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Exhaustive new review article on exoplanets.

January 25th, 2015 No comments

One tends to roll one’s eyes when the topic turns to Georges-Louis Leclerc, Comte de Buffon, the French encyclopedist and pre-revolutionary intellectual luminary.

Buffon sounds regrettably similar to Buffoon, especially considering that The Comte is best-known for some memorable blunders. For example, Georges-Louis came out on the losing side of a tussle with Thomas Jefferson regarding the general valor of the New World fauna. From the wikipedia article:

At one point, Buffon propounded a theory that nature in the New World was inferior to that of Eurasia. He argued that the Americas were lacking in large and powerful creatures, and that even the people were less virile than their European counterparts. He ascribed this inferiority to the marsh odors and dense forests of the American continent. These remarks so incensed Thomas Jefferson that he dispatched twenty soldiers to the New Hampshire woods to find a bull moose for Buffon as proof of the “stature and majesty of American quadrupeds”

Buffon also speculated, in 1778, that the solar system’s planets were the result of a collision between a comet and the Sun, a hypothesis that is completely incorrect. Even in the 1750s, perturbation analyses (such as those carried out by Alexis Claude Clairaut in connection with the successful predictions of the return ephemeris for Halley’s Comet) had made it clearly evident that cometary masses are far smaller than planetary masses.

Buffon, however, was definitively not a buffoon. He came remarkably close to having a full command of all the scientific disciplines, and some of his efforts still sparkle. He calculated that the chance of the Sun rising tomorrow is \(1-(1/2)^x\), where \(x\) is the number of consecutive days that it has risen to date. In his treatment of probability theory, he also stated that one chance in 10,000 is the lowest practical probability — an enormously useful bon mot, on par, say, with Andy Warhol’s remark that “when you think about it, Department Stores are kind of like Museums.”

Buffon’s Histoire Naturelle, which aimed to exhaustively cover all of the natural sciences, ran to 44 quarto volumes, eight of which were written and which appeared after he died, and all of which were out of date the moment they were printed. Even in the 1700s, scientific knowledge was accumulating so rapidly that it was impossible to keep up.

It has been recently hammered home to me that the same situation also now holds true for extrasolar planets. Jack Lissauer and I just finished a review article on exoplanets for the forthcoming second edition of Elsevier’s Treatise on Geophysics. A pre-print is up on today’s arXiv listing. In writing the article, it was painfully clear just how large the literature is, and how fast it is growing…

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Boys, be ambitious!

January 21st, 2015 No comments

When I lived in Japan, I visited Hokkaido University in Sapporo to give an astronomy colloquium. While there, I immediately noticed that an odd motto, “Boys, Be Ambitious!” is attached (in English) with great frequency to the various affairs, both large and small, of the University. One of the astronomy graduate students had the phrase written on a post-it note attached to the screen of his computer. In another building, there was a large mural showing a stern, stiffly dressed 19th-century gentleman exhorting a group of reverent students with a longer version of the phrase:

“Boys, be ambitious! Be ambitious not for money or for selfish aggrandizement, not for that evanescent thing which men call fame. Be ambitious for that attainment of all that a man ought to be.”

Which, upon reflection, seems to be reasonable advice…

The gentleman in the mural, it turns out, is William Clark Smith, the founder and first president of the University of Amherst, Massachusetts. In the mid 1870s, he was enlisted by the Japanese Meiji Restoration government as an Oyatoi Gaikokujin, or “hired foreigner”, to establish an agricultural college in Sapporo (now Hokkaido University) and he made an impression that has lasted well over a century. The Wikipedia article is extensive and quite interesting. On the origination of the motto:

“On the day of Clark’s departure, April 16, 1877, students and faculty of SAC rode with him as far as the village of Shimamatsu, then 13 miles (21 km) outside of Sapporo. As recalled by one of the students, Masatake Oshima, after saying his farewells, Clark shouted, “Boys, be ambitious!”

Upon returning to the United States, and flush with the organizational successes and appreciation that he had garnered in Japan, Clark left his academic career, cultivated an interest in gold and silver mining, and embarked on an abrupt, ambitious, and ultimately disastrous foray into the business world. In 1880, he teamed up with a junior partner, John R. Bothwell, to found what might best be described as a 19th-century incarnation of a metals hedge fund. From offices on the corner of Nassau and Wall Streets in Manhattan, the firm of Clark & Bothwell acquired interests in a slew of silver and gold mines across North America, for which they assumed management and issued stock. Clark, as president, got his contacts and colleagues to invest in the venture, and for a period during 1881, the stocks issued by Clark and Bothwell ran up into multi-million dollar valuations. A classic example of a bubble.

Clark travelled around the country, promoting the company, acquiring new mines, and seeing to their management, while Bothwell appears to have been responsible for back-office operations. Clark, who had no experience in finance, and little real knowlege of mining geology seems to have spun his wheels, while Bothwell, who had a shady history, actively mismanaged the companies. The operation got into debt, with the outcome being all too typically familiar along the lines of When Genius Failed. By the Spring of 1882, they were facing insolvency, investor lawsuits, fraud allegations, and various other problems. Bothwell disappeared on a train trip to San Francisco, never to be seen again, leaving Clark holding the bag. The story played out to the delight of the Massachusetts and national press.

From the Springfield Republican, May 29, 1882:

… it appears form the beginning that he, as manager of the mines has allowed Bothwell, as treasurer, absolute control of the books and finances of the several companies. It doesn’t appear that he ever examined the books, nor had anybody do so for him, or inquired into the financial condition of each mine, or what was being done with their profits; neither has he required from Bothwell such bonds as the latter’s position should require for the safe handling of moneys entrusted to him..

The scandal made the New York Times, which wrote several articles about the affair, including this one, from May 29th, 1882, which I dug out of the archive:


The scandals eventually ruined Clark’s health, and he died four years later, in 1886, at age 60. A cautionary tale for academics everywhere with ambitions to leave the Ivory Tower in search of glittering lucre…

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Census

January 17th, 2015 No comments

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I’ve been putting the finishing touches on a review article covering extrasolar planets that will be posted to arXiv in a few days. The list of to-do’s involves updating the figures, including the one shown just below, which charts \(M\sin i\)‘s of the RV-sourced planets in dark gray and simple radius-derived mass estimates of the transit-sourced planets in red. The steady Moore’s Law-like progression toward ever-lower masses has definitively reached Earth-mass (not to be confused with Earth-like) planets. The process took up only two decades, and was among the more impressive scientific advances of the recent past.

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Here’s an elaboration of the above figure that doesn’t make it into the article, but is interesting nonetheless. On the y-axis is \(K/rms\), which is reasonably well correlated with the signal strength of Doppler velocity discoveries. One can certainly detect planets with confidence at low \(K/rms\), but it requires a large number of independent Doppler velocity measurements. The color corresponds to “astrobiological interest” — surely naive, and probably misplaced, but nonetheless quantifiable by my planet valuation formula.

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The Elysian Fields

January 14th, 2015 No comments

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Credit: NASA/JPL

It feels increasingly awkward and embarrassing to read LaTeXed, peer-reviewed articles that quantify and delineate the habitable zone — the special region surrounding a star that is invariably (and rather fittingly) linked to a particular fairy tale from the Brothers Grimm.

Evolutionary psychologists have speculated that the concept of the afterlife might be inextricably entwined to the evolution of the mind’s ability to reason about the minds of others. A rational world view, however, frustrates ingrained atavistic yearnings and a belief in the supernatural. Habitable planets provide a respectable stopgap to assuage the discomfort of these incompatible poles. Could it be a mere coincidence that the ancient Greek and classical depictions of Elýsion pedíon, the Elysian Fields, are part and parcel the very image of the habitable zone?

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Credit: NASA/SETI/JPL

And they live untouched by sorrow in the islands of the blessed along the shore of deep-swirling Ocean, happy heroes for whom the grain-giving earth bears honey-sweet fruit flourishing thrice a year, far from the deathless gods…

— Hesiod, Works and Days (170)

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Detroit

January 8th, 2015 Comments off

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The submerged summit of the Detroit Seamount ranks among the planet’s gloomiest spots. East of Kamchatka, a mile beneath the waves at 51 51′ N, 167 45′ E, it is second-to-last in the long line of Emperors. Inch by inch, it creeps toward destruction in the Aleutian Trench.

Detroit’s glory days were the late Cretaceous. Back then, it was an active Hawaiian volcano.

Live it fast, you’re gonna there soon. Kauai is five million years old, but underground, the lights have gone out. Over half of the original height and the original land area have disappeared. Rivers gush sediment into the sea. Waimea Canyon juxtaposes verdure and an erosive wasteland. Four wheel drive claws and rends the red dirt.

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Beyond Kauai, the next islands in the chain are Nihoa,

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Necker,

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and the La Perouse Pinnacle,

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whose resemblance to a sinking ship is not just metaphoric.

Before humans arrived, the Hawaiian islands had strange flightless birds. Indeed, each island in the chain developed its own odd avian inhabitants, sculpted by natural selection, and then driven conveyor-like to extinction. Not once, in forty, fifty, sixty tries, did the birds respond by evolving intelligence and doing something about their situation. Probably, there was never enough time.

Or perhaps, that’s something that rarely, if ever, happens.

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lightspeed

January 1st, 2015 Comments off

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Aon Tower, as seen from Lurie Garden in Millennium Park

Millennium Park in Chicago is a remarkable place. Skyscrapers shoulder together and soar up steeply to the north and to the west. The vertiginous effect of their cliff faces is reminiscent of Yosemite Valley.

Lurie Garden is at the center of the park, and is given over largely to native plants that carpeted the Illinois landscape in the interval between the retreat of the glaciers and the advance of the corn fields. In the silence of a photograph with a narrow field of view, it is as if the city never existed.

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Lurie Garden

Restore the sound, and the the buzz and hum of insects are superimposed on the wash of urban noise. A swarm of bees, algorithmic in their efficiency, and attuned to the flowers’ black light glow, collect the nectar. 55% sucrose, 24% glucose and 21% fructose.

When viewed in microwaves and millimeter waves, say from 1 to 100 GHz, the Millennium Park scene displays a similarly jarring juxtaposition. The sky glows with the ancient three degree background radiation — the cosmic static of the Big Bang explosion — subtly brightest in the direction of the Virgo Supercluster. All around, the buildings, the roads and the sidewalks are lit up with manically pulsating wireless transmitters: routers, cell phones, myriad sensors. In highly focused 6 GHz and 11 GHz beams, billions of dollars in coded securities orders streak above the urban canyons on line-of-sight paths linking the data centers of Chicago, Aurora, and suburban New Jersey. The fastest path of all runs through the top of the monolithic Aon Tower, where the signal is amplified and launched onward across the Lake and far into Michigan.

The microwave beams are a new development. In mid-2010, price movements at the Chicago Mercantile Exchange generated reactions in New Jersey nine milliseconds later. The signals traveled on fiber optic cables that meandered along railroad rights-of-way.

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Now, the messages arrive within a few microseconds of the time it would take light to travel in vacuum, galvanizing the swarm of algorithms that are continually jostling and buzzing in the vicinity of the match.

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Angular Power Spectra

December 29th, 2014 Comments off

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It’s worth a scramble to get a window seat on a Hawaiian inter-island flight. The views are full of craggy green cliffs, porcelain ocean, and wispy masses of fog and cloud. Sometimes, several islands are visible at once, and it’s not hard to imagine that the archipelago might extend over the entire globe.

That would be a very different planet, and, in fact, a world covered by hotspot volcanoes might have a surface elevation profile somewhat reminiscent of the WMAP image of the temperature fluctuations in the cosmic microwave background. The WMAP image brings to mind a planet covered in Hawaiian islands.

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Any distribution, \(f(\theta,\phi)\), on the surface of a sphere, be it of temperature, or elevation, or the density of IP addresses, can be expressed as a weighted sum of spherical harmonics

$$f(\theta,\phi)=\sum_{l,m} a_{l,m} Y(\theta,\phi)_{l}^{m}\, ,$$
where the coefficients corresponding to the individual weights, \(a_{l,m}\) are given by
$$a_{l,m}=\int_{\Omega}f(\theta,\phi)Y(\theta,\phi)_{l}^{m \star}d\Omega\, ,$$
and the power, \(C_{l}\) at angular scale \(l\) is
$$C_{l}=\frac{1}{2l+1}\sum_{m=-l}^{l}a_{l,m} {a_{l,m}}^{\star}\, .$$

The power spectrum of the CMB anisotropies peaks at \(l\sim 200\), which corresponds to an angular scale on the sky of \(\Delta \theta \sim 1^{\circ}\), which is very close to the solid angle subtended by the Big Island of Hawaii on the surface of the spherical Earth.

Here’s a recent version of the CMB temperature anisotropy spectrum from the Planck Mission website

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The peaks in the spectrum of CMB temperature anisotropies stem from acoustic oscillations and diffusion damping in the early universe, and they encode all sorts of information about the fundamental cosmological parameters. This, of course, is very well-known stuff: a search on all literature in the ADS database published since 2000, and ranked by citations, lists Spergel et al. 2003, First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters at #1, with 7,914 citations and (rapidly) counting.

Given the similarity between the angular scales of the Hawaiian islands and the main CMB peak, it’s interesting to compute the angular power spectrum of Earth’s bedrock elevation profile. A global relief dataset with one arc-minute resolution is available from NOAA as a 4GB (uncompressed) file. Downsampling by a factor of 100, and applying the “terrain” color map yields a familiar scene

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Computing the power in the first 108 angular modes of the relief distribution in the above data set gives a spectrum that is weighted toward continents and ocean basins rather than archipelagos. There is a pronounced peak at \(l=5\) that reflects the typical angular scale of continents and ocean basins.

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Here is the global relief distribution obtained by summing just the \(l=5\) contributions. It’s right for more or less the same reason that Crates of Mallus was right:

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Using all 108 angular mode families to reconstruct the image gives a fairly credible-looking world map. It’s as if the watercolors ran slightly before they dried. Most critically, the \(l=108\) reconstruction fails to capture the highest peaks and the lowest ocean trenches, and hence more of the dynamic range of the color map is distributed across the globe.

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Degree-wide islands like Hawaii are the exception rather than the rule on Earth’s surface. I believe that this was the concept that former US Vice President Dan Qualye was struggling to express in one of his much-ridiculed pronouncements:

Hawaii has always been a very pivotal role in the Pacific. It is IN the Pacific. It is a part of the United States that is an island that is right here.

(See also his comments on Mars.)

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Skyscraper

December 23rd, 2014 Comments off

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A few weeks ago, I had a flight out of LaGaurdia Airport in New York City. On the drive there, I caught a distant glimpse of the Manhattan skyline. I was startled to see that it is newly altered. Rising from midtown was a silhouette that seemed both impossibly narrow, and taller than any other skyscraper in the far-off cut-out.

Photo Credit: 432 Park Avenue -- processed screenshot

Original Photo: 432parkavenue.com — Photoshop processed screenshot

The Internet, of course, has the story. 432 Park Avenue — $1.25B, 426 meters, the highest rooftop in the city. Many of its floors, especially the higher ones, are monolithic residences, in the process of acquisition by opaque, limited liability corporations, “bank safe deposit boxes in the sky that buyers can put their valuables in and rarely visit.”

Often, the aesthetic informing such projects veers toward the rococo, but 432 Park is minimalist to the core. Every window of the tower is an exact 10 foot by 10 foot square. From the elaborate on-line galleries, it wholly ambiguous whether the surreal bone-parchment interiors already exist or whether they are virtual. Somewhere, in micrometric accuracies of the digital architectural model, lies the pattern of the seasons, the moment of the equinox, the precise angle of sunlight shafting into the cavernous, unvisited, perhaps as-yet unconstructed rooms.

Like the pyramids at Giza — after they were sealed and before they were robbed.

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Dead voices on air

December 18th, 2014 Comments off

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This Fall quarter, I taught a class for undergraduates on order-of-magnitude estimation in physics with a focus on astronomical examples. And on the last day of class, with final exams looming, what could be better that the time-tested stress relievers provided by the Fermi Paradox and the Drake Equation?

In Los Alamos National Laboratory publication LA-103110MS, “Where is Everybody?” An Account of Fermi’s Question, Eric Jones describes how Enrico Fermi, Emil Konopinski, Edward Teller, and Herbert York were diverted into their famous lunch-time conversation in the summer of 1950. While walking to the cafeteria, they were discussing news reports of UFOs, and an associated New Yorker cartoon that explained why the public trash cans in New York City were disappearing.

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The flying saucers of the early 1950s hold a special fascination. A compound of Cold War anxieties — nuclear weapons, communists, infiltrators — they are silvery and remote, icons of minimalist design from a time when the space age was truly, rather than retro- futuristic.

Indeed, much of my own interest in astronomy can be traced to 50’s-era flying saucers. In the Bicentennial summer of 1976, after finishing third grade, I got a paper route delivering the Champaign-Urbana Courier. One of my customers, Mrs. Barbara Houseworth, had a garage full of cast-off books that she collected for an annual drive. I spent a great deal of time examining them whenever I visited to collect the subscription fee. I was particularly drawn to the pulpy paperback books — especially the ones with clay-coated photographic inserts — that covered the Bermuda Triangle, Bigfoot, the Loch Ness Monster, and Flying Saucers. All matters that seemed to merit the most urgent scientific concern.

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At the top of my list was Gray Barker’s They Knew Too Much About Flying Saucers, published in 1956. I was so taken with it that Mrs. Houseworth simply gave me the book.

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Gray Barker was an intriguing character, a closeted gay man in mid-century West Virginia who took a certain delight in channeling the fears and neuroses of the American masses into money-making volumes. Barker’s invention of the three men in dark suits, in particular, achieved a lasting cultural resonance. There is more about him at the UWV Center for Literary Computing, and he is the subject of several recent documentaries.

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The message in the Cold War flying saucer books was crystal clear. Watch the Skies. And I did — on many clear dark Central Illinois nights with a Sears catalog 50mm refracting telescope…

Back to Friday’s class. We adopted the following form for the Fermi-Drake equation
$${N} = \Lambda ~f_{\star \rm{app}}~f_{\rm pl}~f_{\rm quqHP}~f_{\rm life}~f_{\rm macro}~f_{\rm intel}~f_{\rm tech}~L\,,$$
where \(N\) is the number of broadcasting civilizations in the galaxy, \(\Lambda\) is the number of stars formed per year in the Milky Way, \(f_{\star \rm{app}}\) is the fraction of stars with main sequence lifetimes long enough to support the development of a broadcasting civilization, \(~f_{\rm pl}\) is the fraction of stars with planets, \(~f_{\rm HP}\) is the average number of “habitable” planets per star, \(~f_{\rm life}\) is the fraction of these habitable planets that develop life, \(~f_{\rm macro}\) is the fraction of life-bearing planets that develop macroscopic life, \(~f_{\rm intel}\) is the fraction of macroscopic life-bearing planets that develop an “intelligent” life form (e.g. one that can orient itself abstractly in time), \(~f_{\rm tech}\) is the fraction of intelligent species that develop an understanding of the Maxwell Equations and build radios, and \(L\) is the civilization lifetime in years.

We defined and estimated two versions of \(L\). \(L_{\rm radio}\) is the average length of a time that a civilization leaks modulated electromagnetic signals into space. \(L_{\rm extinct}\) is the lifetime of the civilization, marked from the understanding of Maxwell’s equations to the point where the equations are collectively no longer understood.

The first few terms in the equation have been elevated from the realm of science fiction. I’ve adopted values of \(~\Lambda=10\,{\rm stars~yr^{-1}}\), \(~f_{\star \rm{app}}=0.75\), and \(~f_{\rm pl}=0.75\). Note that \(~\Lambda=10\,{\rm stars~yr^{-1}}\) is admittedly on the high side, even for 4.5 Gyr ago when star formation was somewhat more prevelant in the Galaxy.

Here is the table of values for the unknown terms, as estimated by the class members. I tried not to influence the results by telegraphing currently fashionable guesses. Twenty responses were collected:

\(f_{\rm HP}\) \(f_{\rm Life}\) \(f_{\rm Macro}\) \(f_{\rm Intel}\) \(f_{\rm Tech}\) \(L_{\rm Radio}\) \(L_{\rm Extinct}\)
0.10 0.01 0.3 0.1 0.2 1000 100000
0.10 0.70 0.01 0.6 0.001 500 10000
0.40 0.60 0.01 0.1 0.9 500 3000
0.20 0.90 0.08 0.4 0.002 500 500
0.01 0.90 0.05 0.001 0.2 1000 10000
0.01 0.1 0.1 0.01 0.001 1000 1000
0.10 0.01 0.1 0.1 0.01 100 1000
0.40 0.1 0.05 0.5 0.6 100000000 1000000
0.01 0.4 0.01 0.01 0.9 1000 10000
0.30 0.001 0.032 0.6 0.001 200 200
0.01 0.8 0.1 0.7 0.9 1000 1000
0.10 0.0001 0.01 0.001 0.02 500 150
0.10 0.2 0.1 0.01 0.1 10000 100000
0.10 0.9 0.25 0.01 0.5 10000 500000
0.30 0.001 0.01 0.6 0.9 500 3000
0.30 0.05 0.3 0.01 0.01 1000 1000
0.10 0.01 0.1 0.00001 0.00000001 300 5000
0.30 0.01 0.00001 0.01 0.0001 5000 5000
0.05 0.01 0.03 0.3 0.015 1000 150
0.02 0.01 0.1 0.01 0.001 100 100

With results:

Civilizations Currently Broadcasting in the Milky Way Galaxy
Average # 16,875
Median # 0.0016
Standard deviation 73,500
Max 337,500
Min 2.8125e-13

Civilizations Currently Present in the Milky Way Galaxy
Average # 185
Median # 0.013
Standard deviation 735
Max 3,375
Min 2.8125e-13

A smooth distribution of estimates for \(~{N}\) can be generated by drawing randomly from the list of estimates for each uncertain term in the equation, and then repeating for many estimates of \(~{N}\). Here are the histograms of estimates for the number of civilizations broadcasting from the galaxy and the number of civilizations present in the galaxy. The \(x\)-axes are \(\log_{10}N\).

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The estimates point to the possibility that a civilization broadcasts for longer than intelligent members of the species exist. Two people implied this, by submitting values \(L_{\rm radio}>L_{\rm extinct}\). Looking at the table, there is one case where \(L_{\rm radio}\gg L_{\rm extinct} \gg \langle L \rangle\). The large values for \(L\) submitted by this person are causing the Average estimate for \(~{N}\) to substantially exceed the median estimate for \(~{N}\).

Adopting the \({ N=0.002}\) median of this distribution implies we need to look through \(\sim{n=500}\) galaxies to find the nearest broadcasting civilization, and that our nearest neighbors are \(\sim{ 8}\) Megaparsecs away. By the time one receives a message and replies to it, the intended recipient has long since gone extinct.

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Rocket Summer

December 13th, 2014 Comments off

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In 1997, Ray Bradbury’s The Martian Chronicles was reissued by William Morrow Press. It’s a book that’s on my shelf.

In the original edition, published in 1950, the stories were set in what is now the present day, starting with Rocket Summer, dated to January 1999, and ending with The Million Year Picnic, set in October 2026.

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For the 1997 edition, the dates for the stories were all pushed back by thirty one years. The rocket summer still lies sixteen years in the future, but the imposed literary device seems hollow, stop-gap, ineffective. Mars of 1950 is a forever different world than Mars of today, which, satisfyingly, is also populated by two waves of explorers from Earth. Meteor-borne archeobacteria, perhaps still clinging to existence in the warmth of the deep subsurface, and a cadre of faintly autonomous, sometimes faintly anthropomorphic robots and satellites that pine eagerly for attention on social media. 2836 tweets. 1.76M followers.

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