125 Years of Greenwich Longitude

The Prime Meridian at Greenwich Observatory (wikipedia)

We are used today to give the coordinates of a place on Earth using latitude and longitude, indicating longitude in degrees east or west, respectively, of the Greenwich Prime Meridian.

Thus, for example, the small amateur observatory Sternwarte Peterberg near the place where I did grow up is located exactly 7 degrees east of Greenwich.

However, looking up the location on historical maps, I don't find this longitude. Actually, the French engineers who around 1800 drew the first detailed topographic maps of the region did measure longitude with respect to the Paris Observatory. Their Prussian successors used the El Heirro Meridian, which goes back to Ptolemy in the 2nd century, and later switched to coordinates centered at Berlin.

Actually, in the second half of the 19th century, more than a dozen "Prime Meridians" were in use, creating increasing confusion for transport, trade, and communication around the globe.



Thus, in October 1884, delegates from 25 nations met in Washington, DC, at a conference to determine a prime meridian, which should be used as a universal reference for measuring longitude, and for a universal time. 125 years ago, on October 13, 1884, the "International Meridian Conference held at Washington for the purpose of fixing a Prime Meridian and a Universal Day" resolved

"That a meridian proper, to be employed as a common zero in the reckoning of longitude and the regulation of time throughout the world, should be a great circle passing through the poles and the centre of the transit instrument at the Observatory of Greenwich."

and

"That the Conference proposes to the Governments here represented the adoption of the meridian passing through the transit instrument at the Observatory of Greenwich as the initial meridian for longitude."

There was one negative vote, and the delegations from Brazil and France abstained from voting. The French delegation led by astronomer Pierre Jules Janssen, the discoverer of helium, had pleaded for keeping the El Heirro Meridian, but it seems that long tables of data, from tonnages of ships to sales figures of nautical charts and almanachs, all using Greenwich as their reference point, convinced most delegates to officially adopt the de-facto standard.

In 1911, also the French switched to Greenwich longitude and Greenwich time.

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The complete PROTOCOLS OF THE PROCEEDINGS of the International Meridian Conference are available via the Project Gutenberg. The vote on the adoption of Greenwich meridian is reported on page 99.

Light Bulbs and the Solar Energy Production

As of this September, regulations in the European Union ban the the manufacture and import of 100 Watt incandescent light bulbs, as a measure to cut down energy consumption. While this has created a bit of a fuss and lead people to hoard traditional light bulbs, I actually do not remember the last time when I had used a 100 Watt light bulb. I probably won't miss it – unless for a very nice comparison for the energy production of the Sun.

The Earth is at distance r = 150 million km = 1.5 × 10¹¹ m from the Sun. The incoming total electromagnetic energy flux from the Sun at the Earth per unit area, the so-called solar constant, is C = 1360 W/m² = 1.36 × 10³ W/m². Assuming that the energy flux from the Sun is the same in all directions, this means that the energy output per second of the Sun, called luminosity by astronomers, is L = 4 π r² × C = 3.85 × 10²⁶ W. This corresponds, by the way, to the mass equivalent of roughly 5 million metric tons per second: dm/dt = L/c² = 4.27 × 10⁹ kg/s. The Sun has a radius of R = 7 × 10⁸ m. If we naively assume that energy production is the same throughout the whole volume on the Sun, the power density of the solar energy production would amount to ε = L/(4 π/3 R³) = 0.268 W/m³ This is a remarkably tiny number! Of course, energy production in the Sun happens only in the central part, where temperature and density are high enough to sustain nuclear fusion reactions. This central part extends to roughly 10 percent of the solar radius, so that we can estimate the energy production in the core to about ε ≅ 300 W/m³ This is the energy output of three 100 Watt bulbs per cubic metre!

Actually, this back-of-the envelope estimate is not that bad at all. Energy production in the Sun by nuclear reactions is now very well understood, in particular since the "Solar Neutrino Puzzle" has been solved. This knowledge about the Sun's inner parts is encoded in what is called the "Standard Solar Models".

A lot of information and papers on solar models are available from the web site of the late John Bahcall, and from this long list of models, I picked the data set for the model BP2004, which gives all kinds of physical quantities as a function of radial distance from the centre of the Sun.

Energy production can be inferred from the luminosity as a function of radius – there is difference between these quantities when heat is absorbed or released, but this difference is negligible for the current steady state of the Sun's interior. This yields the following figure:



Energy production in the Sun's centre drops to zero beyond roughly one quarter of the solar radius. And in the inner core, it is nearly 300 Watt per cubic metre.

Of course, beyond the energy balance, it's quite unphysical to imagine the solar interior as a vacuum lit by light bulbs. Due to the gravitational pull, density, pressure and temperature are enormous, and beyond anything we can imagine from everyday experience. Here are radial profiles of density, pressure, and temperature of the Sun. Data are taken again from solar model BP2004. Note that the plots now have a logarithmic scale. For better comparison with everyday numbers, I have added the density of water, atmospheric pressure multiplied by a factor of 1 million, and the melting point of iron, multiplied by 100.







There is, of course, another difference between the light from the Sun and a 100 Watt light bulb – that's the spectrum of the light. An incandescent light bulb is a quite inefficient light source, as most of the energy is radiated in the infrared. The solar spectrum, instead, peaks in the visible range.

But, leaving aside the huge differences in density, temperature and ambient pressure, and the different spectra, here is a nice comparison:

My small kitchen has a volume of about 25 cubic metre. So, I should light it with 75 bulbs of 100 Watt each to "simulate" the solar interior. This would be very bright, and blow the fuses, but it is a quantity conveniently to imagine, compared to the huge numbers we usually deal with in astronomy!

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Here is another way to arrive at the order of magnitude of "100 W light bulbs per cubic metre" for the solar energy production – thanks to Bee for insisting on this estimate:

The solar disk in the sky has a diameter of half a degree. The incandescent inner part of a 100 Watt light bulb, with a diameter of about 2.5 cm, appears under an angle of half a degree in a distance of about 3 metres. A spherical cluster of 100 Watt bulbs at a distance r appearing under the same angle and containing (r/ 3 m)² bulbs will produce roughly the same apparent luminosity as the single bulb at a distance of 3 metres. At the distance of the Sun, such a cluster should contain 0.25 × 10²² light bulbs. Actually, the luminosity of the Sun is about 1600 times higher than that - meaning that the Sun is about 1000 times brighter than than a 100 Watt light bulb in a distance of three metres. This seems quite reasonable indeed!

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Virtual Shipspotting

Sabine has arrived in Stockholm, but her household is still in transit. Actually, the latest news from the moving company was that her belongings are on a ship named "Stuttgart Express", en route to Southampton, England, and scheduled to arrive at Stockholm in early October.

On Saturday, out of curiosity, I googled for that ship, and was completely amazed about the amount of information I could find.

The "Stuttgart Express" is a 16-year old cargo vessel, 294 metres long, and with a deadweight of 67680 tons:


The "Stuttgart Express" (photo via www.marinetraffic.com).

According to the ship's itineraries history, the Stuttgart Express has left Halifax, Nova Scotia, on Saturday, August 29 at 20:30 UTC, and reached the English Channel on Friday, September 4, around noon. Though, it didn't stop in Southampton, but went straight on to Antwerp, Belgium, where it arrived at the port on Saturday, September 5, at 9:30 in the morning.



The ship spent Saturday in Antwerp, and left for England early on Sunday morning. However, destination was not Southampton, but a place on the southern bank of the Thames estuary:



No idea what it did there, there seems to be no port, but maybe it has bunkered fuel. Anyway, it left that place this morning before five,



heading for … Bremerhaven, Germany.



Right now, the Stuttgart Express has passed the island of Norderney in the Wadden Sea:



No idea when it will arrive at Southampton to disembark the container, but somehow, the next four weeks have to be spent.

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The Stuttgart Express via www.marinetraffic.com

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Did you know... (VII)

... the origin of the word “travel”?

It goes back to the Old French word travail “suffering or painful effort, trouble” (12c.), from travailler “to toil, labor,” originally “to trouble, torture,” from Vulgar Latin tripaliare “to torture,” from tripalium (in Literary Latin trepalium) “instrument of torture.”

Source: The Online Etymology Dictionary

Yep.

Next time you fly from the East- to the Westcoast, suffering from cheap airline coffee and dull movies, try to imagine you'd have taken the trip 200 years ago...

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See also: Did you know...

• ... that the Eskimos have 98 words for snow?
• ... that the can opener was invented 48 years after invention of the can?
• ... the opposite of eloquent?
• ... why the toast is called toast?
• ... what the Baconian method is?
• ... why Google is called Google?

Ice IX

This afternoon, I stumbled upon this phase diagram of water, showing the different phases of ice. Depending on temperature and pressure, solid water can have a large variety of crystal structures.

I couldn't avoid having a closer look: Ice-Nine exists!


from Landolt-Börnstein: "Physical properties of ice"
(DOI: 10.1007/10201909_90 - free PDF preview)

Fortunately, unlike its mythical cousin, the real Ice-Nine (labelled "IX" in the lower left corner of the diagram) cannot occur at ambient conditions, but exists as a metastable phase only below about -100 centigrade (170 K), and at pressures of a few kbar.

So, no danger that it may accidentally solidify all liquid water...

Fresh Apple Juice

Auenland, as Sabine has dubbed it, has seen this year a rich harvest of all kinds of fruits, especially apples.


Unfortunately, a heavy hailstorm in early July has left its marks on the apples: there is hardly a single fruit without an ugly scar. But they are very tasty nevertheless, and they make an excellent juice. So this is how my brother and me have spent the last two weekends:


We have gathered apples from the trees my family owns around the village,


packed them in my car and brought them to the press of the local fruit-growing and gardening association.


There, the apples are being processed to juice. They are washed and shredded,


and the shred is squeezed in the press.


The gardening association has an apparatus to heat up and pasteurise the juice on-site (the silvery cask in the background on the the right), and fill it in bags to store it. But the most tasty juice is the fresh, untreated one.



Cheers!

Bumblebees can't fly?

Bumblebees are quite impressive insects: They make a nice humming sound, they cause a small stir when flying over patches of dusty ground, and with a mass of nearly a gram, they are heavy enough to bend clover flowers under their weight when landing to feed nectar.



And, of course, bumblebees cannot fly according to the laws of aerodynamics, or so goes the myth. This story, often invoked by people wanting to dismiss results of scientific reasoning, seems to go back to the 1930s, to students of Ludwig Prandtl, a pioneer of aerodynamics at the University of Göttingen in Germany.

As so often, there is some truth also to this myth: If one starts from the assumption that the uplift force comes about as for an airplane wing, this is fine to understand the flight of large birds. But this assumption works much worse for small birds and bats, and it fails for insects such as bumblebees. Obviously, bumblebees have found clever way to fly very different from that of airplanes.

But they don't defy the laws of aerodynamics anymore: The issue of Physical Review Letters of September 4, 2000, besides discussing Prospects of Detecting Baryon and Quark Superfluidity from Cooling Neutron Stars and Magnetic-Octupole Order in Neptunium Dioxide, had a paper by Z. Jane Wang with the unassuming title "Two Dimensional Mechanism for Insect Hovering". But as the abstract explains Resolved computation of two dimensional insect hovering shows for the first time that a two dimensional hovering motion can generate enough lift to support a typical insect weight. The computation reveals a two dimensional mechanism of creating a downward dipole jet of counterrotating vortices, which are formed from leading and trailing edge vortices. [...]". (Phys. Rev. Lett. 85 (2000) 2216-2219).

Snapshots of the vorticity field of the moving wings (black). The illustration, taken from Phys. Rev. Lett. 85 (2000) 2216-2219, shows the formation and dynamics of a "dipole jet" of vortices, which creates the uplift force that allows the insect to hover.

It seems that the rapid motion of insects wings creates tiny vortices in the air that keep them aloft. This is especially important when hovering around a clover bloom. Luckily, bumblebees can fly without reading the PRL.

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• The myth of the bumblebee an its origin is discussed in "The Strange Case Of The Bumble Bee Which Flew" by K.P. Zetie. You can find more background and references in Ivars Peterson's MathTrek of September 13, 2004, "Flight of the Bumblebee".


• For more on the flight of insects, check out the web site of the Animal Flight Group of the Department of Zoology, University of Cambridge, and the web site of the research group of Z. Jane Wang at Cornell University. At the List of publications, you can download, among lots of other papers, the PRL from 2000 as a PDF file. More explanations about her work are in the Cornell Chronicle, "Insect flight obeys the principles of aerodynamics, CU physicist proves", and the Cornell Engineering Magazine, "The Truth about Bumblebees and other insects". On the work of the Cambridge group, and of a Berkeley group who pointed out the role of vortices and viscosity in insect flight, see "The buzz on bumblebees" in the November 2001 issue of plus magazine.

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Physics, Bumblebee Myth

Cookies, Palygorskite, and Maya Blue

A Maya mural paining, on a background of Maya Blue (Source: Wikipedia, and azulmaya.com).

On Thursday the New York Times science news feed linked me to "The Grim Story of Maya Blue". Maya Blue is a bright blue colour that had been used by the Maya people of Central America to paint murals, pottery and artefacts, and for ritual purposes. It's a very persistent pigment that remains even after all others dyes have faded. The New York Times article reports new insights how this pigment actually was produced by the ancient Maya. The frisson of humans painted in Maya Blue before being sacrificed to the Rain God Chaak notwithstanding, I just had a short glance at the article when I was stuck by the mentioning of the mineral used to make the pigment, palygorskite. What a surprise!

Like probably most of you, I guess I never would have heard of palygorskite before, had I not been dealing with a long manuscript about the structure and properties of just this mineral earlier this week. There can be funny coincidences...

Palygorskite, or attapulgite, as it has also been called, is a clay mineral, belonging to a large group of clays known as Fuller's Earth. Technically speaking, it's a magnesium aluminium phyllosilicate with the formula (Mg,Al)₂Si₄O₁₀(OH)·4(H₂O).

This formula looks very complicated, but actually, silicate minerals are quite fascinating stuff. Essentially they are built up of small tetrahedra of silicon atoms surrounded by four oxygen atoms, and octahedra of metal atoms (magnesium and aluminium, in this case) in the centre of six oxygen atoms. Like building bricks from a kid's construction kit, these tetrahedra and octahedra can be combined in a huge number of regular patters, giving rise to the enormous botany of different silicate minerals. In phyllosilicates, the silicon tetrahedra and metal octahedra form planar sheets (hence the name), which then build up layered structures.

Palygorskite has such a layered structure, but actually, it is very uncongested. It does not consist of continuous sheets, but of long bars of layers of metal octahedra sandwiched between silicate tetrahedra. These bars, then, are arranged parallel to each other in a kind of checkerboard pattern, with large, channel-like empty spaces in between.



In this cookie model, the chocolate filling represents the metal octahedra, which are sandwiched between the biscuit, standing for the silicate tetrahedra. You see a cross section through the parallel arrangement of long bars. A more technical illustration is shown in figure below, which has been adapted from the paper On the unusual stability of Maya blue paint: Molecular dynamics simulations, by Ettore Fois, Aldo Gamba, and Antonio Tilocca, Microporous and Mesoporous Materials 57 (2003) 263-272:



The cross section through the basic building bar is marked by the grey rectangle. This basic building block is repeated in a checkerboard pattern in the plane of the figure, and just continues along the axis normal to the figure plane. You can see the silicate tetrahedra, with oxygen atoms at the vertices, and the metal atoms - the large dark-grey spheres surrounded by six oxygen atoms each.

The empty, tunnel-like spaces between the bars are not completely empty, however. Usually they are filled with water molecules. A few of these molecules can be spotted in the illustration above. But if other molecules are around, they can enter the tunnels, and physically bind very efficiently to the silicate framework. For this reason, palygorskite has often been used in medicine: The mineral is not absorbed by the body, but binds acids and toxic substances in the stomach and digestive tract. Thus, it acts as an antidiarrheal medication, for example.

The same thing happens when palygorskite is brought together with Indigo, a dye that can be be extracted, for example, from a plant named Añil, which is native to tropical America.



Indigo molecules fill the channels of the palygorskite structure in a random pattern, as shown in the illustration, which has also been taken from the paper of Ettore Fois, Aldo Gamba, and Antonio Tilocca. The silicate hull shelters the dye molecules, and thus creates the enormous persistence of the pigment and its robustness against harsh climatic conditions, alkali and acid treatment and organic solvents.

How to create this indigo-clay pigment is what the ancient Maya had discovered - that's Maya Blue.

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• Mineralogical details about palygorskite can be found at the databases mindat.org
  and webmineral.com. Webmineral.com has also a very nice JavaApplet to explore interactively the unit cell of palygorskite.


• The peculiar crystal structure of the palygorskite mineral was described for the first time in The structural scheme of attapulgite by W. F. Bradley, American Mineralogist 25 (1940) 405. Bradley used the classical x-ray diffraction technique, and you can have a look at the PDF file of the paper.


• Since the 1940s, mineralogists have applied the whole arsenal of methods provided by modern condensed matter physics to shed light on the structure of palygorskite and its role in the properties of Maya Blue. A very recent review is Pre-columbian nanotechnology: reconciling the mysteries of the maya blue pigment by G. Chiari, R. Giustetto, J. Druzik, E. Doehne and G. Ricchiardi, Applied Physics A: Materials Science & Processing 90 (2008) 3-7 (subscription required).


• For more about the archaeological aspects of Maya Blue, see the entry The Palygorskite and Indigo Mix of Maya Blue at about.com:archaeology as a starting point.

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Astronomical Observatories on Google Maps

A short while ago I've started reading an interesting book about early astronomical tests of the theory of relativity, Einstein's Jury by Jeffrey Crelinsten. I don't want to say more about the book right now - just that I became a bit confused with all the names of US astronomers and observatories mentioned in the text. I thought it may be helpful to put them on a map.

There are web sites and wikipedia entries about all the observatories mentioend, so I decided to play around a bit with Google Maps. There is an "application programming interface", Google Maps API, which can be used to embed customised google maps in web pages, and to add flags and comments to the map. It's actually not so diffcult to use: I registered to get my "API Key", looked at same of the examples and demos (and in the source file of this nice interactive map I had come across by chance a while ago), and after some tinkering, I ended up with this result:

A map of some historical astronomical observatories in the US, ordered from East to West:



I have used the example icon-custom.html from the Google Maps API Examples page. Since the Google Maps API involves JavaScript, which can not be used with the blogger software, I have stored the HTML page with the map and the list of observatories on a separate web server (in case you do not see anything, the server is down, as it happens from time to time), and then used the iframe tag to embedded the page into the blog post.

This API is a fascinating gadget! There are probably hundred times more applications than I can think of right now.

The only thing what still is missing now is a time line ;-)

Did you know... (VI)

... that the Eskimos have 98 words for snow?

Yeah, me too, but it's actually bullshit. One of the more useful side effects of the internet is the busting of urban legends. Though it's useful only if one actually looks for it: Googling 'Eskimo Words for Snow' gives you easily several references that explain not only where the myth comes from, but also what's wrong about it.

The brief explanation is that besides there being several 'Eskimo languages' these are polysynthetic, meaning one can put several nouns with describing adjectives together into one word -- which gives a new word. I.e. there is snow, there is frozen-snow, frozen-and-dirty-snow, frozen-and-dirty-snow-with-a-crust-that-breaks-if-one-steps-on-it, and then there is snow-on-my-outside-chair-waiting-for-springtime.

Reference: Laura Martin, American Anthropologist, Vol. 88, No. 2 (Jun., 1986), pp. 418-423

"Eskimo words are the product of extremely synthetic morphology in which all word building is accomplished by multiple suffixation [...] Furthermore, precisely identical "whole" words are unlikely to recur because the particular combination of suffixes used with a "snow" root, or any other, varies by speaker and situation as well as by syntactic role."

The paper is actually quite entertaining in the way she clarifies earlier claims ("A minimal knowledge of Eskimo grammar would have confirmed the relevance of these facts to the central hypotheses [...]" Ouch.)

Either way, I was shocked to see that the above publication is from '86, since I must have read about it repeatedly, and definitely after '86.

The interesting question is much longer will that story to survive? So, take the poll below and answer the question whether you had heard of the story that the Eskimo's have so-and-so-many words for the one English word 'snow' (the precise number of words doesn't matter)

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See also: Did you know...

• ... that the can opener was invented 48 years after invention of the can?
• ... the opposite of eloquent?
• ... why the toast is called toast?
• ... what the Baconian method is?
• ... why Google is called Google?

Did you know... (V)

... that the can opener was invented 48 years after invention of the can?

Food preservation in cans was patented in 1810 by the British merchant Peter Durand. The first commercial canning factory was opened in England in 1813. In 1846, tin cans could be manufactured at a rate of sixty per hour.

However, though Durand had figured out how to seal food into cans, he just left the consumer with the instruction: "Cut round the top near the outer edge with a chisel and hammer." [Source] This was complicated by the fact that the first tin-coated iron cans were made of thick metal, and often weighed more than the food they held. Usually, the cans were opened with heavy equipment by the clerk in the grocery store [Source].

The first can opener was patented in 1858, by Ezra Warner, and looked like a bent bayonet. It had the big advantage that the user pressed, rather than stabbed it, into the can. A metal guard kept the point from penetrating too far, to “perforate the tin without causing the liquid to fly out.” A second, curved blade could then be worked around the rim to finally remove the lid. Warner’s patent even claimed that “a child may use it without difficulty, or risk.” [Source]


It was only when thinner steel cans could be manufactured in the 1860s that a useful can opener could be invented. In 1866, J. Osterhoudt patented the tin can with a key opener that you can still find today on sardine cans [Source]. And the picture to the right shows a 21st century version of the can-opener.

I wonder whether, in some basement in England, there is a tin can with mixed pickles from 1812 (that however nobody can open with Black&Decker).

So, if you have a great idea don't forget instructions how to open the can, and keep in mind it might take some decades for the details to work out.

See also: Did you know...

• ... the opposite of eloquent?
• ... why the toast is called toast?
• ... what the Baconian method is?
• ... why Google is called Google?

or that bubblewrap was a complete flop with its original marketing idea?

Did you know... (IV)

... the opposite of eloquent?

It's pauciloquent "Uttering few words; brief in speech."

For more '-quents', see this extensive list. You'll find a lot of educated sounding alternatives to lie and blather. E.g.

falsiloquence - deceitful speech
flexiloquent - speaking ambiguously or using words of doubtful meaning
inaniloquent - prone to foolish or empty babbling
mendaciloquence - lying speech

Also good to know:

sialoquent - spitting greatly while speaking

But the best is, nobody will have any idea what you are talking about. Eloquent or not.

See also: Did you know

• ... why the toast is called toast?
• ... what the Baconian method is?
• ... why Google is called Google?

Nabla

Did you know why nabla is called nabla? Well, I didn't know until today. It is named after an instrument somewhat similar to a harp, called by the Greeks the 'psaltery' and by the Hebrews the 'nabla'. Unlike the harp however, the shape of this early string instrument is very geometric: it is pretty much triangular:




The nabla symbol is used in maths (and physics of course) to denote a differential operator. It was introduced by Hamilton around 1837. Its name apparently goes back to a joke by Maxwell. According to Wikipedia, W. Thomson wrote in 1884:

"I took the liberty of asking Professor Bell whether he had a name for this symbol and he has mentioned to me nabla, a humorous suggestion of Maxwell's. It is the name of an Egyptian harp, which was of that shape"

I am kind of glad he didn't suggest to use the Greek name 'psaltery' as I admittedly have no idea how to pronounce it. You might be interested to hear though that it makes an appearance in the bible, Psalm 33:2

"Rejoice in the LORD, O ye righteous: for praise is comely for the upright.
Praise the LORD with harp: sing unto him with the psaltery and an instrument of ten strings. "

The word 'operator' is a very sophisticated expression for a thing that assigns things to things. The telephone operator for example, assigns incoming calls to the desired connection. Its correct mathematical notation is

[source]

An operator can be almost everything. Your kid who never tidies up is an operator that assigns toys to places in your living room. If you buy tickets for the opera, the online booking system is an operator that assigns seats to the audience.

A differential operators specifically acts on functions by differentiating them. The nabla for example, when applied to a scalar field, gives the gradient of that field. If you think about the scalar field as an altitude in a mountain range, then the gradient points towards the direction where the increase is the steepest.

Operators are the core concept of quantum mechanics. Quantities that in a classical theories are functions, like the position or energy of an object, become operators. To make something useful out of them, they now have to act on a function - that being the purpose of an operator. In quantum mechanics, it is the well-known wave-function that they act on.

But the usefulness of the operator concept is that one can deal with them on their own without applying them all the time. It's a bit like replacing 'classical' money with a credit card. If you want to see something 'real' you have to 'apply' it to an ATM to get cash. Most often the result is quantized, say, you can only get multiples of $10 or so. You also typically have an offset, a smallest possible amount that you can get. But for most cases, you are fine dealing with the card itself. You have to be a bit careful though if you use it together with other cards, say the club card (payback card, member card, VIP card, whatever) from your local groceries. For your total, it matters in which order you present them at the register. We say that the operators don't commute: the result depends on the order of use.

The nabla is essentially the operator that, when acting on the wave-function, gives the momentum. That is, up to a constant - in this case a relevant constant. But this may be subject of another post.

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TAGS: PHYSICS, NABLA, MATHEMATICS, OPERATOR

PI day

Today is march 14, or 3/14, as Americans will write - that's π day! It is such an important date that it even has its own website! Unfortunately, if you have a look at the first few decimals of π, you can see that you can't celebrate the π instant at 3 pm something in the afternoon, unless you use a quite awkward scheme to split the hour...

By a curious coincidence, π day is also the birthday of Albert Einstein: He was born on march 14, 1879, in this house in Ulm in southern Germany (the house was destroyed in 1944, so you cannot visit it any more):


(Source: Albert Einstein in Ulm)

As the celebrations of his 125th birthday, and the 100th anniversary of his Annus Mirabilis have brought us many many great websites about Albert Einstein, there is no big point in repeating here anything of all you have for sure read many times.

But did you know that Einstein himself might have had some trouble to recognise PI π in his birthday? As every child learns in school in Germany, dates are written in the form day, month, year. So, Einstein has written his birthday most probably as 14. III. 79, following the conventions of his time and using roman ciphers for the month. That's good to know if you want to make sense out of the date 4. I. 19 - it is January 4th, 1919. That's no special date, it just happens that Einstein lectured about "ponderable bodies" on that day, as he has written down in his lecture notes:


(Source: Albert Einstein Online Archive)

The lecture on 9.11. (that's November 9th, quite an important date in German history) fiel aus wegen Revolution - it was was cancelled "because of revolution"...

Coming back to Einstein and the π day, one might wonder whether Einstein's papers are encoded somewhere in the decimals of π. That's the case if π is a so called normal number. Unfortunately, no one knows so far whether π is normal or not, despite ongoing progress on this question.

The inverse question is much more easy to answer: Does π occur in Einstein papers? If we have a look in the famous Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig? (Annalen der Physik 18 (1905) 639, here as PDF, the famous L = mV² paper), this paper gets by without any π! OK, you may say, that's a short paper. What about the Elektrodynamik bewegter Körper (Annalen der Physik 17 (1905) 891, here as PDF - the electrodynamics of moving bodies, the SRT paper)? Surprise, there are only 4 πs in this 30 page paper, and only in relation with one expression for the energy density. If you really want to get rich in π better invest in Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen (Annalen der Physik 17 (1905) 549, here as PDF, the paper about Brownian motion) - I did not count them all.

What can we learn from all this? The special theory of relativity is not transcendental!

Happy π day!

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TAGS: PI day, Albert Einstein

Eyeglasses and the James Webb Space Telescope

Did you know...


... that "Brille", the German word for eyeglasses, comes from beryl, the name of a transparent crystal?


It seems that eyeglasses are an invention of the Middle Ages. At that time, however, glasses were not made of glass, but from a mineral which comes in a clear, transparent crystalline variety. This material, beryl, was the material the first lenses were carved from.















Cardinal Hugh of St. Cher wearing glasses made of beryl to help his eyesight. This fresco in a church in Treviso, painted in 1352 by Tommaso da Modena, is the oldest known pictorial representation of eyeglasses. (Source: Books, Banks, Buttons: And Other Inventions From The Middle Ages)



Beryl is, chemically speaking, a cyclosilicate, a compound of the light metals beryllium and aluminium with silicon and oxygen. Its chemical formula is Be₃Al₂(SiO₃)₆. In its pure form, beryl is a colourless, clear mineral, but if it is "doped" with trace amounts of other metals, it can have all kinds of colours - and be very precious. Emerald, for example, is a variety of beryl, coloured green by impurities of chromium and, sometimes, iron.

Now, colour centres are a very interesting physics topic of their own, but I was reminded of this beryl story when I came across a comprehensive, freely available paper on the James Webb Space Telescope.

The JWST is a planned satellite telescope which is sometimes called the successor of the Hubble telescope. One of its scopes is to study the first galaxies in the young Universe at a redshift in the range of 5-10. This means that all visible light is shifted far into the infrared. So, the JWST is optimised for observations at the infrared part of the spectrum. It will have a primary mirror with a diameter of 6.5 meters (21 feet 4 inches) which consists of several segments. And these segments will be made of - beryllium.



The primary mirror of the James Webb Space Telescope will consist of 18 honeycomb-shaped segments made of beryllium (Source: NASA)

Metallic beryllium was chosen to produce the mirror because its stiff, light weight, has very small thermal expansion over a wide temperature range and holds its shape at the low 50 Kelvin at which the telescope will operate.

It's a funny coincidence that the same element, which as a main component in a mineral was used to produce the first eyeglasses, will soon help us to look back into the youth of our Universe!

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TAGS: PHYSICS, SCIENCE, JAMES WEBB SPACE TELESCOPE

Happy Birthday Benjamin Franklin!

Gee, it seems whenever Stefan and I attempt to write a post together it ends up being a total disaster. Good morning Stefan! Thanks for the draft, I rewrote it, just so you know! Okay folks, here we go: today is Benjamin Franklin's 301st birthday, and so this blog honors the man who enlightened America, born on January 17th 1706 in Boston.

Did you know...

...that Benjamin Franklin was the first American to own a bathtub?

Well, if you knew that and thought is was funny, Stefan taught me it belongs into the recycle bin of urban legends. But lets try again:

Did you know...

... that Benjamin Franklin was so sure that fresh air was important for good health that he took a daily “air bath”?

Well, I didn't know until today. See, that's what being married is good for, you learn how to get along with your ideas about bathing.


Besides this, Benjamin is known for the invention of the lightning rod, the chimney and the public library.


While I was browsing the web for interesting stuff about Franklin, I found this website where you can have Fun with Franklin. Among other things, you'll learn that a necessary ingredient for a lemon battery is '1 adult helper'. But besides this, upon the mere mentioning of Franklin, I kind of feel the responsibility to remind you 'Never play with electrical cords, wires, switches, or plugs. - Fly kites and model airplanes in a wide open field or park never near overhead electrical wires.'

Yes, yes, you'd have thought after 300 years, people should know:


"(19 March 2006, Belize) Benjamin Franklin reputedly flew his kite in a lightning storm, going on to discover that lightning equals electricity. However, certain precautions must be taken to avoid sudden electrocution. Kennon, 26, replicated the conditions of Ben Franklin's experiment, but without Ben's sensible safety precautions. Dennon was flying a kite with a short string that he had extended with a length of thin copper wire. The copper made contact with a high-tension line, sending a bolt of electrical lightning towards the man. Just bad luck? Kennon's father told listeners his son was an electrician, and "should have known better." Kennon is survived by his parents, six sisters, and five brothers."

Nominee for the Darwin Award 2006

But besides providing an everlasting inspiration for the truly ingenious, Franklin was also actively involved in the first scientific clinical trial:

In the 1780s, the Viennese physician Anton Mesmer came to fame with his theory that "animal magnetism" may be an important determinant for the health of the body and the mind, and that magnetism could be used to cure all kinds of diseases. In a time when electricity was recognized as a driving force for the muscles in the body, this idea could not be easily dismissed as plain nonsense.

Mesmerism: The Operator Inducing a Hypnotic Trance, engraving after Dodd, 1794. Plate from Ebenezer Sibly's book, A Key to Physic, 1794. (Source)

There were many arduous fans of Mesmer and his healing methods. But there were skeptics, too - one of them was Louis XVI, the King of France, who wasn't as mesmerized as his wife, Marie-Antoinette. He wanted to know for sure what was there about these theories of this Austrian physician, and commissioned a report by high-level, international and interdisciplinary committee of experts to find out.

Headed by Franklin, and including the chemist Lavoisier, the botanist Jussieu, and the physician Guillotin, the panel carefully planned and conducted experiments to test Mesmer's hypothesis. In their public report, they concluded that there was no scientific evidence of animal magnetism. Successes of Mesmer's cures could be attributed either to other factors, or to a placebo effect. I bet they'd been interested to hear this frog's idea about animal magnetism.

One could go on and on about Franklin, if you are really interested, you might want to read his autobiography. But from all the interesting things about this great man's life, I want to share with you a quotation that I found about our search for the truth:

"Perhaps the history of the errors of mankind, all things considered, is more valuable and interesting than that of their discoveries. Truth is uniform and narrow; it constantly exists, and does not seem to require so much an active energy, as a passive aptitude of the soul in order to encounter it. But error is endlessly diversified; it has no reality, but is the pure and simple creation of the mind that invents it. In this field the soul has room enough to expand herself, to display all her boundless faculties, and all her beautiful and interesting extravagancies and absurdities."

(In the preface of the 1784 Report of Dr. Benjamin Franklin and other commissioners, charged by the King of France, with the examination of the animal magnetism, as now practised at Paris)

For more fun with Franklin, check out this very professionally designed website, it's just a looker.

PS: Sorry Stefan for messing up your pedagogically valuable essay.

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TAGS: HISTORY OF SCIENCE, USELESS KNOWLEDGE, BENJAMIN FRANKLIN, BATHTUB

This and That

Just some random things:

• Clifford has a very interesting post on 3D imaging of dark matter distribution
  Update: See also Bad Astronomy and Cosmic Variance


• IEEE Spectrum has an article about the reactions to Lee Smolin's book 'The Trouble with Physics', titled Thread-Bare Theories (via qgs)


• I learned yesterday that my post about Micro Black Holes has been selected for the Science Blogging Anthology... since I did not submit my own entry, anybody has an idea who nominated me...? Huh? Anyway, a large THANK YOU to the anonymous fan :-)


• I am about to set up a discussion group here at PI about experimental tests on quantum gravity. From writing this blog it seems to me that the topic is of interest for many readers as well. I have therefore exported a brief summary on a separate blog, where I will (try to) report on the discussion. I hope you contribute lively --->Quantum Gravity in the Lab


• The January issue of Physics Today has a (free) article about Germany's 'excellence initiative' (Exzellenzinitiative of the BMBF) titled Germany singles out universities for excellence
  
• From the category 'Useless Knowledge': Did you know... that Isidore of Seville is the patron saint of the internet?

Naval Amphibious Base, Coronado

Today on Google Earth I saw...

"The Naval Amphibious Base (NAB) Coronado is located just across the bay from San Diego, CA. The base is situated on the Silver Strand, between the San Diego Bay and the Pacific Ocean. NAB Coronado is a major shore command, supporting 27 tenant commands, and is the West Coast focal point for special and expeditionary warfare training and operations. The amphibious base houses Commander Naval Surface Force, US Pacific Fleet, responsible for the training, maintenance and crews of the approximately 90 ships of the Pacific Fleet and Commander Naval Special Warfare Command, US Pacific Fleet. Also located there are most of the Naval Expeditionary and Naval Special Warfare units of the Pacific Fleet as well as the famed Navy Parachute Team, the Leap Frogs."

And here's the design the architect chose for the building:

You find it also on Google Maps.

Source: Google tracks Hitler to San Diego, and my office mate.

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TAGS: GOOGLE MAPS

The National Data Book

The US Census Bureau has released the 2007 statistical abstract. "The Statistical Abstract of the United States, published since 1878, is the authoritative and comprehensive summary of statistics on the social, political, and economic organization of the United States."

The full report with all tables has roughly 1,400 pages, and is available online. You find the abstract on this website.

Some interesting statistics:

• The 2005 population of US residents is ~ 296,410,000 (Table 2).



• The number of admitted immigrants increased from 2004 to 2005 and exceeded the level from 2001, after a significant drop in 2003 (Table 6).



• 15.7% of US citizens (11.2% of children) have no health coverage (numbers from 2004). The rate of non-covered persons is the highest in Texas (25% total /21.4% children), followed by New Mexico (21%/15.3%) and Florida (19.9%/15.1%) (Table 145).



• The most dangerous home furnishing item is the bed. In 2004 it caused 518,441 injuries. Also interesting: 121,094 people suffered injuries caused by their footwear. The statistic counts emergency room treated cases nationwide in 2004 (Table 173).



• The number of reported cases of AIDS decreased slightly from 2003 to its 2004 value of 44,108 (Table 175).



• South Dakota is the only state that did not report any case of Syphilis in 2004 (Table 176).



• The percentage of current cigarette smokers decreased from 2000 to 2004, the average value in 2004 was 20.8%. From the listed groups, black women have the lowest percentage (16.0%) of smokers (Table 191).



• 7.9 % of US citizens age 12 and older classify themselves as 'current users of illicit drugs'. The caption says 'Current users are those who used drugs at least once within month prior to this study'. (Table 194)



• 65.3 % of US citizens are overweight. The statistics I printed has a chocolate smear. (Table 198).



• 2004 in the land of plenty: 13,494,000 households in the US were food insecure. The number of households with hunger among children raised from 0.5 % in 2003 to 0.7 % in 2004 (Table 2004). Though recently the department of agriculture has defined hunger as a non-existent state, see also 'Very low food security'.



• The average US citizen consumed 24.6 gallons of coffee, and 25.2 gallons of beer in 2004 (Table 201).



• 74.1% of doctorates in physical sciences (astronomy, physics and chemistry) are male, 42.0% are foreign citizens, 79.1% are white (status 2004, Table 789).



• In the last quarter of 2005, 22.5% of flights arrived late (more than 15 min) at major US airports. The worst airport is Newark International with 41.9% (Table 1055).



• 6,894 people filed consumer complaints against US airlines in 2005 (Table 1056).



• The number of alternative fueled vehicles in use increased slightly from 2003 to 2004 (Table 1075).



• 42,636 people died in, or as a cause of car accidents in 2004 (Table 1083).



• The median income of households in 2004 was US$ 38,453. The median income White only was $40,469, Black only $23,372. 15.5% of all households have an income under $15.000, and 15.7% have an income over $100.000. (Table 671 and 672).



• The medium household income is the highest in Connecticut with $60,528, and the lowest in West Virginia with $31,504 (Table 687).



• 36,997,000 people (12.7%) live below poverty level, status 2004 (Table 692).



• The US counts 3,510,000 top wealth holders with net worth of $ 1 Million or more. Most of which live in California, followed by New York and Florida (Table 700).

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TAGS: STATISTICS, POVERTY, USA

Did you know... (III)

... why the toast is a toast?

Yesterday, I went to the groceries store and was greeted by an ad saying: It's the toast season! Okay, I wondered, what kind of a tradition is this? Do Canadians toast maple leaves on their bread or what? Upon second inspection however, (I think I need new glasses) the sign turned out to stand in front of the wine department.

So here is why the toast is called toast:

"The word derives from the Latin word 'tostare' (to scorch or roast - i.e. toast ). From Classical times it was common to flavour wine by floating small pieces of toasted bread in it. Sometimes these sippets would be flavoured with spices; at other times the carbon alone would mellow the wine."

Wikipedia clarifies appropriate toasting behaviour in the US and Canada, apparently written by someone who was tired of endless toasty speeches while he had to hold a glass of wine in mid air:

"The following guidelines apply specifically to toasting in Canada and the United States:

• Most people will lightly touch glasses when giving a toast, often saying "toast", "cheers" or a short phrase such as "to us". Toasting without touching glasses is increasingly popular and is regarded by some as a slightly more sophisticated mode of behavior.
• Except during formal occasions [...] it is not very common to "propose a toast" in the more formal sense. However, when someone does make such an gesture, it is almost invariably met with approval regardless of the setting or the occasion.
• If someone wants to "propose a toast as well", this second toast should have a different focus than the first [...] Ideally, this toast is briefer than the first so as not upstage it. Subsequent toasts, if any, should even more succinct.
• Americans and Canadians typically toast only once per gathering, if at all. Even lifting one's glass and saying "cheers" each time a new drink is poured isn't in line with local etiquette and, while not impolite, may be seen as a bit tedious."

Also: since it's the toast season, have a close look at your breakfast before you eat it. It might turn out to have heavenly messages on it. One of the most absurd stories I've heard about eBay is certainly that of the toast with the Virgin Mary face that has been sold for $28.000. Even though a bite is missing from it. What's even more absurd than this toast being sold for such an amount is that it was bought, not by a religious nutcase, but by an internet casino saying the toast had become a "part of pop culture".

Cheers!

See also: Make a toast in 50 different languages

And:

• Did you know... (II)... what the Baconian method is?
• Did you know...(I)... why Google is called Google?

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TAGS: CHRISTMAS , TOAST