I Got A Migraine And Threw Up Because Of This

Raspberry Multiverse

Stephen Hawking’s Grand design is leading to a non symmetric multiverse. However there is reason to suggest a full symmetric multiverse with point symmetry at the centre of a raspberry shaped pulsating bubble multiverse. For an entangled multiverse, each quantum should have its own 12 fold entanglement relation to all 12 opposite (anti) quantums, each located inside one of the 12 universes. The result is called: Poincaré dodecahedral space symmetry.  (see also below: B.F.Roukema) A dodecahedron is also called “Buckyball” An other evidence for space symmetry and the centre of the multiverse is the so called DARK FLOW. Dark flow seems to be found at the edge of the visible universe!! There the “dark flow centre is represented by a so called "Pitch of spacetime”

Fibonacci Sculptures - Part II

These are 3-D printed sculptures designed to animate when spun under a strobe light. The placement of the appendages is determined by the same method nature uses in pinecones and sunflowers. The rotation speed is synchronized to the strobe so that one flash occurs every time the sculpture turns 137.5º—the golden angle. If you count the number of spirals on any of these sculptures you will find that they are always Fibonacci numbers.

© John Edmark

When 25,000 little dice are agitated in a cylinder, they form into neat concentric circles

Behold the magic of compaction dynamics. Scientists from Mexico and Spain dumped 25,000 tiny dice (0.2 inches) into a large clear plastic cylinder and rotated the cylinder back and forth once a second. The dice arranged themselves into rows of concentric circles. See the paper and the videos here.

https://boingboing.net/2017/12/05/when-25000-little-dice-are-ag.html

Neutron Stars Are Even Weirder Than We Thought

Let’s face it, it’s hard for rapidly-spinning, crushed cores of dead stars NOT to be weird. But we’re only beginning to understand how truly bizarre these objects — called neutron stars — are.

Neutron stars are the collapsed remains of massive stars that exploded as supernovae. In each explosion, the outer layers of the star are ejected into their surroundings. At the same time, the core collapses, smooshing more than the mass of our Sun into a sphere about as big as the island of Manhattan.

Our Neutron star Interior Composition Explorer (NICER) telescope on the International Space Station is working to discover the nature of neutron stars by studying a specific type, called pulsars. Some recent results from NICER are showing that we might have to update how we think about pulsars!

Here are some things we think we know about neutron stars:

Pulsars are rapidly spinning neutron stars ✔︎

Pulsars get their name because they emit beams of light that we see as flashes. Those beams sweep in and out of our view as the star rotates, like the rays from a lighthouse.

Pulsars can spin ludicrously fast. The fastest known pulsar spins 43,000 times every minute. That’s as fast as blender blades! Our Sun is a bit of a slowpoke compared to that — it takes about a month to spin around once.

The beams come from the poles of their strong magnetic fields ✔︎

Pulsars also have magnetic fields, like the Earth and Sun. But like everything else with pulsars, theirs are super-strength. The magnetic field on a typical pulsar is billions to trillions of times stronger than Earth’s!

Near the magnetic poles, the pulsar’s powerful magnetic field rips charged particles from its surface. Some of these particles follow the magnetic field. They then return to strike the pulsar, heating the surface and causing some of the sweeping beams we see.

The beams come from two hot spots… ❌❓✔︎ 🤷🏽

Think of the Earth’s magnetic field — there are two poles, the North Pole and the South Pole. That’s standard for a magnetic field.

On a pulsar, the spinning magnetic field attracts charged particles to the two poles. That means there should be two hot spots, one at the pulsar’s north magnetic pole and the other at its south magnetic pole.

This is where things start to get weird. Two groups mapped a pulsar, known as J0030, using NICER data. One group found that there were two hot spots, as we might have expected. The other group, though, found that their model worked a little better with three (3!) hot spots. Not two.

… that are circular … ❌❓✔︎ 🤷🏽

The particles that cause the hot spots follow the magnetic field lines to the surface. This means they are concentrated at each of the magnetic poles. We expect the magnetic field to appear nearly the same in any direction when viewed from one of the poles. Such symmetry would produce circular hot spots.

In mapping J0030, one group found that one of the hot spots was circular, as expected. But the second spot may be a crescent. The second team found its three spots worked best as ovals.

… and lie directly across from each other on the pulsar ❌❓✔︎ 🤷🏽

Think back to Earth’s magnetic field again. The two poles are on opposite sides of the Earth from each other. When astronomers first modeled pulsar magnetic fields, they made them similar to Earth’s. That is, the magnetic poles would lie at opposite sides of the pulsar.

Since the hot spots happen where the magnetic poles cross the surface of the pulsar, we would expect the beams of light to come from opposite sides of the pulsar.

But, when those groups mapped J0030, they found another surprising characteristic of the spots. All of the hot spots appear in the southern half of the pulsar, whether there were two or three of them.

This also means that the pulsar’s magnetic field is more complicated than our initial models!

J0030 is the first pulsar where we’ve mapped details of the heated regions on its surface. Will others have similarly bizarre-looking hotspots? Will they bring even more surprises? We’ll have to stay tuned to NICER find out!

And check out the video below for more about how this measurement was done.

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

Eclipse Across America

August 21, 2017, the United States experienced a solar eclipse! 

An eclipse occurs when the Moon temporarily blocks the light from the Sun. Within the narrow, 60- to 70-mile-wide band stretching from Oregon to South Carolina called the path of totality, the Moon completely blocked out the Sun’s face; elsewhere in North America, the Moon covered only a part of the star, leaving a crescent-shaped Sun visible in the sky.

During this exciting event, we were collecting your images and reactions online. 

Here are a few images of this celestial event…take a look:

This composite image, made from 4 frames, shows the International Space Station, with a crew of six onboard, as it transits the Sun at roughly five miles per second during a partial solar eclipse from, Northern Cascades National Park in Washington. Onboard as part of Expedition 52 are: NASA astronauts Peggy Whitson, Jack Fischer, and Randy Bresnik; Russian cosmonauts Fyodor Yurchikhin and Sergey Ryazanskiy; and ESA (European Space Agency) astronaut Paolo Nespoli.

Credit: NASA/Bill Ingalls

The Bailey’s Beads effect is seen as the moon makes its final move over the sun during the total solar eclipse on Monday, August 21, 2017 above Madras, Oregon.

Credit: NASA/Aubrey Gemignani

This image from one of our Twitter followers shows the eclipse through tree leaves as crescent shaped shadows from Seattle, WA.

Credit: Logan Johnson

“The eclipse in the palm of my hand”. The eclipse is seen here through an indirect method, known as a pinhole projector, by one of our followers on social media from Arlington, TX.

Credit: Mark Schnyder

Through the lens on a pair of solar filter glasses, a social media follower captures the partial eclipse from Norridgewock, ME.

Credit: Mikayla Chase

While most of us watched the eclipse from Earth, six humans had the opportunity to view the event from 250 miles above on the International Space Station. European Space Agency (ESA) astronaut Paolo Nespoli captured this image of the Moon’s shadow crossing America.

Credit: Paolo Nespoli

This composite image shows the progression of a partial solar eclipse over Ross Lake, in Northern Cascades National Park, Washington. The beautiful series of the partially eclipsed sun shows the full spectrum of the event. 

Credit: NASA/Bill Ingalls

In this video captured at 1,500 frames per second with a high-speed camera, the International Space Station, with a crew of six onboard, is seen in silhouette as it transits the sun at roughly five miles per second during a partial solar eclipse, Monday, Aug. 21, 2017 near Banner, Wyoming.

Credit: NASA/Joel Kowsky

To see more images from our NASA photographers, visit: https://www.flickr.com/photos/nasahqphoto/albums/72157685363271303

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

Interesting submission rk1232! Thanks for the heads up! :D :D

How is geometry entangled in the fabric of the Universe?

Geometry can be seen in action in all scales of the Universe, be it astronomical – in the orbital resonance of the planets for example, be it at molecular levels, in how crystals take their perfect structures. But going deeper and deeper into the fabric of the material world, we find that at quantum scale, geometry is a catalyst for many of the laws of quantum-physics and even definitions of reality.

Take for example the research made by Duncan Haldane, John Michael Kosterlitz and David Thouless, the winners of the 2016 Nobel prize in physics. By using geometry and topology they understood how exotic forms of matter take shape based on the effects of the quantum mechanics. Using techniques borrowed from geometry and topology, they studied the changes between states of matter (from plasma to gas, from gas to liquid and from liquid to solid) being able to generate a set of rules that explain different types of properties and behaviors of matter. Furthermore, by coming across a new type of symmetry patterns in quantum states that can influence those behaviors or even create new exotic types of matter, they provided new meaning and chance in using geometry as a study of “the real”.

If the Nobel Prize winners used abstract features of geometry to define physical aspects of matter, more tangible properties of geometry can be used to define other less tangible aspects of reality, like time or causality. In relativity, 3d space and 1d time become a single 4d entity called “space-time”, a dimension perceived through the eye of a space-time traveler. When an infinite number of travelers are brought into the equation, the numbers are adding up fast and, to see how for example, a space-time of a traveler looks for another traveler,  we can use geometric diagrams of these equations. By tracing what a traveler “sees” in the space-time dimension  and assuming that we all see the same speed of light, the intersection points of view between a stationary traveler and a moving one give a hyperbola that represents specific locations of space-time events seen by both travelers, no matter of their reference frame. These intersections represent a single value for the space-time interval, proving that the space-time dimension is dependent of the geometry given by the causality hyperbola.

If the abstract influence of geometry on the dimensions of reality isn’t enough,  take for example one of the most interesting experiments of quantum-physics, the double-split experiment, were wave and particle functions are simultaneously proven to be active in light or matter. When a stream of photons is sent through a slit against a wall, the main expectation is that each photon will strike the wall in a straight line. Instead, the photons are rearranged by a specific type of patterns, called diffraction patterns, a behavior mostly visible for small particles like electrons, neutrons, atoms and small molecules, because of their short wavelength.

Two slits diffraction pattern by a plane wave. Animation by Fu-Kwun Hwang 

The wave-particle duality is a handful, since it is a theory that has worked well in physics but with its meaning or representation never been satisfactorily resolved. Perhaps future experiments that will involve more abstract roles of geometry in quantum fields, like in the case of the Nobel prize winners, will develop new answers to how everything functions at these small scales of matter.

In this direction, Garret Lissi tries to explain how everything works, especially at quantum levels, by uniting all the forces of the Universe, its fibers and particles, into a 8 dimensions geometric structure. He suggests that each dot, or reference, in space-time has a shape, called fibre, attributed to each type of particle. Thus, a separate layer of space is created, parallel to the one we can perceive, given by these shapes and their interactions. Although the theory received also good reviews but also a widespread skepticism, its attempt to describe all known fundamental aspects of physics into one possible theory of everything is laudable. And proving that with laws and theories of geometry is one step closer to a Universal Geometry theory.

The Kakeya Problem

Some time ago I (briefly) mentioned that, along with two other students, I was taking a reading course this semester with Dmitriy Bilyk. It hasn’t quite gone in the direction we were initially expecting, but one of our long detours has been an extended sequence of readings around the the Kakeya conjecture. As far as I know, the Kakeya problem (different from the Kakeya conjecture; more on that later) was the first question that fell respectably under the purview of geometric measure theory. So if nothing else, it is interesting from a historical perspective as a question that kickstarted a whole new field of mathematics.

Okay, but what is the Kakeya problem?

As originally posed, it goes like this: given a disk with diameter 1, it is possible to place down a line segment of length 1 into the set, and rotate it (continuously) an entire 180 degrees. But this is not the smallest-area set for which this kind of rotation is possible:

(all pictures in the post are from the Wikipedia page, which is really good)

This set has area $\tau/16$, half that of the circle. So the question naturally becomes: what is the area of the smallest set that allows this kind of rotation?

The answer is known, and it is…

…

zero, basically.

It’s remarkable, but it’s true: you can construct arbitrarily small sets in which you can perform a 180-degree rotation of a line segment! One way to do it goes like this: in the picture above, we reduced the area of the circle by squeezing it until it developed three points. If we keep squeezing to get more points, then the solid “middle” becomes very small, and the tendrils get very thin, so the area keeps decreasing. However, we can still take a line segment and slowly, methodically, shift it back and forth between the set’s pointy bits, parallel-parking style, to eventually get the entire 180 degrees of rotation.

——

You can’t actually get a set with zero area to work. But the reason for that seemed more like a technicality than something actually substantial. So people changed the problem slightly to get rid of those concerns. Now, instead of trying to get a set where you can rotate a line segment through all 180 degrees, you just have to have a set where you can find a line segment in every direction. The difference being that you don’t need to guarantee any smooth way to “move between” these line segments.

Sets that work for the modified problem are often called Kakeya sets (although some people reserve that for the rotation problem and use Besicovitch sets for the modified one). And indeed, there are Kakeya sets which actually have zero area.

The details involved with going from “arbitrarily small” to “actually zero” are considerable, and we won’t get into them here. The following is a simplification (due to Perron) of Besicovitch’s original construction for the “arbitrarily small” case. We take a triangle which clearly has ½ of the directions the needle might possibly take, and split it up into several pieces in such a way that no directions are lost. Then we start to overlap those pieces to get a set (that still has segments in all the same directions) with much smaller area:

We can do this type of construction twice (one triangle “downward-facing” and the other “left-facing”) and then put those two sets together, guarantee that we get all of 180 degrees of directions.

This Besicovitch-Perron construction, itself, only produces sets which are “arbitrarily small”, but was later refined to go all the way to zero. Again, the technicalities involved in closing that gap are (much) more than I want to talk about now. But the fact that these technicalities can be carried out with the Besicovitch-Perron construction is what makes it “better” than the usual constructions for the original Kakeya problem.

——

I should conclude with a few words about the Kakeya conjecture, since I promised them earlier :)

Despite the essentially-solved status of these two classical Kakeya problems, there is at least one big question still left open. It is rather more technical than the original ones, and so doesn’t get a lot of same attention, but I’d like to take a stab at explaining what’s still current research in this sphere of ideas.

Despite the fact that Kakeya sets can be made to be “small” in the sense of measure, we still intuitively want to believe these sets are “big”. There are many ways we can formalize largeness of sets (in $\Bbb R^n$, in particular) but the one that seems to be most interesting for Kakeya things is the notion of Hausdorff dimension. I won’t define the term here, but if you’ve ever heard someone spouting off about fractals, you’ve probably heard the phrase “Fractals have non-integer dimension!”. This is the notion of dimension they’re talking about.

It is known that Kakeya sets in the plane have Hausdorff dimension 2, and that in general a Kakeya set in $n>2$ dimensions has Hausdorff dimension at least $\frac{n}{2}+1$. The proofs of these statements are… difficult, and the general case remains elusive.

One thing more: you can also formulate the Kakeya conjecture in finite fields: in this setting having “dimension $n$” in a vector space over the field $\Bbb F_q$ means that you have a constant times $q^n$ number of points in your set. Wolff proposed this “technicality-free” version in 1999 as a way to study the conjecture for $\Bbb R$. And indeed, a lot of the best ideas for the problem in $\Bbb R$ have come from doing some harmonic analysis on the ideas originally generated for the finite field case. 

But then in 2008 Zeev Dvir went and solved the finite field case completely. Which on one hand is great! But on the other hand, Dvir’s method definitely can’t be finessed to work in $\Bbb R$ so we still have work to do :P

——

Partially I wanted to write about this because it’s cool in its own right, but I must admit that my main motivation is a little more pragmatic. There was a talk at SEICCGTC 2017 which showed a surprising connection between the Kakeya problem and a certain combinatorial game. So if you think these ideas are at all interesting, you may enjoy reading the next two posts in this sequence about that talk.

[ Post 1 ] [ Next ]