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Saturday, July 30, 2016
Reading List: Parallax
- Hirshfeld, Alan W.
New York: Dover,  2013.
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
model, as opposed to the Earth being at the
center of the universe
was hardly new:
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
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
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
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
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
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
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:
James Bradley, and
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,
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
which was essentially a refractor telescope with its lens
cut in two with the ability to shift the halves and measure the
was able to measure the parallax of the star
by comparison to an adjacent distant star. Shortly
published the parallax of
just two months later,
reported the parallax of
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
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
(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
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.
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.
mission, launched in 1989, measured the parallaxes and
of more than 118,000 stars, with lower resolution data
for more than 2.5 million stars. The
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
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
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
I originally read this book in December 2003. It was a delight to revisit.
More and more as I pick up the pace…
Saturday, July 23, 2016
Reading List: The Frozen Water Trade
- Weightman, Gavin.
The Frozen Water Trade.
New York: Hyperion,  2004.
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
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
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
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
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
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
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
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
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
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
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
I originally read this book in April 2004. I enjoyed it just
as much this time as when I first read it.
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.
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.
Thursday, July 14, 2016
Reading List: Leaving Lisa
- Coppley, Jackson.
Seattle: CreateSpace, 2016.
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
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