stop, but then they sync up a little again and it’s like, “BOOSH we’re still going!”
Somewhat unrelated, but here’s another mathy vid that I didn’t want to see the end of. Which of the three panels captured your attention the most? On the first watch it was the middle panel, on the second watch it was the far left panel for me.
So raise your hand if you knew that in 1963, MIT launched 480,000,000 copper needles into space with the purpose of creating an artificial ionosphere.
‘Cause I sure as hell didn’t.
Wiki: “At the height of the Cold War, all international communications were either sent through undersea cables or bounced off the natural ionosphere. The United States Military was concerned that the Soviets might cut those cables, forcing the unpredictable ionosphere to be the only means of communication with overseas forces.”
And the US Military is not the US Military unless they take DRASTIC MEASURES! So up went the millions of needles. Welcome to Project West Ford.
And what makes it even better is that THEY SCREWED IT UP THE FIRST TIME SO THEY HAD TO DO IT AGAIN. “After a failed first attempt launched on October 21, 1961 (the needles failed to disperse), the project was eventually successful with the May 9, 1963 launch.”
Worldwide criticism? Yup. “British radio astronomers, together with optical astronomers and the Royal Astronomical Society, protested this action. The Soviet newspaper Pravda also joined the protests under the headline “U.S.A. Dirties Space.”"
But some good did come of it: all the protesting eventually resulted in a provision about consultation in the 1967 Outer Space Treaty.
As of 2008, there were still clumps of needles out there. The needles occasionally re-enter, just as they have been since the start of the whole thing.
Another demonstration of just how much “space” is in space.
Edit: Tumblr has led me to this wonderful (and slightly terrifying) video…
…as well as this info:
“What if the moon was the same distance away as the ISS? … While we think of the International Space Station as being, well, way out there in space, it’s not that far. Only around 400 km up, actually. If the Earth was a basketball, then the ISS would only be about a centimeter off its surface.
“On average, our moon resides 384,400 km away from Earth. … Even at that incredible distance, the moon can warp the liquid on the surface of Earth! Which brings me to a major problem with this video … in order to see this, we’d all be dead, and Earth would be very messed up indeed.”
I keep coming back to the kilogram in these science blogs. One day I think I’ll do like a (somewhat) comprehensive history of the SI units, ’cause I find them fascinating.
(I also really like the word kilogram.)
Are you ready to GET YO’ MIND BLOWN?
Okayokayokayokay. So you know how the earth’s magnetic field switches poles every so often? So does the sun’s!
The sun is currently at the peak of its 11 year solar cycle and is about to swap its north magnetic pole for its south and vice versa. According to Stanford University solar physicist Todd Hoeksema, the swapitself isn’t more than 3 to 4 months out. The north pole has actually already flipped; we’re just waiting on the south one to get its butt in gear and head to the opposite side.
So what does this mean for our solar system? What solar physicists focus on during this time is something called the “current sheet.” This is a surface that juts outward from the sun’s equator along which runs an electric current produced by the sun’s magnetic field. The current itself is small but the sheet is freaking huge, and it’s the thing that pretty much keeps the heliosphere (the sun’s magnetic influence) in check.
According to Phil Scherrer, another Stanford solar physicist, the sheet becomes really wavy and warped during a pole swap. So for us here on earth, as we zoom around in our orbit of the sun, we pass in and out of the sheet itself. This can cause disruptive “cosmic weather,” but the warped sheet actually offers the solar system better protection against cosmic rays.
Stanford’s Wilcox Solar Observatory has observed three such polar swaps since 1976. This will be the fourth.
HOW. COOL. IS. THAT. I freaking love the sun.
THE PITCH DROPPED!
AND IT WAS FILMED!
WHAT THE HECK AM I YELLING ABOUT?!
In 1944, an experiment was set up that would last quite a long time. At Trinity College in Dublin, tar pitch was heated and placed into a funnel. The funnel was placed in a jar and was left alone. It’s still sitting there today. Why? Because pitch is something that, at first glance, behaves very much like a solid. It just kinda sits there and if you hit it with something hard enough, it shatters. What they wanted to show with this experiment (which is actually similar to an even longer-lived experiment done in Australia) is that, given time, pitch will exhibit liquid properties. In particular, over a (very long) stretch of time, the pitch in the funnel will succumb to gravity and drop to the bottom of the jar.
So that’s the basic idea. But the big deal in all of this is actually witnessing these drops. Averaging things out between the Australian and Dublin versions of the experiment, it takes somewhere between 7 and 13 years for the drops to happen. That’s a lot of time sitting and watching for a payoff that takes a split-second. Up until now, no one has witnessed it happening.
However, when the Dublin scientists realized last April that a drop was imminent, they did something they could finally do because of today’s technology: they set up a camera to record the pitch* when it finally fell.
And a week ago? VICTORY! On Thursday, July 11th, a pitch drop was not only witnessed, but filmed! See a gif of it here.
And we know it’ll happen again…we just need to wait.
*Actually, I think I read somewhere that they tried this in Australia in like 2000, but the camera wasn’t on when it happened. Oops.
Holy solar-driven demise, Batman. Look at those enormous sunspots.
1785 and 1787—the names for these two groups of spots—are pretty much staring earth in the face right now.
Sun spots are dark areas of intense magnetic activity that, when the activity gets super-intense, spit out energy in the form of solar flares or coronal mass ejections. The flares/ejections fire out clouds of magnetic energy and solar material into space.
And what happens when these things hit earth? Normally, we end up with more extreme aurora that are able to be seen at lower latitudes. But if the storm of magnetism is really strong, satellites can short out and power lines are disabled.
Considering we’re supposed to be at the peak of the current 11-year solar cycle, scientists are watching the spots carefully to see what, if any, flares and ejections they will emit
and how screwed all of us electricity-dependent people will be.
The matrix of LINEAR ALGEBRA!!!
So someone asked the awesome dudes at Ask a Mathematician/Physicist why determinants of matrices are defined in the strange way they are. And one of the opening sentences of the Physicist’s response was:
“The determinant has a lot of tremendously useful properties, but it’s a weird operation. You start with a matrix, take one number from every column and multiply them together, then do that in every possible combination, and half of the time you subtract, and there doesn’t seem to be any rhyme or reason why.”
That needs to be a textbook definition somewhere.
Anyway. This was an especially interesting read for me, since we just learned about the role of the Jacobian matrix’s determinant when performing a change of variables for multiple integrals.
The Physicist has an excellent explanation of it (along with pictures!), but it basically comes down to the fact that the determinant of a 3 x 3 matrix, if we treat the columns of the matrix as vectors, is actually equal to the volume of the parallelepiped (coolest shape name or coolest shape name?) formed by the vectors. Think about if you have two vectors in the xy-plane. You can extend vectors out from each of the tails of the vectors so that you have a parallelogram like this:
Finding the determinant of the 2 x 2 matrix that describes those two vectors is the same as finding the area of the parallelogram formed by them. Add one more dimension and you get a parallelepiped for your shape and a volume for your determinant.
This has a buttload of applications—like I said, when performing a change of variables when doing multiple integration, but also for finding eigenvalues/eigenvectors and determining whether a set of vectors are linearly independent or not.
I was actually planning on making this a longer blog with an actual calculus application, but a) formatting that would take like 80 years for me and I’ve actually got to study sometime tonight and b) I’ve fallen into the “polar coordinates” article on Wiki and I don’t think I’ll be getting out anytime soon. THEY MAKE ME HAPPY, OKAY?!
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).