A Very Brief History of Zero

This post is in honor of Pi Day and Albert Einstein's birthday, both which we celebrate today. Although Pi is known to more than a million digits past the famous 3.14159, my post will be about zero, likely our most important number. 

The number zero is included in the sets of whole and complex numbers but not in the set of natural numbers. Zero is a number placed in the neutral space between the positive and negative numbers on the number line, extending to negative and positive infinite, and thus is neither positive nor negative. Zero has no value and is considered null digit. Mathematicians consider zero an even number based on the premises that if even numbers, when divided by 2 leave no remainder, as odd number do, then is clear that zero is even (1). Moreover, others have stated that it is because if an integer “N” is called even if there exists an integer “M” such that N= 2M. From this, they infer that zeros evenness is clear because zero= 2 multiplied by 0. See (1) and (2) below.

The concept of zero was recognized before the existence of the negative integers was ever considered. Babylonian and Indian mathematicians first thought of the zero around the second to the fourth millennium before the birth of Christ (4000-2000 b. C). However, its real development occurred around 36 b. C. in Mesoamerica. Archeologists hypothesize that other Mesoamerican civilizations like the Olmec may have had some knowledge of the zero much before the Mayans because of number-like hieroglyphs found in their stone calendars, and the values they are supposed to represent. Mayans used mathematics for astronomy and counting. They used their calculations to measure time and to track the stars (2). The use of zero was important because the numeric system depended on the position of the symbol for value; each symbol or glyph represented a level. Zero represented the beginning or no value from where all values originated. The values had additive properties. Precise knowledge of the previous value was crucial to get to the next (4). 

The number zero does not equal emptiness or nothingness. It is the midpoint of our number line and is commonly used to indicate magnitudes or sizes. Think of how we use zeroes every day, in our money, measurements, etc. In fact, the text you are reading now is based on a binary code of ones and zeroes. Mathematics surround us with the number zero playing a central role. 

Cited bibliography

(1)Penner, Robert C. (1999). Discrete Mathematics: Proof Techniques and Mathematical Structures. World Scientific: pg. 34.

(2) “Numeración Maya” retrieved on 2/13/09 from http://es.wikipedia.org/wiki/numeraci%C3%B3n Maya.

(3) Barrow, John D. (2001). The Book of Nothing. Vintage.

(4) Dichl, Richard A. (2004). The Olmecs: America’s First Civilization. Thames & Hudson.

Why Do I Blog?

Most of us blog to communicate ideas, discoveries, news, and the excitement that accompanies discovery. I started this blog with the intention to promote and divulge interesting ideas and information about the sciences that study the past, and the understanding I have gathered through my own experience in learning and research. This, of course, is with the hope of reaching a curious and interested audience.

This ideal is important for several reasons. One is that most of the scientific data we gather through field and cabinet work is later published in specialized journals, but these journals and their content are not really accessible to the general population. Moreover, people do not have the time to keep up with the amount of articles and journals published at all times, or because they are difficult to read.

These create a breach between the most recent scientific discoveries that is of value or interest to us all. Unfortunately, this breach is also a source of mistrust and unhealthy-biased skepticism for science in general, largely due to misunderstanding or ignorance. In fact, this goes against the grain of science communication and education, and it creates a deep gap between mainstream scientific advance and public knowledge.

I have hoped to contribute, although I recognize on a smaller scale, by posting about the things that I am curious about in science, promoting the scientific rationale behind them, and my personal experiences in my journey of learning and researching within these fields. I try to explain processes to find the practicability, or even really the excuse for what we do.

But what is the excuse. What if that curiosity pays off in the long run? It does. Curiosity does pay off in the long run. Look around you. The world that surrounds us is a world created by curiosity, science and technology. Think of the computer or cell phone in which you read these lines. The principles that make these appliances are hundreds of years old, invented or idealized by curious people who had no idea that their curiosities will turn out to be practical or useful to societies of the future.

As a geoscientist, I am trained to use the present as the key to the past. We are constantly trying to recreate and reconstruct the past. But, we try to reconstruct the past in the hope that that knowledge will give us a better present and future. We use models and predictions to hypothesize and reconstruct both the past and the future. So can we reconcile what we do with the practicability of our curiosity in the scheme of time? I think so. Discovering something new or interesting is one of my greatest pleasures. If the present is indeed the only reality and a product construction of our minds, then what better way to spend one's lifetime trying to understand the world that surrounds us, the things that draw our curiosity, even if at the time they seem impracticable or useless. Most of all, sharing and distributing that knowledge makes the quest most rewarding. I think that time has shown that in science no discovery is useless. We must surely always try to answer the whys, and how, where and who of our curiosity, and science allows for that freedom of thought and exploration that can surely fill more than a lifetime, and no doubt continue to better society and enrich human life.

Project Progressus: Archaeology of Conflict

As you can tell from my posts, I love history, either in the rocks, fossils, or human records. I have recently joined Project Progressus an international research group interested in the archaeology of belic conflicts and the material and collective memories that these events have left behind in Cuba and Latin America.

Project Progressus has a self-titled blog page of which Odlanyer Hernández de Lara, a Cuban archaeologist with extensive work experience in Cuba and Argentina, is the editor and main contributor of blog Progressus. Odlanyer is also the editor in chief of Cuba Arqueológica, a journal that specializes in Caribbean archaeology, but particularly in the communication of advances in archaeological research in Cuba.

The explosion of the USS Maine in the bay of Havana on February 15, 1898, as depicted by an unknown artist for the Muller Luchsinger & Co New York. This incident launched the Spanish-American War or the "splendid little war" as was dubbed by Secretary of State John Hay. 

The scope of the project is to promote and communicate advances concerning the recovery of the material remains and collective memories of battle-conflict archaeology in Cuba and Latin America. This includes not only elucidating aspects of relatively modern conflicts such as the Spanish-American war and the Cuban Missile Crisis but also of conflicts earlier in the colonial period. My colleagues and I will be contributing by participating in field work, workshops, organization, and writing additional posts to increase accessibility to the archaeological information that the project will generate.

I am excited to enter Progressus not only because I will be contributing to the body of historical knowledge and deepen my own about colonial Cuba, but also because I will get the opportunity to collaborate and learn from great archaeologists with a deep understanding of this subject.

Without much ado, the reader is thus redirected to Progressus page for further information and interesting future posts.

Fossil Leaves of the Yumuri River Gorge in Matanzas, Cuba

Fossilized plants are among the rarest types of fossils. This is because there are many factors that prevent or allow for their preservation. One of these factors is the delicate nature and chemical composition of the plant leaves themselves. Leaves are delicate, thin, and devoid, except in rare instances, of hard or mineralized parts, and thus become fossils under very special conditions; often in exceptional conditions.

Plant remains become fossils usually as carbon or oxide films within clay or mud sediments. The chances of preservation increase if coupled with rapid burial in quiet, low energy water environments where they can absorb water, sink and settle to the bottom where they become covered with sediment and preserved. If in addition, the sediment is low in oxygen, there is less decomposition and increasing preservation. In this way, fossil leaves provide an array of indicators to the surrounding environment and their origin, and thus open a wide window to the past.

Fig. 1: Fossilized leaf and seed on the river gravels at the Yumuri river site. 

This is the case of the Yumuri River gorge, near Matanzas city, in northwestern Cuba. It represents an interesting example of both fossil leaf assemblage and good preservation (Fig. 1 and 2). These fossil leaves represent an interesting case in the study of Cuban, and even the Caribbean palaeoflora. The first fossil plants in Cuba were reported by the German Johannes Felix in 1882. Ever since, fossil plants have been sporadically reported from Jurassic to the Holocene fossils (Leon, 1929) (Iturralde and Rojas, catalog available here).

The fossil leaves of the Yumuri river gorge are found within the complex arrangement of sandstone conglomerates and fossil muds of El Abra member, a variation of the Canimar formation (Iturralde, 1969). These are a mixture of small and medium pebbles, with rare fish and crab fossils within the finer sediments. This formation is very localized, existing only along the river gorge. It apparently dates between the late Miocene and the middle Pliocene. If so, this fossil leaf deposit can provide a great insight into the poorly known flora and paleoclimate of the region during that the last 6 million years. In itself a great wealth of information into the Cuban past.

Fig. 2: Sands and gravels beds of the Abra Member of the Canimar Fm. on the banks
of the Yumuri river gorge.

Let us start with the fossil leaves.

The shape and area of the leaves, and the type of sediment in which they are preserved, can provide an array of approximations (proxies) into the past climate and formation history of this deposit. There is a correlation between environment and the shape of plant leaves (Wilf et al. 1998 and 2000. Also, see Lindner, 2007 and citations therein). Plants with large leaves and smooth edges are most common in tropical and subtropical climates. Inversely, leaves with lobed and serrated edges, as is the case of maples, are indicative of temperate, colder climates.  The larger the area of the leaf is positively correlated with local weather such as precipitation and temperature (op. cit.). The Abra leaves, with their smooth edges, and mostly smooth elongated leaves, suggest warm, mean annual temperatures (MATs), likely greater than or about 28 degrees Celsius. The leaf margin analysis (of LMA based on the mm^2 area of the leafs) suggests warm tropical climate with mid-range precipitation (see Wilf et al. 1998 for tables).

Fig. 3: Small leaf within its fine sand tomb. Note the raised bumps on the surface, and the smooth edges.

When leaves fall they are usually spread very close to their source (Lindner, 2007). In this way, they can represent a very true local floral assemblage. The task of identifying the leaf species from El Abra was first tackled by  E. W. Berry, who reported over a dozen of species (Berry, 1936). These were mostly new species; a study that now will need revision, and is a poor indicator of age. Berry had already reported on fossil plants from the Pleistocene deposits in another of Matanzas's famous site, the San Felipe Tar Pits, near Marti (Berry, 1934). These studies of palaeofloras was followed by the notes of Roca (1922), and later Leon (1929).

Overall, the Abra fossil leaves suggests a past tropical warm and humid coastal biome. This would agree with the higher temperatures of the Pliocene, especially those of the mid-Pliocene. But once more, the better chronology is wanting here.

Fig. 4: A very small leaf attests to the fine degree of preservation of oxidized film.

Fig. 5: This curved leaf may be an indication, that at least some leafs were dry
when they sank to the bottom sediments of the river.

The Abra leaves show other interesting details which pertain to their physical state at the time of burial (taphonomy). Some of the leaves seem to have been preserved in a dry state. Meaning that at least some of the leaves that were preserved were dry and probably windblown by the time of deposition. This is the case of the leaf in Fig. 5, which compares with a dried example of a Mahogany Swietenia mahagoni Fig. 6 below. See how it is curved and curled?

Fig. 6: A modern example of a fallen, dry Mahogany tree leaf,
very similar to that of Fig. 5 above.

Because the sediments were so fine a mixture of mud and sands, leaf detail was preserved. Including in some examples, the original state of the leaves as they were being pressed and preserved into the thin films they are now.

The fossil plants occur only within the beds of fine sediments. These fine sediments indicate a low energy deposition environment, such as still or quiet waters, or single event deposition, such a flood that settled out quickly (Lindner, 2007). This is so because low energy waters usually do not move larger-coarser gravels, pebbles or boulders. Only larger energy events can. Especially if they are to be moved for longer distances along the flood plains of a shallow river bank. The mixture of sands and gravels of multiple sizes may support this. This is observable in the beds where the finer clasts overlie the heavier larger ones. This is called, in sedimentation stratigraphy, a graded bedding.

Fig. 7: Assemblage of fossil leaves encased in the sediment,
at various levels of deposition. Look at the bent leaf above.

These graded beds form a succession of finer beds, following larger thicker sandy beds, which indicate a cyclic variation in the formation of the deposit that can be indicative of migrating river beds, or flooding planes as stated above.These beds have marked limits in-between them, indicating abrupt changes in sedimentation regimes. Some have considered them to be variations in a river- sea level influence- regression and transgression or increasing/decreasing sea level (Iturralde, 1969). This makes sense being so close to the mouth of the bay, and if indeed this region had been a shallow, young delta in the past, much before it was lifted as it is now.

Fig. 8: Possible seed encased in fossil leaves
Note the abrupt bed plane bellow the plant fossils. 

In conclusion, taking all these variations of evidence together we can reconstruct a wooded river margin, shallow, low energy, and prone to flooding, in a tropical/subtropical climate. The clastic material is most likely coming from erosion of higher inner valley lands, filtering through the incipient river gorge into the flood plains of the river deltas into the yet nonexistent bay of Matanzas.

Fig. 9: Eroded and exposed fossil leaf at El Abra, Yumuri River Gorge in Matanzas.

This is part of one of my ongoing projects and much more work needs to be done. For instance, one of the greatest problems is defining the actual age of the sediments since there are a lot mixture and reworking of younger and older material within the same beds. The other would be to revise the taxonomy of the plants involved, and other organisms found in the deposit.

If you are a plant taxonomist who can identify these fossil plants and would like to collaborate, contact me.

In the mean time stay tuned!

Cited Literature

For a catalog of Cuban plants see Estudios de Plantas Fosiles de Cuba, prepared by the National Museum in Cuba.

For other interesting fossil plant discoveries in the circum-Caribbean see Velez-Juarbe Caribbean Paleobiology blog.

Berry, E. W. 1934. Pleistocene plants from Cuba. Torrei Botanical Club 61(5): 237-240.

Berry, E. W. 1936. A Miocene flora from the Gorge of Yumuri river, Matanzas, Cuba. John Hopkins Studies in Geology 13: 1-135.

Iturralde-Vinent, M. see his literature regarding Matanzas on Biblioteca Digital Cubana de Geociencias.

Lindner Dustra, T. 2007. Paleobotany and Paleoclimatology, Part 2: Leaf Assemblages (Taphonomy, Paleoclimatology, and Paleogeography) pp. 179-202 in Part 3 of E. A. M. Koutsoukos Applied Stratigraphy, Topics in Geobiology, volume 23.

Leon, Hermano. 1929. La flora flosil de Cuba en la actualidad. La Salle: 1-6pp.

Roca, M. 1922. Nota aserca de un yacimiento de fosiles vegetales del Abra de Yumuri, Matanzas, Cuba. Memorias de la Sociedad Cubana de Historia Natural 4: 120-124.

Wilf, P. S. L. Wing, D. R. Greenwood, and C. L. Greenwood. 1998. Using fossil leaves as paleo-precipitation indicators: an Eocene example. Geology, 26: 203-206.

Wilf, P. and C. C. Labanderia. 1999. The response of plant-insect associations to Paleocene-Eocene warming. Science 284: 2153-2156.

Dominican Republic: A Story of Caves and Bats

"In the island, which I have said before was called Hispaniola, there are very lofty and beautiful mountains, great farms, groves and fields, most fertile both for cultivation and for pasturage, and well adapted for constructing buildings. The convenience of the harbors in this island, and the excellence of the rivers, in volume and salubrity, surpass human belief, unless one should see them"

Letter of Christopher Columbus to King Ferdinand and Queen Isabella of Spain, 1492



The heights of Pico Duarte (3098 m), and the Cordillera Central. Behind, the Chain de la Selle or Sierra Baoruco.

November 2004 found me on the island of Hispaniola. To my great pleasure and experience, I was more than very excited to go. His research concentrated on the study of a peculiar group of bats called natalids for his doctoral dissertation (see results here). That study entitled surveying and studying living populations of these bats in their natural habitats, and visiting the island of Hispaniola was essential.

Practically straight out of the plane, we were scouting for areas to set our mistnets and observe our first bats. On that first night, near the quintessential city of Santo Domingo, we captured a female fig-eating bat Phyllops falcatus (haitiensis), which was weighted, measured, and released. The efforts were rewarded by the company of researchers Adrian Tejedor, Kevin Murray and Nelson Marcano.



Fig-eating bat Phyllops falcatus (haitiensis) near Santo Domingo, Dominican Republic.

Next day, and after many hours of bureaucratic roundabouts, we set out west, across the mountains of the Sierra de Neiba and on to the Valley of Neiba on our way to Barahona. We were looking for a fisherman town called Los Patos, and a set of caves perched in the mountains of Barahona. Several other scientists had marked this location as a site of interest for bat researchers (Miller, 1916-1929), and we were following their footsteps.



End hills of the Sierra Baoruco, in the small fishermen town of Los Patos, near Barahona.

The caves 1 and 2 of Los Patos are almost vertical, inside the belly and atop the hills from which the ocean is visible. The rocks there are limestone conglomerates, which with time and erosion rolled down and covered the beach in a thick blanket of polished pebbles. Such surface made our sleep there somewhat uncomfortable, but the view was spectacular.


Los Patos beach, near Barahona, looking towards the Caribbean Sea.



View from the mouth of Cueva de Los Patos 1, over looking the Caribbean Sea.

Inside the caves laid examples of the ancient fauna, represented by delicate fossils. The floors had guano and the walls had bats. The species we observed included ghost-faced bats Mormoops blainvillei, large fruit-eating bats Brachyphylla nana, Artibeus jamaicensis, the pollen and nectar eaters Monophyllus redmani and Phyllonycteris obtusa, plus large-eared insectivorous Macrotus waterhousei. The bat and bird faunas were exquisitely diverse.

Cueva de Los Patos 1-2. Roost of large fruit bats Brachyphylla nana (pumila) and Phyllonycteris obtusa.

Large-eared bat Macrotus waterhousei. This is the large subspecies waterhousei, which lives on Hispaniola.



However, the natalids, Natalus major and Chilonatalus micropus, the goal of the expedition almost, eluded us. Our single Ch. micropus was caught late one night, as we were putting away the mist net. Just then came this low, butterfly-like, flying bat into the net. So far, this remains the only reported Ch. micropus roost site on Hispaniola (Tejedor, 2011: 35).

Chilonatalus micropus from Los Patos Cave 2

Under the chilly effect of the mountains, we headed back to Santo Domingo. On our way through the valley of the Cordillera Central towards the south, we stopped at Bani, birthplace of Maximo Gomez (1836-1905). Gomez was a brave and dedicated General of Cuban wars for independence between 1868 and 1898, and the later Cuban-Spanish-American War. Cuban history values the great contribution from this Dominican generalissimo (see fig. below).

General Maximo Gomez, early 1900s. From Library of American History, Vol.VII.

The roads crossing through the central valley of the Cordillera Oriental to Sabana del Mar, on the south coast of Samana Bay, were very deteriorated or non-existing, rough, and dangerous. But these were filled with interesting flora and fauna that we stopped to observe.

Hispaniolan giant Tarantula Phormictopus cancerides

One of our first encounters was this Hispaniolan giant Tarantula (Phormictopus cancerides), and one or two Ashy-faced owls (Tyto glaucops). While asking for directions in the town of Sabana de la Mar, we spotted a large bat flying around a light post in the main central park. We parked to take a closer look. It must have been nearly 12 am, and we were dead tired, but stunned to see a large bulldog fisher bat (Noctilio leporinus) apparently eating insects attracted by the light of the lamp post!

Noctilio leporinus on the central plaza of Sabana del Mar. The white dots are likely insects captured in the glare.

Finally, that night we arrived a natural reserve station on the Haitises Park. The Haitises are a conglomerate of natural wonders. It has a high diversity both in fauna and flora, and interesting  formations called "mogotes" or in this case known as "haitises". These are conic karst hills, like the mogotes of my previous post on Pinar del Rio, western Cuba. These, however, are formed on younger limestone, smaller, and covered with more vegetation, but similarly impressive.



Conic karts, limestone formation of the Haitises as we saw them from our boat.
Courtesy and Copyright of Adrian Tejedor.

Conic karts, limestone formation of the Haitises as we saw them from our boat.
Courtesy and Copyright of Adrian Tejedor.

This variation of karst formation or karst geomorphology (as in geological manifestations of the terrain), was formed by dissolution of the limestone over time. In the Caribbean islands similar karstic formations are present, but most profusely in Cuba, Jamaica, this region of Hispaniola, and in Puerto Rico. However, they are all distinct in their level of maturity. The oldest and thus more mature are those of Pinar del Rio in Cuba, whereas those of Hispaniola and Puerto Rico are formed on most recent rocks.

Massive limestone haitises in the bay of Samana. One can almost imagine
how C. Columbus saw the Tainos right on these beaches he was there.

To get to these rounded hills, which from afar looked like elephants half submerged in the waters of the San Lorenzo bay, we had to ride on a small boat. This boat took our party along the crannies and crevices between the massive rock domes of the Haitises. We were looking for the intricate cave systems that honeycomb these formations, so important to our research since they were to host the fauna we sought.



Railroad Cave appears from within the drowned elephants that are the karst hills of the Haitises.

One of these caves was Cueva de la Linea, or Railroad Cave, known to us from the early research of William M. Gabb, William L. Abbott, Gerrit S. Miller,  and later that of Krieger (1928-29).

Railroad Cave is near an abandoned railway track near the bay of San Lorenzo. The area is surrounded by crescent sandy beaches, marshes, and caves. The most notable caves being  Simmons's Cave, Boca del Infierno cave (the Mouth of Hell), and Railroad cave, which is known locally as Cueva del Templo (cave of the temple).

William M. Gabb explored caves around this area between 1869 and 1871, finding extensive evidence of pre-Columbian inhabiting. Exploration continued calling the attention of William L. Abbott who explored several of these caves, including Railroad cave in 1883 and then in 1916. It was the former which enticed the National Museum to send Gerrit S. Miller later that year, and then again in 1928 with H. Krieger. It was this last party which carried out serious archeological and paleontological research there (1929).

Sunlit Cueva de la Linea or Railroad cave in Samana Bay.

The Ciguayan tainos inhabited these beach caves, and their former presence is felt by their many shell heaps (Strombus pugilis) at their entrances and the unforgettable cave art in their anterooms. The shell heaps also include the bones of the animals the Tainos used for food, such as hutias, manatees, conchs and fish, and are generally called kitchen middens in the archeological jargon. One can't help but imagine what Columbus saw when he visited the bay of Samana to observe an eclipse of the moon in 1492. Then, the natives lived on the north shore of the bay.

No doubt we enjoyed this particular cave much. The pictographs and petroglyphs, like those the figure below, carved into the cave rock, depicted faces, handprints, and sketches of animals like egrets, dogs, sharks, and others. Moreover, there were large bat colonies in very hot rooms separated by small water intrusions, deep into the cave system.

Ciguayan Taino petroglyph at Cueva de la Linea, Samana.
One of the many human artistic representations of the area.

Moving inside these hot rooms was uncomfortable because the extreme temperature and smell of bat urine made breathing difficult. Often we had to stop and hold on to the wet walls to catch our breath before moving on forward. In the center of these rooms, there were accumulations of bat excrements and all kind of invertebrate fauna that feeds on deceased bats and the guano on the floor. The same guano that is often mined as a natural fertilizer.



Natalus major in its roost, Cueva de Cristian, Hato Mayor.



A colony of the sought after Natalus major, inside a well-vented room Cueva de Cristian, Hato Mayor.

But what was the purpose of all this?

Fieldwork is not an easy task and is well accompanied by multiple difficulties that researchers must endure reaching their goals. From sleeping on cave floors infested with ticks and roaches, to having no food or commodities, to being attacked by the native fauna (people included).

It is sad that much destruction occurs well within the boundaries of several national parks and other areas. Illegal burning, cutting, and cave guano extraction threatens and disturbs the natural fauna. This includes the nests of the Palm crows, the endangered Ridgway's hawk, Hispaniola amazon parrots, natalid bats, and a myriad of plant life; living organisms in general, but especially those that are endangered or vulnerable already. Many of the well-forested areas are cleared for avocado, coconut, and plantain plantations or tourism. Therefore, it is important that we document the existing flora and fauna so that we can establish sensitive plans of protection, so that the wonderful areas are not lost to posterity, and that other may enjoy its natural wonders in the same way that we have.

Samana peninsula and San Lorenzo bay seen from atop one of the Haitises.
A scenery reminder of the natural wonders that must be protected from complete human destruction.
Once these are gone, they are gone forever.

The experience of research, not just traveling to exotic places to see interesting organisms, but with the hope of discovering something new, is very rewarding. In the end, our efforts are towards a better understanding of the natural environment that surrounds us all.

We think these environments and their organisms are worth preserving, but one blog cannot capture the natural complexity and beauty of these amazing islands. The world would surely be a dull place without these magnificent ecosystems. We should strive to protect them, instead of destroying them.


Cited Literature

Krieger, H. W. 1929. Archeological and historical investigations in Samana, Dominican Republic. US National Museum Bulletin, 147.

Tejedor, Adrian. 2011. Systematics of funnel-eared bats (Chiroptera: Natalidae). Bulletin of the American Museum of Natural History, 353.