NGC 3324.

Fill your void

NASA’s Message-In-A-Bottle: The Interstellar Constellation

The picture above represents one of the most beautiful things we’ve ever done.

Here’s a short thought experiment and story:

Somewhere one day a person, who may or may not be somewhat like you, might be looking through their telescope.

They might see something strange, approaching the planet.

They contact the authorities.

A mission is conceived to rendezvous with the object.

Astronauts carefully seal the mysterious asteroid in a large container and bring it back to the planet for scientists to study.

The whole world would be tense, waiting for news to break of what this strange thing is.

Its enigmatic shape gives it away as almost certainly not being natural.

Finally a nervous person approaches the media and crowds outside the lab.

With a shaking hand the person wipes sweat from their brow. They look up briefly before speaking, as if half expecting something to be there.

“The asteroid… is not from the solar system. It hurtled here at great speeds from a distant star.

It’s old. We’re not sure yet how old, but it’s clearly been a long time since it was home.

Inside the asteroid is a golden disc. We’ve managed to remove the disc. It has markings… and sounds etched into it.”

It was a little longer before the contents of the disc were deciphered. The scientists realized that the strange 14-branches of lines on the disc were binary. Yes or no. The simplest language in the universe, and a mathematical one.

A language that might be used to communicate with cosmic neighbors.

Across countless years and an unimaginable gulf of empty darkness, something was telling us, “Yes, yes, yes, no, no, yes, no, yes, no, yes, no, no, yes, yes, no, yes, yes, no…”

But yes to what? No to what?

The media exploded when an astronomer announced the binary series and the lengths of the branches corresponded exactly to the fingerprint-like beacons of 14 pulsars.

Around the world researchers mapped out where the center of the constellation should be, where the center of the 14 branches from their perspective night sky was.

They knew almost immediately but didn’t want to believe.

The star in the center of the constellation, the place where this message came from…

A news anchor looked into a camera, a somber look on their face:

“Astronomers have triangulated the location of the alien spacecraft. It came from a distant star which you can see in your telescopes. It’s the large red one.

It’s pretty to us but was a very different sort of star when this message was sent to us. Our space telescopes have confirmed that there’s a rocky planet in orbit around the star… there’s no atmosphere on it now as the star’s growth has boiled away any atmosphere there might have been.

Could those aliens still be alive somehow? Did they survive the incineration of their home?

As much as we ask these questions all we’ve got are the recordings they left on a sturdy golden record.

When played we hear strange sounds in an alien tongue. Deciphered, the recording reads,

“Hello, from the children of planet Earth…””

This story, believe it or not has already begun.

A few decades ago, NASA, working with Dr. Carl Sagan compiled a golden record to go aboard the Voyager spacecrafts. 

Voyager 1 launched from Earth in 1977. It left the solar system and entered interstellar space in 2013.

In 1 billion years, that golden record will still be readable and the sounds engraved thereon still readable.

NASA used the unique, lighthouse-like rhythms of specific pulsars to generate a map, a sort of interstellar constellation that, no matter where in the Milky Way you are, will always point to our Sun at the center.

It’s a beautiful message. For a billion years the sounds of children speaking across the universe will survive. For a billion years the sounds of a heartbeat of someone in love will be carried from star to star. 

That heartbeat, that love, will flow across the cosmos for a billion years.

For a billion years our interstellar message-in-a-bottle will drift among the current of starlight, perhaps until one day a person, who may or may not be somewhat like you, might look through their telescope and see a strange asteroid drifting towards their planet…

(Image credit: NASA)

An Adaptable Species: Part 2 of 4 (Part 1) Episode 11: The Immortals, Cosmos: A SpaceTime Odyssey

F-22 Raptor with a launch of the Space Shuttle in the background.

How to stabilize a wobbly table?

You are in a restaurant and you find that your table wobbles. What do you do?  Most people either put up with it, or they attempt to correct the problem by pushing a folded table napkin under one of the legs. But mathematicians can go one better. A couple of years ago, four mathematicians published a research paper in which they proved that if you rotate the table about its center, you will always find an orientation where the table is perfectly stable.

This problem - as a math problem - has been around since the 1960s, when a British mathematician called Roger Fenn first formulated it. In 1973, the famous math columnist Martin Gardner wrote about the problem in his Scientific American column, presenting a short, clever, intuitive argument to show how rotation will always stop the wobble. Here is that argument.

This only works for a table with equal legs, where the wobble is caused by an uneven floor. However uneven the floor, a table will always rest on at least three legs, even if one leg is in the air. Suppose the four corners are labeled A, B, C, D going clockwise round the table, and that leg A is in the air. If the floor were made of, say, sand, and you were to push down on legs A and B, leaving C and D fixed, then you could bring A into contact with the floor, but leg B would now extend into the sand. Okay so far?

Here comes the clever part. Since all four legs are equal, instead of pushing down on one side of the table, you could rotate the table clockwise through 90 degrees, keeping legs B, C and D flat on the ground, so that it ends up in the same position as when you pushed it down, except it would now be leg A that is pushed into the sand and legs B, C, and D are all resting on the floor. Since leg A begins in the air and ends up beneath the surface, while legs B, C, and D remain flat on the floor, at some point in the rotation leg A must have first come into contact with the ground. When it does, you have eliminated the wobble.The result follows from the Intermediate Value Theorem (Proof).

For more - VIDEO: Fix a Wobbly Table (with Math) by Numberphile.

Consider an interval I = [a, b] in the real numbers ℝ and a continuous function f : I → ℝ. Then, Version I. if u is a number between f(a) and f(b), f(a) < u < f(b)   (or  f(a) > u > f(b) ), then there is a c ∈ (a, b) such that f(c) = u.

This argument seems convincing, but making it mathematically precise turned out to be fairly hard. In fact, it took over 30 years to figure it out. The solution, presented in the paper Mathematical Table Turning Revisited, by Bill Baritompa, Rainer Loewen, Burkard Polster, and Marty Ross, is available online at Mathematical table turning revisited 19, Nov 2005, http://Arxiv.org/abs/math/0511490

The result follows from the Intermediate Value Theorem.  But getting it to work proved much harder than some other equally cute, real-world applications of the IVT, such as the fact that at any moment in time, there is always at least one location on the earth’s surface where the temperature is exactly the same as at the location diametrically opposite on the other side of the globe. As the authors of the 2005 solution paper observe, “for arbitrary continuous ground functions, it appears just about impossible to turn [the] intuitive argument into a rigorous proof. In particular, it seems very difficult to suitably model the rotating action, so that the vertical distance of the hovering vertices depends continuously upon the rotation angle, and such that we can always be sure to finish in the end position.” The new proof works provided the ground never tilts more than 35 degrees. (If it did, your wine glass would probably fall over and the pasta would slide off your plate, so in practice this is not much of a limitation.) Is the theorem any use? Or is it one of those cases where the result might be unimportant but the math used to solve it has other, important applications?…… “I have to say that, other than the importance of the IVT itself, I can’t see any application other than fixing wobbly tables. Though I guess it does demonstrate that mathematicians do know their tables”-  Mathematician Keith Devlin.

[SOURCE - MAA.org, K. Devlin, Feb. 2007]

[PDF] On the stability of four legged tables, A. Martin, 15 Aug. 2006:  Proving that a perfect square table with four legs , place on continuous irregular ground with a local slope of at most 14.4 degrees and later 35 degrees, can be put into equilibrium on the ground by a “rotation” of less than 90 degrees. And Discussing the case of non-square tables and make the conjecture that equilibrium can be found if the four feet lie on a circle.

Also, I think we can add an actual argument: “The table would be stability (not wobble) if their four legs contact the ground - not necessarily that they have lie on the same flat surface ”, then everything will be easier to approach the problem that the authors wrote.

Vela Supernova Remnant : The plane of our Milky Way Galaxy runs through this complex and beautiful skyscape. At the northwestern edge of the constellation Vela the telescopic frame is over 10 degrees wide, centered on the brightest glowing filaments of the Vela Supernova Remnant, an expanding debris cloud from the death explosion of a massive star. Light from the supernova explosion that created the Vela remnant reached Earth about 11,000 years ago. In addition to the shocked filaments of glowing gas, the cosmic catastrophe also left behind an incredibly dense, rotating stellar core, the Vela Pulsar. Some 800 light-years distant, the Vela remnant is likely embedded in a larger and older supernova remnant, the Gum Nebula via NASA

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Engineers are preparing to test the parachute system for NASA’s Orion spacecraft at the U.S. Army Yuma Proving Ground in Yuma, Arizona. During the test, planned for Wednesday, Aug. 26, a C-17 aircraft will carry a representative Orion capsule to 35,000 feet in altitude and then drop it from its cargo bay. Engineers will test a scenario in which one of Orion’s two drogue parachutes, used to stabilize it in the air, does not deploy, and one of its three main parachutes, used to slow the capsule during the final stage of descent, also does not deploy. The risky test will provide data engineers will use as they gear up to qualify Orion’s parachutes for missions with astronauts. On Aug. 24, a C-17 was loaded with the test version of Orion, which has a similar mass and interfaces with the parachutes as the Orion being developed for deep space missions but is shorter on top to fit inside the aircraft.