Climate modeling: there's no app for that—not yet

Someday we may be able to say, “Climate modeling—there's an app for that.”

                                                                                                Brian Hayes, 2014.

Climate models come in various levels of simplicity—or complexity. Therefore, Isaac M. Held of the Geophysical Fluid Dynamics Laboratory in Princeton proposes to compare and rank models by placing them into a hierarchical system [1].

Brian Hayes illustrates that climate models not only differ in complexity by what geophysical details they capture via model design, but that—from a user point of view—they also differ in code availability & readability, interface design, interactivity options, patchwork structure and applied programming language [2]. Certain implementations are still based on FORTRAN, a computer language from the punched-card era. Although mathematically powerful, this is not the first language you are thinking of when building an app for smart devices.

Encouragingly and convincingly, Hayes argues for the importance of simple climate models as precursors or complements to those with higher complexity: “primitive” models are able to capture and highlight unique patterns and behavior, such as a self-reinforcing effect. For example, a model with latitudinally striped Earth zones, which can respond to adjustments in the solar constant, the albedo of land and ice, and a greenhouse-effect parameter, succeeds in capturing a feedback loop in which cooling promotes ice cover, followed by further cooling of Earth's average temperature [bit-player.org/extras/climate/ebm.html].

Certainly, climate models exhibit uncertainties with respect to prediction of future climates. Some models, however, successfully decode and reproduce aspects of the past climate evolution. If models of manageable complexity are able to show us what triggers sudden climate shifts, we may be interested to have them at our fingertips—as apps for educational or entertaining purpose. Virtually experimenting with Earth climate is okay. Any other climate experiments will have critical consequences.

Keywords: computational models, computer simulation, evolution of Earth's climate, climate change, understanding models, feedback mechanism.

References and more to explore
[1] Isaac M. Held: The Gap between Simulation and Understanding in Climate Modeling. American Meteorological Society November 2005, pp. 1609-1614. Online: www.gfdl.noaa.gov/bibliography/related_files/ih0501.pdf.
[2] Brian Hayes: Clarity in Climate Modeling. American Scientist November-December 2014, 102 (6), pp. 422-425.
Online: www.americanscientist.org/issues/pub/clarity-in-climate-modeling.

What do we know about precursors of the modern place-value systems for numerals?

A place-value system for writing numerals consists of a fixed set of symbols (digits), including a cipher for zero. Each symbol has a defined meaning and value depending on its position relative to other symbols within a composed number. In a number encoded by using the base-ten number system, for example, positions from right to left correspond to increasing positive powers of ten. More flexible, less systematic systems, such as the letter-based system of Hebrew numerals, apply a larger set of digits, but typically lack a symbol for zero. Yet, these less rigid concepts for number representation bear striking similarities with the rational, strictly positional, digit-minimized systems of today—including the dual, octal, decimal and hexadecimal number system.

How did place-value systems evolve? The history of the place-value idea can only be guessed at by relying on a few documents and some preserved specimens of counting boards. Joseph Mazur summarizes our fragmentary knowledge:

George Gheverghese Joseph tells us in his book The Crest of the Peacock that, aside from the Babylonians' clever sexagesimal (base 60) positional system, our modern place-value system is exclusively Indian. And yet Robert Kaplan, in his book The Nothing That Is: A Natural History of Zero, tells us that our system was Indian, but originated with the Greeks. Without solid written proof, there is no way of filling in the blanks of history. All we really know is that somehow, in some time and place, the clever place-value idea was transmitted from the Indians to the Arabs and later to the Europeans.

                                                                                              Joseph Mazur, 2014.

Reference
Joseph Mazur: Enlightening Symbols. Princeton University Press, Princeton and Oxford, 2014; page 38.

What is a biovermiculation or bioverm?

A biovermiculation, frequently called bioverm, is a microbial community exhibiting a patterned growth within an extreme environment. Bioverms are of interest in overlapping natural-science disciplines such as geomicrobiology, speleology and astrobiology. Michael Lemonick, who also points out the significance of biosignatures and biofilms for astrobiological research, inspiringly illustrates the artlike biostructures of bioverms, which make

patterns on the cave walls, including spots, lines, and even networks of lines that look almost like hieroglyphs. Astrobiologists have come to call these patterns biovermiculations, or bioverms for short, from the word “vermiculation ,” meaning decorated with “irregular patterns of lines, as though made by worm tracks.”  

It turns out that patterns like these aren't made only by microorganisms growing on cave walls. “It happens on a variety of different scales, usually in places where some resource is in short supply,” says Keith Schubert, a Baylor University engineer who specializes in imaging systems and who came to Cueva de Villa Luz [a poisonous cave near Tapijulapa in Mexico] to set up cameras for long-term monitoring inside the cave. Grasses and trees in arid regions create bioverm patterns as well, says Schubert. So do soil crust, which are communities of bacteria, mosses, and lichens that cover the ground in deserts.

                                                                                              Michael Lemonick, 2014.

Are these patterns, which are based on simple rules of growth and competition for resources, a universal signature of life?

Keywords: biology, ecology, pattern formation, growth patterns, competition for resources, network architectures, scaling.

Reference
Michael D. Lemonick: The Hunt for Life Beyond Earth. National Geographic July 2014, 226 (1), 26-45.

What is a biofilm?

A biofilm is

a community of microbes bound together in a viscous, gooey blob. 

                                                                                              Michael Lemonick, 2014.

Such biofilms are ubiquitous on Earth—likely growing in your shower and frequently found on other inorganic surfaces in wet environments as well as on organic surfaces including those of plants. If found beyond Earth (for example, in caves of Mars), biofilms would take on the role of exciting biosignatures for alien life and thrive—indicating that we, or at least “our” microbes, are not alone.

Reference
Michael D. Lemonick: The Hunt for Life Beyond Earth. National Geographic July 2014, 226 (1), 26-45.

What are biosignatures?

Biosignatures are

visual or chemical clues that signal the presence of life, past or present, in places where scientists won't have the luxury of doing sophisticated laboratory experiments. 

                                                                                              Michael Lemonick, 2014.

Those places include niche environments on Earth as well as possible habitats on other planets and moons of our solar system and on exoplanets and their moons.

Reference
Michael D. Lemonick: The Hunt for Life Beyond Earth. National Geographic July 2014, 226 (1), 26-45.

Don't dig new trenches: Complement your creative work by writing openly and understandably about mathematics

Writing about mathematics offers freedoms of explanation that complement the dense texture of meaning captured by mathematical symbols. 

                                                                                              Mircea Pitici, 2014.

Mathematicians are innovators, tinkerers and thinkers. They typically represent their ideas, definitions, algorithms and proofs in condensed formulations and symbol-loaden notations. In his Introduction to The Best Writing On Mathematics, 2013 (Princeton University Press, 2014), editor Mircea Pitici argues for the “inestimable educational and social value” of “talking plainly about mathematics.” He writes that mathematicians should seek validation outside their discipline and narrow community. Pitici explains: 

Mathematics and its applications are scrutable only as far as mathematicians are explicit with their own assumptions, claims, results, and interpretations. When these elements of openness are missing mathematicians not only fail to disrupt patterns of entrenched thinking but also run the risk of digging themselves new trenches. 

                                                                                                                  

The terms of caratage and weight-fraction fineness for gold concentrations of alloys

Gold (Au) is a precious metal. It is so precious that it has a special unit of purity: karat, also spelled carat. Frequently used unit symbols are kt or k.  Uppercase K is also in use, but may conflict with the symbol for the temperature unit Kelvin.

The term caratage refers to the purity of gold, i.e. the fraction of pure gold when this metallic element is alloyed with other chemical elements. Karat purity—using the kt unit symbol—is defined as follows:

Karat purity = (24 · M_Au/M_tot) kt 

M_Au is the mass of pure gold in a material sample and M_tot is the total mass of that sample. Thus, pure gold corresponds to 24 kt.

C. J. Raub reviews the composition of various gold alloys in relation to color and other properties [1].  He provides his readers with the following understanding of carat alloys:

The gold concentration of alloys can be expressed either in terms of caratage, 24 carat representing the pure element gold, or in finess which is the weight fraction expressed in 1000ths ( ‰). In European countries, 8, 14 and 18 carat jewellery is most common. (333, 585 and 750 ‰). 
                                                                                                                  C. J. Raub, 1999.

Dissolution reactions of gold alloys and reaction rates depend on the karat value. Nitric acid, aqua regia and other testing solutions are employed to determine the karat of a gold sample [2]. Testing materials and reagents are typically obtained from a jewelers' supply store.

Gold is known to be malleable. For many applications, a gold material with highest hardness at highest caratage is wanted—such that the material keeps its shape and guarantees wear resistance under ambient conditions. The 990 gold-titanium alloy with a fineness of 23.75 kt (24 · 990/1000)  is such a material, which has been developed as a fine gold alloy with desirable color, durability, and mechanical properties [3].

Keywords: gold alloys, purity calculation, concentration units, unit symbols, unit conversion.

References and more to explore
[1]  C. J. Raub: Gold Metal and Gold Alloys in Jewellery. In Hubert Schmidbaur, editor: Gold - Progress in Chemistry, Biochemistry and Technology. John Wiley & Sons, Chichester, England, 1999; page 110.
[2] Philadelphia Museum of Art: Finishing Techniques in Metalwork. Determination of Gold Karat [www.philamuseum.org/booklets/7_44_85_1.html?page=3].
[3] G. Gafner: The development of 990 gold-titanium, and its production, use, and properties. J. S. Afr. Inst. Min. Metall. 1989, 89 (6), pp. 173-181 [www.saimm.co.za/Journal/v089n06p173.pdf].