Early names for Lake Tahoe: Mountain Lake, Lake Bigler, Lake Bonpland

The name of Lake Tahoe derives from the word the Washoe Indians used to name the lake: da ow a ga. Walking the Eagle Trail Loop near the Upper Eagle Falls above Emerald Bay at the southwestern part of Lake Tahoe in California, you can find an interpretative board that mentions a few other names the lake had, before it became the well-known tourist destination it is today: When Lieutenant John Charles Frémont (see A common place-name of the West: Fremont) and Charles Preuss sighted the lake from a ridge near Carson pass on Valentine's Day, 1844, while attempting a winter crossing of the Sierra Nevada (all still Mexican territory then), they originally named it Lake Bonpland, although early maps also reflect the name Mountain Lake. At high elevation, located between Californian mountain peaks of the Sierra Nevada and the Carson Range of Nevada, the latter was an appropriate name for this alpine lake. However, in 1852 the California legislature renamed it to Lake Bigler, after John Bigler, the 3rd governor of California. After 1860, the Washoe-language-based name, Tahoe, became popular and Lake Tahoe has since resisted any further name changes.

Keywords: history, geography, place-name origins, place-name synonyms

Petroleomics, petroleome, and their counterparts in protein chemistry

The term petroleomics refers to the chemical study of petroleum including its physicochemical characterization and the identification of its molecular constituents. The noun petroleomics reminds us of the word proteomics in protein chemistry standing for the study of proteins including their molecular and supramolecular structures and functions.
The term petroleome refers to the entire amount of a petroleum sample. The goal is to know the complete chemical composition of petroleomes. Again, an analogous word for a similar concept in protein chemistry comes to mind: proteome, composed from protein and genome.
The word petroleomics was coined by Alan G. Marshall at the National High Magnetic Field Laboratory at Florida State University, where he and his group is working on analytical methods for the compositional characterization and molecular description of petroleum fractions such as asphaltenes [1].

Keywords: petrochemistry, word analogy

References and literature
[1] Celia Henry Arnaud: Digging Into Asphaltenes • Mass spectrometry uncovers chemical details of petroleum's most recalcitrant fraction. Chemical & Engineering News September 21, 2009, Volume 87, Number 38, pp. 12-17.
[2] Oliver C. Mullins, Eric Y. Sheu, Ahmed Hammani and Alan G. Marshall: Asphaltenes, Heavy Oils, and Petroleomics. Springer, New York, 2007. DOI: 10.1007/0-387-68903-6 (PDF versions of all chapters).
[3] Oliver C. Mullins: Petroleomics and Structure-Function Relations of Crude Oils and Asphaltenes (Chapter 1 in [2]).
DOI: 10.1007/0-387-68903-6_1.

A sobriquet for asphaltene: “cholesterol of petroleum”

While cholesterol promotes clogging of arteries in biological systems, asphaltene can cause clogging of pipes in refining facilities and of pores and channels in geochemical systems such as underground rocks of oil-field reservoirs. Hence, the sobriquet “cholesterol of petroleum” for asphaltenes [1]. These are complex mixtures consisting of aromatic and heterocyclic compounds. Asphaltenes occur in crude oil along with saturated, unsaturated, and aromatic hydrocarbons and hetero-functionalized derivatives thereof.
The “19th-century definition” of asphaltenes, obtained as petroleum fractions, focuses on the solubility of asphaltene constituents in other organic solvents [1]: The asphaltene fraction comprises components that are soluble in toluene but insoluble in n-heptane or n-pentane.
To model and predict asphaltene properties such as as viscosity and aggregation [2] behavior and to optimize petroleum processing operations, a detailed molecular understanding of asphaltene is required. The “cholesterol-like” activity of asphaltene depends on intra- and extramolecular interactions of its molecular constituents.

Keywords: petrochemistry, thermodynamics of petroleum, nickname of petroleum fraction, analogy

References
[1] Celia Henry Arnaud: Digging Into Asphaltenes • Mass spectrometry uncovers chemical details of petroleum's most recalcitrant fraction. Chemical & Engineering News September 21, 2009, Volume 87, Number 38, pp. 12-17.
[2] Narve Aske, Harald Kallevik, Einar Eng Johnson and Johan Sjöblom: Asphaltene Aggregates from Crude Oil and Model Systems Studied by High-Pressure NIR Spectroscopy. Energy & Fuels 2002, 16, pp. 1287-1295. DOI: 10.1021/ef020065i.

A common place-name of the West: Fremont

Browsing a map of California, it is not hard to find a place-name that has the word Fremont in it. This name refers to John Charles Frémont, who literally put many parts of the western United States on the map. When he was born in Savannah, Georgia, on January 21, 1813, his name was spelled John Charles Fremon [1]. His father was the French teacher Charles Fremon. John Charles grew up in Charleston, South Carolina, where he adopted the french spelling of his name: Frémont. He became a lieutenant in the army corps of engineers in Washington and was sent west for surveying expeditions during the time when James Knox Polk was the president of the United States. Walter Borneman summarizes Frémont's westward drift as follows [1]:

John Charles Frémont was, and remains, something of an enigma. To his defenders, Frémont will always be “the Pathfinder of the West,” the quintessential explorer marching westward, ever westward. To his detractors, Frémont was an opportunistic bungler, a man who—had it not been for the political connections and journalistic talents of his wife and the dedicated services of his mountain man guides, including Kit Carson—might have simply marched off history's map.
As usual with someone who elicits such strong and divergent passions, the truth lies somewhere in between. Certainly, there is no denying that the West is covered with place-names—Frémont peaks, lakes, rivers, towns, and counties— that mark his paths.

The acute accent over the letter e in his name is now often dropped in American-English writings. If still alive, Frémont would not be pleased!

Reference
[1] Walter R. Borneman: Polk • The Man Who Transformed the Presidency and America. Random House Trade Paperback Edition, New York, 2009; pages 182-184.

A new English verb from the German language: to hocker

Hockern is a new recreational activity on the rise in Germany and elsewhere. The German verb hockern is derived from the masculine noun Hocker, meaning milking stool. Hockern can be translated into English as to busy oneself with a milking stool or to do tricks with a milking stool. To simplify translations, I would suggest to use hocker—as a regular verb—in English. It rhymes with soccer and is inflected in the same way as the verb tinker: He hockers. She hockered. They are hockering. Since the vowel e is unstressed, there is no doubling of the consonant r.
A person that hockers, may be called a hockerer or hocker gymnast.
If you are not yet convinced that hockern is a new sport, which needs to be verb-ized into English, you may just want to sit on your Hocker and watch while others are hockering along.

Keywords: creativity, gymnastics, body dynamics, fun; linguistics, English words, German words

More on Hockern
Hockern / Sport with a German Milking Stool, Feb. 06, 2008.
Hockern in Frankfurt... (video)
Kieler Kneipensport "Hockern" (Spiegel Online)
Freizeit: Locker vom Hocker (Märkische Allgemeine, September 12, 2009)

Group-theoretical confusion, rhyming words and non-rhyming names

The words rage and age definitely rhyme. The pairs rhyme–time and group–loop are spelled differently, but still do rhyme. We expect rhyming words in songs and rhymes. Sometimes, however, the fact that words do not rhyme at line's end is intended. The following song, that captures a panic during an epoch of exciting discoveries in group theory [1], is a case in point:

The floodgates were opened! New groups were the rage!
(And twelve or more sprouted, to greet the new age.)
By Janko and Conway and Fischer and Held
Mc Laughlin, Suzuki, and Higman, and Sims.

No doubt you noted the last lines don't rhyme.
Well, that is, quite simply, a sign of the time.
There's chaos, not order, among simple groups;
And maybe we'd better go back to the loops.

The panic of the 1960s and 1970s is over, unless you fear the Monster. Now finite simple groups are classified (completely?) and group theorists have their Atlas of Finite Groups, also known as Atlas of Symmetry (a “Rosetta Stone of science”), where groups are mapped out by beginning with A5 and finishing with M, the Monster that might as well been called the Friendly Giant or the Fischer-Griess group (see page 336 in [1]).
The names of mathematicians, mentioned in the above song, refer to Zvonimir Janko, John Horton Conway, Bernd Fischer, Dieter Held, Jack McLaughlin, Michio Suzuki, Graham Donald Higman, and Charles Sims.

Keywords: rhyme, mathematicians, symmetry, history of group theory, classification of finite simple groups

Reference
[1] Marcus du Sautoy: Symmetry. A Journey into the Patterns of Nature. First Harper Perennial Edition, Harper Collins Publishers, New York, 2009; page 306.

Abbreviation: Trhd. for trailhead

The composed noun trailhead is sometimes abbreviated as trhd. My example shows a sign at the end of the Jobs Peak Ranch Trail in the eastern part of Douglas County, Nevada. If you arrived here by coming from the Jobs Peak Ranch Trailhead, it will take you another 1.4 miles to return to where you started. Instead, looking in the other direction, a sign informs you that you may continue on to reach the Fay-Luther Trhd. after 2.0 miles. In fact, the units in miles have been omitted on both signs; probably another form of abbreviating.

Great dodecahedron versus Platonic dodecahedron

The dodecahedron is a Platonic solid along long with the tetrahedron, cube, octahedron and icosahedron. The faces of these five highly symmetric, three-dimensional objects are regular polygons (equilateral triangle, square and regular pentagon). A “spherical composition” of a specific number of same-type polygons (12 pentagons in the dodecahedron case) forms a Platonic solid. Each pair of adjacent polygons share an edge. The building polygons are not allowed to intersect, according to a condition imposed by Theaetetus, a colleague of the philosopher Plato, after which the Platonic solids are named. But what if they are allowed to intersect? Marcus du Sautoy “answers” this question with the following historical observation [1]:

To everyone's surprise, in 1809 a new shape had been built out of these 12 pentagons [that were known to build the Platonic dodecahedron]. Theaetetus had insisted that the faces of his shapes should not cut into each other. But what if you relaxed this condition? A mathematics teacher in Paris had found a new way to piece 12 pentagons together to make a new symmetrical shape that was christened the great dodecahedron. Although it looks like a shape built from lots of irregular triangles, it consists of 12 intersecting pentagons. The shape satisfies all the conditions for a Platonic solid except for the fact that the faces cut into each other. How many other strange and beautiful shapes like this might be out there? Three others were soon discovered, and mathematicians began to wonder where the new list might end.

Should these polyhedra with intersecting regular polygons be named anti-Theaetetian solids? Since they look star-shaped, they are otherwise addressed as stellated polyhedra [2].
Whatever they are named, there are only four of them as Augustin-Louis Cauchy (1789-1857) proved by successfully answering the question of the French Academy of Science (founded in 1666), which had dedicated a prize in 1811 for “proving beyond doubt that the five Platonic solids plus the four new solids were all the three-dimensional shapes that you could build from identical regular polygons” [1].

Keywords: solid geometry, nomenclature of polydedra

References and further reading and visualizing
[1] Marcus du Sautoy: Symmetry. A Journey into the Patterns of Nature. First Harper Perennial Edition, Harper Collins Publishers, New York, 2009; pages 164-166.
[2] Chapter VI “Star-Polyhedra” in the book by H. S. M. Coxeter: Regular Polytopes. Dover Publications, New York, 1973.
[3] Image of a great dodecahedron and more at Wolfram

An Argand diagram is a Wessel diagram is a Gauss diagram

An Argand diagram is a two-dimensional coordinate system for the presentation of complex numbers. The scaling on the horizontal axis gives the real part and the scaling on the vertical axis gives the imaginary part of a complex number. Although Jean-Robert Argand (1768-1822) is usually credited for geometrically picturing complex numbers this way, Marcus du Sautoy provides a detailed look into the origin of complex number presentation [1]:

Gauss [Carl Friedrich, (1777-1855)] had actually used a picture of the imaginary numbers as a mathematical tool in his proof [of the Fundamental Theorem of Algebra], but he kept it hidden for many years, fearing he would be laughed at by a mathematical establishment still wedded to the language of equations and formulae. But because the image was so powerful and gave imaginary numbers a physical reality, it was only a matter of time before others hit upon the idea. Two amateur mathematicians, the Dane [/Norwegian] Caspar Wessel [(1745-1818)] and the Swiss Jean Argand, independently proposed similar pictures in pamphlets they published. Argand, who was the last of the three to have the idea, is the person whose name became attached to the picture we now call the Argand diagram. Credit is rarely just.

Hence, the terms Wessel diagram or Gauss diagram would as well be justified.

Instead of using the word diagram for a figure, that illustrates complex numbers and their relationships graphically, the word plane is often used: Argand plane instead of Argand diagram. Other synonymous terms for Argand plane are complex plane or z-plane; giving credit to the complex numbers z = a + bi again!

Keywords: mathematics, geometry, algebra, history, graphical illustration, synonymous expressions

References
[1] Marcus du Sautoy: Symmetry. A Journey into the Patterns of Nature. First Harper Perennial Edition, Harper Collins Publishers, New York, 2009; page 153.
[2] Orlando Merino: A Short History of Complex Numbers. University of Rhode Island, 2006; PDF-file.

The word “via” as noun and preposition

The word via has a Latin origin, meaning way or road as in Via Appia (Appian Way), which is the name of a Roman road that connected Rome to Brindisi in what is now southern Italy.

In English, this meaning of connecting is still present when via is used as a noun—even on a microscale. In microelectronic engineering, for example, the short word via is used to name an interconnect hole or through-hole on an integrated circuit. A via connects two conductive layers separated by a dielectric layer. Vias are typically etched through dielectric layers and then filled with a conductive metal to make an electrical connection.

The word via is also used as a preposition with meanings by way of or by means of (as in sending via email). With via, one can emphasize an applied process (as in separating via distillation). Typically, via can be replaced by prepositions such as by, through, or with with a slight loss of nuance. Also, a detour or unexpected route is often expressed via via: She came from Cyprus via Canada to Chicago.

Synonyms in mathematics: remainder and residue

The remainder is what is “left over” when an integer is divided by a non-zero integer. For example, the division of 11 by 7 results in 1 and leaves the remainder 4. In the terminology of number theory, this can be written as 11 ≡ 4 mod 7 (in words: 11 and 4 are congruent modulo 7 or, synonymously, 4 is a residue of 11 modulo 7) .
In general notation: a ≡ b mod m, expressing that the difference a-b is an integral multiple of m. The symbol b represents the remainder or residue.

Note: The German word for remainder or residue is the masculine noun Rest. Infrequently, the word rest can be found in English-language math texts, used as a synonym for remainder or residue.

Keywords: arithmetics, mathematics, number theory, division, English language, German language

Symmetry from the Greek words “syn” and “metros”

The five regular polyhedra (tetrahedron, hexahedron or cube, octahedron, dodecahedron and icosahedron) are often cited as an expression of perfect symmetry. These polyhedra are today called Platonic solids after the Greek Philosopher Plato. He thought they were so fundamental that they must be the basic building units shaping the material world. The word symmetry began shaping at around the same time, when Plato founded his science and philosophy institution in Athens in 387 BC. In his book about symmetry [1], Marcus du Sautoy explains how the word symmetry made its way into the English language, from Greek via Latin:

It is the Greek language that assigned a name to the common trait that bound Plato's five objects [Platonic solids] together: symmetros. In the first century AD the Roman author Pliny the Elder bemoaned Latin's lack of a word for symmetry. Symmetros combines the Greek words syn, meaning ‘same’, and metros, meaning ‘measure’. Together they describe something ‘ with equal measure’. Symmetry for the Greeks was reserved for describing an object in which some of the internal physical dimensions were the same across the shape. In symmetrical solids the edges were all the same length, the faces all had the same area, and the angles between adjacent faces were all equal. Symmetry is about measurement and geometry. It would take some time for symmetry to become recognized as a mathematical property that goes beyond simple measurement, although the Greek philosophers were beginning to explore the idea of symmetry as a powerful image beyond physical shapes.

Keywords: geometry, mathematics, etymology, history, Greek, Latin

Reference
[1] Marcus du Sautoy: Symmetry. A Journey into the Patterns of Nature. First Harper Perennial Edition, Harper Collins Publishers, New York, 2009.

Truth, untruth, and probability

Truth and untruth are opposites. Where does probability fit in? As we talk about the probability that a proposition is true, we often suggest we have an idea of the provability of the proposition's truth. At the root of the noun probability (and also the noun probe) and the adjective probable is the Latin verb probare, meaning to try or to test. The English noun proof and the verb prove have the same Latin roots. Therefore, the words probability and provability do not just look alike, they have the same meaning from an etymological viewpoint. This has recently been illustrated by Chandler Davis in a discourse on mathematical reasoning [1]:

There is no doubt that the idea of probability was close to the idea of truth at the early stage [16th century]—etymologically, “probable” is “provable”, and even today, “probity” means utter reliability—and the emerging notion of something having positive probability had to be disentangled from the different notion of appearing credible. This fascinating story has been closely studied in recent years, especially by Ian Hacking and Lorraine Daston, and I have nothing to add to their work.

Keywords: etymology, mathematics, logic, philosophy, Latin

Reference
[1] Chandler David: The Role of the Untrue in Mathematics. The Mathematical Intelligencer Summer 2009, Volume 31, Number 3, pp. 4-8.

The conjunction “but” often means “and”

The words and and but are coordinating conjunctions. Whereas and is typically symmetric (the phrases before and after and can be interchanged without changing meaning), but is asymmetric. The word but is used to coordinate or subordinate a clause of concession or exception. However, but is also used in a way that implies an and connection [1]:

Let me begin with a mantra of 20th-century math education: “ ‘but’ means ‘and’.” We all know that this makes partial sense: namely, if one says “John is poor but happy” one is asserting both “John is poor” and “John is happy”. Nevertheless “but” is a major component in the structure of thought (like “nevertheless”), and the version having “but” as the connective is not the same as the conjunction of the two simple assertions. Many English speakers would find “John is poor but happy” cogent but not “John is rich but happy”. You will easily find more and subtler everyday examples. Examples within mathematics are subtler, inexhaustible, but [!] more elusive; […]

Even when but takes on the meaning of and, but stays syntactically asymmetric.

Keywords: natural language, coordinators, mathematics, logic, reasoning, precision

Reference
[1] Chandler David: The Role of the Untrue in Mathematics. The Mathematical Intelligencer Summer 2009, Volume 31, Number 3, pp. 4-8.

Acronym: REACH for Registration, Evaluation and Authorisation of Chemicals

REACH is the European Community approach to prospective risk management of new chemicals. The REACH regulation is effective since June 1, 2007. The goal is to protect humans and the environment and to place responsibilities to the chemical industry in terms of gathering information on physicochemical and ecotoxicological properties of chemical products and their safe handling. The European Chemicals Agency (ECHA), located in Helsinki, Finland, has details in the languages of the EU member countries:

• Danish: Det Europæiske Kemikalieagentur
  
• Dutch: Europees Agentschap voor chemische stoffen
  
• English: European Chemicals Agency
  
• French: Agence européenne des produits chimiques
  
• German: Europäische Chemikalienagentur
• Italian: Agenzia europea per le sostanze chimiche
  
• Polish: Europejska Agencja Chemikaliów
  
• Portuguese: Agência Europeia dos Produtos Químicos
• Spanish: Agencia Europea de Sustancias y Preparados Químicos

A complete, language-dispatching list of ECHA-links is available at http://echa.europea.eu.

In German, REACH is typically stated as Registrierung, Bewertung, Zulassung und Beschränkung chemischer Stoffe. With this translation, the regulation activity of authorisation (authorization) splits into acceptance (Zulassung) and limitation or restriction (Beschränkung) of chemical substances. In fact, in some other language versions the acceptance/restriction breakdown is made as well. The restriction aspect did not make it into the acronym. This certainly is the least favored regulation outcome on the part of manufacturers and, further, its inclusion into the acronym would have made it unpronounceable; so it was just left out to reach REACH.