Weekend Diversion: An Optical Illusion For Your Ears

The sounds you hear are affected by what you see. Experience it for yourself!


“It is the function of art to renew our perception. What we are familiar with we cease to see. The writer shakes up the familiar scene, and, as if by magic, we see a new meaning in it.” -Anais Nin

We’re all used to trusting our senses for information about this world. And while there are certainly plenty of illusions that lead us astray, they almost always come up as tricks that our eyes play on us. Have a listen to Thievery Corporation’s song, The Supreme Illusion,

https://play.spotify.com/track/2T6WDL5LJmT85XdN6Uz1jz

while I introduce you to a whole kind of illusion that involves your ears!

Image credit: Fromkin, Victoria and Robert Rodman. An Introduction to Language. 5th ed. Fort Worth: Hartcourt Brace Jovanovich College Publishers, 1993. Via http://www2.uncp.edu/home/canada/work/caneng/phono.htm.

You all know how to pronounce the different consonants, and how to make a plethora of different sounds with your mouth. For example, if you wanted to make the “B” sound, you’d purse your lips together, and burst them outwards at the moment you wanted to create that distinctive “B”.

In fact, just by looking at a snapshot of someone’s mouth, you can often tell what the next consonant sound they make is going to be!

Image credit: screenshot from BBC Two.

Well, looking at someone’s mouth who’s about to make that “B” sound, you’d most certainly never confuse it with a sound that you make by blowing air between your upper teeth and your bottom lip, like the “F” sound. Right? I mean, it’s hard to get more different — from a consonant perspective — than those two sounds.

The “F” sound is unmistakeable, right?

Image credit: screenshot from BBC Two.

Believe it or not, if you listen to the “B” sound while you watch someone’s mouth go through the motions of an “F” sound, you will hear the “F”!

Not only will you hear the “F” sound, but you’ll even hear it even if you know it’s coming. And it’s coming.

Try it. Watch the video below.

https://www.youtube.com/watch?v=G-lN8vWm3m0

This amazing phenomenon is known as the McGurk effect, and I must have watched the above video five or six times already, because no matter how hard I try, my sight overrules my ears! With other optical illusions, I can sometimes overrule them and “see through” the illusion once I’ve figured it out, but I can’t with this one. The only way to overcome it, as far as I can tell, is to close my eyes. Only then do I always hear the true sound.

So I went to look for other examples, and look what else it works with!

https://www.youtube.com/watch?v=aFPtc8BVdJk

Do you hear the “Ga” (or maybe the “Ca” or “Da”) sound coming out of this guy’s mouth? Replay it and close your eyes, and listen again. Your brain pulls both the audio and visual stimuli together and does its best to interpret the confusing signals, but this illusion is incredibly robust!

Image credit: Esther Wiersinga-Post (edits by me), via http://www.ai.rug.nl/nl/project/integratie.html.

There are all kinds of videos of this illusion out there, but what I’m most fascinated by is that some types of brain damage to the left hemisphere, increase the effect, while other types as well as disorders such as dyslexia, autism, alzheimer’s or schizophrenia lead to reduced McGurk effects.

This is the first hearing illusion I’ve ever come across, and this is a spectacular one. (If you haven’t checked out our Comments of the Week this week, go and check it out.) Hope you enjoyed it, and have a great weekend, too!


A version of this post originally appeared on Scienceblogs. If you have a question or comment, head over there to the Starts With A Bang forum and weigh in!

Next Story — How did the Universe get its first supermassive black holes?
Currently Reading - How did the Universe get its first supermassive black holes?

Illustration of the distant galaxy CR7, which last year was discovered to house a pristine population of stars formed from the material direct from the Big Bang. Image credit: M. Kornmesser / ESO.

How did the Universe get its first supermassive black holes?

How they get so big so fast is a mystery. Could “direct collapse” be the solution we’re seeking?


“For something to collapse, not all systems have to shut down. In most cases, just one system is enough.” -Robert Kiyosaki

At the center of almost every large galaxy lies a supermassive black hole, millions or even billions of times the mass of our Sun in scale. Our Universe has been around for 13.8 billion years, which you might think is plenty of time to form a black hole that large. Yet the farther and farther back in time we look, every supermassive black hole we measure seems to have roughly the same mass as the ones today. In other words, while the largest-scale structures in the Universe:

  • giant elliptical galaxies,
  • ultra-massive clusters with thousands of times the mass of the Milky Way,
  • and galactic filaments that are hundreds of millions of light years across,

took billions of years to form, there are ultra-massive black holes that have been around as far back as we can see.

An illustrated timeline of the Universe’s history. Image credit: European Southern Observatory (ESO).

They don’t predate stars, but they are found in the earliest massive galaxies we know how to measure. The crazy explanation is that the Universe was born with these cosmic behemoths, but that flies in the face of everything else we know about structure formation, including the magnitudes and mass/size scales of the fluctuations that gave rise to everything we see today. The new physics that would have to be hypothesized to create a Universe that was born with extremely large black holes is not only preposterous, it’s incredibly constrained by observations of the cosmic background light populating the cosmos.

The fluctuations in the Cosmic Microwave Background, as seen by Planck. Image credit: ESA and the Planck collaboration.

But there are two “mundane” explanations, or explanations that don’t involve any new fundamental physics beyond that which we currently know.

  1. A huge set of starbursts — a giant rush of catastrophic star-formation — triggered the formation of a great many stellar-mass black holes in just a few million years. Over time, they merged together and migrated towards the center of the galaxy, giving rise to a supermassive black hole in very short order.
  2. A supermassive black hole formed by direct collapse of matter into a very large, massive black hole all at once, providing the seed for ultramassive black holes to grow over a relatively short timescale.

The first scenario, by a great many people, is thought to be the simplest explanation, since we see plenty of evidence of how this could work, even today.

The starburst galaxy Henize 2–10, located 30 million light years away. Image credit: X-ray (NASA/CXC/Virginia/A.Reines et al); Radio (NRAO/AUI/NSF); Optical (NASA/STScI).

Star formation is known to occur in bursts, with the greatest rates of star formation occurring in the first three billion years of the Universe, and falling ever since. When stars form en masse, they produce stars of all different masses and colors, including copious numbers of stars over 20, 50, 100 or even 200 solar masses. These massive, blue, hot stars are both the brightest and the shortest lived, and they end their lives in core-collapse supernovae, almost all of which give rise to black holes. Because of the dynamics of gravity, the way these most massive objects work is that they interact with the other stars around them, kick them around while sinking to the center of a cluster-or-galaxy, and then merge together. It’s a simple, conservative scenario. But it might also be insufficient.

Last year, the galaxy CR7 was discovered: a strong candidate for having a truly pristine population of stars. Pristine means that this would be the very first time stars were forming inside this galaxy since the Big Bang, and the science supports this view quite strongly. Yet if we look at even this galaxy, we find something spectacular about it: it also exhibits evidence for a supermassive black hole. And while the starburst explanation is tempting, it may not line up completely with what we see. In a paper written earlier this year, scientists Aaron Smith, Volker Bromm and Abraham Loeb came up with a different explanation: perhaps they were seeing the first evidence for a direct-collapse black hole!

The X-ray and optical images of a small galaxy containing a black hole many tens of thousands of times the mass of our Sun. These black holes may have arisen first in the Universe by the direct collapse of matter. Image credit: X-ray: NASA/CXC/Univ of Michigan/V.F.Baldassare, et al; Optical: SDSS; Illustration: NASA/CXC/M.Weiss.

This galaxy, sending light from 13 billion years ago, has to see that light travel throughout the expanding Universe, where its wavelengths get stretched from ultraviolet through the visible portion of the spectrum and all the way into the infrared. Still, the hottest, bluest stars — which it’s rich in — cause intense ultraviolet emission from the atoms present: hydrogen and helium. These emission lines originate from slightly different parts of the galaxy, and thanks to the incredible technology of the 2015 observations detecting them, we were able to determine that the hydrogen emissions appear to be moving quickly, at 160 km/s, relative to the helium emissions. When Smith, Bromm and Loeb try to model these emissions using simulations, they find that a massive source of radiation must be present at the center, creating an ionized bubble and driving an expanding shell of gas out from the center.

A rich nebula of gas, pushed out into the interstellar medium by the hot, new stars formed in the central region. Image credit: Gemini Observatory / AURA.

There are two explanations to consider: either there’s a massive star cluster at an incredibly high temperature of 100,000 K, or there’s a massive black hole driving it. The big difference between the two models is that the massive black hole produces the offset speed between the hydrogen and helium as well as the incredible size of the region (over 50,000 light years!) while the primordial massive star cluster does not.

These are simulations only, however; if you want to confirm your picture, you need evidence to decide one way or the other. The way we’ll be able to determine whether there truly is a massive black hole will be observational, and it will involve looking for the characteristic radio emissions from black holes.

A small section of the Karl Jansky Very Large Array, one of the world’s largest and most powerful arrays of radio telescopes. Image credit: John Fowler, under a cc-by-2.0 license.

The largest, most advanced radio telescope arrays in the world are on the verge of being up to the task! The evidence pointing to the existence of direct-collapse black holes is tantalizing and suggestive, but we’re not over the threshold yet. In order to get there, we need to see the proof. But the theoretical possibility has been raised, and the gauntlet has been thrown down. It’s time to collect the evidence and let nature decide!


This post first appeared at Forbes, and is brought to you ad-free by our Patreon supporters. Comment on our forum, & buy our first book: Beyond The Galaxy!

Next Story — Cassini prepares for its final, suicidal mission
Currently Reading - Cassini prepares for its final, suicidal mission

A natural color view of Saturn, its rings edge-on and its largest moon, Titan, as viewed from the Cassini spacecraft. Image credit: NASA/JPL/Space Science Institute.

Cassini prepares for its final, suicidal mission

After nearly 20 years in orbit around Saturn, Cassini prepares to say goodbye.


“All the atoms of our bodies will be blown into space in the disintegration of the solar system, to live on forever as mass or energy.” -Carolyn Porco

In 1997, NASA’s Cassini spacecraft was launched for a journey to Saturn, where it would study our Solar System’s ringed world as never before.

Visible and radio images of Saturn’s rings and their structure, as delivered by Cassini. Image credit: NASA/JPL/Space Science Institute.

It delivered beyond our wildest expectations, presenting breathtaking new views of the least dense planet known.

Saturn in eclipse, perhaps the most stunning image of the planet ever taken. Image credit: NASA/JPL/Space Science Institute.

It viewed Saturn in eclipse, discovering two new, outer rings in the process.

An infrared view of Saturn, along with its ring’s shadows on the planet’s atmosphere. Image credit: NASA / JPL / Space Science Institute.

Its infrared eyes viewed Saturn’s hazes beneath the top-level clouds.

A false-color image highlighting Saturn’s hurricane over its north pole, inside the much larger hexagon-shaped feature. Image credit: NASA/JPL-Caltech/SSI.

The north pole of Saturn was found to possess a strange hexagonal storm, thought to be stable over century-long timescales.

Descent Imager/Spectral Radiometer (DISR) image of Titan taken at 2km altitude during the descent. Image credit: ESA/NASA/JPL/University of Arizona.

The Huygens probe released by it descended onto Titan, its largest moon, discovering an incredible landscape, liquid methane lakes and even waterfalls.

Iapetus, the second Saturn moon ever discovered, as imaged by Cassini. Image credit: NASA / JPL-Caltech / Space Science Institute / Cassini.

The mystery of Iapetus, its two-toned moon, was solved as well: dark material from the captured comet, Phoebe, causes the ice on one side to sublimate and settle on the other.

The captured Kuiper Belt object, Phoebe, now one of Saturn’s moons. Image credit: NASA/JPL/Space Science Institute.

Enceladus, an icy, outer moon, was found to contain a subsurface water-ice ocean, which erupts in spectacular geysers.

This is a false-color image of jets (blue areas) in the southern hemisphere of Enceladus taken with the Cassini spacecraft narrow-angle camera on Nov. 27, 2005. Image credit: NASA/JPL/Space Science Institute.

The rings were determined to be made up of 99.9% water-ice, and are at least hundreds of millions of years old.

One of Saturn’s small moons passing in its orbit through a gap in the rings. Image credit: NASA/JPL/Space Science Institute.

And finally, it discovered and viewed the largest storm in the Solar System’s known history: 2011′s Saturnian hurricane.

Image credit: NASA / JPL-Caltech / Space Science Institute, of the great storm’s evolution over a period of 8 months.

Mostly Mute Monday tells the story of a single astronomical phenomenon or object in visuals, images and video in no more than 200 words. Cassini will end its mission in 2017 by crashing into Saturn, thereby avoiding any possible contamination of moons with organics on them.

This post first appeared at Forbes, and is brought to you ad-free by our Patreon supporters. Comment on our forum, & buy our first book: Beyond The Galaxy!

Next Story — Ask Ethan: How Small Can A Piece Of The Universe Be And Still Expand?
Currently Reading - Ask Ethan: How Small Can A Piece Of The Universe Be And Still Expand?

The stars, galaxies and clusters shown here are individually bound together, but do not expand as the Universe does. Image credit: NASA/ESA Hubble Space Telescope.

Ask Ethan: How Small Can A Piece Of The Universe Be And Still Expand?

Galaxy-sized? Human-sized? Atom-sized? Even smaller? How tiny can a bit of space be and still expand?


“We now have the best picture of how galaxies like our own formed their stars.” -Casey Papovich

The expansion of the Universe has a long and amazing history. When Hubble first noticed the relationship between a galaxy’s distance from us and how redshifted its light was, he knew immediately it was a consequence of Einstein’s General Relativity. When Hubble announced his discovery, Einstein immediately recanted his cosmological constant — a “fudge factor” to keep the Universe static — and called it his greatest blunder. But while the space between galaxies expands, atoms, human beings and planets remain the same size over time. What determines this? Jeroen van Rijn wants to know:

What scale limit if any are we talking about when we say the universe expands? Does it mean Planck length isn’t a constant so much? Do atom’s orbits grow corresponding with this stretching of space or does the strong force counteract this?
The “raisin bread” model of the expanding Universe, where relative distances increase as the space (dough) expands. Image credit: NASA / WMAP science team.

The expanding Universe is a tough phenomenon to wrap your head around, because it’s very counterintuitive. Perhaps the best analogy is to imagine that the fabric of space is like a ball of dough, suspended in an oven in zero gravity. As the dough bakes, the bread leavens and rises, and it expands uniformly in all directions. But that’s just for empty space, or space with nothing in it. What if you wanted to have space that contained things like matter: protons, atoms, humans, planets, galaxies or even clusters of galaxies? There are two ways you could imagine the expansion.

The balloon/coin analogy of the expanding Universe. The individual structures (coins) don’t expand, but the distances between them do in an expanding Universe. Image credit: E. Siegel, from his book Beyond The Galaxy.

One is like the surface of a balloon with coins glued to it, where the coins themselves don’t change as the balloon’s surface expands. The Universe gets bigger and bigger, and all the space between the individual particles — or individual galaxies — grows as well. A coin will appear to recede from a nearby coin at a particular rate, while a coin twice as far away will appear to recede at double that rate. The think is that any coin will perceive that same effect: its perceived speed, and hence the redshift (stretching) of the light, will appear to depend solely on the distance of the coin you’re looking at in this expanding space. This much we know happens, and we’ve known it since the 1920s. This was the very same relationship that “Hubble’s Law” demonstrated to us was at play in the Universe.

If everything expanded as the Universe did, then the coins would need to be replaced by paint. Image credit: “Fun with Astronomy” by Mae and Ira Freeman, via http://amzn.to/2aKd9qD.

But the other way you could imagine this is by considering the surface of a balloon with objects painted onto it. As the balloon inflates and its surface expands, it carries the mark of the paint along with it. Sure, the distant objects will all move away from one another in accord with Hubble’s Law, but in this case, the objects themselves would also expand along with the fabric of space.

So what is it that the Universe does? What scale does space expand on? One thing we can do is check the Universe itself. When we look out at the distant galaxies, we should see them redshifted and smaller/lower in mass, as greater distances also mean earlier times.

The evolution of Milky Way-like galaxies throughout different epochs in the Universe. Image credit: NASA, ESA, C. Papovich / Texas A&M University, H. Ferguson / STScI, S. Faber / University of California, Santa Cruz and I. Labbe / Leiden University.

We do see that, but we also see some important other signatures:

  • The galaxies have the same spectral lines at high redshifts, telling us that the sizes and properties of atoms billions of years ago are the same as they are today.
  • That the physical size of the galaxies are determined by their masses alone; that galaxies of the same mass today and at early times are the same physical size.
  • And that the way the cosmic web (and large-scale structure) grows or doesn’t is dependent only on the amount of mass present in a given region of space.
The absorption lines at a variety of redshifts show that the fundamental physics and sizes of atoms have not changed throughout the Universe, even as the light has redshifted due to its expansion. Image credit: NASA, ESA, and A. Feild (STScI).

So it looks like it’s the “coins” analogy rather than the “paint” analogy. When we look out at the Universe, we see that the fabric of space itself expands in all circumstances unless there’s another force that works to bind an object together. This actually fits in theoretically with what we expect completely, because unlike we commonly think of it, the expansion isn’t a force, but is rather a rate. When something becomes bound together, it doesn’t matter what the force doing the binding is, whether it’s a nuclear force in the case of protons and nuclei, whether it’s an electromagnetic force in the case of atoms, cells or humans, or whether it’s a gravitational force in the case of planets, stars, galaxies or even clusters of galaxies.

Wide-field image of the Coma cluster of galaxies. Image credit: Adam Block/Mount Lemmon SkyCenter/University of Arizona.

While the fabric of space itself expands, it expands at a certain speed-per-unit-distance. (In reality, this is just units of inverse time.) As a rule-of-thumb, if the force between any two objects causes them to attract at a greater rate than the expansion of the Universe would cause the space between them to expand, then they no longer act like paint; they act like coins. Our bodies are bound together; every atom is bound together; our local group is already bound together; even the entire Coma cluster of galaxies (above) is bound together! But it’s important to remember that this is all relative. The expansion of the Universe doesn’t affect our local group or anything within it because our local group is too tightly bound for that, but go outside of it and space itself continues to expand. This is why distant galaxies (and other bound structures) continue to recede from us, even as individually we’re all locally bound to our own regions of space.

The various groups and clusters we can see here — including our local group — are all individually bound, but the space between each of them is expanding. Image credit: Andrew Z. Colvin under a c.c.a.-s.a.-3.0 license.

But we can go to arbitrarily small regions of space in the unbound regions, where there is no matter present, and we’d find that any sized-region — light years, kilometers, microns, proton-sized, or Planck-sized (or even smaller) — expands in direct accord with Hubble’s Law. The rate of the expansion of space, in General Relativity, allows you to treat the fabric of space as though it’s completely continuous, with no need to quantize it as you might in quantum physics. This remains valid for the expansion of the Universe, right up until the moment where you put a bound structure inside it! There’s no fundamental limit to how small a bit of space can be and still expand, but it needs to either be empty or sufficiently large so that the “structure” that you’re in can’t overcome the expansion itself.


This post first appeared at Forbes, and is brought to you ad-free by our Patreon supporters. Comment on our forum, & buy our first book: Beyond The Galaxy!

Next Story — The Least Likely Record To Fall This Olympics, And Beyond
Currently Reading - The Least Likely Record To Fall This Olympics, And Beyond

Usain Bolt breaks the all-time record in the Men’s 100m dash at the 2009 world championships with a time of 9.58s. Screenshot from the HD television broadcast.

The Least Likely Record To Fall This Olympics, And Beyond

If you thought Usain Bolt’s 9.58s world record time in the 100 meters was ever in jeopardy, this shows how unlikely that was.


“A lot of legends, a lot of people, have come before me. But this is my time.” -Usain Bolt

Sunday, August 14th: the two-time defending gold medalist and world record holder in the men’s 100 meters, Usain Bolt, steps to the starting line. He’s won six olympic gold medals — the 100m, 200m, and 4x100m relay in 2008 and 2012 apiece — and current holds the record in all three events at 9.58s, 19.19s and 36.84s. He’s won three 100m world championships, at the 2009 events in Berlin (where he set the all-time record), and again in 2013 and 2015. He owns the three fastest times in 100m history: 9.58s, 9.63s and 9.69s (which two others have tied), and has never tested positive for doping, unlike his closest American rivals, Tyson Gay and Justin Gatlin. This Olympics, at the age of 29, he faces off against his closest rivals, including Gatlin, teammate Yohan Blake and a new crop of young superstars, all capable of sub-10s times.

And no one touches the world record.

Usain Bolt with his official world record time in 2009. Image credit: American Foreign Press.

“How did you know that?” There’s a reason we run these races in the first place, after all. At the 1991 world championships, what most people considered to be a past-his-prime Carl Lewis stepped to the line in the 100m finals against the record holder, Leroy Burrell, and the strongest field of sprinters ever assembled. Lewis himself was a decorated former world record holder, having won Olympic gold and set world records in the event 1984 and 1988 (once Ben Johnson was stripped after a positive steroid test), but had never broken the 9.9s barrier. At the age of 30, many wrote Lewis off, with some calling him washed-up. Yet he ran the race of his life, finishing in 9.86s and setting the world record in the process.

Carl Lewis delights in his 1991 victory at the World Championships, setting a new world record at 9.86s in the event. Image credit: ROMEO GACAD/AFP/Getty Images.

That world record would progress many times over the next few years. Burrell would re-take the record in 1994 with a run of 9.85s, Donovan Bailey would shave the time down to 9.84s in 1996, Maurice Green would improve that to 9.79s in 1999, breaking the 9.8s barrier. Then in 2005, Asafa Powell burst onto the scene, breaking the record with a time of 9.77s, eventually improving that down to 9.74s in 2007, just before the Beijing Olympics. But Bolt’s 9.69s in the 2008 Olympic finals has never been beaten, except by Bolt himself, with his 9.58s time in the 2009 world championship finals and his 9.63s in the 2012 Olympic finals.

The progression of the men’s 100 meter world record times. (Official, non-steriod results only.) Image credit: E. Siegel.

With a number of runners hovering around the 9.7s mark, how can we be so sure that Bolt’s 9.59s won’t be challenged again so soon? While you can never be sure, the progression of world records in running events often follows a simple mathematical formula. In the early eras, the record progresses at a roughly steady rate — appearing to follow a straight line — as training, technique, equipment and overall physiques improve steadily. As time moves forward, progress typically occurs in small increments, as human beings find it more difficult to make progress towards such an elusive goal. Bolt himself may be an outlier in a number of aspects, but he’s certainly within the realm of what’s humanly possible. But physically, there’s going to be an overall limit: not of an infinitely fast time, but of a time that’s fundamentally limited by the physiology of the human body.

The skeletal muscle fiber signatures of champion sprint runners as compared to other athletes and non-athletes. Image credit: Scott Trappe et al., Journal of Applied Physiology, 15 June 2015 Vol. 118 no. 12, 1460–1466.

There’s a mathematical curve we can fit to the world record progression that encapsulates all of that behavior as simply as possible: by modeling that with an exponential function. In general, you want the number of parameters in your model to be as small as possible, and it must be significantly smaller than the number of data points you have to fit it to. An exponential curve is the simplest, fewest-parameter model (only 3) that captures all of the relevant behavior we discussed. And compared to those three parameters, we have 19 data points to go on.

The Men’s 100 meter world record progression (red points) and the fit of the simple three-parameter exponential model for expected times. Note how ahead-of-schedule Bolt’s 9.58s time still is today. Image credit and analysis: E. Siegel.

There are a few incredible things to learn from this:

  1. The ultimate time that human males should be able to reach in the 100m dash is somewhere around the 9.2s mark, based on their performance to date.
  2. Bolt’s 9.58s time is such an outlier that we wouldn’t expect athletes to achieve it again until the late 2030s or early 2040s, following this progression.
  3. And that Bolt’s very existence has changed what we think humanity’s limits are. Without him, our limits would appear to be more than a tenth of a second slower.

All of this is even more remarkable when you consider that all of Bolt’s nearest competitors — Gay, Blake, Gatlin and Powell — have been banned or suspended at least once for doping violations, while Bolt has never ever failed a drug test.

Bolt winning his first Olympic gold medal in the 100m in a time of 9.69s, despite slowing up at the end. Image credit: Wikimedia Commons user SeizureDog under a c.c.a.-2.0 license.

Predicting how this trend will continue in the future is a difficult task, and no simple model is every going to encapsulate the full capabilities of the human body over time with just three parameters. But even a simple analysis like this shows that Bolt is a generation ahead of his time. No one has ever won gold in the 100m, 200m and 4x100m relay in two consecutive Olympics — much less three — like Bolt has. I’d be very surprised if Bolt broke his own record before he retires, but I’d be even more shocked if anyone else came close to challenging it. As Olympic champion Michael Johnson put it, a runner capable of surpassing Bolt’s time “hasn’t been born yet.”


This post first appeared at Forbes, and is brought to you ad-free by our Patreon supporters. Comment on our forum, & buy our first book: Beyond The Galaxy!

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