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Quantumaniac is where it’s at - and by ‘it’ I mean awesome.

Over here I post a ton of physics / math / general interesting posts in an attempt to make your brain feel good. My aim is to be as informative as possible, all while posting fascinating things that hopefully enlighten us both a little to the mysteries of our truly wondrous universe(s?). Plus, how would you know if the blog exists or not unless you observe it? Boom, just pulled the Schrödinger’s cat card. Now you have to check it out - trust me, it said so in an equation somewhere.

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The Arms of M106 

The spiral arms of bright galaxy M106 sprawl through this remarkable multiframe portrait, composed of data from ground- and space-based telescopes. Also known as NGC 4258, M106 can be found toward the northern constellation Canes Venatici. The well-measured distance to M106 is 23.5 million light-years, making this cosmic scene about 80,000 light-years across. Typical in grand spiral galaxies, dark dust lanes, youthful blue star clusters, and pinkish star forming regions trace spiral arms that converge on the bright nucleus of older yellowish stars. But this detailed composite reveals hints of two anomalous arms that don’t align with the more familiar tracers. Seen here in red hues, sweeping filaments of glowing hydrogen gas seem to rise from the central region of M106, evidence of energetic jets of material blasting into the galaxy’s disk. The jets are likely powered by matter falling into a massive central black hole.

Credit: Image Data - Hubble Legacy Archive, Robert Gendler, Jay GaBany, Processing - Robert Gendler, NASA

Trifid Nebula

Clouds of glowing gas mingle with dust lanes in the Trifid Nebula, a star forming region toward the constellation of the Archer (Sagittarius). In the center, the three prominent dust lanes that give the Trifid its name all come together. Mountains of opaque dust appear on the right, while other dark filaments of dust are visible threaded throughout the nebula. A single massive star visible near the center causes much of the Trifid’s glow.

The Trifid, also known as M20, is only about 300,000 years old, making it among the youngest emission nebulae known. The nebula lies about 9,000 light years away and the part pictured here spans about 10 light years.

Source: APOD

Mickey Mouse Crater on Mercury

NASA’s messenger spacecraft, in order around the planet Mercury, has found this giant crater (about 105 km wide) topped with two smaller impact basins that come together to form the recognizable Mickey Mouse shape. Messenger (short for Mercury Surface, Space Environment, Geochemistry and Ranging) mission scientists said: 

The shadowing helps define the striking ‘Mickey Mouse’ resemblance, created by the accumulation of craters over Mercury’s long geologic history.

This view of Mickey is a good example of pareidolia (another being the famous ‘face on Mars’), a phenomenon in which the human brain recognizes familiar shapes and characterizations in random images. 

Image Source: Flickr

Spaun - the Most Realistic Artificial Human Brain Yet

A group of neuroscientists and software engineers at the University of Waterloo in Canada are claiming to have built the world’s most complex, large-scale model simulation of the human brain. The simulated brain, which runs on a supercomputer, has a digital eye which it uses for visual input, a robotic arm that it uses to draw its responses — and it can pass the basic elements of an IQ test.

The brain, called Spaun (Semantic Pointer Architecture Unified Network), consists of 2.5 million simulated neurons, allowing it to perform eight different tasks. These tasks range from copy drawing to counting, to question answering and fluid reasoning. At this point, you should watch the video below to get a rough idea of how Spaun works — and then read on to find out why Spaun is so interesting.

Now, the nitty-gritty details. Spaun has a 28×28 (784-pixel) digital eye, and a robotic arm which can write on some paper. Every interaction with Spaun is through its 784-pixel eye. The scientists flash up a bunch of numbers and letters, which Spaun reads into memory, and then another letter or symbol acts as the command, telling Spaun what to do with its memory. The output of the task is then inscribed by the robotic arm.

Spaun’s brain consists of 2.5 million neurons that are broken down into a bunch of simulated cranial subsystems, including the prefrontal cortex, basal ganglia, and thalamus, which are wired together with simulated neurons that very accurately mimic the wiring of a real human brain. The basic idea is that these subsystems behave very similarly to a real brain: Visual input is processed by the thalamus, the data is stored in the neurons, and then the basal ganglia fires off a task to a part of the cortex that’s designed to handle that task.

All of this computation is performed in a physiologically accurate way, with simulated voltage spikes and neurotransmitters. Even the limitations of the human brain are simulated, as you can see in the video below, with Spaun struggling to store more than a few numbers in its short-term memory.

The end result is a brain that is mechanistically simple (2.5 million neurons isn’t really much to write home about), but which is surprisingly flexible. By implementing just a handful of very basic tasks, it’s interesting to see how complex behavior begins to emerge. There are some tantalizing hints as to how the brain evolved: starting with simple tasks, and then building upon and weaving them together to build complex functionality. 

Moving forward, the research team, led by Chris Eliasmith, wants to imbue Spaun with adaptive plasticity — the ability to rewire its neurons and learn new tasks simply by doing, rather than being pre-programmed. 


Videos of Spaun

Modeling the Price of Different Sized TVs

It really started with a joke.

“Oh, you need a new TV? You should get a 70 inch. Wait, what about the 80 inch TV? Well, those quite a bit more expensive than the 70 inch TV”

I really hadn’t looked carefully at TV prices so I wasn’t aware that the price increased dramatically with size. I’m aware now.

You can probably guess what comes next. Yes, I need to go to Amazon and look up the prices of different sized TVs. Now, there is a problem comparing TVs of different sizes. You could have a 42 inch TV with more features than a 60 inch and that could have an impact on the price. What I need are TVs that are the same model except for size. Fortunately, I was able to find some models just like that from Sharp, Samsung and Vizio. Along with this, I have the lowest prices for the different size ranges as advertised by the Walmart website.

Screenshot 1 18 13 1 50 pm

The different brands seems to be similar enough that we can look at this all as one set of data. So, what happens when you double the size of a TV? Does the price also double? No. A 40 inch TV is much less than half the cost of an 80 inch TV. Well maybe the size is proportional to the area of the TV.

First, let’s look at the listed “size” vs. the actual area. The standard measurement for a TV is to give the diagonal distance from one corner to the opposite. We also know that a standard HDTV has a 16:9 aspect ratio. Maybe this diagram will be useful.

Screenshot 1 19 13 7 56 pm

It doesn’t matter how big your TV is. If it’s an HDTV, the ratio of height to width will be 9/16. Here, I just have some constant in there (a) to get the actual size. Using the Pythagorean theorem, we can find the length of the diagonal based on the side lengths – you can see that parameter a survives. But this isn’t really right either. I want the area in terms of the quantity s (which I am using as the length of the diagonal). From this expression, I can get an expression for a in terms of s:

Screenshot 1 20 13 11 12 am

I probably shouldn’t have evaluated that square root since it looks like I will just square that value anyway. Now for the area (which I will label as A).

Screenshot 1 20 13 11 25 am

Let’s just check this really quickly. What if I have a 40 inch TV? It would have a height of 19.61 inches and a width of 34.86 inches. This would give it an area of 683.6 inch2. Now, if I use the above formula with a diagonal of 40 inches, I get the same value.

Now for the plot of TV price vs. screen area.

Screenshot 1 20 13 2 43 pm

That doesn’t look as linear as I would like it to be. Look at that 80 inch TV. It doesn’t fit very well with the linear function comparing area and price.

More Data

That doesn’t really improve anything. My last option is to forget about my first assumption. What if the different TV manufactures follow different models? Here is a plot of price vs. screen area for the Sharp, Target, and average Walmart TVs with separate linear fits.

Screenshot 1 21 13 7 59 am

This gives three different price functions for TVs in terms of screen area.  (Yes, I know I left off some of the brands of TVs – but they mostly fit with the lower sized models so I left them off for a cleaner graph)

Screenshot 1 21 13 8 03 am

What does this tell us? First, if Walmart sold a TV with no screen (zero area) – it would cost you -$21.64. Yes, they would have to give you money. This could be my new job – buying zero-inch TVs and collecting the money. But really, does this make sense? Yes. It must mean that if they are basing the price on the area of the TV then they are subsidizing this price. Otherwise, your Target TV would cost 21 dollars more. And look at the Sharp TVs. They have a zero-inch price of almost $4,000. Of course, maybe this just indicates the sale price of these devices and not an actual price. What do I know? I am just making up economic stuff here.

So, How Much? 

In this case, I have a question in my mind. What if there was a 100 inch TV? How much should that cost? What about a 200 inch TV? Of course, these are the diagonal measurements and not the area. So, let me re-write the price function in terms of diagonal size (s) instead of the area.

Screenshot 1 21 13 8 26 am

Now that the price is a function of size, I can just plop in the size to get a price. With this, a 100 inch TV should cost $10,706. A 200 inch TV would cost $54,806 dollars. That’s a serious TV. Now, this is just using the Sharp price function since I have data for larger TVs from them. What if Walmart made a 200 inch TV with their same pricing model? It would cost just $4,888. Not too bad.

One more thing. What if you want a free TV? How big would a Sharp TV be if it was free? Here, I can put in a price of zero dollars and then solve for the size.

Screenshot 1 21 13 8 35 am

That’s bigger than the TV I have right now. OK Sharp, I will take my free 52 inch TV. I will even pay for the shipping. Just send me an email and I will give you my address.

Oh – someone is probably going to ask if they can use my data.  Sure.  Here it is in a Google Docs spreadsheet.  Have with it.

Source: Dot Physics

Japan to Build World’s Largest Wind Farm

In the wake of the devastating 2011 earthquake and tsunami that struck the island nation, officials in Japan have announced plans for building the largest wind farm in the world. The country plans to eventually shut down all of its nuclear plants and replace them with wind and solar plants.

Currently, the largest wind farm in the world is off the coast of Suffolk in the U.K. Called the Greater Gabbard farm, it produces 504 megawatts of power using 140 turbines. The new farm planned for Japan is expected to produce 1 gigawatt using just 143 turbines.

Instead of anchoring each turbine directly to the ocean floor, the plan is to mount them on floating steel frames that will be anchored to the continental shelf below. To keep them upright, ballast will be used underneath. Construction of the huge wind farm is expected to be complete by 2020. Project managers say that sufficient testing has been done with the design to ensure the new farm will not be harmed by earthquakes, tsunamis or typhoons.


Is Pink a Color? 

MinutePhysics, a popular YouTube channel, posted a video a little while back saying that there is no pink light. This seems to have sparked a debate over whether or not pink is a color - an issue not really brought up by the original video. So, is pink a color? As usual, science is more complicated than you’d initially believe.

Since this is a physics blog, let’s go with the usual physical understanding of what ‘color’ is. Every color, effectively, is just a certain frequency of light. Electromagnetic radiation is characterized by its wavelength, frequency, intensity, etc. When the wavelength is within the visible spectrum (the range of wavelengths humans can visually perceive, approximately from 390 nm to 700 nm), it is known as “visible light,” a range which we breakdown as Roy G. Biv. 

There is no single frequency which our brains correspond to “pink” light. Then, how does pink exist? Effectively, pink is a combination of red and violet light - two colors from opposite sides of the visible spectrum. Since these two colors are literal opposites on the visible spectrum, pink could not exist as a fundamental frequency in nature (if you tried to average out the frequencies and “mix” them, you’d arrive at a color somewhere near the middle of the spectrum, around yellow or green). Thus, pink isn’t a fundamental frequency floating out there in space - a single frequency that we could call “pink” doesn’t exist. 

Hold on Tumblr bro, Pink obviously exists, I see it on Nicki Minaj all the time! 

Yes, yes - what we perceive as Pink does exist on its own, but does that necessarily make it a true color? Will Pink be excluded from the highly exclusive Color Club much like Pluto was ousted from the Planetary Patrol?

Take a second to look around you, you’ll see tons of objects - probably many colored ones. When you look at, for example, a red object - that object absorbs all of the other frequencies except red, and it reflects red back to you. However, when you look at a pink object - you are not seeing pink wavelengths of light. An object would appear pink because wavelengths of both red and violet are being reflected - and our brains perceive it as a new “color,” namely pink.

On a very fundamental level, pink is not a fundamental part of the universe - because no color is. The universe is chock full of electromagnetic radiation, and the only truly fundamental properties of it are wavelength, amplitude, frequency, etc. Color is a phenomenon completely produced by your brain - it’s how we perceive the light. Even different animals perceive light differently than us - like certain animals that can see beyond the visible spectrum, including infrared light. As biologist Timothy H. Goldsmith wrote for Scientific American, “color is not actually a property of light or of objects that reflect light, it is a sensation that arises within the brain.” So, by existing only as a human means of understanding the universe, pink is just as “real” as any other color. 

So, there you have it - pink is not a part of the light spectrum, it is the effect of our brains filling the gap between blue and violet, but does that make it any less of a color than anything else? 

Let’s look at two common definition for what a color is - one artistic and one scientific. 

Scientific Definition: The sensation produced by the effect of light waves striking the retina of the eye. The color of something depends mainly on which wavelengths of light it emits, reflects, or transmits.

Artistic Definition: Color is the element of art that is produced when light, striking an object, is reflected back to the eye.

While there is no fundamental definition of color in all respects, personally, I’d say that pink fits both of these descriptions. Since no color is a fundamental property of the universe, pink does not exist as a part of the visible spectrum, but since all colors are just fabrications of our brain, I have to side with pink here. There are intelligent people on both sides of this debate, and one’s interpretation of definition seems to be how one decides whether to draw the line or not to exclude pink. Where do you stand?

Further Reading

Physics of a Broken Swing Image

Surely by now, someone online has clearly shown this image to be fake. Instead, let’s use this as an example looking at the way people think about forces and motion.

  • Forces and Circular Motion

Suppose something is moving around in a circle. Maybe it is a amusement park swing. Here is a force diagram for one of the riders:

Screenshot 1 17 13 2 21 pm

There are only two forces on the swinger. There is of course the gravitational force pulling down. The only other force is the tension in the chain pulling on the swinger in the direction of the chain. Then why does the swinger move in a circular path? A component of the tension force pulls up to counter act the gravitational force. The other part of the tension from the chain pulls towards the center of the circle. It is this part of the tension force that makes the swinger move in a circle.

If you like, you can break all forces into two types. If a force is in the same (or opposite) direction as the motion (velocity) of an object, that force will cause the speed to either increase or decrease. If the force is perpendicular to the direction of the velocity, this force will cause the object to change directions. Of course you can have a force that both speeds up an object and causes it to turn.

Really, that is it. That is the only physics that you need to get this swinger to move around in a circle. Sure, there is a relationship between the angle the swing is at and the speed that the swinger moves, but for now we can leave that alone.

  • What Would Really Happen?

If the chain suddenly breaks, what happens next? Well, the force diagram becomes a little bit simpler. It would just look like this:

Screenshot 1 17 13 3 13 pm

This gravitational force would cause the velocity to change in the downward direction. So, clearly, it would fall down since before the chain broke it wasn’t moving in the vertical direction at all. But what else would it do? Here is a diagram of the swinger from the top view.

Screenshot 1 17 13 3 18 pm

In this view (after the chain broke), you can’t see the only force pulling on the swinger – the gravitational force is pulling down. Since there aren’t any forces pushing the swinger to the left or right, from the top the swinger would just go in a straight line.

In the faked image, the falling swinger is clearly moving away from the swing in a path perpendicular to the way he was originally moving.

  • Why Would a Faker Get This Wrong?

Many people seem to think that if an object is moving in a circle there is a force pushing outward from the center of the circle. This is the fabulous and mythical centrifugal force. Even though the centrifugal force is fake, it can still be useful in some ways. However, the point is that if you are in a stationary frame then there IS NO force pushing outward.

1: (Source)

2: (Source)

Kurt Gödel - Logician and Interesting Figure

Kurt Gödel was an Austrian-American mathematician, philosopher - and is considered one of the most significant logicians in human history, comparable to figures like Aristotle. Gödel is best known for his two incompleteness theorems, published in 1931 when he was 25 years old, as well as making important contributions to proof theory. 

  • He was bros with Einstein. 

He’s also rather well known for a strong friendship with Albert Einstein, who found themselves living in Princeton at the same time. They both worked at the Princeton Institute for Advanced Study, and were known to take long walks together to and from work. The nature of their conversations was a mystery to the other Institute members. Economist Oskar Morgenstern recounts that toward the end of his life Einstein confided that his “own work no longer meant much, that he came to the Institute merely…to have the privilege of walking home with Gödel”.

  • He found a loophole in the U.S. Constitution. 

On December 5, 1947, Einstein and Morgenstern accompanied Gödel to his U.S. citizenship exam, where they acted as witnesses. Gödel had confided in them that he had discovered an inconsistency in the U.S. Constitution, one that would allow the U.S. to become a dictatorship. Einstein and Morgenstern were concerned that their friend’s unpredictable behavior might jeopardize his chances. Fortunately, the judge turned out to be Phillip Forman. Forman knew Einstein and had administered the oath at Einstein’s own citizenship hearing. Everything went smoothly until Forman happened to ask Gödel if he thought a dictatorship like the Nazi regime could happen in the U.S. Gödel then started to explain his discovery to Forman. Forman understood what was going on, cut Gödel off, and moved the hearing on to other questions and a routine conclusion.

  • He starved himself to death. 

In the later years of his life, Gödel had an obsessive fear of being poisoned. He refused to eat any food that hadn’t been prepared by his wife, Adele. Late in 1977, Adele was hospitalized for six months. During her absence, he refused to eat, eventually starving to death. He weighed 65 pounds (approximately 30 kg) when he died.

Stickney Crater - Phobos

Stickney Crater, the largest crater on the martian moon Phobos, is named for Chloe Angeline Stickney Hall, mathematician and wife of astronomer Asaph Hall. Asaph Hall discovered both the Red Planet’s moons in 1877. Over 9 kilometers across, Stickney is nearly half the diameter of Phobos itself, so large that the impact that blasted out the crater likely came close to shattering the tiny moon. This stunning, enhanced-color image of Stickney and surroundings was recorded by the HiRISE camera onboard the Mars Reconnaissance Orbiter as it passed within some six thousand kilometers of Phobos in March of 2008. Even though the surface gravity of asteroid-like Phobos is less than 1/1000th Earth’s gravity, streaks suggest loose material slid down inside the crater walls over time. Light bluish regions near the crater’s rim could indicate a relatively freshly exposed surface. The origin of the curious grooves along the surface is mysterious but may be related to the crater-forming impact.