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Saturday, July 30, 2016

Reading List: Parallax

Hirshfeld, Alan W. Parallax. New York: Dover, [2001] 2013. ISBN 978-0-486-49093-9.
“Eppur si muove.” As legend has it, these words were uttered (or muttered) by Galileo after being forced to recant his belief that the Earth revolves around the Sun: “And yet it moves.” The idea of a heliocentric model, as opposed to the Earth being at the center of the universe (geocentric model), was hardly new: Aristarchus of Samos had proposed it in the third century B.C., as a simplification of the prevailing view that the Earth was fixed and all other heavenly bodies revolved around it. This seemed to defy common sense: if the Earth rotated on its axis every day, why weren't there strong winds as the Earth's surface moved through the air? If you threw a rock straight up in the air, why did it come straight down rather than being displaced by the Earth's rotation while in flight? And if the Earth were offset from the center of the universe, why didn't we observe more stars when looking toward it than away?

By Galileo's time, many of these objections had been refuted, in part by his own work on the laws of motion, but the fact remained that there was precisely zero observational evidence that the Earth orbited the Sun. This was to remain the case for more than a century after Galileo, and millennia after Aristarchus, a scientific quest which ultimately provided the first glimpse of the breathtaking scale of the universe.

Hold out your hand at arm's length in front of your face and extend your index finger upward. (No, really, do it.) Now observe the finger with your right eye, then your left eye in succession, each time closing the other. Notice how the finger seems to jump to the right and left as you alternate eyes? That's because your eyes are separated by what is called the interpupillary distance, which is on the order of 6 cm. Each eye sees objects from a different perspective, and nearby objects will shift with respect to distant objects when seen from different eyes. This effect is called parallax, and the brain uses it to reconstruct depth information for nearby objects. Interestingly, predator animals tend to have both eyes on the front of the face with overlapping visual fields to provide depth perception for use in stalking, while prey animals are more likely to have eyes on either side of their heads to allow them to monitor a wider field of view for potential threats: compare a cat and a horse.

Now, if the Earth really orbits the Sun every year, that provides a large baseline which should affect how we see objects in the sky. In particular, when we observe stars from points in the Earth's orbit six months apart, we should see them shift their positions in the sky, since we're viewing them from different locations, just as your finger appeared to shift when viewed from different eyes. And since the baseline is enormously larger (although in the times of Aristarchus and even Galileo, its absolute magnitude was not known), even distant objects should be observed to shift over the year. Further, nearby stars should shift more than distant stars, so remote stars could be used as a reference for measuring the apparent shift of those closest to the Sun. This was the concept of stellar parallax.

Unfortunately for advocates of the heliocentric model, nobody had been able to observe stellar parallax. From the time of Aristarchus to Galileo, careful observers of the sky found the positions of the stars as fixed in the sky as if they were painted on a distant crystal sphere as imagined by the ancients, with the Earth at the center. Proponents of the heliocentric model argued that the failure to observe parallax was simply due to the stars being much too remote. When you're observing a distant mountain range, you won't notice any difference when you look at it with your right and left eye: it's just too far away. Perhaps the parallax of stars was beyond our ability to observe, even with so long a baseline as the Earth's distance from the Sun. Or, as others argued, maybe it didn't move.

But, pioneered by Galileo himself, our ability to observe was about to take an enormous leap. Since antiquity, all of our measurements of the sky, regardless of how clever our tools, ultimately came down to the human eye. Galileo did not invent the telescope, but he improved what had been used as a “spyglass” for military applications into a powerful tool for exploring the sky. His telescopes, while crude and difficult to use, and having a field of view comparable to looking through a soda straw, revealed mountains and craters on the Moon, the phases of Venus (powerful evidence against the geocentric model), the satellites of Jupiter, and the curious shape of Saturn (his telescope lacked the resolution to identify its apparent “ears” as rings). He even observed Neptune in 1612, when it happened to be close to Jupiter, but he didn't interpret what he had seen as a new planet. Galileo never observed parallax; he never tried, but he suggested astronomers might concentrate on close pairs of stars, one bright and one dim, where, if all stars were of comparable brightness, one might be close and the other distant, from which parallax could be teased out from observation over a year. This was to inform the work of subsequent observers.

Now the challenge was not one of theory, but of instrumentation and observational technique. It was not to be a sprint, but a marathon. Those who sought to measure stellar parallax and failed (sometimes reporting success, only to have their results overturned by subsequent observations) reads like a “Who's Who” of observational astronomy in the telescopic era: Robert Hooke, James Bradley, and William Herschel all tried and failed to observe parallax. Bradley's observations revealed an annual shift in the position of stars, but it affected all stars, not just the nearest. This didn't make any sense unless the stars were all painted on a celestial sphere, and the shift didn't behave as expected from the Earth's motion around the Sun. It turned out to be due to the aberration of light resulting from the motion of the Earth around the Sun and the finite speed of light. It's like when you're running in a rainstorm:

Raindrops keep fallin' in my face,
More and more as I pick up the pace…

Finally, here was proof that “it moves”: there would be no aberration in a geocentric universe. But by Bradley's time in the 1720s, only cranks and crackpots still believed in the geocentric model. The question was, instead, how distant are the stars? The parallax game remained afoot.

It was ultimately a question of instrumentation, but also one of luck. By the 19th century, there was abundant evidence that stars differed enormously in their intrinsic brightness. (We now know that the most luminous stars are more than a billion times more brilliant than the dimmest.) Thus, you couldn't conclude that the brightest stars were the nearest, as astronomers once guessed. Indeed, the distances of the four brightest stars as seen from Earth are, in light years, 8.6, 310, 4.4, and 37. Given that observing the position of a star for parallax is a long-term project and tedious, bear in mind that pioneers on the quest had no idea whether the stars they observed were near or far, nor the distance to the nearest stars they might happen to be lucky enough to choose.

It all came together in the 1830s. Using an instrument called a heliometer, which was essentially a refractor telescope with its lens cut in two with the ability to shift the halves and measure the offset, Friedrich Bessel was able to measure the parallax of the star 61 Cygni by comparison to an adjacent distant star. Shortly thereafter, Wilhelm Struve published the parallax of Vega, and then, just two months later, Thomas Henderson reported the parallax of Alpha Centauri, based upon measurements made earlier at the Cape of Good Hope. Finally, we knew the distances to the nearest stars (although those more distant remained a mystery), and just how empty the universe was.

Let's put some numbers on this, just to appreciate how great was the achievement of the pioneers of parallax. The parallax angle of the closest star system, Alpha Centauri, is 0.755 arc seconds. (The parallax angle is half the shift observed in the position of the star as the Earth orbits the Sun. We use half the shift because it makes the trigonometry to compute the distance easier to understand.) An arc second is 1/3600 of a degree, and there are 360 degrees in a circle, so it's 1/1,296,000 of a full circle.

Now let's work out the distance to Alpha Centauri. We'll work in terms of astronomical units (au), the mean distance between the Earth and Sun. We have a right triangle where we know the distance from the Earth to the Sun and the parallax angle of 0.755 arc seconds. (To get a sense for how tiny an angle this is, it's comparable to the angle subtended by a US quarter dollar coin when viewed from a distance of 6.6 km.) We can compute the distance from the Earth to Alpha Centauri as:

1 au / tan(0.755 / 3600) = 273198 au = 4.32 light years

Parallax is used to define the parsec (pc), the distance at which a star would have a parallax angle of one arc second. A parsec is about 3.26 light years, so the distance to Alpha Centauri is 1.32 parsecs. Star Wars notwithstanding, the parsec, like the light year, is a unit of distance, not time.

Progress in instrumentation has accelerated in recent decades. The Earth is a poor platform from which to make precision observations such as parallax. It's much better to go to space, where there are neither the wobbles of a planet nor its often murky atmosphere. The Hipparcos mission, launched in 1989, measured the parallaxes and proper motions of more than 118,000 stars, with lower resolution data for more than 2.5 million stars. The Gaia mission, launched in 2013 and still underway, has a goal of measuring the position, parallax, and proper motion of more than a billion stars.

It's been a long road, getting from there to here. It took more than 2,000 years from the time Aristarchus proposed the heliocentric solar system until we had direct observational evidence that eppur si muove. Within a few years, we will have in hand direct measurements of the distances to a billion stars. And, some day, we'll visit them.

I originally read this book in December 2003. It was a delight to revisit.

Posted at 21:39 Permalink

Saturday, July 23, 2016

Reading List: The Frozen Water Trade

Weightman, Gavin. The Frozen Water Trade. New York: Hyperion, [2003] 2004. ISBN 978-0-7868-8640-1.
In the summer of 1805, two brothers, Frederic and William Tudor, both living in the Boston area, came up with an idea for a new business which would surely make their fortune. Every winter, fresh water ponds in Massachusetts froze solid, often to a depth of a foot or more. Come spring, the ice would melt.

This cycle had repeated endlessly since before humans came to North America, unremarked upon by anybody. But the Tudor brothers, in the best spirit of Yankee ingenuity, looked upon the ice as an untapped and endlessly renewable natural resource. What if this commodity, considered worthless, could be cut from the ponds and rivers, stored in a way that would preserve it over the summer, and shipped to southern states and the West Indies, where plantation owners and prosperous city dwellers would pay a premium for this luxury in times of sweltering heat?

In an age when artificial refrigeration did not exist, that “what if” would have seemed so daunting as to deter most people from entertaining the notion for more than a moment. Indeed, the principles of thermodynamics, which underlie both the preservation of ice in warm climates and artificial refrigeration, would not be worked out until decades later. In 1805, Frederic Tudor started his “Ice House Diary” to record the progress of the venture, inscribing it on the cover, “He who gives back at the first repulse and without striking the second blow, despairs of success, has never been, is not, and never will be, a hero in love, war or business.” It was in this spirit that he carried on in the years to come, confronting a multitude of challenges unimagined at the outset.

First was the question of preserving the ice through the summer, while in transit, and upon arrival in the tropics until it was sold. Some farmers in New England already harvested ice from their ponds and stored it in ice houses, often built of stone and underground. This was sufficient to preserve a modest quantity of ice through the summer, but Frederic would need something on a much larger scale and less expensive for the trade he envisioned, and then there was the problem of keeping the ice from melting in transit. Whenever ice is kept in an environment with an ambient temperature above freezing, it will melt, but the rate at which it melts depends upon how it is stored. It is essential that the meltwater be drained away, since if the ice is allowed to stand in it, the rate of melting will be accelerated, since water conducts heat more readily than air. Melting ice releases its latent heat of fusion, and a sealed ice house will actually heat up as the ice melts. It is imperative the ice house be well ventilated to allow this heat to escape. Insulation which slows the flow of heat from the outside helps to reduce the rate of melting, but care must be taken to prevent the insulation from becoming damp from the meltwater, as that would destroy its insulating properties.

Based upon what was understood about the preservation of ice at the time and his own experiments, Tudor designed an ice house for Havana, Cuba, one of the primary markets he was targeting, which would become the prototype for ice houses around the world. The structure was built of timber, with double walls, the cavity between the walls filled with insulation of sawdust and peat. The walls and roof kept the insulation dry, and the entire structure was elevated to allow meltwater to drain away. The roof was ventilated to allow the hot air from the melting ice to dissipate. Tightly packing blocks of uniform size and shape allowed the outer blocks of ice to cool those inside, and melting would be primarily confined to blocks on the surface of the ice stored.

During shipping, ice was packed in the hold of ships, insulated by sawdust, and crews were charged with regularly pumping out meltwater, which could be used as an on-board source of fresh water or disposed of overboard. Sawdust was produced in great abundance by the sawmills of Maine, and was considered a waste product, often disposed of by dumping it in rivers. Frederic Tudor had invented a luxury trade whose product was available for the price of harvesting it, and protected in shipping by a material considered to be waste.

The economics of the ice business exploited an imbalance in Boston's shipping business. Massachusetts produced few products for export, so ships trading with the West Indies would often leave port with nearly empty holds, requiring rock ballast to keep the ship stable at sea. Carrying ice to the islands served as ballast, and was a cargo which could be sold upon arrival. After initial scepticism was overcome (would the ice all melt and sink the ship?), the ice trade outbound from Boston was an attractive proposition to ship owners.

In February 1806, the first cargo of ice sailed for the island of Martinique. The Boston Gazette reported the event as follows.

No joke. A vessel with a cargo of 80 tons of Ice has cleared out from this port for Martinique. We hope this will not prove to be a slippery speculation.

The ice survived the voyage, but there was no place to store it, so ice had to be sold directly from the ship. Few islanders had any idea what to do with the ice. A restaurant owner bought ice and used it to make ice cream, which was a sensation noted in the local newspaper.

The next decade was to prove difficult for Tudor. He struggled with trade embargoes, wound up in debtor's prison, contracted yellow fever on a visit to Havana trying to arrange the ice trade there, and in 1815 left again for Cuba just ahead of the sheriff, pursuing him for unpaid debts.

On board with Frederic were the materials to build a proper ice house in Havana, along with Boston carpenters to erect it (earlier experiences in Cuba had soured him on local labour). By mid-March, the first shipment of ice arrived at the still unfinished ice house. Losses were originally high, but as the design was refined, dropped to just 18 pounds per hour. At that rate of melting, a cargo of 100 tons of ice would last more than 15 months undisturbed in the ice house. The problem of storage in the tropics was solved.

Regular shipments of ice to Cuba and Martinique began and finally the business started to turn a profit, allowing Tudor to pay down his debts. The cities of the American south were the next potential markets, and soon Charleston, Savannah, and New Orleans had ice houses kept filled with ice from Boston.

With the business established and demand increasing, Tudor turned to the question of supply. He began to work with Nathaniel Wyeth, who invented a horse-drawn “ice plow,” which cut ice more rapidly than hand labour and produced uniform blocks which could be stacked more densely in ice houses and suffered less loss to melting. Wyeth went on to devise machinery for lifting and stacking ice in ice houses, initially powered by horses and later by steam. What had initially been seen as an eccentric speculation had become an industry.

Always on the lookout for new markets, in 1833 Tudor embarked upon the most breathtaking expansion of his business: shipping ice from Boston to the ports of Calcutta, Bombay, and Madras in India—a voyage of more than 15,000 miles and 130 days in wooden sailing ships. The first shipment of 180 tons bound for Calcutta left Boston on May 12 and arrived in Calcutta on September 13 with much of its ice intact. The ice was an immediate sensation, and a public subscription raised funds to build a grand ice house to receive future cargoes. Ice was an attractive cargo to shippers in the East India trade, since Boston had few other products in demand in India to carry on outbound voyages. The trade prospered and by 1870, 17,000 tons of ice were imported by India in that year alone.

While Frederic Tudor originally saw the ice trade as a luxury for those in the tropics, domestic demand in American cities grew rapidly as residents became accustomed to having ice in their drinks year-round and more households had “iceboxes” that kept food cold and fresh with blocks of ice delivered daily by a multitude of ice men in horse-drawn wagons. By 1890, it was estimated that domestic ice consumption was more than 5 million tons a year, all cut in the winter, stored, and delivered without artificial refrigeration. Meat packers in Chicago shipped their products nationwide in refrigerated rail cars cooled by natural ice replenished by depots along the rail lines.

In the 1880s the first steam-powered ice making machines came into use. In India, they rapidly supplanted the imported American ice, and by 1882 the trade was essentially dead. In the early years of the 20th century, artificial ice production rapidly progressed in the US, and by 1915 the natural ice industry, which was at the mercy of the weather and beset by growing worries about the quality of its product as pollution increased in the waters where it was harvested, was in rapid decline. In the 1920s, electric refrigerators came on the market, and in the 1930s millions were sold every year. By 1950, 90 percent of Americans living in cities and towns had electric refrigerators, and the ice business, ice men, ice houses, and iceboxes were receding into memory.

Many industries are based upon a technological innovation which enabled them. The ice trade is very different, and has lessons for entrepreneurs. It had no novel technological content whatsoever: it was based on manual labour, horses, steel tools, and wooden sailing ships. The product was available in abundance for free in the north, and the means to insulate it, sawdust, was considered waste before this new use for it was found. The ice trade could have been created a century or more before Frederic Tudor made it a reality.

Tudor did not discover a market and serve it. He created a market where none existed before. Potential customers never realised they wanted or needed ice until ships bearing it began to arrive at ports in torrid climes. A few years later, when a warm winter in New England reduced supply or ships were delayed, people spoke of an “ice famine” when the local ice house ran out.

When people speak of humans expanding from their home planet into the solar system and technologies such as solar power satellites beaming electricity to the Earth, mining Helium-3 on the Moon as a fuel for fusion power reactors, or exploiting the abundant resources of the asteroid belt, and those with less vision scoff at such ambitious notions, it's worth keeping in mind that wherever the economic rationale exists for a product or service, somebody will eventually profit by providing it. In 1833, people in Calcutta were beating the heat with ice shipped half way around the world by sail. Suddenly, what we may accomplish in the near future doesn't seem so unrealistic.

I originally read this book in April 2004. I enjoyed it just as much this time as when I first read it.

Posted at 22:26 Permalink

Thursday, July 21, 2016

New: The Army's Flying Saucer

The Army's Flying Saucer recounts the curious story of the Avro Canada VZ-9 Avrocar, an actual flying saucer developed for the U.S. Army in the late 1950s as a flying Jeep.

Posted at 21:55 Permalink

Sunday, July 17, 2016

New: Slide Rule

I've just posted Slide Rule, an introduction to this venerable computing tool, in which several simple physics problems are worked out in detail, ranging from loading a turnip truck to interstellar flight.

Posted at 00:31 Permalink

Thursday, July 14, 2016

Reading List: Leaving Lisa

Coppley, Jackson. Leaving Lisa. Seattle: CreateSpace, 2016. ISBN 978-1-5348-5971-5.
Jason Chamberlain had it all. At age fifty, the company he had founded had prospered so that when he sold out, he'd never have to work again in his life. He and Lisa, his wife and the love of his life, lived in a mansion in the suburbs of Washington, DC. Lisa continued to work as a research scientist at the National Institutes of Health (NIH), studying the psychology of grief, loss, and reconciliation. Their relationship with their grown daughter was strained, but whose isn't in these crazy times?

All of this ended in a moment when Lisa was killed in a car crash which Jason survived. He had lost his love, and blamed himself. His life was suddenly empty.

Some time after the funeral, he takes up an invitation to visit one of Lisa's colleagues at NIH, who explains to Jason that Lisa had been a participant in a study in which all of the accumulated digital archives of her life—writings, photos, videos, sound recordings—would be uploaded to a computer and, using machine learning algorithms, indexed and made accessible so that people could ask questions and have them answered, based upon the database, as Lisa would have, in her voice. The database is accessible from a device which resembles a smartphone, but requires network connectivity to the main computer for complicated queries.

Jason is initially repelled by the idea, but after some time returns to NIH and collects the device and begins to converse with it. Lisa doesn't just want to chat. She instructs Jason to embark upon a quest to spread her ashes in three places which were important to her and their lives together: Costa Rica, Vietnam, and Tuscany in Italy. The Lisa-box will accompany Jason on his travels and, in its own artificially intelligent way, share his experiences.

Jason embarks upon his voyages, rediscovering in depth what their life together meant to them, how other cultures deal with loss, grief, and healing, and that closing the book on one phase of his life may be opening another. Lisa is with him as these events begin to heal and equip him for what is to come. The last few pages will leave you moist eyed.

In 2005, Rudy Rucker published The Lifebox, the Seashell, and the Soul, in which he introduced the “lifebox” as the digital encoding of a person's life, able to answer questions from their viewpoint and life experiences as Lisa does here. When I read Rudy's manuscript, I thought the concept of a lifebox was pure fantasy, and I told him as much. Now, not only am I not so sure, but in fact I believe that something approximating a lifebox will be possible before the end of the decade I've come to refer to as the “Roaring Twenties”. This engrossing and moving novel is a human story of our near future (to paraphrase the title of another of the author's books) in which the memory of the departed may be more than photo albums and letters.

The Kindle edition is free to Kindle Unlimited subscribers. The author kindly allowed me to read this book in manuscript form.

Posted at 21:32 Permalink