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Agronomía Colombiana

Print version ISSN 0120-9965

Agron. colomb. vol.32 no.1 Bogotá Jan./Apr. 2014

Effect of edaphic and foliar applications of different doses of zinc on the yield of the Criolla Colombia cultivar

Efecto de la aplicación edáfica y foliar de zinc sobre el rendimiento del cultivar Criolla Colombia

Andrés López 1, Manuel Iván Gómez2, and Luis Ernesto Rodríguez2

1 Plant Genetic Resources, TibaitatáResearch Center, Corporación Colombiana de Investigación Agropecuaria (Corpoica). Mosquera (Colombia).
2 Department of Agronomy, Faculty of Agricultural Sciences, Universidad Nacional de Colombia. Bogota (Colombia).

Received for publication: 5 July, 2013. Accepted for publication: 19 March, 2014.

The present study was carried out in a Typic Hapludand soil in the municipality of 'El Rosal' (Colombia) and aimed to compare the yield performance of the cultivar Criolla Colombia under foliar applications of Zn chelate (0, 1, 2 and 3 kg ha-1) and edaphic applications of granulated Zn sulfated (0, 1, 2 and 3 kg ha-1). A split-plot, randomized complete block design, with four repetitions per treatment, was employed. In each category, the evaluated variables were: tuber weight and number of tubers. The results revealed that the 3.0 kg ha-1 edaphic application rendered a quadratic yield behavior with a relative increase of 7.9 t ha-1 (136%) for the first category tuber weight and 9.5 t ha-1 (68%) for total weight. In turn, the foliar application of the same dose resulted in a 5.8 t ha-1 (93%) relative increase and a first category tuber total weight increase of 3.8 t ha-1 (24%). Under the edaphic and foliar Zn applications, the number of tubers underwent 77 and 86% increases, respectively, with respect to the control. These results show the importance of Zn in photoassimilate accumulation efficiency, structure differentiation and tuber quality in this short-cycle crop.

Key words: fertilization, diploid potato, micronutrients, tubers, Andean crops.

Esta investigación se realizó en el municipio de El Rosal (Colombia), en un suelo Typic Hapludand y tuvo como objetivo evaluar el efecto de la aplicación edáfica de sulfato de Zn granulado (0, 1, 2 y 3 kg ha-1), comparado con la aplicación foliar de quelato de EDTA Zn (0, 1, 2 y 3 kg ha-1) sobre el potencial del rendimiento del cultivar Criolla Colombia. Se utilizó un diseño de parcelas divididas en bloques completos al azar y cuatro repeticiones por tratamiento. Las variables evaluadas fueron: peso y número de tubérculos por categorías. Los resultados muestran que ante la aplicación edáfica de una dosis de Zn de 3,0 kg ha-1, el rendimiento presenta un comportamiento cuadrático, con un incremento relativo de 7,9 t ha-1 (136%) para el peso de los tubérculos de categoría primera, y de 9,5 t ha-1 (68%) para el peso total. Ante la aplicación foliar de la misma dosis, se observó un incremento relativo de 5,8 t ha-1 (93%) para el peso de los tubérculos de categoría primera y de 3,8 t ha-1 (24%) para el peso total. El número de tubérculos registró un aumento de 77% y de un 86% en la aplicación edáfica y foliar, con respecto al testigo, estos resultados muestran la importancia que tiene el Zn en la eficiencia de acumulación de fotosíntatos, diferenciación de sus estructuras y calidad de los tubérculos en un cultivo de ciclo corto como Criolla Colombia.

Palabras clave: fertilización, papa diploide, micronutrientes, tubérculos, cultivos andinos.

In Colombia, the name "yellow diploid potato" (Papa Criolla) refers to those morphotypes that exhibit yellow rind and flesh (egg yolk phenotype) (Rodríguez et al., 2009). This type of potato was initially classified as Solanun phureja (Hawkes, 1990), later on as the Solanun tuberosum Phureja Group (Huamán and Spooner, 2002), and, recently, as the Solanun tuberosum Andigenum Group (Spooner et al., 2007, Rodríguez et al., 2010). Although it can be cultivated between 2,000 and 3,000 m a.s.l., its optimum range is from 2,300 to 2,800 m a.s.l. (Becerra-Sanabria et al., 2007).

Colombia is known as the number one diploid potato producer worldwide, planting 8,500 ha a year, from which a hundred thousand tons are harvested in the departments of Cundinamarca, Nariño and Boyaca (Herrera and Rodríguez, 2012), producing exports of 1,000 t yearly (Fedepapa, 2012).

Those who have managed to export this product report promising experiences due to its good international acceptance, resulting from its unique taste. However, it is necessary to solve problems related to a homogeneous, constant and sufficient supply, in order to adequately satisfy the demands of international contracts. For this reason, it is necessary to improve the production, transformation and commercialization processes (Herrera and Rodriguez, 2012), Stressing the call for crop technology research and dissemination and for the adoption of good agricultural practices (GAP) with an emphasis on the proper management of soil fertility and water.

The variety Criolla Colombia exhibits an erect growth habit, intense lilac flowers, and good development of its light green foliage. Having no dormant period and a tuber potential yield of 15 t ha-1, this plant produces rounded tubers with half-depth eyes and an intense yellow rind and flesh (Rodríguez et al., 2009).

Within potato cropping, fertilization is one of the most remarkable production costs, reaching figures of about 39% (Porras, 2005). Although Colombia has developed a strong tradition for the modernization of this crop, which has good industrialization and exportation potential (Martínezet al., 2006), supply price increments and inadequate crop management limit productivity and threaten the competitiveness of the system (Rodríguez et al., 2009). For this reason, current research aims to identify yield limiting factors and innovative cropping practices. Among the latter, those dealing with soil fertility strive for an integral and balanced nutritional management with special emphasis on micro-nutrients, an aspect that has been insufficiently investigated. Integral fertilization is one of the most efficient practices for assuring the full expression of a plant's genetic potential, resulting in better yields, both in terms of quality and quantity (Castro and Gómez, 2010).

Interest in micro-nutrients has recently captured the attention of plant nutrition and physiology specialists, since, in many agro-ecosystems, these minerals limit productivity, although this is frequently not so evident (Kirkby and Römheld, 2007). Hence, their adequate supply does not only determine considerable yield increments, but also an advantageous utilization of nitrogen and phosphorus fertilization (Kirkby and Römheld, 2007).

Micro-nutrients in potato crop fertilization (the case of Zn)

The fact that micro-nutrients are present in much lower concentrations than macro-nutrients in plant tissues indicates that they are likely to play different roles in growth and metabolism (Kirkby and Römheld, 2007), which is the most frequent case. These low concentrations reflect the role played by these nutrients as enzymatic reaction activators and as part of the prosthetic groups of metalloproteins, which are capable of catalyzing redox processes through electron transference (mainly the transition elements: Fe, Mn, Cu and Mo). Micro-nutrients are also likely to form complexes, linking an enzyme to a substrate, which is the case with Fe and Zn. Some of these minerals, such as Mn, Zn and Cu, are known to be present in superoxido diminutasa (SD) isozymes, which act as sweeping systems that eliminate toxic oxygen radicals, thus protecting biomembranes, DNA, chlorophyll and proteins (Kirkby and Römheld, 2007). The main functions of micro-nutrients are presented in Tab. 1.

Zinc is absolutely essential to healthy plant growth and optimum yields in all agricultural and horticultural crops (Alloway, 2004). In contrast with Fe, Mn, Cu and Mo, Zn is a transition element that is, therefore, not subjected to valence changes. Zn is absorbed as a divalent cation (Zn+2) and transported through the xylem either freely or as a part of organic acids. Not oxidized or reduced by plant metabolism, Zn+2 acts as an enzymatic cofactor or metallic component (Marschner, 1995). Some of these metalloenzymes bind to other enzymes and their substrates, while, in other cases, Zn forms tetrahedral complexes with N and O, which are particularly coupled to S in a variety of organic compounds (Vallee and Auld, 1990; Kochian, 1991; Kirkby and Römheld, 2007).

Higher plants produce few Zn containing enzymes, which play catalytic, coactivating and structural roles (Vallee and Auld, 1990; Vallee and Falchuk, 1993). Among these enzymes, we can count carbonic anhydrase (CA), RNA polymerase and alcohol dehydrogenase; the latter promoting the production of ethanol from aldehyde in root apexes under anaerobic conditions (Clavijo, 2001). When this mineral is coupled to catalytic enzymes, its atoms are separated from one another by chains of three amino acids; the most frequent one being histidine, followed by glutamine and asparagine. Zn atoms with structural functions are usually coordinated with S groups, together with cystein. These complexes constitute stable structures that play important roles in DNA replication and genetic expression (Coleman, 1992).

The biochemical paths involving Zn affect plants in several ways, such as protein and sugar metabolism (the latter comprising photosynthesis and the conversion of starch into sugars), auxins (a growth regulator) synthesis, pollen formation (Sharma et al., 1990) and membrane integral maintenance (Brown et al., 1987; Alloway, 2004).

Many Zn dependent enzymes play important roles in the metabolism of proteins, carbohydrates and auxins. For example, a deficiency of this element reduces the activity of carbonic anhydrase (CA), which, being present in chloroplasts and the cytoplasm, facilitates the transference of CO2/HCO3 for the photosynthetic fixation of CO2 (Marschner and Cakmak, 1989; Cakmak, 2000). Also affected by Zn deficiency, the enzyme 1,6bifosfato regulates C6 sugars in the chloroplast and the cytoplasm, where it is located; whilealdolasa promotes the transference of C3 photosynthates from chloroplasts to the cytoplasm, where it regulates metabolite flow via glycolytic processes (Marschner and Cakmak, 1989; Cakmak, 2000).

Auxin (specifically IAA) metabolism alterations are closely associated with Zn deficiency symptoms such as intervein chlorosis (which goes from green to light yellow) and short internodes (Arce et al., 1991), as well as delayed growth, small leaves, and leaf necrosis as secondary effects of P and Fe toxicity (Ramírez, 2004). If the auxin metabolism route is affected by Zn is not clear yet, but tryptophan, whose production requires this mineral, is a likely precursor of IAA synthesis. Anyway, it is clear that Zn deficiency diminishes the amount of synthesized IAA, which is, additionally, subjected to more intense oxidative degradation processes (premature tissue ageing) (Kirkby and Römheld, 2007).

Zinc deficiency is also closely related to N metabolism, in as much as it reduces the concentration of proteins and increases that of aminoacids (Kirkby and Römheld, 2007; Bell and Dell, 2008); thus, determining disease propensity through a higher exudation of these low molecular weight components (phytosiderophores) and turning over in the plant resulting from altered root and shoot growth patterns (Ramírez, 2004). There is growing evidence that the cell membrane structural integrity and permeability maintenance roles played by Zn protect the plant against the attack of pathogens on roots and new sprouts (Kirkby and Römheld, 2007; Bell and Dell, 2008).

Protein synthesis inhibition resulting from Zn deficiency is largely determined via RNA reduction, which is, in turn, provoked by a lower Zn polymerase activity, reduced structural integrity of ribosomes and higher RNA degradation. With this mineral's deficiency, the mentioned growth arrestment brings along lower carbohydrate consumption levels and, consequently, lower photosynthetic rates. This leads to a larger production of oxygen radicals, which, not being removed, intensify Zn deficiency symptoms, especially under intense luminosity (Kirkby and Römheld, 2007).

Marschner (1995) suggests that the isozyme superoxido dismutasa (SOD or Cu-Zn-SOD), which contains Zn, plays an important role in the removal of superoxidized radicals (O2-) and, therefore, in protein and membrane protection against oxidation. Zinc controls the production of free radicals, which are toxic, by interfering in NADPH oxidation and in their actual removal. Through the action of these radicals, Zinc deficiency leads to the breakage of the double bonds of phospholipids and polyunsaturated fatty acids in the cell membrane, which, in this way, becomes more permeable and tends to allow the loss of sugars, aminoacids and potassium. The damaged lipid membrane and IAA oxidation produce chlorophyll destruction and, thus, necrosis and atrophied growth of the leaves (Marschner and Cakmak, 1989).

Foliar and edaphic Zn absorption

The approximate Zn concentrations in the granitic, igneous rock and basaltic fractions of the earth's crust are, respectively, 40, 70, and 100 mg kg-1 of soil (Taylor, 1964); while sedimentary rocks such as limestone, sandstone and shale contain 16, 20 and 95 mg kg-1 of soil, respectively (Turekian and Wedepohl, 1961). The total Zn content in soils varies from 3 to 770 mg kg-1, whereas the world average is 64 mg kg-1 (Kabata-Pendias and Pendias, 1992).

Soil fertility is usually measured in terms of nutrient availability for plants. However, a soil with elevated mineral levels is not necessarily fertile because several factors, such as compaction, drainage, drought, diseases or pests, may limit nutrient availability. For this reason, the concept of fertility should also include chemical, physical and biological criteria (Pumisacho and Sherwood, 2002).

Regarding soils, Zn deficiency is caused in crops by low native levels of this element, a lack of associated minerals in the pedogenetic process, basic or calcareous reaction media, a lack of organic matter, salinity, downpouring, a loss of the arable layer due to erosion, which in turn results from steep topography or continuous tillage, and possible antagonisms between P and Fe. Although low Zn availability may occur in an ample series of soils, the deficiency of this nutrient is more thoroughly expressed in sandy soils (Alloway, 2008; Bell and Dell, 2008).

With zinc sulphate being the most frequent Zn compound employed in fertilization, other important fertilizers are: ZnEDTA (Zn chelate) and Zn nitrate (Alloway, 2008). These fertilizers can be applied to the soil or directly to the plant (foliar application). Zinc sulphate (ZnSO4 4H2O) applications to the soil range between 2 and 20 kg ha-1, while foliar applications use 0.3 to 0.5% solutions, with the highest Zn chelate translocation rates being obtained with EDTA-Zn and ZnSO4.

Foliar fertilization is actually a complement to soil fertilization. It is intended for the correction of micronutrient deficiencies and the recovery of the plant when affected by adverse biotic or abiotic conditions. The efficiency of this fertilization method is a function of crop age, foliar area, time of year, application method and mobility of the mineral in question (Pumisacho and Sherwood, 2002).

Under full foliar fertilization, potato yield has been reported to increase by 5 t ha-1. Zinc chelate applications have been found to increase yield by up to 2.6 t ha-1. Positive responses to foliar fertilization are mainly attributed to low sulphur, zinc and manganese levels. Two to four fertilizer doses at intervals of 21 d starting at flowering are usually recommended for micronutrient deficiency correction via foliar application (Pumisacho and Sherwood, 2002).

In this context, the objective of the current study was to evaluate the effects of edaphic and foliar Zn applications on the yield of the variety Criolla Colombia under the conditions of a Bogota Plateau soil. This will facilitate formulating fertilization strategies under which this plant is capable of satisfying its need for specific nutrients, such as Zn in this case, when they are not available.

Materials and methods

This research was conducted on the San Gabriel farm, in the municipality of El Rosal (Cundinamarca, Colombia) (2,685 m a.s.l.; with a precipitation of 825 mm year-1; annual average temperature of 13°C; and 81% relative humidity) on a Typic Hapludand loamy soil with strongly acid reaction and low cationic exchange capacity; but with good levels of Ca, probably due to the effects of previous soil amendments. Showing no aluminum limitations, it did present Mg misbalances. Native Zn was at moderate to adequate levels (4-6 mg kg-1), but the P/Zn ratio, which was above 10, might have absorbed the mineral in question. Regarding other ionic ratios, the P and Ca levels might have determined the K, Mg, B and Zn deficiencies. These analyzes were performed in the Universidad Nacional de Colombia, Soils Laboratory, Bogota (Tab. 2).

Plant material

The experiment made use of 2-4 cm seed-tubers of the cultivar Criolla Colombia, which are typically round shaped and feature medium-depth eyes, an intense yellow flesh and rind, an early maturation (120 d), a specific gravity of 1.088, no dormant period, and an average yield of 13-15 t ha-1 (Rodríguez et al., 2009).

The zinc application was intended as a complement to the conventional fertilization plan (kg ha-1): N, 88.39; P2O5, 232.09; K2O, 113.29; CaO, 56; MgO, 70.75; and S, 6. The zinc sources employed for the trial were Microzinc® (Microfertisa, Bogota) (20% granulated Zn sulphate) and EDTA- Zn chelate, 12% soluble powder.

The band application of ZnSO4 to the plot was carried out together with that of the other fertilizers. Thus, the Zn doses were 0, 1, 2 and 3 kg ha-1. Likewise, each foliar Zn dose was fractioned into five applications starting on day 30 after planting and continuing on days 37, 44, 51 and 58.

The foliar applications were carried out with a 20 L RoyalCondor® sprayer pump (Progen, Bogota). Each dose was applied with 300 L ha-1 of water. Additionally, the water was treated with MF-Acidurez® SP, 0.25 g L-1 (Microfertisa, Bogota) (hardness corrector and pH reducer) and Herbox-SL (Exro, Bogota) 0.75 cm3 L-1 (hypotensive coadjuvant) to improve the application efficiency of the element in question.

Experiment design

The experiment was carried out under a split-plot, randomized complete block design with four repetitions, considering the Zn application dose as factor A (0, 1, 2, 3 kg ha-1) and the application technique (edaphic or foliar) as factor B. The experimental units corresponded to 21.6 m2 plots with 0.9 m between furrows and 0.3 m between plants.

Studied variables

The yield was assessed in terms of number of tubers and tuber production weight in two size categories. Thus, the following variables were measured: class 1 yield (C1Y, corresponding to the weight of those tubers with a diameter larger than 4 cm); class 2 yield (C2Y, 2-4 cm tubers); and commercial yield (CY), which grouped categories 1 and 2. Regarding the number of tubers in 120 m2, NC1T represented class 1 tubers (diameter > 4 cm); NC2T, 2-4 cm diameter tubers; and NTT, classes 1 and 2. The harvest took place on day 105 after sowing.

Statistical analysis

The statistical treatment of the data consisted of an analysis of variance (ANOVA) carried out in SAS v9.0 (SAS Institute, Cary, NC) and Office Excel®Â (Microsoft Corporation, Washington DC), comparing two factors: Zn dose (0, 1, 2, 3 kg ha-1) and application technique (edaphic and foliar) with their corresponding interactions. As the data passed the normality test, each variable was further scrutinized by Bartlett's variance homogeneity test, which indicated the general fulfillment of this assumption except for the total number of tubers.

The homogeneous variables were evaluated through analysis of variance. Those showing significant differences were further analyzed through orthogonal contrasts. Finally, a tendency line was adjusted for those variables showing Zn dose effects. The variable total number of tubers (TN1) was elevated to the power of two, thus stabilizing its variances, which allowed for proceeding to the ANOVA.

Results and discussion

Provided that, except for the total number of tubers (TC), all variables showed normal behavior, we resorted to Levene and Bartlett's homogeneity tests. As this variable showed no variance homogeneity, it required a transformation to stabilize the data. The remaining variables were found to be homocedastic. As a consequence, the analysis of variance was carried out with the original data.

Class 1 yield (C1Y)

This variable revealed significant differences between Zn doses within both foliar and edaphic application methods. However, no such difference was found between them or resulting from their interaction with the mineral doses. The contrast analysis showed how this variable was positively correlated to the Zn dose for each application technique. Table 3 shows how the 3 kg ha-1 dose had a positive effect on the crop, as can be seen from the yield increase data: 7.9 t ha-1 (136%) for the edaphic application and 5.8 t ha-1 (93%) for the foliar application.

This positive effect exerted by Zn on total yield indicates a better efficiency in the growth processes and assimilate conversion, translocation and accumulation (Gómez et al., 2007). In working with the stubborn onion, Gómez et al. (2007) observed that the simultaneous application of Zn and Mn resulted in better class 1 yields (35.36 t ha-1) than those obtained without the incorporation of these micronutrients in the N P K Mg fertilization program.

Class 2 yield (C2Y)

This variable presented a linear interaction between the studied factors. That is to say, each application method had a different behavior in face of the Zn dose. Tab. 3 allows one to observe how yield was still positively correlated to the edaphic Zn dose, albeit not as strongly as in class 1. The 3 kg ha-1 Zn dose gave the best result, with a 1.9 t ha-1 yield increase (19%) with respect to the control. The foliar Zn application had a different behavior. The dose that allowed the best results was 2 kg ha-1, which resulted in an increase of 1.3 t ha-1 (14%).

This difference between the treatments was probably due to the foliar P/Zn ratio, which has been investigated by Marschner (1995) and by Khan and Ajakaiye (1976). These authors detected an antagonism between these two minerals, resulting from the fact that excessive amounts of P (P/Zn ratios above 55) reduce yield. Specifically, P excesses lead to the production of Zn metabolic disorders consisting of the synthesis of insoluble compounds containing this mineral, all of which limit its long distance absorption (Marschner, 1995). Pumisacho and Sherwood (2002), stated that, in the case of the potato, P is a critical nutrient for the initial yield and development of the plant, in as much as it promotes root growth and rapid tuber formation.

Commercial yield (CY)

As in the case of C1Y, CY only revealed significant differences between the Zn dose treatments, but not between their application methods, which exhibited a linear behavior, as in CY1. Said differences were observed within both the foliar and edaphic application techniques. Table 3 shows how the edaphic application rendered a 9.5 t ha-1 (68%) yield increase with the 3.0 kg ha-1 Zn dose, while the foliar application resulted in a 4.5 t ha-1 (29%) increase with the 2.0 kg ha-1 dose.

The observed yield increases in C1Y, C2Y and CY were probably caused by correlated photosynthesis and hormone synthesis increments. Among the latter, auxins are particularly important, as far as they participate directly in root development, in agreement with similar remarks by Gómez (2005). In addition, auxin metabolism not only promotes stem and coleoptile elongation through better solute intake and protein and polysaccharide synthesis and storage, but - as stated by Salisbury and Ross (2000) - adventitious root formation and vascular differentiation as well.

Number of class 1 tubers (NC1T)

Although the studied Zn doses had significant effects on this variable, the application techniques did not, just as they showed no mutual interaction as well, which implies that they had an independent behavior. The contrast analysis applied to this data highlights the important role played by Zn in short-cycle crops such as the diploid potato, in which this nutrient allows better structure differentiation and filling due to more efficient assimilate accumulation (Gómez et al., 2007).

The percent variation in the number of tubers revealed a positive effect of Zn fertilization on diploid potato yield (Tab. 4), as far as the greatest variations were observed in the class 1 tubers, in agreement with the NC1T and NT data. In effect, a 77% increase was observed in the class 1 tubers with the edaphic application treatment, while the foliar one resulted in a 86% increase. In contrast, the class 2 tubers were found to decrease, even to a level below that of the control under both application methods. Since commercial yield contains more class 1 than class 2 tubers, these data indicate that the plant is behaving more efficiently in terms of tuber filling.

The observed increase in the number of class 1 tubers might be associated with a positive response to Mg, as also reported by Pérez et al. (2008). In evaluating this same variety, these authors suggest that Zn stimulates Mg utilization because they both play active roles in photosynthesis.

The results of the present research correspond with those of Gómez (2006), who reported a 25% yield increase with regards to the control in Zn treated stubborn onions. Similarly, Peña et al. (1999) found that 7 kg ha-1 doses of this mineral increase onion yield (Gómez et al., 2007).

Technical optimum

As the observed crop response correlates to Zn dose, its optimum was sought with a polynomial regression (Fig. 1). However, under the foliar application method, this increase was only marginal with the 3 kg ha-1 dose (Fig. 2), implying that, at elevated doses, plant yield diminishes, probably due to a phytotoxic reaction or to the P/Zn ratio. In turn, a linear response was observed under the edaphic application method (Fig. 2), which suggests that the optimum dose has to be sought by increasing the Zn application until there is a yield decline.

The positive response obtained in the current study with the 3 kg ha-1 dose corroborates reports by Gómez et al. (2007) and Murphy and Walash (1972), according to which the best yield response was found with the 3.5 kg ha-1 dose; therefore, resulting in a recommended Zn dose of 3.4 to 4.5 kg ha-1.

Zinc is an important nutrient, as far as it enhances crop efficiency by improving both P absorption and size and weight quality.

The positive response obtained in the current foliar and edaphic Zn application trial could be fruitfully applied by diploid potato growers on the Bogota Plateau in order to optimize crop yield. However, a comprehensive evaluation of plant nutrition in this case calls for an assessment of dry weight productivity and Zn interaction with other elements.

The application technique is of great interest, as far as it is part of an integrated plant nutrition management strategy. Although the edaphic method is the most frequent, economical and efficient one, foliar applications are also attractive after considering the series of soil factors that limit Zn absorption, which make them a means of quick micronutrient supply.

Based on the linear behavior exhibited by the edaphic Zn fertilization, future research should aim at determining an optimum Zn application level by taking into consideration marginal points and further elevated doses, so as to find toxicity levels, which are observable through yield decreases.

The authors express their gratitude to Manuel Caicedo, General Manager of Sociedad Agraria de Transformación (Agrarian Society for Transformation at El Rosal, Cundinamarca), for his collaboration and to Microfertisa for its technical and economic support.

Literature cited

Alloway, B. 2004. Zinc deficiency in crops: causes and corrections. Department of Soil Science, The University of Reading, Reading, UK.         [ Links ]

Alloway, B.J. 2008. Zinc in soils and crop nutrition. 2nd ed. International Zinc Association (IZA); International Fertilizer Industry Association (IFA), Brussels.         [ Links ]

Arce, J.P., B. Storey, and C.G. Lyons. 1991. Effectiveness of three different Zn fertilizers and two methods of application for the control of 'little-leaf' in peach trees in South Texas. HortScience 26(5), 497.         [ Links ]

Becerra-Sanabria, L.A., S.L. Navia-de Mosquera, and C.E. Ñústez-López. 2007. Efecto de diferentes niveles de fósforo y potasio sobre el rendimiento del cultivar "Criolla Guaneña" en el departamento de Nariño. Rev. Latinoam. Papa 14(1), 51-60.         [ Links ]

Brown, P.H., R.M. Welch, and E.E. Cary. 1987. Nickel: a micronutrient essential for higher plants. Plant Physiol. 85(3), 801-803.         [ Links ]

Cakmak, I. 2000. Possible roles of zinc in protecting plant cells from damage by reactive oxygen species. New Phytol. 146, 185-2005.         [ Links ]

Clavijo, J. 2001. Metabolismo de los nutrientes en las plantas. pp. 11-28. In: Silva M., F. (ed.). Fertilidad de suelos, diagnóstico y control. 2nd ed. Sociedad Colombiana de la Ciencia del Suelo (SCCS), Bogota.         [ Links ]

Bell, R.W. and B. Dell. 2008. Micronutrients for sustainable food, feed, fibre and bioenergy production. International Fertilizer Industry Association (IFA), Paris.         [ Links ]

Coleman, J.E. 1992. Zinc proteins: enzymes, storage proteins, transcription factors, and replication proteins. Annu. Rev. Biochem. 61, 897-946.         [ Links ]

Hawkes, J.G. 1990. The potato: evolution, biodiversity and genetic resources. Belhaven Press, Smithsonian Institution Press, London, Washington DC.         [ Links ]

Fedepapa, Federación Colombiana de Productores de Papa. 2012. Indicadores 2012. Rev. Papa 25, 45-46.         [ Links ]

Herrera, A.O. and L.E. Rodríguez. 2012. Tecnologías de producción y transformación de papa criolla. Facultad de Agronomía, Universidad Nacional de Colombia, Bogota.         [ Links ]

Huamán, Z. and D.M. Spooner. 2002. Reclassification of landrace populations of cultivated potatoes (SoÂlanum sect. Petota). Amer. J. Bot. 89(6), 947-965.         [ Links ]

Gómez, M. 2005. Guía técnica para el manejo nutricional de los cultivos: diagnostico, interpretación y recomendación de planes de fertilización. Microfertisa, Bogota.         [ Links ]

Gómez, M. 2006. Manual técnico de fertilización de cultivos. Microfertisa, Bogota.         [ Links ]

Gómez, M., H. Castro, C. Gómez, and F. Gutiérrez. 2007. Optimización de la producción y calidad en cebolla cabezona (Allium cepa) mediante el balance nutricional con magnesio y micronutrientes (B, Zn y Mn), Valle Alto del rio Chicamocha, Boyacá. Agron. Colomb. 25(2), 339-348.         [ Links ]

Castro, H. and M.I. Gómez, M. 2010. Fertilidad de suelos y fertilizantes. pp. 217-303. In: Burbano O., H. and F. Silva M. (eds.). Ciencia del suelo. Principios básicos. Sociedad Colombiana de la Ciencia del Suelo (SCCS), Bogota.         [ Links ]

Kabata-Pendias, A. and H. Pendias. 1992. Trace elements in soils and plants. 2nd ed. CRC Press, Boca Raton, FL.         [ Links ]

Kirkby, E. and V. Römheld. 2007. Micronutrientes na fisiologia de plantas: funções, absorçÃ£o e mobilidade. Informações Agronômicas No. 118. Internacional Plant Nutrition Institute (IPNI), Norcross, GA.         [ Links ]

Kochian, L. 1991. Mechanism of micronutrient uptake and translocation in plants. pp. 229-296. In: Mortvedt, J.J., F.R. Fox, L.M. Shuman, and R.M. Welch (eds.). Micronutrients in agriculture. Book Series No. 4. Soil Science Society of America, Madison, WI.         [ Links ]

Marschner, H. 1995. Mineral nutrition of higher plants. 2nd ed. Academic Press, San Diego, CA.         [ Links ]

Marschner, H. and I. Cakmak. 1989. High light intensity enhances chlorosis and necrosis in leaves of zinc, potassium and magnesium deficient beans (Phaseolus vulgaris) plants. J. Plant Physiol. 134(3), 308-315.         [ Links ]

Martínez, H., N. Pinzón, and C. Barrios. 2006. La cadena de la papa en Colombia. Una mirada global de su estructura y dinámica 1991-2005. Observatorio Agrocadenas Colombia, Ministerio de Agricultura y Desarrollo Rural (MADR); Inter-American Institute for Cooperation on Agriculture (IICA), Bogota.         [ Links ]

Murphy, L.S. and L. M. Walsh. 1972. Correction of micronutrient deficiencies with fertilizers. pp. 371-381. In: Micronutrientes in agriculture Zn, Fe, B, Mo, Cu, Mn. Soil Science Society America, Madison, WI.         [ Links ]

Pérez, L.C., L.E. Rodríguez, and M.I. Gómez. 2008. Efecto del fraccionamiento de la fertilización con N, P, K y Mg y la aplicación de los micronutrientes B, Mn y Zn en el rendimiento y calidad de papa criolla (Solanum phureja) variedad Criolla Colombia. Agron. Colomb. 26(3), 477-486.         [ Links ]

Porras, P. 2005. Problemática general del sistema productivo de papa con énfasis en fisiología y manejo de suelos. pp. 1-4. In: I Taller Nacional sobre Suelos, Fisiología y Nutrición Vegetal en el Cultivo de Papa. Centro Virtual de Investigación de la Cadena Agrolimentaria de la Papa (Cevipapa), Bogota.         [ Links ]

Pumisacho, M. and S. Sherwood. 2002. El cultivo de la papa en Ecuador. Instituto Nacional de Investigaciones Agropecuarias (INAP); International Potato Center (CIP), Quito.         [ Links ]

Ramírez, C. 2004. Nutrición mineral y producción vegetal. pp. 57-68. In: Manejo productivo, poscosecha y exportación en fresco de hierbas aromáticas culinarias, temporada 2004-2005. Universidad Nacional de Colombia, Bogota.         [ Links ]

Rodríguez, L.E., C. Ñústez, and N. Estrada. 2009. Criolla Latina, Criolla Paisa y Criolla Colombia, nuevos cultivares de criolla para el departamento de Antioquia (Colombia). Agron. Colomb. 23(3), 287-301.         [ Links ]

Rodríguez, F., M. Ghislain, A.M. Clausen, S.H. Jansky, and D.M. Spooner. 2010. Hybrid origins of cultiÂvated potatoes. Theor. Appl. Genet. 121, 1187-1198.         [ Links ]

Salisbury, F. and W. Ross. 2000. Fisiología de las plantas. Células: agua, soluciones y superficies. Thomson Editors Spain; Paraninfo, Madrid.         [ Links ]

Sharma, P.N., C. Chatterjee, S.C. Agarwala, and C.P. Sharma. 1990. Zinc deficiency and pollen fertility in maize (Zea mays). Plant Soil 124, 221-225.         [ Links ]

Spooner, D.M., J. Núñez, G. Trujillo, M. del R. Herrera, F. Guzmán, and M. Ghislain. 2007. Extensive simple sequence repeat genotyping of potato landraces supports a major reevaluation of their gene pool structure and classification. PNAS 104, 19398-19403.         [ Links ]

Taylor, S. 1964. Abundance of chemical elements in the continental crust: a new table. Geochim. Cosmochim. Acta 28, 1273-1286.         [ Links ]

Turekian, K. and K. Wedepohl. 1961. Distribution of the elements in some major units of the earth's crust. Geol. Soc. Amer. Bull. 72(2), 175-192.         [ Links ]

Vallee, B. and D. Auld. 1990. Zinc coordination, function and structure of zinc enzymes and other proteins. Biochemistry 29, 5647-5659.         [ Links ]

Vallee, B. and K. Falchuk. 1993. The biochemical basis of zinc physiology. Physiol. Rev. 73, 79-118.         [ Links ]


Robert Provine, Ph.D., a neuroscientist in his book Laughter: A Scientific Investigation, states that laughter establishes or restores a positive emotional climate and a sense of connection between two people, who literally take pleasure in the company of each other. In no particular order, here are 35 benefits of laughter:Read More →

Cosmetic Treatment


The MAFIC plans to conduct a scientific research expedition at the Atacama Desert in Chile in April 2018. Part of their ongoing investigation of Mars analogues on the Earth is to inform on the interpretation of the data that is relayed from the rovers currently on the surface of Mars. The objective is to combine four different datasets (microbiology, mineralogy, gas chemistry, and remote sensing) to formulate a comprehensive understanding of the patterns left behind by extremophile microorganisms inhabiting such environments. This expedition will take them to the fumaroles located in the volcanoes from the Atacama region. Under these extreme testing conditions, they require the most trustworthy cases for protecting their valuable scientific equipment.

To be able to complete their multidisciplinary research, the MAFIC team will need to bring out many pieces of highly sensitive equipment for mineralogical and microbial analysis. Much of this equipment is very precisely calibrated and therefore must be handled with extreme care – so our cases were their unanimous choice.

Follow MAFIC’s research updates on Twitter and on their website.


My child has a murmur in the heart

The murmur constitutes the first reason to refer a child to the pediatric cardiologist. It is a “noise” that we pediatricians can hear when we auscultate the child’s heart, and most of the times it is of no significance. In that case we call it “innocent murmur” and it is found roughly in 3 out of 4 healthy children, and that is the reason why many times the pediatrician does not comment about it.

The identification of a cardiac murmur, and its characterisation as innocent or not, could be compared to listening to music. It is necessary to pay attention to its intensity, tone or frequency, timbre, wavelength and duration. And it is the pediatrician’s and/or the cardiologist’s task to determine if that murmur seems really innocent or if it can hide a congenital heart disease, that is to say, a heart disease. But this is not always easy, since it requires, in addition to knowledge and experience, a silent environment and time, which very often are absent by the excessive healthcare work found in consultations or emergency services. Even in the best conditions and with a good auscultation, a small percentage of cardiac pathologies “escape” us.

But, what must I do if a murmur is detected in my child’s heart? As simple as following the pediatrician’s indications. Most cases of innocent murmurs appear or vary according to the position of the child, and increase their intensity when the heart rate increases, for example with fever, nervousness or after exercising. It is thus that many times it is detected, or the parents are informed about it, in an emergency service, when, for example, the child has fever or bronchitis, although very probably the pediatrician had already described it as innocent and was doing a clinical follow-up.

Then, how can it be confirmed that a murmur is innocent or warns us of that 2% of congenital heart diseases which cannot be detected by auscultation? The answer is to make a cardiac ultrasound scan, an innocuous test which is similar to the ultrasound scans in pregnancy, and which is performed by children cardiologists, or adult ones with experience with children. By means of this test we are able to see the heart and its structures, and check if that “small noise” is due or not to some alteration in it and, if necessary, we can refer the child to a centre specialized in congenital heart diseases where the pathology will be dealt with.

So, in general, it is necessary to convey calm to mums and dads when the pediatrician informs them of a murmur in the heart, because, besides being nothing important many times, we can always confirm it with an echography and obtain the result in about 15-30 minutes.

In fact, the American Heart Academy recommends to perform an echocardiogram in all children under the age of 2 years having a cardiac murmur although the child does not have any symptoms, or at any age if there were doubts regarding its nature.

Whatever to be able to listen with calm to that sound that gives us peace since we are in the maternal womb: boom, boom. Boom, boom.

Published on 25 february 2012 in Diario Información of Alicante


Twenty Arguments for God – A Summary

Twenty Arguments for God – Twenty – Pascal’s Wager

20. Pascal’s Wager

Consider the following diagram:

Twenty Arguments for God – Nineteen – The Common Consent Argument

19. The Common Consent Argument

This proof is in some ways like the argument from religious experience (18) and in other ways like the argument from desire (16). It argues that:
It is most plausible to believe that they have not.
Therefore it is most plausible to believe that God exists.
It seems far more likely that those who refuse to believe are the ones suffering from deprivation and delusion—like the tone-deaf person who denies the existence of music, or the frightened tenant who tells herself she doesn’t hear cries of terror and distress coming from the street below and, when her children awaken to the sounds and ask her, “Why is that lady screaming, Mommy?” tells them, “Nobody’s screaming: it’s just the wind, that’s all. Go back to sleep.”
Reply: If people were wrong about the theory of heliocentrism, they still experienced the sun and earth and motion. They were simply mistaken in thinking that the motion they perceived was the sun’s. But if God does not exist, what is it that believers have been experiencing? The level of illusion goes far beyond any other example of collective error. It really amounts to collective psychosis.
For believing in God is like having a relationship with a person. If God never existed, neither did this relationship. You were responding with reverence and love to no one; and no one was there to receive and answer your response. It’s as if you believe yourself happily married when in fact you live alone in a dingy apartment.
Question 2: But isn’t there a very plausible psychological account of religious belief? Many nonbelievers hold that belief in God is the result of childhood fears; that God is in fact a projection of our human fathers: someone “up there” who can protect us from natural forces we consider hostile.
In fact, the argument begs the question. We seek psychological explanation only for ideas we already know (or presume) to be false, not those we think to be true. We ask, “Why do you think black dogs are out to kill you? Were you frightened by one when you were small?” But we never ask, “Why do you think black dogs aren’t out to kill you? Did you have a nice black puppy once?”

In the course of history, millions of people have believed in god and they can’t all be wrong can they? Well yes they can. Millions of people have believed in gods that are not the Christian god, does the author think they are all wrong? Of course he does.

The author would have us believe that because religious belief has been wholeheartedly accepted, promoted and foisted on others for as long as there is a history of humanity, then that must make it true. The author isn’t drawing a distinction between religions here, all religions are lumped into the same basket so as to weight the scales in favour of the Christian god. Should this methodology be taken seriously?

This one doesn’t. Testimony means little to nothing when it’s that blatantly biased.

The question is asked if it’s really plausible to believe that if there is no god then all those acts of worship over the course of mankind’s religious history were never once directed to a real object. Well there are many idols that have been on the receiving end of that worship so it seems that the author has a rather skewed perception of what it was that all those religions have worshiped. The author, it appears, assumes that all those religions were really focused on the single god that he believes in.

The comparison with heliocentrism is puzzling. I assume the author means geocentrism, which isn’t a theory but an hypothesis. The origin for the belief was observation of the sun and moon, the correction of the false idea and the establishment of the fact of heliocentrism was further evidence that is measurable and repeatable today. God, in the meantime, is still only an idea, one which Christians will not allow to be tested, measured or otherwise detected.

Ditto the comparison with falsely believing yourself to be married. I can go home and experience conversations over a home cooked meal and then correctly load the dishwasher afterwards. In the meantime all prayers to god and other methods of communication are decidedly one-sided. The author is trying desperately to assert the existence of god using every day experiences while failing to address that his god can not be seen, touched, heard or tested for.

Not accepting that religious belief can be explained naturally, is not the same as it not being possible, it just means that in the religious mind, religious belief overrides everything else.

Can you hear the strawman claxon sounding? I have no recollection of ever having heard this argument, I am pretty sure this is the first time I have responded to any form of it. Kids form a belief in god because they are taught it. Either from parents or from other trusted adults. They don’t naturally gravitate to it because of fear. It’s not a coherent argument but it does make for a good set-up to plug the work of Paul Vitz who asserts

an alienation from the human father that results in rejection of God

More of that nonsense here (, if you can bare it.

Twenty Arguments for God – Eighteen – The Argument from Religious Experience

18. The Argument from Religious Experience

Some sort of experience lies at the very core of most people’s religious faith. Most of our readers have very likely had such an experience. If so, you realize, in a way no one else can, its central importance in your life. That realization is not itself an argument for God’s existence; in fact, in the light of it you would probably say that there is no need for arguments. But there is in fact an argument for God’s existence constructed from the data of such experiences. It is not an argument which moves from your own personal experience to your own affirmation that God exists. As we said, you most probably have no need for such an argument. Instead, this argument moves in another direction: from the widespread fact of religious experience to the affirmation that only a divine reality can adequately explain it.
It is difficult to state this argument deductively. But it might fairly be put as follows.
Many people of different eras and of widely different cultures claim to have had an experience of the “divine.”
It is inconceivable that so many people could have been so utterly wrong about the nature and content of their own experience.
Therefore, there exists a “divine” reality which many people of different eras and of widely different cultures have experienced.
Does such experience prove that an intelligent Creator-God exists? On the face of it this seems unlikely. For such a God does not seem to be the object of all experiences called “religious.” But still, he is the object of many. That is, many people understand their experience that way; they are “united with” or “taken up into” a boundless and overwhelming Knowledge and Love, a Love that fills them with itself but infinitely exceeds their capacity to receive. Or so they claim. The question is: Are we to believe them?
There is an enormous number of such claims. Either they are true or not. In evaluating them, we should take into account:
the consistency of these claims (are they self-consistent as well as consistent with what we know otherwise to be true?);
the character of those who make these claims (do these persons seem honest, decent, trustworthy?); and
the effects these experiences have had in their own lives and the lives of others (have these persons become more loving as a result of what they experienced? More genuinely edifying? Or, alternatively, have they become vain and self-absorbed?).
Suppose someone says to you: “All these experiences are either the result of lesions in the temporal lobe or of neurotic repression. In no way do they verify the truth of some divine reality.” What might your reaction be? You might think back over that enormous documentation of accounts and ask yourself if that can be right. And you might conclude: “No. Given this vast number of claims, and the quality of life of those who made them, it seems incredible that those who made the claims could have been so wrong about them, or that insanity or brain disease could cause such profound goodness and beauty.”
It is impossible to lay down ahead of time how investigation into this record of claims and characters will affect all individuals. You cannot say ahead of time how it will affect you. But it is evidence; it has persuaded many; and it cannot be ignored. Sometimes—in fact, we believe, very often—that record is not so much faced as dismissed with vivid trendy labels.

It’s not new or surprising that people who are religious have expereinces that they interperet in support of that religion. Often these experiences are very important to them. In some cases you could even say that they treasure them. People with vastly different religious creeds will use similar experiences to support their own beliefs.

Can these experiences be explained in any other way? Well yes, the human mind is very good at seeing patterns, especially patterns that do not exist, it is so easy to do this that a great many illusions are based specifically on this attribute. In addition, the human mind will interperet things according to it’s own biases. That is, if something can’t be explained easilly, then the mind will jump to its default unexplained bias. This could be religious, conspiracy, aliens or any number of other imagined explanations. The sheer number of experiences that people are prepared to attribute to these isn’t an argument for the existence of any of them but a clear demonstration of how lazy our cognitive functions are. Investigating and testing for the actual explanation requires a darn sight more effort than assuming your superstition of choice is correct. Which is exactly why these kinds of experiences are seen by the religious as confirmation of their religion.

In my time I’ve had a fair number of experiences that were interpreted as religious. To be completely frank and honest, there is one very significant one which I have no explanation for, does that mean the Christian god is real? Of course not. Way back at the beginning of my journey away from Christianity I learnt about the scientific explanation for an experience that matched one of my own (Sleep Paralysis). It was this moment that caused me to seriously question my religiously interpreted experiences. It was only when I questioned them in this manner that I realised that I had been duped all along.

Religious experience, by it’s very nature, is a very subjective thing and when mixed with a spoonful of bias, it becomes highly unreliable. This is exactly why we should not trust religious experience and it should not be taken as confirmation of anyone’s preferred god.

Twenty Arguments for God – Seventeen – The Argument from Aesthetic Experience

17. The Argument from Aesthetic Experience

There is the music of Johann Sebastian Bach.
Therefore there must be a God.
You either see this one or you don’t.

What do I do with this one? Question the sincerity of the author? Roll out an ad hominem by insulting the authors intelligence?

Do I call POE? Do I ask if the whole thing is an elaborate troll?

Do I counter by saying that there is also shit and vomit, therefore there is no god?

I’m stumped, not because the sentences are compelling, but because this is not an argument. To take it seriously or to give it serious thought is insulting.

Twenty Arguments for God – Sixteen – The Argument from Desire

16. The Argument from Desire

Twenty Arguments for God – Fifteen – The Argument from Conscience

15. The Argument from Conscience

Since moral subjectivism is very popular today, the following version of, or twist to, the moral argument should be effective, since it does not presuppose moral objectivism. Modern people often say they believe that there are no universally binding moral obligations, that we must all follow our own private conscience. But that very admission is enough of a premise to prove the existence of God.
Isn’t it remarkable that no one, even the most consistent subjectivist, believes that it is ever good for anyone to deliberately and knowingly disobey his or her own conscience? Even if different people’s consciences tell them to do or avoid totally different things, there remains one moral absolute for everyone: never disobey your own conscience.
Now where did conscience get such an absolute authority—an authority admitted even by the moral subjectivist and relativist? There are only four possibilities.
From something less than me (nature)
From me (individual)
From others equal to me (society)
From something above me (God)
Let’s consider each of these possibilities in order.
How can I be absolutely obligated by something less than me—for example, by animal instinct or practical need for material survival?
How can I obligate myself absolutely? Am I absolute? Do I have the right to demand absolute obedience from anyone, even myself? And if I am the one who locked myself in this prison of obligation, I can also let myself out, thus destroying the absoluteness of the obligation which we admitted as our premise.
How can society obligate me? What right do my equals have to impose their values on me? Does quantity make quality? Do a million human beings make a relative into an absolute? Is “society” God?
The only source of absolute moral obligation left is something superior to me. This binds my will, morally, with rightful demands for complete obedience.
Thus God, or something like God, is the only adequate source and ground for the absolute moral obligation we all feel to obey our conscience. Conscience is thus explainable only as the voice of God in the soul. The Ten Commandments are ten divine footprints in our psychic sand.
Addendum on Religion and Morality
In drawing this connection between morality and religion, we do not want to create any confusion or misunderstanding. We have not said that people can never discover human moral goods unless they acknowledge that God exists. Obviously they can. Believers and nonbelievers can know that knowledge and friendship, for example, are things that we really ought to strive for, and that cruelty and deceit are objectively wrong. Our question has been: which account of the way things really are best makes sense of the moral rules we all acknowledge—that of the believer or that of the non-believer?
If we are the products of a good and loving Creator, this explains why we have a nature that discovers a value that is really there. But how can atheists explain this? For if atheists are right, then no objective moral values can exist. Dostoyevsky said, “If God does not exist, everything is permissible.” Atheists may know that some things are not permissible, but they do not know why.
Consider the following analogy. Many scientists examine secondary causes all their lives without acknowledging the First Cause, God. But, as we have seen, those secondary causes could not be without the First Cause, even though they can be known without knowing the First Cause. The same is true of objective moral goods. Thus the moral argument and the various metaphysical arguments share a certain similarity in structure.
Most of us, whatever our religious faith, or lack of it, can recognize that in the life of someone like Francis of Assisi human nature is operating the right way, the way it ought to operate. You need not be a theist to see that St. Francis’s life was admirable, but you do need to be a theist to see why. Theism explains that our response to this believer’s life is, ultimately, our response to the call of our Creator to live the kind of life he made us to live.
There are four possible relations between religion and morality, God and goodness.
Religion and morality may be thought to be independent. Kierkegaard’s sharp contrast between “the ethical” and “the religious,” especially in Fear and Trembling, may lead to such a supposition. But (a) an amoral God, indifferent to morality, would not be a wholly good God, for one of the primary meanings of “good” involves the “moral”—just, loving, wise, righteous, holy, kind. And (b) such a morality, not having any connection with God, the Absolute Being, would not have absolute reality behind it.
God may be thought of as the inventor of morality, as he is the inventor of birds. The moral law is often thought of as simply a product of God’s choice. This is the Divine Command Theory: a thing is good only because God commands it and evil because he forbids it. If that is all, however, we have a serious problem: God and his morality are arbitrary and based on mere power. If God commanded us to kill innocent people, that would become good, since good here means “whatever God commands.” The Divine Command Theory reduces morality to power. Socrates refuted the Divine Command Theory pretty conclusively in Plato’s Euthyphro. He asked Euthyphro, “Is a thing pious because the gods will it, or do the gods will it because it is pious?” He refuted the first alternative, and thought he was left with the second as the only alternative.
But the idea that God commands a thing because it is good is also unacceptable, because it makes God conform to a law higher than himself, a law that overarches God and humanity alike. The God of the Bible is no more separated from moral goodness by being under it than he is by being over it. He no more obeys a higher law that binds him, than he creates the law as an artifact that could change and could well have been different, like a planet.
The only rationally acceptable answer to the question of the relation between God and morality is the biblical one: morality is based on God’s eternal nature. That is why morality is essentially unchangeable. “I am the Lord your God; sanctify yourselves therefore, and be holy, for I am holy” (Lev. 11:44). Our obligation to be just, kind, honest, loving and righteous “goes all the way up” to ultimate reality, to the eternal nature of God, to what God is. That is why morality has absolute and unchangeable binding force on our conscience.
The only other possible sources of moral obligation are:
a. My ideals, purposes, aspirations, and desires, something created by my mind or will, like the rules of baseball. This utterly fails to account for why it is always wrong to disobey or change the rules.
b. My moral will itself. Some read Kant this way: I impose morality on myself. But how can the one bound and the one who binds be the same? If the locksmith locks himself in a room, he is not really locked in, for he can also unlock himself.
c. Another human being may be thought to be the one who imposes morality on me—my parents, for example. But this fails to account for its binding character. If your father commands you to deal drugs, your moral obligation is to disobey him. No human being can have absolute authority over another.
d. “Society” is a popular answer to the question of the origin of morality “this or that specific person” is a very unpopular answer. Yet the two are the same. “Society” only means more individuals. What right do they have to legislate morality to me? Quantity cannot yield quality; adding numbers cannot change the rules of a relative game to the rightful absolute demands of conscience.
e. The universe, evolution, natural selection and survival all fare even worse as explanations for morality. You cannot get more out of less. The principle of causality is violated here. How could the primordial slime pools gurgle up the Sermon on the Mount?
Atheists often claim that Christians make a category mistake in using God to explain nature; they say it is like the Greeks using Zeus to explain lightning. In fact, lightning should be explained on its own level, as a material, natural, scientific phenomenon. The same with morality. Why bring in God?
Because morality is more like Zeus than like lightning. Morality exists only on the level of persons, spirits, souls, minds, wills—not mere molecules. You can make correlations between moral obligations and persons (e.g., persons should love other persons), but you cannot make any correlations between morality and molecules. No one has even tried to explain the difference between good and evil in terms, for example, of the difference between heavy and light atoms.
So it is really the atheist who makes the same category mistake as the ancient pagan who explained lightning by the will of Zeus. The atheist uses a merely material thing to explain a spiritual thing. That is a far sillier version of the category mistake than the one the ancients made; for it is possible that the greater (Zeus, spirit) caused the lesser (lightning) and explains it; but it is not possible that the lesser (molecules) adequately caused and explains the greater (morality). A good will might create molecules, but how could molecules create a good will? How can electricity obligate me? Only a good will can demand a good will; only Love can demand love.

This argument opens by offering a rephrasing of the moral argument.

Modern people often say they believe that there are no universally binding moral obligations …

So far I don’t have any issues; there is no evidential support for universally binding moral obligations, so there is no reason to say otherwise. However, tacked on the end is.

… that we must all follow our own private conscience.

It’s a strange phrase, and not one that I hear, so I have no idea which modern people allegedly often say it.

“Consistent subjectivist” is an oxymoron really since subjectivity tends to imply non consistency so the existence of a consistent subjectivist is something I remain to be convinced of. No need to dwell on that though as it was covered in the last post. I disagree with the whole sentence, I am not aware of any subjectivists who think that way. Please, if you are one, step forward and educate me.

I’m fairly sure that I can find an example of when I’ve acted against what my conscience was screaming at me. In fact, isn’t that exactly what feelings of guilt do? They highlight when we’ve acted against our own conscience. It seems that in the rush to assert something as true (without support of course) the author has tripped over and put a massive head sized hole in the side of the argument.

Now where did conscience get such an absolute authority

It doesn’t have absolute authority, but hey ho, let’s read the options.

From something less than me (nature)
From me (individual)
From others equal to me (society)
From something above me (God)

What we have here is a prime example of framing the answer to suit the desired result. Does the author’s conscience not limit how much dishonesty is allowed?

How can I be absolutely obligated by something less than me

I don’t know, first one should demonstrate that absolute obligations actually exist, saying they do doesn’t make them so.

This is good to know, and it is nice to see it acknowledged so frankly. Though I do take issue with the word ‘discover’. Moral good is a human description of human behaviour; it is an attribute we individually ascribe to acts. It’s not something you find, like money down the back of the sofa.

I agree. Unfortunately there is no evidence that values are a thing that we discover, they are descriptions we ascribe. Which means ….

I agree! Objective moral values have not been shown to exist, so atheists must be right! Huzzah! Cue the fanfare and let the confetti burst forth!

That’s not the end if though; the argument then has a huge section which assumes its opening assumption is correct and assumes that the god it’s trying to establish exists. The circularity is more dizzying than the previous argument.

Reference is made to Divine Command Theory:

But wait.

I agree with the power play part, is that good enough to dismiss Divine Command Theory as an argument? It seems the author thinks so, so now I’m a little puzzled, many theists subscribe to Divine Command Theory, but this one seems not to. Dissention in the ranks?

Never mind, let’s skip right to the end

Not in the slightest, the scientific method is used to detect and describe the effect the brain has on behaviour. One does not need to be atheist to accept that. We see altruism in non human animals. Evolutionary theory can describe conscience as an emerging property as well as morality and other related behaviours. Assigning them to a god brings it’s own set of issues like how do we tell the difference between those god-given traits and evolved traits? Not to mention the absolute lack of support for the existence of any god.

Like every argument before it, this one can’t demonstrate with any certainty the bold claims it makes. It relies on bare faced assertions and prays that no one will notice.

Twenty Arguments for God – Fourteen – The Moral Argument

14. The Moral Argument

But the atheistic one is incompatible with there being moral obligation.
Therefore the “religious” view of reality is correct.

The first line of the quoted piece reads

Isn’t it immoral to lie?

In the first four lines, this argument opens with an unsupported assertion, makes a false dichotomy, makes another unsupported assertion and then posits an unsafe conclusion. It’s a terrible way to start an argument!

The claim that it is an objective fact that we are obligated to be moral is a religious claim that can only be true if there is a god that has created us subservient to this ‘fact’. That god hasn’t been demonstrated and so the claim is suspect. To try and then use this claim as proof that that god exists is circular reasoning.

Humans behave according to their biases and their desires; this is an entirely subjective behaviour pattern. That the religious doubt it is because of their bias towards a controlling god and their desire for everyone else to fall in line. That is an entirely subjectively moral behaviour based on their peculiar biases and desires. Need further proof against objectivity? Go to any church and checklist the behaviours of the membership, do they all act in the same way in the same situations? No they don’t. Then there can’t be an objective standards ruling their behaviour, therefore their behaviour is subjectively driven.

In the reply to question 1 we see a rare bit of honesty, the argument does indeed assume objectivism and the argument does indeed fail if is false.

Therein lies the fatal flaw in this argument, from beginning to end the objective morality is assumed and used to argue for ‘religion’, yet at no point is there any reference to anything supporting objectivity. There is a half-hearted attempt at dissing subjectivity which ironically supports it.

almost no one is a consistent subjectivist.

That is the whole point of subjectivity! Consistency is neither implied nor expected, we act and behave according to our motivation at the time. By definition that means there will be inconsistency. That inconsistency is the evidential support for subjectivity. In claiming that morals are objective, the author has actually demonstrated exactly why morals are subjective. Subjective morality does not support the god hypothesis and this one on it’s own should be enough to declare the Christian god does not live, long live humanity!

Twenty Arguments for God – Thirteen – The Ontological Argument

13. The Ontological Argument

The ontological argument was devised by Anselm of Canterbury (1033-1109), who wanted to produce a single, simple demonstration which would show that God is and what God is. Single it may be, but far from simple. It is, perhaps, the most controversial proof for the existence of God. Most people who first hear it are tempted to dismiss it immediately as an interesting riddle, but distinguished thinkers of every age, including our own, have risen to defend it. For this very reason it is the most intensely philosophical proof for God’s existence; its place of honor is not within popular piety, but rather textbooks and professional journals. We include it, with a minimum of discussion, not because we think it conclusive or irrefutable, but for the sake of completeness.
Anselm’s Version
“God” means “that than which a greater cannot be thought.”
Suppose that God exists in the mind but not in reality.
Then a greater than God could be thought (namely, a being that has all the qualities our thought of God has plus real existence).
But this is impossible, for God is “that than which a greater cannot be thought.”
Therefore God exists in the mind and in reality.
Question 1: Suppose I deny that God exists in the mind?
Reply: In that case the argument could not conclude that God exists in the mind and in reality. But note: the denial commits you to the view that there is no concept of God. And very few would wish to go that far.
Question 2: Is it really greater for something to exist in the mind and in reality than in the mind alone?
Reply: The first premise of this argument is often misunderstood. People sometimes say: “Isn’t an imaginary disease better than a real one?” Well it certainly is better—and so a greater thing—for you that the disease is not real. But that strengthens Anselm’s side of the argument. Real bacteria are greater than imaginary ones, just because they have something that imaginary ones lack: real being. They have an independence, and therefore an ability to harm, that nothing can have whose existence is wholly dependent on your thought. It is this greater level of independence that makes them greater as beings. And that line of thinking does not seem elusive or farfetched.
Question 3: But is real being just another “thought” or “concept”? Is “real being” just one more concept or characteristic (like “omniscience” or “omnipotence”) that could make a difference to the kind of being God is?
Reply: Real being does make a real difference. The question is: Does it make a conceptual difference? Critics of the argument say that it does not. They say that just because real being makes all the difference it cannot be one more quality among others. Rather it is the condition of there being something there to have any qualities at all. When the proof says that God is the greatest being that can be “thought,” it means that there are various perfections or qualities that God has to a degree no creature possibly could, qualities that are supremely admirable. But to say that such a being exists is to say that there really is something which is supremely admirable. And that is not one more admirable quality among others.
Is it greater to exist in reality as well as in the mind? Of course, incomparably greater. But the difference is not a conceptual one. And yet the argument seems to treat it as if it were—as if the believer and the nonbeliever could not share the same concept of God. Clearly they do. They disagree not about the content of this concept, but about whether the kind of being it describes really exists. And that seems beyond the power of merely conceptual analysis, as used in this argument, to answer. So question 3, we think, really does invalidate this form of the ontological argument.
Modal Version
Charles Hartshorne and Norman Malcolm developed this version of the ontological argument. Both find it implicitly contained in the third chapter of Anselm’s Proslogion.
The expression “that being than which a greater cannot be thought” (GCB, for short) expresses a consistent concept.
But what must be so is so.
Therefore, GCB (i.e., God) exists.
Question: Just because GCB must be thought of as existing, does that mean that GCB really exists?
Reply: If you must think of something as existing, you cannot think of it as not existing. But then you cannot deny that GCB exists; for then you are thinking what you say cannot be thought—namely, that GCB does not exist.
Possible Worlds Version
This variation on the modal version has been worked out in great detail by Alvin Plantinga. We have done our best to simplify it.
Maximal excellence: To have omnipotence, omniscience and moral perfection in some world.
Maximal greatness: To have maximal excellence in every possible world.
There is a possible world (W) in which there is a being (X) with maximal greatness.
But X is maximally great only if X has maximal excellence in every possible world.
Therefore X is maximally great only if X has omnipotence, omniscience and moral perfection in every possible world.
In W, the proposition “There is no omnipotent, omniscient, morally perfect being” would be impossible—that is, necessarily false.
But what is impossible does not vary from world to world.
Therefore, the proposition, “There is no omnipotent, omniscient, morally perfect being” is necessarily false in this actual world, too.
Therefore, there actually exists in this world, and must exist in every possible world, an omnipotent, omniscient, morally perfect being.

A more lengthy telling of the argument (if you want it) is here: and here:

In summary, because it is possible to think that there is nothing that is greater than the Christian god, the Christian god is the greatest thing ever and is therefore real. Well colour me unimpressed because I am pretty sure that I can think of a god eating monster that eats gods for fun, especially gods which are greater than those which exist only in the mind. Therefore my god eating monster just ate all the gods so there’s none left. The end.

Jesting aside, this argument is all about the limits of the human mind. The argument posits that the no human can imagine anything greater than X and because something existing is greater than something imagined, the imagined Christian god must be real. The argument makes no allowance for someone else thinking of something greater than the Christian god, there really is nothing about this argument that makes any sense.

I take issue with the phrase ‘philosophical proof’ at the start because I dispute that philosophy can prove any such thing using arguments like this. Proof would be a demonstration of that god that is unambiguous and could not be attributed to anything else. Thinking it real and claiming that that means it is real is not a proof for anything and it is disingenuous to suggest otherwise.

Getting into the grit of the argument itself, it stumbles massively when it says that god must exist both in thought and reality because it’s not possible to think of something greater. It’s a blunt assertion with no support. It is always possible to think of something greater and it is the utmost arrogance to think that because you have imagined in your mind what you think is the greatest possible god, that that god must therefore exist. Thinking something is real doesn’t make it real.

The argument also seems to be implying that when something that exists is thought about, that something exists both in reality and in the mind! No it doesn’t. What is in the mind is simply a mental representation. Like a photocopy isn’t the real thing and it’s copy and a reflection isn’t the real thing and it’s copy.

The argument really does back flip itself into a knot of nonsense.

The argument certainly is imaginative, I’ve got to give it that, but what it imagines isn’t real and the leap from the imagined greatest ever god to that god being real is missing a great many steps and it does not follow in the slightest.

Twenty Arguments for God – Twelve – The Argument from the Origin of the Idea of God

12. The Argument from the Origin of the Idea of God

This argument, made famous by Rene Descartes, has a kinship to the ontological argument (13). It starts from the idea of God. But it does not claim that real being is part of the content of that idea, as the ontological argument does. Rather it seeks to show that only God himself could have caused this idea to arise in our minds.
It would be impossible for us to reproduce the whole context Descartes gives for this proof (see his third Meditation), and fruitless to follow his scholastic vocabulary. We give below the briefest summary and discussion.
We have ideas of many things.
These ideas must arise either from ourselves or from things outside us.
One of the ideas we have is the idea of God—an infinite, all-perfect being.
This idea could not have been caused by ourselves, because we know ourselves to be limited and imperfect, and no effect can be greater than its cause.
Therefore, the idea must have been caused by something outside us which has nothing less than the qualities contained in the idea of God.
But only God himself has those qualities.
Therefore God himself must be the cause of the idea we have of him.
Therefore God exists.
Consider the following common objection. The idea of God can easily arise like this: we notice degrees of perfection among finite beings—some are more perfect (or less imperfect) than others. And to reach the idea of God, we just project the scale upward and outward to infinity. Thus there seems to be no need for an actually existing God to account for the existence of the idea. All we need is the experience of things varying in degrees of perfection, and a mind capable of thinking away perceived limitations.
But is that really enough? How can we think away limitation or imperfection unless we first recognize it as such? And how can we recognize it as such unless we already have some notion of infinite perfection? To recognize things as imperfect or finite involves the possession of a standard in thought that makes the recognition possible.
Does that seem farfetched? It does not mean that toddlers spend their time thinking about God. But it does mean that, however late in life you use the standard, however long before it comes explicitly into consciousness, still, the standard must be there in order for you to use it. But where did it come from? Not from your experience of yourself or of the world that exists outside you. For the idea of infinite perfection is already presupposed in our thinking about all these things and judging them imperfect. Therefore none of them can be the origin of the idea of God; only God himself can be that.

I believe the Descartes argument that is mentioned at the top is summarised here:

ideas [of things] must arise either from ourselves or from things outside us.

We all have ideas, this is part of being human, sometimes our ideas are nonsense and sometimes they are correct. They are all out own. How does an idea come from outside of us when the idea happens inside our brain? Is there a demonstration of how an idea comes to us from outside of us? How do we tell the difference between the two idea types?

This idea [of an all-perfect god] could not have been caused by ourselves

With the failure to address how there are ideas that we don’t come up with ourselves, how could anyone support this claim? The claim is interesting, but its premise is not shown so why should the claim be accepted?

the idea must have been caused by something outside us

How? What is the mechanism? The author is running with the idea as though it’s true. Who came up with the idea that there are ideas that come from outside us? If that idea came from within someone, how could we know it to be true?

Therefore God exists.

Whose idea of god exists? Does every Christian describe the same god? Do they all exist? if a Christian’s idea of god is flawed or incorrect does that means it’s their own idea of god and not an external idea? Does that cancel out this argument?

It one believes the author, it seems that only the Christian god could have planted the idea of the Christian god into our minds because we’re too weak and limited in our thinking to invent that god ourselves? Really!?

One only has to read the Bible to see that the Christian god has many human characteristics, disproportionate vengeance, annihilation of the disliked, inconsistency. It’s all there.

If it’s specifically the Christian idea of god that has been given to humans from god, how come there are so many other gods that humans think about? Is the Christian god really that much more special that it would be impossible for humans to come up with it on their own?

As a final thought, I am genuinely astonished that this argument is presented seriously. In fact this argument makes me wonder if the whole list of 20 arguments is someone having a massive laugh at the expense of those Christians who buy it and reference it on an all too regular basis.


Missing Toddler Nalani Johnson Found Dead in Western Pennsylvania

BURRELL TOWNSHIP, Pa. — The body of missing toddler Nalani Johnson has been found in western Pennsylvania, according to investigators.

An Amber Alert was issued Saturday when police say Johnson was abducted, and crews had been searching for her since.

Investigators say Johnson’s body was discovered in Pine Ridge Park in Burrell Township, Indiana County Tuesday afternoon, according to WNEP.

A woman is in custody in the case after the Nalani’s father, Paul Johnson, said a driver abducted his daughter on Saturday evening in Penn Hills, Pennsylvania, according to police documents and a news release.

Paul Johnson said he was riding in a car with Lyft and Uber stickers with his daughter and two friends, according to a criminal complaint filed by the Allegheny County police.

The driver of the car was Sharena Nancy, a woman with whom Johnson was in the beginning of an “intermittent romantic relationship” with, Allegheny County Police Superintendent Coleman McDonough said at a press conference Tuesday.

The couple became acquainted over social media in the past few months and spent several hours together with Johnson’s daughter and another friend on Saturday, before an argument ensued while the woman was driving, McDonough said.

While police did not elaborate on the details of the argument, McDonough said it was significant enough that Johnson and his other friend decided to exit the car.

Johnson told detectives he tried calling the driver’s cellphone multiple times, but she never picked up, so he called 911 around 5 p.m. ET.

Nancy told detectives that Johnson sold the child to an individual for $10,000 and asked her to complete the drop-off, according to the complaint.

Nancy told detectives she encountered a silver SUV with out-of-state license plates parked on the side of the road and did as she had been instructed, passing the toddler and the car seat over to a woman standing next to the car and then driving off. Nancy told police she saw a second woman inside the SUV.

McDonough said Tuesday they have no evidence to corroborate Nancy’s version of events, adding that Johnson and his family have been cooperative with the ongoing investigation.

CNN was unable to identify or reach an attorney for Nancy.

Nalani’s grandmother, Taji Walsh, told KDKA that Nancy’s account of the events is not true. Her son, whom she calls “PJ,” is Nalani’s father.

CNN Wire contributed to this report.


Savoy’s Schofield named Beefeater MIXLDN UK champion

Twelve contenders took part in the national final but Schofield took the title after impressing the judges with his Mother’s Milk cocktail.Tying into the competition’s theme of the evolution of London, his cocktail was inspired by 24 Milk Street, a residence previously incinerated in the Great Fire of London that was later home to renowned Victorian chef Isabella Beeton.

Schofield will represent the UK in the global finals in January 2016


RSA release, the RSA has been analyzed for vulnerabilities.

RSA Attacks

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by Ron Rivest, Adi Shamir, and Len Adleman, the RSA cryptosystem was first revealed
in the August 1977 issue of Scientific American. The RSA is most commonly used
for providing privacy and ensuring authenticity of digital data. RSA is used by
many commercial systems. It is used to secure web traffic, to ensure privacy and
authenticity of Email, to secure remote login sessions, and it is at the heart
of electronic credit-card payment systems.

its initial release, the RSA has been analyzed for vulnerabilities. Twenty
years of research have led to a number of intriguing attacks, none of them is
devastating. They mostly show the danger of wrong use of RSA. RSA encryption in
its simple form is explained as follow.

N = p*q be the product of two large primes of the same size (n/2 bits
each).  A typical size for N is n=1024
bits, i.e.309 decimal digits.

e, d be two integers satisfying

= 1 mod ? (N)

? (N) = (p-1) (q-1).

N = RSA modulus,

e = encryption exponent, and

d = called the decryption exponent.

pair (N, e) is the public key. The pair (N, d) is called the secret key and
only the recipient of an encrypted message knows it.

message M is encrypted by computing,

C =
Memod N.

decrypt the ciphertext C, the authentic receiver computes

Cdmod N.Cd = Med = M
(mod N)

last equality is based on Euler’s theorem.

Factoring Large Integers

is known as the first attack on RSA public key (N, e). After getting the
factorization of N, an attacker can easily construct ? (N), from which the
decryption exponent d = e-1mod? (N) can be found. Factoring the modulus is
referred to as brute-force attack. Although factorizing the modulus has been
improving, the current state of the art of this attack is unable to post a
threat to the security of RSA when RSA is used properly.

is that with very large numbers, factoring takes an unreasonable amount of time.
it been proven that factoring is not equivalent.

the Message Space

small, then one could simply try to encrypt every possible message block, until
an insurmountable task because the block sizes are quite large.

Guessing d

possible attack is a known ciphertext attack. This time the attacker knows both
the plaintext and ciphertext (they simply has to encrypt something). They then
try to crack the key to discover the private exponent, d. This might
to the original plaintext. Once d has been discovered it is easy to find
the factors of n. Then the system has been broken completely and all
further ciphertexts can be decrypted.

possible ds to try. This method is a factorizing algorithm as it allows
us to factor n. Since factorizing is an intractable problem we know this
is very difficult. This method is not the fastest way to factorize n.
Therefore one is suggested to focus effort into using a more efficient
algorithm specifically designed to factor n.

Cycle Attack

attack is very similar to the last. The idea is to encrypt the ciphertext

in algorithm is to use the public exponent of the public key to re-encrypt the
text. However any exponent should work so long as it is coprime to (p-1).(q-1)
(where p, q are factors of the modulus). So using an exponent such as 216
fast exponentiation, we use only 16 modular squarings and 1 modular
The trouble is that we cannot be sure that it is coprime to (p-1).(q-1).
In practice, many RSA systems use 216 + 1 as the encrypting exponent
for its speed.

the cycle attack, the encrypting exponent could be chosen to make
the system more efficient. Many RSA systems use e=3 to make encrypting
faster. However, there is a vulnerability with this attack. If the same message
Remainder Theorem.

Common Modulus

assumption that generating the same modulus N = p*q for all users of a system,
and user is provided with a unique pair (ei, di) from which user I forms a
public key (N, ei) and a secret key (N, di) may seem to work providing that a
trusted central authority provides the unique pairs.

would choose the public modulus securely and generate pairs of encryption and
employees/users. The reason for doing this is to make it convenient to manage
and to write software for. But, the resulting system is insecure since Bob who
is unable to decipher Alice’s cipher due to not having Alice private key d Alice
he however, can factor N using his own exponents.

blinding eavesdrop  obtain a valid
signature on a message of his choice by asking user to sign a random
“blinded message”. In that case, user 1 does not know what message is
actually signing and most signature schemes apply a “one-way hash” to
the message prior to signing, thus the attack is not a serious concern. Let (N,
d) be user 1’s  private key and (N, e) be
public key. Assume that an adversary wants user 1’s  signature on a message M ? Z*N. Being a smart move,
user 2 should refuse to sign M. Otherwise eavesdrop can compute S = S’ / ? mod
N and obtains user 1’s signature S on the original M.

Se =
(S’)e/ ?e= (M’)ed / ?e ? M’ / ?e= M (mod N)

Faulty Encryption

the situation where an attacker, Malory, has access to the communication
channel used by Alice and Bob. In other words, Malory can listen to anything
that is transmitted, and can also change what is transmitted. Alice wishes to
talk privately to Bob, but does not know his public key. She requests by
sending an email, to which Bob replies. But during transmission, Malory is able
of Bob, changing (e,n) to (e’,n). When Alice receives the faulty key, she encrypts
the prepared message and sends it to Bob (Malory also gets it). But of course,
Bob cannot decrypt it because the wrong key was used. So he lets Alice know and
they agree to try again, starting with Bob re-sending his public key. This time
Malory does not interfere. Alice sends the message again, this time encrypted
with the correct public key.

Therefore she can now apply the common modulus attack to retrieve Alice’s
message, assuming that Alice was foolish enough to encrypt exactly the same
message the second time.

most powerful attacks on low public exponent RSA are based on a Copper-smith

theorem provides an algorithm for efficiently finding all roots of f modulo N that are less than X = N1/d.
The algorithm’s running time decreases as X gets smaller. The strength of this theorem
is its ability to find small roots of polynomials modulo a composite N.

of Coppersmith’s Theorem:

stereotyped messages in RSA (sending messages whose difference is less than N1/e
can compromise RSA)

proof of RSA-OAEP (constructive security proof).

related RSA messages (sending the same message to multiple recipients)

N = p*q if the high bits of pare known.

algorithm that can get the private key for RSA in deterministic polynomial time
can be used to factor N in deterministic polynomial time.

integers with a large smooth factoring a proscribed interval.·Finding roots of modular multivariate polynomials.

Hastad’s broadcast attack

first application of Coppersmith’s theorem and the improvement to an old attack
is Hastad’s Broadcast Attack.

Bob wishes to send an encrypted message M to a number of parties P1, P2,……Pk.
Each party has its own RSA key (Ni, ei). We assume M is less than all the Ni’s.
Idealistically, to send M, Bob encrypts it using each of the public keys and
sends out of the ith ciphertext to pi. An attacker Eve can
eavesdrop on the connection out of Bob’s sight and collect the k transmitted ciphertexts.

simplicity, suppose all public exponents ei, are equal to 3. A
simple arguments shows that Eve can recover M if k ? 3. Indeed, Bob obtains C1,
C2, C3,

Where,                            C1= M3mod
N1, C2= M3mod N2, C3= M3mod

that gcd(Ni, Nj) = 1 for all i ? j since otherwise Eve
can factor some of the Ni’s. Hence, applying the Chinese Remainder Theorem (CRT)
to C1, C2, C3 gives a C’ ?ZN1N2N3
satisfying C’ = M3mod N1N2N3. Since M is less than all the Ni’s, we
have M3< N1N2N3. Then C' = M3 holds over the integers. Thus, Eve may recover M by computing the real cube root of C'. More generally, if all public exponents are equal to e, Eve can recover M as soon as k > e. The attack is feasible only when a small e is
used. To stimulate Hastad’s result, if M is m bits long, Bob could send Mi=
i2m+ M to party Pi. Since Eve obtains encryptions of
different messages, he can’t mount the attack.

Hastad showed that this linear padding is insecure. In fact, he proved that
applying any fixed polynomial to the message prior to encryption does not
prevent the attack. Suppose that for each of the participants P1…
Pk, Bob has a fixed public polynomial fi ? ZNi x.
To broadcast a message M, Bob sends the encryption of fi (M) to party
Pi. By eavesdropping, Eve learns Ci= fi (M) ei
mod Ni for i =1… k. Hastad showed that if enough parties are
involved, Eve can recover the plaintext M from all the ciphertexts. In more
generality, Hastad proved that a system of univariate equations modulo
relatively prime composites, such as applying any fixed polynomial g1 (M)
= 0 mod Ni, could be solved if sufficiently many equations are provided. This
attack suggests that randomized padding should be used in RSA encryption.

Coppersmith’s short pad attack

The Franklin-Reiter attack is considered to be an artificial attack because why
should Bob send Alice the encryption of related messages? Coppersmith
strengthened the attack and proved an important result on padding. Coppersmith
showed that if randomized padding suggested by Hastad is used improperly then RSA
encryption is not secure. A naive random padding algorithm might pad a plaintext
M by appending a few random bits to one of the ends. The following attack
points out the danger of such simplistic padding. Suppose Bob sends a
properly-padded encryption of M to Alice. An attacker, Eve, intercepts the ciphertext
and prevents it from reading its destination. Bob notice that Alice did not
respond to his message and decides to resend M to Alice. He randomly pads M and
transmits the resulting ciphertext. Eve now has two ciphertexts corresponding

Timing attacks

us consider a smartcard that stores a private RSA key. An attacker may not be
able to see its content and expose the key. However, the precise time of
decryption the card takes can help an attacker find or discover the private
decryption exponent d. Repeated squaring algorithm can be used for this attack
which is explained as follow:

• Let d = dn, dn-1… d0
(binary of d)

• Set z = M and C = 1. For i=0 … n do:

• (1)
if di= 1 set C = C. z mod N

• (2)
z = z * z mod N

• C at the end has the value Mdmod

Random Faults

speed up the computation of Md mod N, Implementations of RSA
decryption and signatures frequently use the Chinese Remainder Theorem. Instead
of working modulo N, the signer Bob first computes the signatures modulo p and q
and then combines the result using the Chinese Remainder Theorem.

first computes,

 Cp= Mdpmod p and Cq=
Mdqmod q

Where dp= d mod (p -1) and dq=
d mod(q-1).

then C = T1Cp+ T2Cq(mod

whereT1= { 1 mod p and T2=
{0 mod p 0 mod q } 1 mod q}

running time of the last CRT step is negligible compared to the two
exponentiations. p and q are half the length of  N. Since simple implementations of
multiplication take quadratic time, multiplication modulo p is four times
faster than modulo N. Furthermore, dp is half the length of d and consequently
computing Mdp mod p is eight times faster than computing Mdp
mod N. Overall signature time is thus reduced by a factor of four. Many RSA
implementations use this method to improve performance.

6 Conclusion

years of research aimed to break the RSA produced some insightful attacks, but
no serious attack has been found yet. Currently, it appears that proper RSA
implementation can provide the required security in the digital world. Four
main classes of RSA attacks were found: (1) elementary attacks that show the
misuse of the system, (2) low private exponent to show how serious it gets when
a low private is used, (3) low public exponent attacks, and (4) attacks on the
RSA implementation.

use of RSA and properly padding a message before encryption can defeat the
explained attacks.


The ketogenic diet (KD) is widely used as a weight loss strategy and, more rarely, as therapy for some diseases. In many sports weight control is often necessary (boxing, weightlifting, wrestling, etc) but the KD is not usually considered. Our hypothesis is that KD might be used to achieve fat loss without affecting negatively strength/power performance.