Philomen and Baucis:   Hospitable hosts
Just as the stranger was about to knock for the fifth and final time, the door opened slowly.  Through the slit the stranger could see a single eye regarding him sternly.  Behind the eye was a sliver of a warm, well-furnished interior.
     "What do you want?" a gruff voice demanded.  The eye moved from the stranger who had knocked to his larger companion standing just off to the left.
     "Please," the smaller stranger replied, "we are visitors to this town.  We have neither a friend nor food.   May we humbly ask for some food and a place to rest?"
     The door opened slightly more, enough to reveal an entire face.  At first austere, the homeowner's countenance suddenly brightened with amusement.  "Yeah, you may ASK!"
     He slammed the door.  The strangers heard the bolt engaged and the listened to the  man inside make a disparaging comment to his family, all of whom laughed gleefully at his biting remark.
     The two strangers looked upon each other sadly as they walked off the porch.    This reception -or lack thereof- merely confirmed what they had decided twenty slammed doors before:  The quaint hamlet of Phyrgia was wicked and inhospitable.  Throughout the day, both of them went from house to house: two dirty, rag-adorned supplicants pleading for food and shelter.   Each response seemed more hostile and cruel than the one which preceded it.   They had been cursed, mocked, and once even swatted with a broom.    They encountered angry grimaces for hours.     After this latest rebuff they realized that they had visited each home except for the isolated little cottage poised on the side of a large hill.      It didn't look like a promising prospect: its dilapidated exterior showed its age.    However, these two strangers were determined to try every home in Phrygia. As they climbed the hillside, they could see crevices and bare spots on the cottage walls:  it looked as though it were quite drafty.   Were it not for light billows of smoke issuing from a back opening, they might have concluded that the shack was abandoned.   As they reached the home, the men saw that it was certainly old:  as though it could have been destroyed by a well aimed wind gust.     Not exactly the home of people with much to offer strangers.
      "I'll give your hand a rest," the larger stranger said to his friend.  He knocked on the door and stood back a step, for he saw that this door opened toward the outside, unlike all the other nicer homes in town.   After a moment's silence, he knocked again.   He heard a rustling behind the door and a muffled voice.   As he stood forward to knock again, the door flew open.   The stranger was struck by the door and then by the clumsy old fellow who had stumbled outside.
     "Hello?" the old man asked.  He recovered his balance before looking up with fright at the large figure before him.  "Oh, my Heavens, look at you!"
    The elderly fellow then clasped his hands and muttered nervously.  "M...m..may I help you?"
    The stranger told him that he and his friend were new in town, quite tired and hungry.  "May we humbly ask for food and rest?"
    "Well," the man answered after a prolonged gulp. "of course.  Please come in.  Both of you."
     The two strangers followed the twitching little man into his small, but curiously neat domicile.  It was a single room with a bed in the corner, a fire stove, cauldron and bench in the other corner.  Between both corners was a door looking out onto a wide expanse of sloping green.   A small bare shelf hung on one wall.  A rickety table and some chairs occupied the room's center.  The home had little else besides. "You're most kind," the larger man said as the two entered the home and closed the door.
     "Not at all," his host replied with an uneasy smile.  "I make it a personal rule never to refuse the requests of seven foot tall strangers.   Make yourselves comfortable." he said, gesturing to a bench located next to their fire and  cauldron.   "Baucis!" he called to the open back door.  "We have visitors!" 
        A rather elderly woman, who had been out back tending to the couple's one goose, hobbled into the house.    She smiled warmly at the seated guests.   "Welcome," she said, stepping forward with a handful of cabbage leaves.   "Philemon, you old satyr, you didn't tell me you were expecting visitors."
         "I wasn't, but, um, here they are.  They're hungry, tired and, um, " he reduced his voice to a  completely audible whisper, "tall."   He raised his hand well above his head for emphasis, in case his wife wasn't sure what he meant.
         "Then, we should feed them well, indeed,"  Baucis told him.   "Dinner will be ready in a few moments.  I'm afraid we can offer you only cabbage soup and wine."
         The strangers both nodded "That is most gracious of you," the larger one replied, smirking slightly.
         "How can I help?" Philemon asked, grabbing and then accidentally dropping two wine cups from the shelf.   "Oh, dear," he said, stooping slowly down to retrieve the cups.
         Suppressing her exasperation, Baucis told her husband to stoke the fire while she prepared the soup and wine, the latter of which was little more than vinegar diluted with water.
         Philemon managed with great effort to build up the fire.   He spent a few minutes  blowing on the embers and then a few more coughing on the ashes, some of which fell in great clouds upon the smaller stranger.   Horrified, Philemon muttered profuse apologies to his ashen-legged guest as he frantically tried to wipe the ashes off the amused man's lap.   After nursing the pain from a couple of violent knee swats, the smaller stranger gently but firmly grabbed Philemon's hands, assuring him that he needn't bother, for he was not at all offended.
         The meal arrived a few minutes later. During the dinner the strangers spoke rarely, preferring instead to listen with amusement to the old couple speak of themselves.   They were poor farmers who had lived in that house for more than fifty years.  They bought it for a pittance soon after their wedding. They spoke of  their fondness -wholly unreciprocated- of the neighbors whom they had often invited to dine with them.  None ever accepted, hence their joy at receiving these two men, whose names they had neither requested nor received.  The old couple noticed that when the strangers did converse, they spoke Latin and Aeolic Greek more eloquently than anybody they had ever met.  The visitors switched between both languages seamlessly, as though drawing the two tongues together into an elegant tapestry of sound.   Baucis was particularly delighted by their conversation, regretting that they didn't speak more.
           At one point, as the strangers spoke, Philemon watched his wife finish her cup of wine.   Being enthralled by the visitors, she didn't notice her husband as he went to fill some of her cup with his own.    (Something he did almost each night.)    The elegant sound tapestry was torn by Philemon's uncharacteristically loud shout.  "Heavens!"
           The three others lurched back a bit, both startled and a bit appalled by this sudden exclamation.
           "What is the matter!?"  Baucis demanded. 
           Philemon merely pointed to the cup she had just drained.
           It was full again.
           Being aware of her husband's generous nature and knowing that he refilled her wine cup every night, she merely replied, "Yes, I see it. Thank you, my dear."
           "I didn't put any wine in your cup."
            Baucis looked at her cup, full to the rim.  Unlike the wine that she had poured into the cup earlier, this wine was of the finest vintage: its aroma, itself, seemed  intoxicating.   The elderly couple cast grave expressions toward the visitors.  Even in the ancient world, most people hardly ever encountered any supernatural phenomena.    This simple old couple on a hillside certainly never had.   A cup that filled itself with rich wine was a special sign.   A sign, they wrongly assumed, of divine displeasure.
            They reacted as most people with no experience in mystical realms would react.
            "We humbly beg your pardon!" Philemon pleaded, hoisting himself up faster than one would think such an elderly man could manage. In haste, he toppled over the soup bowl, splattering cabbage soup to the ground.  Even the generally imperturbable Baucis trembled as she rose from the table.  The strangers regarded them both curiously.
            Philemon aplogized profusely for the meal, confessing that it was not the finest food they had to offer.  "We have been mean and meager to our guests,"  he said to the sky.  "We implore the gods to forgive us our stinginess. We have a goose we can prepare for their dining."
            "I'll fetch it!" Baucis said, moving swiftly toward the back door.
            The next few minutes were a pandemonium of chaos.   The old couple chased the terrified goose into the house.   Being much younger and fearful , the goose ran for its life with the two desperate humans pursuing it as quickly as their fragile bones would allow them.    They shouted at it, grabbed at it, and once tried to corner on the bed, only to have it flee between Philemon's legs with a flutter of dislodged white feathers.   The strangers looked at each other and laughed aloud.  This wild goose chase was certainly one of the most amusing displays they had ever witnessed.
            After the goose fled outside again, the couple stood breathless by the bed.    The strangers arose to address them.
            "You needn't bother to feed us any more," the larger one assured them.  "I am certain the gods are not displeased with you."
            "They're not?" Baucis asked, her wrinkled old man shaking by her mouth.
            "No, we're not," the smaller stranger said with a chortle.    The rags the man had worn dissolved, revealing elegant clothing:  gold emblazoned tapestries that the two had formed earlier with their voices: a trick which only the Olympians could perform.
            "You have been hosts to the gods," the larger visitor announced.  "I am  Zeus, your servant, and this is my companion, Hermes."
            After a moment of open mouthed silence, the old man, not knowing the proper greeting for a visiting god, diverted his eyes and spoke. "Ah....h...hello there..."  
            Baucis kept her eyes locked on them and simply bowed with an arm pressed against her chest. 
            Zeus approached them  "Despite your poverty, you have been generous.   Despite our strangeness, you have been hospitable.   I am the guardian of all lonely travelers and you have been most kind to us.  I am indeed most pleased."   Both Zeus and Hermes bowed to them.  Zeus summoned them to follow him outside their front door.  They saw, to their shock, a large lake where the village had stood merely an hour before.   The light of the setting sun made it look like an ocean of amber.   
            "What happened?"  Philemon asked breathlessly.
            Hermes waved his hand toward the submerged village.  "This day was destined to bring a flood  covering the land.   We visited each home and were turned away by the selfish and wicked.    Only one home received us:   yours.   While the others were succumbing to the deluge, we were dining.  The flood moved up this mountain, but we arrested its ascent.   Of all Phrygia, only you two remain."
             The elderly couple looked down upon the water which covered their neighbors: those folks who had universally regarded them with either cold suspicion or open ridicule.   
             Baucis sniffed silently to herself.  Philemon bowed his head and wiped his eye.   A strong hand was laid upon his shoulder.  "Let's go back inside."
             Once inside, Zeus offered them their greatest wish.    They told him that they wanted to become his priests and to spend the rest of their lives together.    Zeus granted this request at once.   Baucis and Philemon were moved to a great palace, where, surprisingly, they lived for many more years as attendants to the king of the gods.
             One day, far in the future, at the onset of a slightly chilled evening similar to the one on which they had first encountered Zeus and Hermes years before, they were standing together admiring the sunset. Suddenly, they both felt their feet becoming rooted to the ground.  Bark was growing rapidly up their bodies.   Knowing that their extraordinarily long lives as humans were drawing to a close,  Philemon and Baucis reached for each other just as their arms were transforming into branches.    Philemon smiled at his wife's face just before it became covered by bark.  He softly whispered, "You never thanked me for marrying you."  Philomen and Baucis  became an oak and lime tree, which often grow together and share a trunk.  It was a custom for people to drape wreaths over their branches as a tribute to the elderly couple's kindness and generosity.  

THE SOUTHWORTH PLANETARIUM

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2019-2020:  CLXXXII

THE DAILY ASTRONOMER

Wednesday, July 22, 2020

Remote Planetarium 69:   The Drake Equation

So, now we ask a question:   how many advanced races exist in the Milky Way Galaxy?  We recognize that we are at something of a disadvantage when addressing this issue because we know of only one life bearing planet and we're living on it.    The importance of asking this question pertains to the search for extraterrestrial life.   If life is exceedingly rare so that a given spiral galaxy like the Milky Way might only harbor a few life-bearing worlds, we shouldn't expect to detect any life at all, at least not with the methods currently available to us.     However, if life is so common that millions or even hundreds of millions of life- bearing worlds are scattered throughout the galaxy, we should find a trace of at least one of them before long.       Yet, how can we begin to take a census of the Milky Way's advanced races?

We can't.

However, we can try to estimate the number through use of the "Drake Equation," a mathematical marvel that combines science and speculation.   It was formulated by radio astronomy pioneer Frank Drake (1930 -  ) who has been searching for extraterrestrial signals for many decades.  

If you're feeling a bit uneasy, don't be.   The aim of today's lesson is to work through the Drake Equation piece by piece.       

N      =  number of advanced civilizations in the Milky Way Galaxy

This is the quantity we're trying to determine with all these values.   As we shall see, N can vary widely from person to person, depending on their assumptions about some of the factors within the equation.       We know that the minimum value of N is 1 because of Earth.  Of course, some might insist that based on human behavior the minimum could be zero.   Well, bah humbug to that bunch.

R   = rate of star formation in the galaxy

According to recent estimates, about three solar masses of material are converted into stars each year.   That material is not necessarily transformed into three stars.    Remember that most stars are less massive than the Sun.    This matter could be turned into as many as seven or eight stars.      Or, perhaps, just one star more massive than the Sun.      Also, statistics is a tricky business.     Some years will experience more star formation than others.    We remember also that star formation requires millions of years.   By star formation, we refer to the point at which the star becomes active by thermonuclear fusion reactions.    

fp = fraction of stars with planets

Based on what astronomers have discovered so far, we can assume that many stars have planets.      Analysis of the Kepler Space Telescope findings shows that one in six stars has an Earth-sized planet in a tight orbit.  About twenty percent have a "Super Earth" in orbit around them.  (A Super Earth is one that is more massive than Earth but considerably less massive than gas giant planets.)      

ne  =  number of planets within a star's "ecoshell" or habitable zone

Astronomers estimate that 40 billion worlds within the Milky Way Galaxy are likely revolving within the habitable zones of their parent stars.   Eleven billion of these might be orbiting Sun-like (G type) stars.    These estimates are all based on the Kepler Space Telescope findings.   Data collected from future missions might induce astronomers to modify these estimates to some extent.

fl  = fraction of those planets on which life develops

Now we've careened headlong into the realm of speculation.    Unfortunately, the data point available in our own solar system.  As we learned earlier this week, Venus, Earth and Mars are all within the Sun's habitable zones.   However, Earth alone contains life.  That gives us a 1:2 ratio of life-bearing worlds to non-life bearing words in the solar system.   Were that ratio to apply to other solar systems, we could assert that life proliferates throughout the galaxy.    Our estimate becomes even more optimistic if we find conclusive evidence that life actually did develop on Mars early in its history.  That discovery would support the notion that life arises quickly when conditions are conducive to its inception.   Of course, it would also suggest that life can be readily snuffed out, as well.   

fi  =  fraction of living species that develops intelligence

Now we're truly limited.      Based on our solar system, the rate of intelligent life developing on a life-bearing world is one hundred percent. A beautiful 1/1 fraction.   Approximately 3.7 billion years ago, the first traces of primordial life developed on the young, toxic Earth.  Now, we're in the age of space stations and 5 G networks.   This fraction will remain wholly unknown, unless, of course, some alien emissaries visit Earth and present us with a comprehensive list of life-bearing worlds and intelligent life-bearing worlds.    On the other hand, if we accept that microbial life did arise on Mars before it was eradicated, then this fraction becomes 1/2.       Both fractions, however, are predicated only on our own solar system and therefore might not be indicative of the galaxy in general. 

fc = fraction releasing detectable signals into space

Well, we know we did, although we needed 3.7 billion years to develop the capability.         During that immense amount of time, Earth sustained asteroid bombardments and snowball Earth epochs, to name just two of the perils life has confronted over the course of Earth's natural history.        The greatest mass extinction, the Permian-triassic event, occurred 250 million years ago.    That mass extinction devastated 96 percent of all ocean species and a majority of the other life forms, as well.     Earth life literally required millions of years to recover from that extinction event.       It is possible that life on other worlds was completely destroyed by some great extinction.    We just know that life on Earth survived.  

L  = length of time releasing detectable signals

Two ways to approach this last value.    First, radio was invented in the late 19th century.  By the 1940's humans developed atomic bomb technology.   Not much later the nuclear stockpile we amassed was so large it could have wiped out Earth life ten times over.    Humans were transmitting signals for slightly more than half a century before they were at risk of self-annihilation.          Secondly, many modern radio signals don't propagate like the original waves did.      Many of today's broadcasts are not broadcasting into space anymore.   Even if the outer space broadcasting ended altogether today, humans have been transmitting detectable signals for more than a century.       Again, Earth is our only data point and might not be representative of other life-bearing planets, if they exist in the first place.  

The Drake Equation is not intended to settle the issue of how many advanced civilizations exist in the galaxy. Instead, it provides us with a method by which to estimate that number: one that will likely remain unknown for an immensely long time. 

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