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RIP Professor Maryam Mirzakhani
Professor Maryam Mirzakhani, the first woman awarded the Fields Medal prize died of breast cancer on 15 July 2017. Read this informative tribute by +John Baez.
Maryam Mirzakhani, 1977 - 2017

She died yesterday, a mathematician who had not yet reached the height of her powers: the first Fields medalist from Iran, and also the first woman to win that honor. Here's what I wrote when she won:

As a child in Tehran, she didn't intend to become a mathematician - she just wanted to read every book she could find! She also watched television biographies of famous women like Marie Curie and Helen Keller. She started wanting to do something great... maybe become a writer.

She finished elementary school while the Iran-Iraq war was ending, and took a test that got her into a special middle school for girls. She did poorly in math her first year, and it undermined her confidence. “I lost my interest in math," she said.

But the next year she had a better teacher, and she fell in love with the subject. She and a friend became the first women on Iranian math Olympiad team. She won a gold medal the first year, and got a perfect score the next year.

After getting finishing her undergraduate work at Sharif University in Tehran in 1999, she went on to grad school at Harvard. There she met Curtis McMullen, a Fields medalist who works on hyperbolic geometry and related topics.

Hyperbolic geometry is about curved surfaces where the angles of a triangle add up to less than 180 degrees, like the surface of a saddle. It's more interesting than Euclidean geometry, or the geometry of a sphere. One reason is that if you have a doughnut-shaped thing with 2 or more holes, there are many ways to give it a hyperbolic geometry where its curvature is the same at each point. These shapes stand at the meeting-point of many roads in math. They are simple enough that we can understand them in amazing detail - yet complicated enough to provoke endless study.

Maryam Mirzakhani took a course from McMullen and started asking him lots of questions. “She had a sort of daring imagination,” he later said. “She would formulate in her mind an imaginary picture of what must be going on, then come to my office and describe it. At the end, she would turn to me and say, ‘Is it right?’ I was always very flattered that she thought I would know.”

Here's a question nobody knew the answer to. If an ant walks on a flat Euclidean plane never turning right or left, it'll move along a straight line and never get back where it started. If it does this on a sphere, it will get back where it started: it will go around a circle. If it does this on a hyperbolic surface, it may or may not get back where it started. If it gets back to where it started, facing the same direction, the curve it moves along is called a closed geodesic.

The ant can go around a closed geodesic over and over. But say we let it go around just once: then we call its path a simple closed geodesic. We can measure the length of this curve. And we can ask: how many simple closed geodesics are there with length less than some number L?

There are always only finitely many - unlike on the sphere, where the ant can march off in any direction and get back where it started after a certain distance. But how many?

In her Ph.D. thesis, Mirzakhani figured out a formula for how many. It's not an exact formula, just an 'asymptotic' one, an approximation that becomes good when L becomes large. She showed the number of simple closed geodesics of length less than L is asymptotic to some number times L to the power 6g-6, where g is the number of holes in your doughnut.

She boiled her proof down to a 29-page argument, which was published in one of the most prestigious math journals:

• Maryam Mirzakhani, Growth of the number of simple closed geodesics on hyperbolic surfaces, Annals of Mathematics 168 (2008), 97–125,

This is a classic piece of math: simple yet deep. The statement is simple, but the proof uses many branches of math that meet at this crossroads.

What matters is not just knowing that the statement is true: it's the new view of reality you gain by understanding why it's true. I don't understand why this particular result is true, but I know that's how it works. For example, her ideas also gave here a new proof of a conjecture by the physicist Edward Witten, which came up in his work on string theory!

This is just one of the first things Mirzakhani did. She's now a professor at Stanford.

"I don't have any particular recipe," she said. "It is the reason why doing research is challenging as well as attractive. It is like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out."

She has a lot left to think about. There are problems she has been thinking about for more than a decade. "And still there’s not much I can do about them," she said.

"I can see that without being excited mathematics can look pointless and cold. The beauty of mathematics only shows itself to more patient followers."

I got some of my quotes from here:

and some from here:

They're both good to read. For a mathematically informed obituary, see this by Terry Tao:

The animated gif is a clip from this video:


Animated Photo

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+John Baez on the science of red sprites: "Sprites are quite different from lightning. They're not electric discharges moving through hot plasma. They involve cold plasma - more like a fluorescent light."
Red sprites

Far above a thunderstorm in the English Channel, red sprites are dancing in the upper atmosphere.

You can't usually see them from the ground - they happen 50 to 90 kilometers up. People usually photograph them from satellites or high-flying planes. But this particular bunch was videotaped from a distant mountain range in France by Stephane Vetter, on May 28th.

Sprites are quite different from lightning. They're not electric discharges moving through hot plasma. They involve cold plasma - more like a fluorescent light.

They're quite mysterious. People with high speed cameras have found that a sprite consists of balls of cold plasma, 10 to 100 meters across, shooting downward at speeds up to 10% the speed of light... followed a few milliseconds later by a separate set of upward moving balls!

Sprites usually happen shortly after a lightning bolt. And about 1 millisecond before a sprite, people often see a sprite halo: a faint pancake-shaped burst of light approximately 50 kilometres across 10 kilometres thick.

Don't mix up sprites and ELVES - those are something else, for another day:

You also shouldn't confuse sprites with terrestrial gamma-ray flashes. Those are also associated to thunderstorms, but they actually involve antimatter:

A lot of weird stuff is happening up there!

The photo is from here:


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Hidden Secrets of Parasitic Plants
Dr +Tommy Leung has written about a common but mysterious parasite, buried deep in the roots of other trees and plants in Brazil (and also found in other parts of Central and South America). Unlike other plant parasites, the Langsdorffia hypogaea is is wholly dependant on its host. Unless you know what to look for, this parasite will easily escape your gaze; however, once you recognise its red, mushroom-like flowers, you'll find they are widespread. The flowers only appear during the dry seasons and it is the only external signs of this parasitic plant. Dr Leung writes:

Parasitic plants are important parts of many ecosystems due to the wide range of organisms they interact with. While they can be detrimental to the host plant's growth and reproduction, they are also a food source for many animals. For most parasitic plants very little is known about their basic natural history, let alone the impact they have on the surrounding environment.

Find out about how this parasitic plant pollinates and its secrets yet to be uncovered by science.
Red Flowers And Parasitic Tubers
I've written a new Parasite of the Day post! This one is about a type of parasitic plant from Central and South America that lives as a parasitic tuber attached to the roots of its host plant, and sprouts red flowers that pokes out the ground like mushrooms. To read more about this parasitic plant, follow the link below.

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Very interesting article by +Neha Jain  on the use of natural anti-microbal "cocktails" by ants.

To test if ants enhance the antimicrobial properties of resin, Chapuisat and his team enclosed worker ants with resin and nest materials, such as twigs and small stones, for two weeks. They found that resin that had been in contact with the ants provided greater protection against the fungus Metarhizium brunneum—which can be deadly—than resin kept away from ants.

Please read the full article on the link on .

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On any given day, about 90,000 kilograms of dust and small rocks hit the Earth. What happens when something larger is on a collision course with Earth?

Asteroid Hunters by Carrie Nugent was quite an enjoyable read. It's short, informative, and quite relevant as the recent fly-by of "2014 JO25", an asteroid with a diameter of 650 meters demonstrated.

If you've ever been interested in how scientists really detect potential planet (or hemisphere) killer, or how they might deflect them then this is an excellent book to start with.

read more on  (includes link to a TED Talk on the subject).

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Have you seen this article claiming, "Ancient stone carvings confirm how comet struck Earth in 10,950BC, sparking the rise of civilisations."? The paper behind this claim has some inconsistencies with established research. First, the authors are not experts in the field of archaeology nor astronomy. Second, the researchers base their interpretations on the works of discredited authors. Third, there is no evidence of the population decline they claim. Read more from +Jeff Baker, who argues: "This is a poorly researched paper that should not be getting the attention it is currently receiving." 
When I first saw this article in my stream, I was skeptical of the findings. The first thing I noticed was that the primary author is in an engineering department. Martin Sweatman is apparently a chemical engineer. There is nothing about his biography with the University of Edinburgh to suggest he has the background to discuss either astronomical theories or archaeological theories.

His co-author on the paper is a bioengineer who has done research into Parkinson’s Disease. Again, his biography doesn’t suggest he has any expertise in astronomy or archaeology.

In the Telegraph article, they acknowledge that some of their interpretations of the images at Gobekli Tepe were originally made by Graham Hancock. Among Hancock’s other arguments are that Antarctica is Plato’s Atlantis. The civilization Plato described is, according to Hancock, buried under the ice sheet. Hancock claims that Antarctica was originally located in the mid-Atlantic, but, galloping plate tectonics shifted the location of the continent to the South Pole, in less than a generation.

Looking at the article (which you can read here: ), they start out citing Clube and Napier for the astronomy portion of their paper. I had never heard of these two astronomers nor their Neo-Catastrophist theories, so I googled them. I came upon this critique of their theories:

Basically, it is a crap theory that doesn’t fit with any established astronomical model. Oh, and Clube and Napier cite Velikovsky, like Hancock he is a pseudo-scientist/charlatan.

After discussing Clube and Napier, Sweatman and Tsikritsis mention the Washington Scablands as evidence of rapid melting of the glaciers. The Scablands were created by a series of large scale floods involved with the release of water from the Pleistocene Lake Missoula. Geologists estimate these floods occurred between 18,000 and 13,000 years ago.

The carvings at Gobekli Tepe are thought to date to ca. 9,000 BCE, or 2,000 years after the beginning of the Younger Dryas (which Sweatman and Tsikritsis argue was caused by fragments of a comet hitting North America).

They further argue that the animals depicted on the pillars are similar to constellations that, according to a computer model, would have been visible in the sky ca. 11,000 BC. This is an extreme leap of logic. We have no way of knowing what constellations the inhabitants of that time period would have seen in the night sky. That people 2,000 years later would still use the same names is a stretch. Without a written language, which wasn’t developed for another 6,000 years, it is unlikely that the same names would have remained as the “constellations” changed shape.

These two authors also claim that there was a catastrophic population decline associated with the Younger Dryas. There is, to my knowledge, no evidence for such an event. Even in North America, the possibility of a large scale population decline is disputed.

This is a poorly researched paper that should not be getting the attention it is currently receiving.

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Tribute to Astrophysicist Vera Rubin, the "Mother" of Dark Matter
Astrophysicist Professor Vera Rubin, National Medal of Science awardee who confirmed the existence of dark matter, died on 25 December 2016.

Dark matter is "the invisible material that makes up more than 90% of the mass of the universe." Rubin's pioneering work progressed from 1965 to the late 1970s. Her webpage describes the beginning of this discovery:

"By the late 1970s, after Rubin and her colleagues had observed dozens of spirals, it was clear that something other than the visible mass was responsible for the stars’ motions. Analysis showed that each spiral galaxy is embedded in a spheroidal distribution of dark matter — a “halo.” The matter is not luminous, it extends beyond the optical galaxy, and it contains 5 to 10 times as much mass as the luminous galaxy. The stars' response to the gravitational attraction of the matter produces the high velocities. As a result of Rubin's groundbreaking work, it has become apparent that more than 90% of the universe is composed of dark matter."

Rubin's research remained prolific until the early 2000s, as she continued to study various models for the composition of the dark halos. Among her most recent publications was an examination of the rotation curves of spiral galaxies.

Until her retirement, Rubin worked at the Carnegie Institution for Science Department of Terrestrial Magnetism in Washington, D.C. She was awarded the National Medal of Science in 1993. She was also a member of the National Academy of Sciences and in 1996, she received the Royal Astronomical Society’s Gold Medal, the first woman to do so 168 years after Caroline Hershel (1828).

Neta Bahcall of Princeton University describes Rubin's scientific significance: “A pioneering astronomer, the ‘mother' of flat rotation curves and dark-matter, a champion of women in science, a mentor and role model to generations of astronomers.”

Carnegie Science describes Rubin's scientific impact extends far beyond her pioneering research: "She was an ardent feminist, advocating for women observers at the Palomar Observatory, women at the Cosmos Club, Princeton, and she even advised the Pope to have more women on his committee."

See +Yonatan Zunger's tribute to Professor Rubin in the linked post.

Learn more
Read some background on Rubin from Carnegie Science:

See Rubin's biography and publications: #stemwomen #astrophysics #astronomy
And in the continuing march of the Angel of Death, I am sad to report that Vera Rubin died today at the age of 88. Rubin was most famous as the discoverer of dark matter: the invisible and still-mysterious substance which makes up 85% of the mass of the universe.

Dark matter had been hypothesized back in the 1930's, but it wasn't until the 1970's that it was finally observed. Rubin was studying distant galaxies when she noticed that the rotation speed of their outer edges didn't jibe with the speed they should have based on the amount of visible matter.

You can tell how fast something is moving relative to you using the Doppler effect: the same thing that makes a siren sound higher-pitched as it moves towards you and lower-pitched as it moves away. It works because sound looks like a sine wave of rising and dropping pressure, and pitch corresponds to the time between successive peaks. When the source is moving towards you, the first peak emitted by the siren is already moving towards you at the speed of sound, but the second peak will get there sooner than expected, because it had the benefit of moving towards you at the siren's speed for one more period and then being sent off at the speed of sound. This means that if you know the original pitch of the siren, you can even figure out how fast it's moving based on the pitch you hear.

The same trick works with light, only now instead of pitch, it's color that depends on the time between peaks; things appear bluer when they approach, and redder when they recede. Since starlight contains a lot of easily measured standard lights in it - colors like those that Hydrogen and Helium emit when heated, and which have a very distinct pattern when viewed through a prism - we can measure the speed of distant stars and galaxies. And by comparing the speed of the left and right edges of a galaxy, you can tell how fast it's spinning.

But we've known how to calculate the orbits of stars since Kepler, and from the amount of light a galaxy emits, we can make a pretty good guess at how heavy it is. From that, you would conclude that the stars at the outside of a galaxy should be moving more slowly than the ones at its center, in a nicely predictable way.

But that's not what Rubin saw! Instead, she discovered that the stars at the outside were moving at the same speed as the ones at the center - something only possible if there was some extra, invisible mass pulling them.

What Rubin discovered was that there is an invisible halo of "dark matter" surrounding each galaxy, nearly ten times as massive as the galaxy itself. It's "dark" in the plainly literal sense: unlike stars, it's not actively on fire and glowing.

In the decades since, dark matter has become a core area of study in astrophysics. Using the same techniques and ever-more-sophisticated telescopes, including dedicated satellite observatories, we've mapped the presence and motion of dark matter in greater detail, and discovered that it's far more mysterious than we first suspected. For example, we know it's not made up of ordinary atomic or molecular stuff, because its dynamics is all wrong; neither is it made up of massive neutrinos or any other kind of matter we understand.

(There's also dark energy, an even more widespread and invisible field, discovered a few decades later. Unlike dark matter, which attracts things by gravity, dark energy seems to provide a universe-spanning, diffuse, but very distinctly measurable repulsive force. It's even less understood than dark matter; most scientists suspect that if we understood these things well, we'd know a lot more about the nature of the universe)

Rubin therefore sits in the pantheon of the great astronomers of the 20th century. Alas, her death means she will not get the Nobel Prize that many have been arguing she deserves for a very long time: the prize cannot (by the terms of its founding grant) be awarded posthumously. But she remains one of the most important researchers in the field, and her work will continue to have a profound impact on our understanding of Nature for generations to come.

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Community Service Announcement
About a month ago, several members of our Community shared an important but disturbing article on Medium revealing that we had an abuser in our midst. You can read the original and continually updated post here:

As the story gained traction and readership, more and more people - many of them friends, colleagues, and associates of our Science on Google+ community - came forward with their own contributions and acknowledgments of abuse: psychological manipulation, financial malfeasance amounting to tens of thousands of dollars, emotional abuse, sexual assault. The damage has been wide-ranging and traumatic.

Situations like this are shocking to anyone of good conscience, and this case strikes particularly close to home: the perpetrator, Scott Lewis, was formerly a moderator in this community. We were not aware of his abusive behavior during his brief tenure as a moderator, and his profile has been removed from our Member list. We at Science on Google+ absolutely reject and oppose his deplorable, harmful actions. We are aware that Scott used his position as a moderator of our community to leverage other science outreach opportunities with various organisations such as Hubble Space Telescope and the Space Telescope Science Institute. In an effort to prevent him from continuing to leverage our name, we issue this unequivocal statement denouncing his behavior.

Scott exploited our trust and his position of modest influence to take advantage of community members - you, the heart of this community; members of the moderation team; and others directly or indirectly associated with Science on Google+ - for his own personal and nefarious gain. In this circumstance as in our daily science and science communication, we feel a strong obligation to:

- Disclosure
- Clarity, Transparency, and Openness
- and Support

As such, while being respectful of the privacy of the victims of this exploitation, we offer this post to ensure that everyone is aware of these events and we offer these resources to help any victims who have not yet come forward:

A. Because of the expanding scope of this situation, the volunteers who published the original article also launched an informal and private support network for victims. If you feel the need, if you have been victimized or can add your voice to the existing chorus of supporters, please visit the link at the top of this post and message the good folks who brought us awareness.

B. Please feel free to post in the Guidelines/Feedback to Mods section of our community, but NOTE THAT WE ARE NOT ABLE TO OFFER CONFIDENTIALITY IF YOU POST IN SCIENCE ON GOOGLE+.

C. Feel free to direct message any of the community moderators, but know that we are not professional counselors and will likely refer you to resources better equipped to provide assistance (some are linked in the original Medium article). We would also like to direct your attention to a well constructed guide that +A.V. Flox recently put together regarding abuse and intervention. You can view the guide by clicking on the following link:

If you number among the victims, know that you did not bring this upon yourself and that you are not alone. We are, as always, here to help in whatever capacity we are able. You are why we built and maintain this community, and we very much want it to be a friendly, safe, and educational place to visit. We value you tremendously.

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Fond memories
Do you know the difference between semantic and episodic memory? If not read on.
Remember, it's #FidoFriday.
Fugazza et al, recently published work demonstrating that dogs have episodic-like memory. What's episodic memory? It's your personal recollection of an event, but not to be confused with autobiographical memory. Semantic memory is recollection of facts, e.g., knowing the capital of Iowa. To distinguish between episodic memory and autobiographical memory, remember autobiographical memory includes semantic memory, e.g., the names of the places in your memories.

In this study, dogs were trained to mimic the trainer when the trainer gave the command "do it". It's called Do as I Do training. To get at episodic memory, the dogs were then trained to lie down after watching the owner do a task, like touch an umbrella or jump over a chair. Then the dogs were surprised by being asked, "do it". They had to remember what was done 1 minute earlier and 1 hour earlier. As with many of us, the dogs did much better at the shorter delay of 1 minute.

You can read more about memory types here:
Episodic Memory: Definition and Examples

The full article is here:
Recall of Others’ Actions after Incidental Encoding Reveals Episodic-like Memory in Dogs

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The importance of Peer Review
+Brian Koberlein explains a bit about EM drive and the importance of peer review.
Jury Of One's Peers

The reactionless thruster known as the EM Drive has stirred heated debate over the past few years. If successful it could provide a new and powerful method to take our spacecraft to the stars, but it has faced harsh criticism because the drive seems to violate the most fundamental laws of physics. One of the biggest criticisms has been that the work wasn’t submitted for peer review, and until that happens it shouldn’t be taken seriously. Well, this week that milestone was reached with a peer-reviewed paper. The EM Drive has officially passed peer review.

It’s important to note that passing peer review means that experts have found the methodology of the experiments reasonable. It doesn’t guarantee that the results are valid, as we’ve seen with other peer-reviewed research such as BICEP2. But this milestone shouldn’t be downplayed either. With this new paper we now have a clear overview of the experimental setup and its results. This is a big step toward determining whether the effect is real or an odd set of secondary effects. That said, what does the research actually say?

The basic idea of the EMDrive is an asymmetrical cavity where microwaves are bounced around inside. Since the microwaves are trapped inside the cavity, there is no propellent or emitted electromagnetic radiation to push the device in a particular direction, standard physics says there should be no thrust on the device. And yet, for reasons even the researchers can’t explain, the EM Drive does appear to experience thrust when activated. The main criticism has focused on the fact that this device heats up when operated, and this could warm the surrounding air, producing a small thrust. In this new work the device was tested in a near vacuum, eliminating a major criticism.

What the researchers found was that the device appears to produce a thrust of 1.2 ± 0.1 millinewtons per kilowatt of power in a vacuum, which is similar to the thrust seen in air. By comparison, ion drives can provide a much larger 60 millinewtons per kilowatt. But ion drives require fuel, which adds mass and limits range. A functioning EM drive would only require electric power, which could be generated by solar panels. An optimized engine would also likely be even more efficient, which could bring it into the thrust range of an ion drive.

While all of this is interesting and exciting, there are still reasons to be skeptical. As the authors point out, even this latest vacuum test doesn’t eliminate all the sources of error. Things such as thermal expansion of the device could account for the results, for example. Now that the paper is officially out, other possible error sources are likely to be raised. There’s also the fact that there’s no clear indication of how such a drive can work. While the lack of theoretical explanation isn’t a deal breaker (if it works, it works), it remains a big puzzle to be solved. The fact remains that experiments that seem to violate fundamental physics are almost always wrong in the end.

I’ve been pretty critical of this experiment from the get go, and I remain highly skeptical. However, even as a skeptic I have to admit the work is valid research. This is how science is done if you want to get it right. Do experiments, submit them to peer review, get feedback, and reevaluate. For their next trick the researchers would like to try the experiment in space. I admit that’s an experiment I’d like to see.

Paper: Harold White, et al. Measurement of Impulsive Thrust from a Closed Radio-Frequency Cavity in Vacuum. Journal of Propulsion and Power. DOI: 10.2514/1.B36120 (2016)

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