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

Islamic Art

Most everyone is familiar with geometry and patterns.  The above image by Richard Henry is included here to give some mathematical frame of reference.  The artistic emphasis of these ideas gained prominence due to certain religious rules in Islamic religious texts forbidding the portrayal of human forms in worship.  Additionally, the advanced mathematical discoveries in the middle east brought about some wonder toward the patterns of these ideas.  The underlying message in such geometries, within the Islamic context, is the infinite and natural power of God.  It is important to note that ideas like zero, our decimal counting system, and algebra originated from India and the middle east.  Arabic calligraphy is also similarly celebrated and made the subject of  many past and current Islamic art.  

Incredible “EPIC” View Of The Moon Passing In Front Of The Earth

This is real, folks. It is not a computer-generated animation. NASA’s DSCOVR (Deep Space Climate Observatory) satellite took these incredible shots on July 16 using its Earth-facing EPIC camera from its vantage point between the Earth and the Sun, a million miles away!

DSCOVR sits at what’s known as the L1 Lagrangian point, where the gravitational pull of the Earth and Sun balance out in such a way that satellites positioned there can remain in stable orbit while using minimal energy:

Image: NASA/NOAA

This view of the far side of the Moon reminds us that it is anything but dark. The Moon is tidally locked, meaning that we see the same face all the time, but the sun regularly shines on the side that we don’t see (we’re just seeing a new or crescent moon when that happens). The far side also lacks the dark plains, or maria, that texture the Earth-facing side, made of basalt laid down by ancient lunar lava flows, reminding us that our lunar satellite has a complex geologic history:

NGC 3324.

Credit: NASA, ESA and the Hubble Heritage Team (STScI/AURA)

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.

The One-Year Mission

First off, what is the One-Year Crew? Obviously, they’re doing something for a year, but what, and why?

Two crew members on the International Space Station have just met the halfway point of their year in space. NASA Astronaut Scott Kelly and Russian Cosmonaut Mikhail Kornienko are living in space for 342 days and will help us better understand the effects of microgravity on the human body.

Why 342 days and not 365? Thought you might ask. Due to crew rotation schedules, which involve training timelines and dictate when launches and landings occur, the mission was confined to 342 days. Plenty of time to conduct great research though!

The studies performed throughout their stay will yield beneficial knowledge on the medical, psychological and biomedical challenges faced by astronauts during long-duration spaceflight.

The weightlessness of the space environment has various effects on the human body, including: Fluid shifts that cause changes in vision, rapid bone loss, disturbances to sensorimotor ability, weakened muscles and more.

The goal of the One-Year Mission is to understand and minimize these effects on humans while in space.

The Twins Study

A unique investigation that is being conducted during this year in space is the Twins Study. NASA Astronaut Scott Kelly’s twin brother Mark Kelly will spend the year on Earth while Scott is in space. Since their genetic makeup is as close to identical as we can get, this allows a unique research perspective. We can now compare all of the results from Scott Kelly in space to his brother Mark on Earth.

But why are we studying all of this? If we want to move forward with our journey to Mars and travel into deep space, astronauts will need to live in microgravity for long periods of time. In order to mitigate the effects of long duration spaceflight on the human body, we need to understand the causes. The One-Year mission hopes to find these answers.

Halfway Point

Today, September 15 marks the halfway point of their year in space, and they now enter the final stretch of their mission. 

Here are a few fun tidbits on human spaceflight to put things in perspective:

1) Scott Kelly has logged 180 days in space on his three previous flights, two of which were Space Shuttle missions. 

2) The American astronaut with the most cumulative time in space is Mkie Fincke, with 382 days in space on three flights. Kelly will surpass this record for most cumulative time in space by a U.S. astronaut on October 16.

3) Kelly will pass Mike Lopez-Alegria’s mark for most time on a single spaceflight (215 days) on October 29.

4) By the end of this one-year mission, Kelly will have traveled for 342 days, made 5,472 orbits and traveled 141.7 million miles in a single mission. 

Have you seen the amazing images that Astronaut Scott Kelly has shared during the first half of his year in space? Check out this collection, and also follow him on social media to see what he posts for the duration of his #YearInSpace: Facebook, Twitter, Instagram. 

Make sure to follow us on Tumblr for your regular dose of space: http://nasa.tumblr.com

Flying Across The Universe Part 2 (From Top to Bottom: Cone Nebula, Omega Nebula, Carina Nebula, and Lupus 3)

(Part 1)

Credit: ESO.org