Size matters

Something odd happens when we consider scales much larger or smaller than our ordinary experience; our imagination fails.

It's why people seem not to comprehend the difference between millionaires and billionaires.  Millionaires are wealthy, yes.  But billionaires?  

If a person with a billion dollars gave away a million dollars a day, 365 days a year -- in other words, creating one new millionaire every day -- (s)he wouldn't run out for almost three years.  The fact that people lump together millionaires and billionaires as both simply "rich" indicates we don't have a good way to conceptualize how big a billion actually is.

The same thing happens when you look at anything that's very small.  In my biology classes, we did a lab where students learned how to estimate measurements using a microscope.  Knowing the magnification and the field diameter (the actual width of the bit of the slide you're looking at), it's a fairly simple calculation to estimate the size of (for example) a cell.

What I found the most interesting was that after performing the calculation, most students had no clue whether the answer they'd come up with was even within the ballpark.  Most of the time, if they did make an error, it was a simple computational goof; but the curious thing was that they couldn't tell if they were even in the right realm.  0.001 meters?  0.000001 meters?  0.000000000001 meters?  All looks pretty similar -- "small."

(Then there's the student who multiplied when she should have divided, and told me that a plant cell was 103 meters in diameter.  "Don't you think that's a bit... on the large size?" I asked her.  She responded, "Is it?"  I told her 103 meters was a little longer than a typical football field.  She responded, "Oh.")

This problem crops up in fields like subatomic physics (on one end) and, germane to today's topic, astrophysics (on the other).  What got me thinking about it was a paper this week in the journal Astronomy and Astrophysics about a distant quasar with the euphonious name VIK J2348-3054.  Quasars are extraordinarily luminous objects which were a puzzle for a long time -- viewed through earthly telescopes they appear as single dim, star-like spots, but based on their redshifts they are enormously far away (and thus, even to be visible at all from that distance their actual luminosity has to be crazy high).  The current models support quasars as being supermassive black holes at the centers of young galaxies, emitting high-energy radiation and particles as they swallow vast amounts of gas and dust in a wildly spinning whirlpool called an accretion disk.

[Image credit: M. Kornmesser/European Southern Observatory]

An energy output that high causes disruption in the entire region surrounding it.  It heats and/or blows away gas and dust nearby, which overcomes the gravitational collapse of clumps of material and thus suppresses star formation.  And this quasar is so powerful it has stopped the formation of new stars in a region with a radius of over sixteen million light years.

Stop and ponder that for a moment.

Sixteen million light years isn't just big, it's abso-fucking-lutely enormous.  It's six times the distance between the Milky Way and the Andromeda Galaxy.  Put into units that more of us are comfortable with, this is about 160,000,000,000,000,000,000 kilometers.

Of course, I'm not sure how much even that helps.  Once again, our imaginations simply fail us.  Perhaps this will frame it better; the fastest human-made vehicle, Voyager 1, is traveling at about 61,000 kilometers per hour.  At this rate, Voyager 1 will have covered one light year in about eighteen thousand years.  And that's not even the distance to the nearest star, Proxima Centauri (if it was heading that direction, which it's not).

To travel the distance that has been cleared by this quasar, Voyager 1 would take a bit less than three hundred billion years -- about twenty times the age of the universe.

I don't even know how to wrap my brain around a number this big.  I may not have the difficulty with numbers my long-ago student had with her football-field-sized plant cell, but I have sat here all morning trying to understand what it means for something to work over this kind of size range, and I just can't manage it.

The inevitable result is that this kind of thing makes us feel pretty small.  I'm actually okay with that.  The universe is a grand, beautiful, and abso-fucking-lutely enormous place.  It's a good thing to look up into the night sky and feel awe, to realize that every star you see is (relatively speaking) close by, occupying a small spherical region in one arm of a completely ordinary galaxy, of which there are millions more scattered across the vastness of space.

We humans get a little big for our britches, sometimes.  A dose of humility is needed every so often.

And if it comes from the realm of science, so much the better.

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A matter of scale

In Douglas Adams's brilliant book, The Hitchhiker's Guide to the Galaxy, a pair of alien races, the Vl'Hurg and the G'gugvuntt, spent millennia fighting each other mercilessly until they intercept a message from Earth that they misinterpret as being a threat.  They forthwith decide to set aside their grievances with each other, and team up for an attack on our planet in retaliation:

Eventually of course, after their Galaxy had been decimated over a few thousand years, it was realized that the whole thing had been a ghastly mistake, and so the two opposing battle fleets settled their few remaining differences in order to launch a joint attack on our own Galaxy...

For thousands more years the mighty ships tore across the empty wastes of space and finally dived screaming on to the first planet they came across -- which happened to be the Earth -- where due to a terrible miscalculation of scale the entire battle fleet was accidentally swallowed by a small dog.

I was reminded of the Vl'Hurg and G'gugvuntt while reading the (much more serious) book The View from the Center of the Universe, by physicist Joel Primack and author and polymath Nancy Abrams.  In it, they look at our current understanding of the basics of physics and cosmology, and how it intertwines with metaphysics and philosophy, in search of a new "foundational myth" that will help us to understand our place in the universe.

What brought up Adams's fictional tiny space warriors was one of the most interesting things in the Primack/Abrams book, which is the importance of scale.  There are about sixty orders of magnitude (powers of ten) between the smallest thing we can talk meaningfully about (the Planck length) and the largest (the size of the known universe), and we ourselves fall just about in the middle.  This is no coincidence, the authors say; much smaller life forms are unlikely to have to have the complexity to develop intelligence, and much larger ones would be limited by a variety of physical factors such as the problem that if you increase length in a linear fashion, mass increases as a cube.  (Double the length, the mass goes up by a factor of eight, for example.)  Galileo knew about this, and used it to explain why the shape of the leg bones of mice and elephants are different.  Give an animal the size of an elephant the relative leg diameter of a mouse, and it couldn't support its own weight.  (This is why you shouldn't get scared by all of the bad science fiction movies from the fifties with names like The Cockroach That Ate Newark.  The proportions of an insect wouldn't work if it were a meter long, much less twenty or thirty.)

Pic from the 1954 horror flick Them!

Put simply: scale matters.  Where it gets really interesting, though, is when you look at the fundamental forces of nature.  We don't have a quantum theory of gravity yet, but that hasn't held back technology from using the principles of quantum physics; on the scale of the very small, gravity is insignificant and can be effectively ignored in most circumstances.  Once again, we ourselves are right around the size where gravity starts to get really critical.  Drop an ant off a skyscraper, and it will be none the worse for wear.  A human, though?

And the bigger the object, the more important gravity becomes, and (relatively speaking) the less important the other forces are.  On Earth, mountains can only get so high before the forces of erosion start pulling them down, breaking the cohesive electromagnetic bonds within the rocks and halting further rise.  In environments with lower gravity, though, mountains can get a great deal bigger.  Olympus Mons, the largest volcano on Mars, is almost 22 kilometers high -- 2.5 times taller than Mount Everest.  The larger the object, the more intense the fight against gravity becomes.  The smoothest known objects in the universe are neutron stars, which have such immense gravity their topographic relief over the entire surface is on the order of a tenth of a millimeter.

Going the other direction, the relative magnitudes of the other forces increase.  A human scaled down to the size of a dust speck would be overwhelmed by electromagnetic forces -- for example, static electricity.  Consider how dust clings to your television screen.  These forces become much less important on a larger scale... whatever Gary Larson's The Far Side would have you believe:

Smaller still, and forces like the strong and weak nuclear forces -- the one that allows the particles in atomic nuclei to stick together, and the one that causes some forms of radioactive decay, respectively -- take over.  Trying to use brains that evolved to understand things on our scale (what we term "common sense") simply doesn't work on the scale of the very small or very large.

And a particularly fascinating bit, and something I'd never really considered, is how scale affects the properties of things.  Some properties are emergent; they result from the behavior and interactions of the parts.  A simple example is that water has three common forms, right?  Solid (ice), liquid, and gaseous (water vapor).  Those distinctions become completely meaningless on the scale of individual molecules.  One or two water molecules are not solid, liquid, or gaseous; those terms only acquire meaning on a much larger scale.

This is why it's so interesting to try to imagine what things would be like if you (to use Primack's and Abrams's metaphor) turned the zoom lens one way and then the other.  I first ran into this idea in high school, when we watched the mind-blowing short video Powers of Ten, which was filmed in 1968 (then touched up in 1977) but still impresses:

Anyhow, those are my thoughts about the concept of scale.  An explanation of why the Earth doesn't have to worry about either Vl'Hurgs and G'gugvuntts, enormous bugs, or static cling making your child stick to the ceiling.  A relief, really, because there's enough else to lose sleep over.  And given how quickly our common sense fails on unfamiliar scales, it's a good thing we have science to explain what's happening -- not to mention fueling our imaginations about what those scales might be like.

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Guest post: Smaller than a dust mote

Today we're fortunate to feature a guest post by my friend, fellow blogger, and twin-separated-at-birth, Andrew Butters, whose blog Potato Chip Math is a must-read.  Like myself, Andrew is a devotee of astronomy, and here he'll take us on a voyage into deep space -- and give you a change of perspective you might never have considered.

Enjoy!

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I'll admit it, I'm a space nerd. I have been since high school and only got more intense when I started studying Applied Physics at university. There is a lot of weird science at the astronomical level and to comprehend it you have to wrap your head around concepts that you won't ever encounter in your daily life and then understand how to measure them. The two measurements that trip up just about everyone who hasn't studied them are time and distance. At an astronomical level those two things are astonishingly gigantic, so much so that to the average person they might as well have no meaning at all.

This is why, when I read a recent article on space.com, my mind, which studied this at a university level for several years, was sufficiently blown. Space.com does a decent job putting in lay terms what authors Linhua Jiang, Nobunari Kashikawa, Shu Wang, Gregory Walth, Luis C. Ho1, Zheng Cai, Eiichi Egami, Xiaohui Fan, Kei Ito, Yongming Liang, Daniel Schaerer, and Daniel P. Stark of the published article, "Evidence for GN-z11 as a luminous galaxy at redshift 10.957," explained in painstaking mathematical and scientific detail for the journal Nature Astronomy. I'll summarize it even further: space is fucking huge.

In the article, the authors prove rather conclusively that the farthest observable galaxy to date is a whopping 13.4 billion light years away. Don't let the word "years" in there fool you. A light year is a measure of distance and 13.4 billion of them are the equivalent of 127 nonillion kilometers (127,000,000,000,000,000,000,000,000,000,000 km). To put that into a different perspective, there are 3600 seconds in an hour, a million seconds is a little over 11.5 days, and a billion seconds is 31.7 years. What about 127 nonillion seconds? That's 4.25 x 10^22 centuries or roughly five orders of magnitude longer than the age of the Universe itself.

So, space is huge. So what? Well, for me, it puts my existence on this third rock spinning in circles around a rather average sun as part of a rather average galaxy into perspective. As with any good conversation on this topic, it’s probably a good idea to lead with a little Carl Sagan. Many of you have seen this picture before:

[NASA – Image in the public domain]

It was taken in 1990 by the Voyager I probe on February 14 at the request of Carl Sagan. It took a decade for the request to come to fruition, but after it did here’s what he had to say about it:

"We succeeded in taking that picture [from deep space], and, if you look at it, you see a dot. That’s here. That’s home. That’s us. On it, everyone you ever heard of, every human being who ever lived, lived out their lives. The aggregate of all our joys and sufferings, thousands of confident religions, ideologies and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilizations, every king and peasant, every young couple in love, every hopeful child, every mother and father, every inventor and explorer, every teacher of morals, every corrupt politician, every superstar, every supreme leader, every saint and sinner in the history of our species, lived there on a mote of dust, suspended in a sunbeam.

"The Earth is a very small stage in a vast cosmic arena. Think of the rivers of blood spilled by all those generals and emperors so that in glory and in triumph they could become the momentary masters of a fraction of a dot. Think of the endless cruelties visited by the inhabitants of one corner of the dot on scarcely distinguishable inhabitants of some other corner of the dot. How frequent their misunderstandings, how eager they are to kill one another, how fervent their hatreds. Our posturings, our imagined self-importance, the delusion that we have some privileged position in the universe, are challenged by this point of pale light.

"Our planet is a lonely speck in the great enveloping cosmic dark. In our obscurity – in all this vastness – there is no hint that help will come from elsewhere to save us from ourselves. It is up to us. It’s been said that astronomy is a humbling, and I might add, a character-building experience. To my mind, there is perhaps no better demonstration of the folly of human conceits than this distant image of our tiny world. To me, it underscores our responsibility to deal more kindly and compassionately with one another and to preserve and cherish that pale blue dot, the only home we’ve ever known." — Carl Sagan, speech at Cornell University, October 13, 1994

To give you an idea of exactly how far away Voyager I was when it took that photograph, here’s a picture, though it’s not to scale. As we’ll see in a bit the scale of the Solar System, and indeed the Universe, is staggeringly massive.

Joe Haythornthwaite and Tom Ruen [CC BY-SA 4.0], from Wikimedia Commons

How far away is that? It’s far. I mean, really far. The Pale Blue Dot photograph was taken 6 billion kilometers away. Voyager 1 launched in September 1977 and traveled at an average speed of roughly 60,000 km/h, and it still took thirteen years for it to get that far away. Neptune, the most distant planet in the Solar System takes 165 years to make a single trip around the Sun. When Neptunians say, “Winter is coming,” and have a look of concern on their faces it’s for good reason.

What if the Moon were the size of a single pixel on your screen right now? It’s a cool exercise to ponder and it gives us a real sense of the vastness of our surroundings. In fact, someone thought it was so cool that they created a model for it. Spend a few minutes scrolling (and scrolling and scrolling and scrolling) through it.

If the Moon Were 1-Pixel

This is all well and good, but what about beyond our Solar System? We orbit but one star out of hundreds of billions in our galaxy alone and our galaxy is but one of trillions in the observable Universe. To get a sense of what lies immediately beyond our Sun there are a couple of really cool, interactive sites you can visit Our Stellar Neighborhood, http://stars.chromeexperiments.com/, which allows you to zoom and pan and view 100,000 of the nearest stars. Solar System Model, https://www.solarsystemscope.com/, is a similar tool, but this one has more features and also includes options to show spacecraft, constellations, dwarf planets, comets, and a lot more. Still, nothing we’ve seen so far gets us out of our galaxy, the Milky Way, at the center of which is a black hole.

What about beyond our galaxy? A few years ago, while pondering the vastness of the Universe, some smart person at NASA decided that they would take the Hubble Telescope and point it at a small square of nothingness to see what they could see. Suffice it to say they were not disappointed.

https://www.nasa.gov/mission_pages/hubble/science/xdf.html

Every bit of light you see in that picture is a galaxy. In each galaxy are hundreds of billions of stars. This picture represents only a fraction of a fraction of a fraction of the sphere of our night sky. To photograph the rest of it you would need to take another 12,913,983 pictures.

Which is all fine and dandy, but again, people have a hard time comprehending the scale. All of our reference points are too small and too slow. Fortunately, someone at NASA put together something that shows that even if you travel at the upper limit for speed – the speed of light – it takes a really long time to get anywhere. One could say that the speed of light in that respect is rather slow. Put another way, space is huge.

How long it takes for light to travel between the Earth and the Moon

How long it takes for light to travel between the Earth and Mars 

Finally, for anyone wondering where God and religion fit in, I will leave you with this (enlarge the photo when it loads and scroll): 

[Source link]

~ Andrew


Other Important and Interesting Links:

Ten Female Astronomers

Ten Inspiring Women in Science

Eight Free Science Resources

Levels of Infinity

Space Missions

Two Trillion Galaxies

LA to New York Earth Timeline

Exoplanet Orbits

A Virtual Universe

Daylight Map

ISS Payload Camera

Scale of Solar System & Universe

Black Hole Size Comparison

How Big is the Universe?

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This week's Skeptophilia book recommendation is apt given our recent focus on all things astronomical: Edward Brooke-Hitching's amazing The Sky Atlas.

This lovely book describes our history of trying to map out the heavens, from the earliest Chinese, Babylonian, and Native American drawings of planetary positions, constellations, and eclipses, to the modern mapping techniques that pinpoint the location of stars far too faint to see with the naked eye -- and objects that can't be seen directly at all, such as intergalactic dust clouds and black holes.  I've always loved maps, and this book combines that with my passion for astronomy into one brilliant volume.

It's also full of gorgeous illustrations showing not only the maps themselves but the astronomers who made them.  If you love looking up at the sky, or love maps, or both -- this one should be on your list for sure.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]