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The Expanding Universe: How the Universe Got Bigger As We Measured It

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Since before history began, we have tried to understand our world and our place in it. To the earliest hunter-gatherer tribes, this meant little more than knowing the tribe's territory. But as people began to settle and trade, knowing the wider world became more important, and people became interested in the actual size of it. Aristarchus of Samos (310-230 BC) made the earliest surviving measurements of the distance between objects in space. By carefully measuring the apparent size of the Sun and Moon and carefully observing the terminator of the Moon when half full, he concluded that the Sun was 18-20 times farther away than the Moon. The actual value is 400, but he was on the right track; he just didn't have precise enough measurements.


A diagram from Aristarchus' work, "On Size and Distances," describing how to work out the relative distances.

Meanwhile, Eratosthenes of Cyrene (276-195 BC) was working on the size of the Earth. He came upon a letter stating that at noon in Syene (modern-day Aswan) on the summer solstice, one could look down a well and see all the way to the bottom because the Sun was precisely overhead. Eratosthenes already knew the distance between Alexandria and Syene, so all he had to do was observe the angle of the Sun on the summer solstice there and then do a little math. Assuming a spherical Earth, he computed the circumference to be 252,000 stadia, which works out to 39,690 km -- which is less than a 2% error compared to the real value. A directly measured size now existed for the world. But what of the heavens? The work of Aristarchus wasn't accurate enough. After figuring out how to reliably predict eclipses, Hipparchus (190-120 BC) used them to get a better estimate of the ratio of distance between Moon and Sun. He concluded that the Moon was 60.5 Earth radii away, and the Sun was 2,550 Earth radii away. His lunar distance was pretty accurate -- that works out to 385,445 km to the Moon, which is pretty close to the actual distance, an average of 384,400 km -- but for the Sun it worked out to 16 million km, about 136 million km short of the actual distance.

Above left: A dioptra, a predecessor to both the astrolabe and the theodolite, of a type similar to the one Hipparchus used to make his measurements.

When Ptolemy (AD 90-168) came along, the Universe shrank for a while.

Using the epicycles he assumed must exist within his geocentric universe, he estimated the distance to the Sun to be 1,210 Earth radii, and the distance to the fixed stars to be 20,000 Earth radii away; using modern values for the Earth's average radius, that gives us 7,708,910 km to the Sun and 127,420,000 km to the fixed stars. Both of those are woefully small (Ptolemy's universe would fit within the orbit of Earth), but they get even smaller if we use his smaller estimate for the Earth's circumference -- he estimated the Earth to be about 1/6 the size it actually is. (And therein hangs a tale, for Christopher Columbus would try to use Ptolemy's figure when plotting his journey west to the Orient, rather than the more accurate ones that had been developed in Persia since then.)


Ptolemy's world; at the time, the best map that existed of the known world.

By the end of the 16th Century, the size of the Earth was pretty well defined, but the size of the Universe remained challenging. Johannes Kepler solved the puzzle of orbital motion and calculated the ratio of the distance between Sun and various planets, enabling accurate predictions of transits. In 1639, Jeremiah Horrocks made the first known observation of a transit of Venus. He estimated the distance between Earth and the Sun at 95.6 million km, the most accurate estimate to date (and about 2/3 the actual distance). In 1676, Edmund Halley attempted to measure solar parallax during a transit of Mercury, but was unsatisfied with the only other observation made. He proposed that further observations be made during the next transit of Venus, in 1761. Unfortunately, he did not live that long.



Jeremiah Horrocks, observing the transit of Venus by the telescopic projection method.

In 1761, acting on the recommendations of the late Edmund Halley, scientific expeditions set out to observe the Transit of Venus from as many places as possible. More expeditions set out in 1769 for the second transit of the pair, including a famous journey by Captain James Cook to Tahiti, and in 1771, Jerome Lalande used the data to calculate the Sun's average distance as 153 million km, far larger than previously estimated, and the first time the measurement was close to right. Further transits in 1874 and 1882 refined the distance to 149.59 million km. In the 20th Century, it has been refined further using radio telemetry and radar observations of the inner planets, but it has not strayed much from that value. The size of the solar system was now known.

Above left: Sketch depicting the transit circumstances, as reported by James Ferguson, a Scottish self-taught scientist and inventor who participated in the transit observations.

But the universe is bigger than the solar system. In the 1780s, William Herschel mapped the visible stars in an effort to find binary stars. He found quite a few, but he also worked out that the solar system was actually moving through space, and that the Milky Way was disk shaped. The galaxy, which was at that time synonymous with Universe, was eventually estimated to be about 30,000 light years across -- an inconceivably large distance, but still far too small.

Hershel's map of the galaxy could not tell how far away any of the stars were; stars get dimmer as they move away, but you can only use this to calculate their distance if you know how bright they are to begin with, and how can you know that? In 1908, Henrietta Leavitt found the answer: she noticed that Cepheid variable stars had a direct relationship between their luminosity and the period of their variation, allowing astronomers to deduce exactly how bright they are to start with. Harlow Shapley immediately applied this discovery and found three amazing things when he mapped all the visible Cepheids: the Sun is actually nowhere near the center of the galaxy, the center of the galaxy is obscured by vast amounts of dust, and the galaxy is at least ten times larger than anyone had ever suspected -- so vast that it would take light 300,000 years to cross it. (Shapley was overestimating a bit; it's actually more like 100,000 light years or so.)

Above left: Henrietta Leavitt, one of the few women in astronomy and the only one on this list; she got little recognition for her discovery at the time.

In 1924, Edwin Hubble produced the next major revolution. Using the new 100-inch telescope at Mount Wilson Observatory, he located Cepheids in the Andromeda Nebula, a spiral nebula in which no stars had previously been resolved. He calculated these Cepheids were 1.2 million light years away, putting them far beyond Shapley's wildest estimate for the size of the galaxy. Therefore, Andromeda was not a part of our galaxy at all; it was an entirely separate "island universe," and most likely the same was true of other spiral nebulae. This meant the Universe was very likely far larger than anyone could hope to measure. It could even be infinite.


At left: The 100-inch telescope at Mount Wilson Observatory, where Hubble did his work. It was the world's largest telescope until 1948.

And then Hubble found something even more astonishing. In 1929, Hubble compared the spectra of near and far galaxies, based on distances already known by observations of Cepheid variables. The spectra of more distant ones were consistently redder, and for nearly all of them, there was a linear relationship between redshift and distance. Due to the Doppler Effect, this meant they were receding. He wasn't sure what to make of this observation at the time, but in 1930, Georges Lemaître pointed out a possible solution: he suggested that the universe was expanding, carrying galaxies along with it, and that at one time it had all be compacted down impossibly tight. Hubble went with this and calibrated the apparent expansion against the distance to known standard candles, calculating the age of the most distant objects to be 1.8 billion light years.


At left: Georges Lemaître, who happened to also be a Catholic priest. He died in 1966, shortly after learning about the Cosmic Microwave Background radiation, which further reinforced his theory of the Big Bang.

This was much too small, and in 1952, Walter Baade figured out why: there are actually two kinds of Cepheids, and Hubble had been observing the ones that Leavitt had not baselined. After characterizing this new population of Cepheids, he recalculated from Hubble's observations and brought the Universe's minimum age up to 3.6 billion years. In 1958, Allan Sandage improved it more, to an estimated 5.5 billion years.

Astronomers started to ratchet up their observations of ever more distant objects. In 1998, studies of very distant Type 1A supernovae revealed a new surprise: not only is the universe expanding, but the rate of the expansion is increasing. Today, the Universe is usually estimated to be 13.7 billion years old -- or, more accurately, the most distant things we can observe appear to be that far away. The catch, of course, is that we're observing them in the past. They're actually further away now -- assuming, of course, that they even still exist. A lot can happen in 13.75 billion years. And now that we know the universe's expansion is accelerating, they are even farther away by now. The current estimate for the actual size of the observable universe is 93 billion light-years in diameter, a tremendous size that the human brain cannot begin to fathom on its own, vastly overwhelming the tiny universe of the ancient Greeks.


NASA artist's concept of the progenitor of a Type 1a supernova -- a neutron star stealing matter from a supergiant companion until eventually enough matter is collected to trigger a supernova.

The understanding of the size of the Universe has gone from being impressed by the distance to the Sun, to the size of the solar system, to the vastness of the galaxy, to the staggering distance to neighboring galaxies, to the mindbendingly complicated distances to things that we can only see as they were an impossibly long period of time ago. What will we discover as we measure the Universe tomorrow?

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iStock // Ekaterina Minaeva
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Man Buys Two Metric Tons of LEGO Bricks; Sorts Them Via Machine Learning
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iStock // Ekaterina Minaeva

Jacques Mattheij made a small, but awesome, mistake. He went on eBay one evening and bid on a bunch of bulk LEGO brick auctions, then went to sleep. Upon waking, he discovered that he was the high bidder on many, and was now the proud owner of two tons of LEGO bricks. (This is about 4400 pounds.) He wrote, "[L]esson 1: if you win almost all bids you are bidding too high."

Mattheij had noticed that bulk, unsorted bricks sell for something like €10/kilogram, whereas sets are roughly €40/kg and rare parts go for up to €100/kg. Much of the value of the bricks is in their sorting. If he could reduce the entropy of these bins of unsorted bricks, he could make a tidy profit. While many people do this work by hand, the problem is enormous—just the kind of challenge for a computer. Mattheij writes:

There are 38000+ shapes and there are 100+ possible shades of color (you can roughly tell how old someone is by asking them what lego colors they remember from their youth).

In the following months, Mattheij built a proof-of-concept sorting system using, of course, LEGO. He broke the problem down into a series of sub-problems (including "feeding LEGO reliably from a hopper is surprisingly hard," one of those facts of nature that will stymie even the best system design). After tinkering with the prototype at length, he expanded the system to a surprisingly complex system of conveyer belts (powered by a home treadmill), various pieces of cabinetry, and "copious quantities of crazy glue."

Here's a video showing the current system running at low speed:

The key part of the system was running the bricks past a camera paired with a computer running a neural net-based image classifier. That allows the computer (when sufficiently trained on brick images) to recognize bricks and thus categorize them by color, shape, or other parameters. Remember that as bricks pass by, they can be in any orientation, can be dirty, can even be stuck to other pieces. So having a flexible software system is key to recognizing—in a fraction of a second—what a given brick is, in order to sort it out. When a match is found, a jet of compressed air pops the piece off the conveyer belt and into a waiting bin.

After much experimentation, Mattheij rewrote the software (several times in fact) to accomplish a variety of basic tasks. At its core, the system takes images from a webcam and feeds them to a neural network to do the classification. Of course, the neural net needs to be "trained" by showing it lots of images, and telling it what those images represent. Mattheij's breakthrough was allowing the machine to effectively train itself, with guidance: Running pieces through allows the system to take its own photos, make a guess, and build on that guess. As long as Mattheij corrects the incorrect guesses, he ends up with a decent (and self-reinforcing) corpus of training data. As the machine continues running, it can rack up more training, allowing it to recognize a broad variety of pieces on the fly.

Here's another video, focusing on how the pieces move on conveyer belts (running at slow speed so puny humans can follow). You can also see the air jets in action:

In an email interview, Mattheij told Mental Floss that the system currently sorts LEGO bricks into more than 50 categories. It can also be run in a color-sorting mode to bin the parts across 12 color groups. (Thus at present you'd likely do a two-pass sort on the bricks: once for shape, then a separate pass for color.) He continues to refine the system, with a focus on making its recognition abilities faster. At some point down the line, he plans to make the software portion open source. You're on your own as far as building conveyer belts, bins, and so forth.

Check out Mattheij's writeup in two parts for more information. It starts with an overview of the story, followed up with a deep dive on the software. He's also tweeting about the project (among other things). And if you look around a bit, you'll find bulk LEGO brick auctions online—it's definitely a thing!

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iStock
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Here's How to Change Your Name on Facebook
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iStock

Whether you want to change your legal name, adopt a new nickname, or simply reinvent your online persona, it's helpful to know the process of resetting your name on Facebook. The social media site isn't a fan of fake accounts, and as a result changing your name is a little more complicated than updating your profile picture or relationship status. Luckily, Daily Dot laid out the steps.

Start by going to the blue bar at the top of the page in desktop view and clicking the down arrow to the far right. From here, go to Settings. This should take you to the General Account Settings page. Find your name as it appears on your profile and click the Edit link to the right of it. Now, you can input your preferred first and last name, and if you’d like, your middle name.

The steps are similar in Facebook mobile. To find Settings, tap the More option in the bottom right corner. Go to Account Settings, then General, then hit your name to change it.

Whatever you type should adhere to Facebook's guidelines, which prohibit symbols, numbers, unusual capitalization, and honorifics like Mr., Ms., and Dr. Before landing on a name, make sure you’re ready to commit to it: Facebook won’t let you update it again for 60 days. If you aren’t happy with these restrictions, adding a secondary name or a name pronunciation might better suit your needs. You can do this by going to the Details About You heading under the About page of your profile.

[h/t Daily Dot]

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