Being an innocent youngster and a math professor at the same time

Martin Gardner's autobiography has posthumously been published [1,2]. Known for his Scientific American math column, Martin Gardner was fascinated by recreational mathematics, magic tricks and scientific research and he knew how to fascinate others. Persi Diaconis tells us that he wrote the following blurb for one of Gardner's books [2]:  

Warning: Martin Gardner has turned dozens of innocent youngsters into math professors and thousands of math professors into innocent youngsters.

Persi Diaconis, 2013.

Diaconis admits that he was one of those youngsters. Who else? I assume, the number of Gardner enthusiasts is growing exponentially.

Keywords: inspiration, recreation, magic, puzzle solving, mathematics.

References and more to explore
[1] David Singmaster: Master puzzler. Nature, September 19, 2013, 501 (7467), pp. 314-315. doi: 10.1038/501314a.
[2] Martin Gardner with Persi Diaconis and James Rand: Undiluted Hocus-Pocus. Princeton University Press, Princeton, New Jersey, 2013; page xvii.

Molecular chatterboxes: genes talking to genes

When genes became damaged or mutated, their hosting cells may turn malignant. Such cancerous cells can grow into tumors over time. Understanding of cancer, a group of diseases medically known as malignant neoplasm, relies on  the basic concept of uncontrolled, misregulated growth of cells into nearby parts of a patient's body. In addition to genetic changes, many other factors contribute to the biochemistry of malignancy, including body-occupying bacteria and the complex biomolecular interactions switching certain genes on and off. George Johnson summarize the new insight into the physics and informatics of cancer as follows: 

In the end, all biology comes down to genes talking to genes—within the cell or from cell to cell—in a constant molecular chatter. I had not considered, however, that the genes in human tissues can also exchange information with the genes residing in the microbes that occupy our bodies. Cancer is a disease of information, of mixed-up cellular signaling. Now there is another realm to explore.

George Johnson, 2013.

The new realm goes beyond the cell-centric mechanism of repeated mutation acquirement stimulating abnormal growth. A new paradigm that hopefully provides the needed insight to come forward with new treatments and advances in curing cancer.  

Keywords: cell biology, oncology, medicine, epigenetics, cancer treatment.

Reference
George Johnson: The long trail of cancer's. Scientific American, November 2013, 309 (5), 2012; pp. 60-63 [www.scientificamerican.com/article.cfm?id=book-excerpt-george-johnson-explores-the-latest-discoveries-about-cancer].

As well as we like: accurate(ly) versus efficient(ly)

Doing something well can mean to do it accurately or efficiently, or both. Julian Havil is asking the question how well an irrational number can be approximated by a rational number; and—within this context—he discusses the distinction between the adjectives accurate and efficient or, to be more accurate, the adverbs accurately and efficiently:

If by well we mean accurately, then the answer is as well as we like. It is intuitively clear that the accuracy of rational approximation can, in theory, be chosen to be what we will: there are plenty of rationals and as many as we could desire as close as we desire to our chosen number; consider the decimal expansion of the irrational number, truncated as we please. Yet, there is a hidden cost, as we shall see. Alternatively, if by well we mean efficiently the story is more complex since some numbers are more amenable to rational approximation than others - and from this relative compliance we can draw important distinctions [...]

Julian Havil, 2012.

Well done! 

Keywords: semantics, adjectives, adverbs, word disambiguation, approximation.

Reference
Julian Havil: The Irrationals. Princeton University Press, Princeton and Oxford, California, 2012; page154.

Elementary versus simple

Mathematics makes a nice distinction between the usually synonymous terms elementary and simple, with elementary taken to mean that not much mathematical knowledge is needed to read the material and simple to mean that not much mathematical ability is needed to understand it.

Julian Havil, 2012.

When the mathematically different meanings of these two adjectives collapse into one, the adjective complex makes for a suitable antonym. Julian Havil discusses the distinct meanings of the adjectives elementary and simple within mathematical context. He also provides an example in which their distinct meanings become difficult to grasp or where both words even regain identical meaning: the proof that ζ(3) is an irrational number, which has been achieved in quite different ways by (1) Roger Apéry, (2) Frits Beukers, (3) Wadim Zudilin, and others. An interesting, yet complex topic—even when illustrated in simple terms. 

Keywords: semantics, adjectives, antonym, word disambiguation.

Reference
Julian Havil: The Irrationals. Princeton University Press, Princeton and Oxford, California, 2012; pp. 152-153.

Named and unnamed mathematical constants: from anonymous to famous

Mathematical constants are either anonymous or famous, with fame a reflection of the constant's importance.

Julian Havil, 2012.

Along his compellingly illustrated path through the history of irrational numbers—delivering insights for mathematicians and non-mathematicians—Julian Havil introduces readers to interesting constants beyond the “famous constants” π and e [1]: the Conway Constant (also written Conway's Constant [2]), for instance, which isn't exactly famous. Neither is it anonymous, as it is named after the English mathematician John Horton Conway, who introduced and analyzed the look-and-say sequence leading to the discovery of the Conway Constant [3].

Anonymous constants may become famous. The Conway Constant and its look-and-say sequence should be of interest in the study of self-descriptive processes such as molecular self-replication; and, thus, will contribute to biomolecular modeling and advances in macromolecular chemistry and biochemistry [4].

Keywords: mathematics, special numbers, rationals, irrationals, transcendentals.

References and more to explore
[1] Julian Havil: The Irrationals. Princeton University Press, Princeton and Oxford, California, 2012; pages 136 and 137.
[2] Wolfram MathWorld: Conway's Constant [mathworld.wolfram.com/ConwaysConstant.html].
[3] John H. Conway: The Weird and Wonderful Chemistry of Audioactive Decay. Eureka 1986, 46, pp. 5-18 (see TOC on www.archim.org.uk/archives/eureka/#46).

by Óscar Martín

[4] Óscar Martín: Look-and-say biochemistry: Exponential RNA and Multistranded DNA. American Mathematical Monthly 2006, 113(4), pp. 289-307 [www.maa.org/publications/periodicals/american-mathematical-monthly/american-mathematical-monthly-april-2006].

Óscar Martín

by Ó Óscar Martín

One of the most attractive little villages anywhere in the American West: Genoa, Nevada

Genoa and peaks of the Carson Range seen from Discovery Trail

Genoa in Nevada is a small town that started as a settlement of Mormon pioneers in the 1850s and is today a charming community attracting both new residents and visitors from far and near. David W. Toll intimately describes this historic town as follows:

Genoa (pronounced Juh-NO-uh) IS THE OLDEST permanent settlement within the present state of Nevada, and one of the most attractive little villages anywhere in the American West. Established as a trading post in 1851 to serve the wagon trains as a resting place between the open desert and the granite barricade of the Sierra Nevada, Mormon Station (as it was called then) became a small farming center. It is now a gentrified enclave of the wealthy.

David W. Toll, 2002.

The Genoa Historic District attracts tourists. The surrounding river fork lands arouse bird watchers' interest. And the slopes and canyons of the Carson Range invite outdoor enthusiasts to challenge that granite barricade and its steep drop-offs. Old and young—wealthy or not—explore the scenic sites and tracks of the Genoa Trail System with a multitude of hiking, biking and horseback-riding options. Situated in the biologically-diverse Great Basin/Sierra Nevada transition zone in the Carson Valley, Genoa has a lot to offer to those who enjoy educational and recreational activities. The nearby River Fork Ranch and nature preserve provides interpretive sites and trails through ranch land. To see these plains and the mosaic of Genoa neighborhoods from a higher perspective, hiking and climbing the Genoa Waterfall Trail, Sierra Canyon Trail or Discovery Trail will do. Genoa: a little village with an expansive trail network.

Keywords: history, gentry, traveling, outdoors, recreation.

Reference
David W. Toll: The Complete Nevada Traveler. The Affectionate and Intimately Detailed Guidebook to the most Interesting State in America. Gold Hill Publishing Company, Inc., Virginia City, Nevada, 2002.

A geological wonderland: Lassen Volcanic National Park in northeastern California

California's Lassen Volcanic National Park is an easily accessible “Ring of Fire” hot spot rich in volcanic episodes. Visitors enjoy to explore this dramatic landscape. Volcanologists are dreaming of solving the intriguing puzzles that lie and evolve underneath its surface. Tim I. Purdy introduces Lassen Volcanic as follows [1]:

Lassen Volcanic National Park is a geological wonderland—home to four different types of volcanoes. While Lassen Peak is the most prominent feature in the park, it just happens to be the world's largest plug dome volcano. The peak gained notoriety with its eruptions of 1914-15.

The four different volcano types—to which Purdy refers—have to be the same types illustrated in the Kohm Yah-mah-nee Visitor Center and mentioned in the 20-minute park film The Story Behind the Landscape shown there and at the Loomis Museum auditorium: plug dome (like Lassen Peak), cinder cone, shield volcano and composite volcano (or strata dome or stratovolcano). These are the four main kinds into which geologists group volcanoes [2]. But there are other terms as well as type variations including cryptodome, mud volcano, supervolcano, submarine volcano and subglacial volcano.

A plug dome, generally named lava dome or volcanic dome, forms and evolves by the flow of highly viscous lava, like dacite, through its vent or veins. Typically the lava does not flow very far—otherwise it would build a gently sloping shield volcano. The viscous mass piles up, fills the volcano's crater, is cooling and solidifying around the rim or at the cone top, and grows a plugging dome by expansion from within the volcanic vent—hence its name. According to the park brochure, this is how Lassen Peak originated, since it started to take shape about 27,000 years ago as a volcanic vent on the northern flank of ancestral Brokeoff Volcano. The latter was a big composite volcano, which built up 400,000 to 600,000 years ago through countless eruptions until it broke down due to hydrothermal activity and weathering. 

Keywords: geology, volcanology, volcano classification, lava flow.

References and more to explore
[1] Tim I. Purdy: Lassen Volcanic. Lahontan Images, Susanville, California, 2009: Introduction.
[2] USGS: Principal Types of Volcanoes [pubs.usgs.gov/gip/volc/types.html].