brief communications dimensional structure. A critical issue in and Engineering, 1304 West Green Street, creating photonic materials is how to fill the Urbana, Illinois 61801, USA interstitial space completely with a compo- e-mail: p-braun@uiuc.edu nent that has a high refractive index. We therefore electrodeposited group II­VI semi- 1. Joannopoulos, J. D., Meade, R. D. & Winn, J. N. Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, conductors into colloidal sediments, filling New Jersey, 1995). the interstitial space with materials of high 2. Holland, B. T., Blanford, C. F. & Stein, A. Science 281, 538­540 refractive index (Fig. 1). The electrodepo- (1998). 3. Wijnhoven, J. E. G. J. & Vos, W. L. Science 281, 802­804 (1998). sited materials still allow the colloidal tem- 4. Zakhidov, A. A. et al. Science 282, 897­901 (1998). plate to be removed, which is necessary to 5. Vlasov, Y. A., Yao, N. & Norris, D. J. Adv. Mater. 11, 165­169 maximize the refractive-index contrast. (1999). Electrodeposition should be an ideal 6. Biswas, R., Sigalas, M. M., Subramania, G. & Ho, K.-M. Phys. Rev. B 57, 3701­3705 (1998). way to fill topologically complex structures 7. Busch, K. & John, S. Phys. Rev. E 58, 3896­3908 (1998). because it starts from deep within the struc- 8. Lin, S. Y. et al. Nature 394, 251­253 (1998). ture and then grows out towards the 9. Fleming, J. G. & Lin, S. Y. Opt. Lett. 24, 49­51 (1999). exposed surfaces. We obtained microporous 10.Imhof, A. & Pine, D. J. Nature 389, 948­951 (1997). 11.Klein, J. D. et al. Chem. Mater. 5, 902­904 (1993). cadmium­selenium (CdSe) structures by 12.Edamura, T. & Muto, J. Thin Solid Films 235, 198­201 (1993). potentiostatic11 deposition in the interstitial space of a polystyrene colloidal template (Fig. 1a,b). Cadmium sulphide (CdS) was also grown by galvanostatic12 (Fig. 1c) and addendum potentiostatic (results not shown) deposi- Colour categories in a stone-age tribe tion in colloidal assemblies, again yielding J. Davidoff, I. Davies, D. Roberson three-dimensionally periodic structures Nature 398, 203­204 (1999) after the template is removed. The colour-naming pattern of Berinmo speakers may Because both CdS and CdSe have high appear consistent with that obtaining in tritanopia1, a refractive indices (2.5 at 600 nm and 2.75 at colour-vision disorder that has an increased frequency in 750 nm, respectively), these structures can other tropical areas2 and can arise from chronic exposure have deep gaps in their photonic band to short-wavelength light3. Furthermore, it could be structure after the template is removed. CdS argued that an isolated tribe may have become tritanopic and CdSe are promising materials for pho- through a shared genetic defect. However, our Berinmo tonic applications because, unlike most speakers were not tritanopic. They were tested with the other high-refractive-index materials, they City University Colour Vision Test4 that specifically assesses are optically transparent in the visible and tritanopia. The test consists of ten plates, and all speak- near-infrared region of the spectrum. ers who failed any of the plates were eliminated from our One of the critical requirements for the Figure 1 Electrodeposition in colloidal assemblies. a, Schematic study. The failure rate was 7 out of 83 speakers tested existence of a true omnidirectional photonic representation of the experimental set-up. b, c, Scanning electron during the course of the study. band gap is three-dimensional periodicity micrographs of the product. b, CdSe potentiostatically deposited in and uniformity. Our template-directed elec- 1. Pokorny, J., Smith, V. C., Verriest, G. & Pinckers, A. J. L. G. the interstitial space of a polystyrene colloidal assembly formed Congenital and Acquired Color Vision Defects (Grune & trodeposition of semiconductors results in from polystyrene spheres 0.466 m in diameter. After the elec- Stratton, New York, 1979). three-dimensional structures (Fig. 1b,c), as trodeposition, the polystyrene template was fully dissolved with 2. Davies, I. R. L., Laws, G., Corbett, G. G. & Jerrett, D. J. Pers. Ind. indicated by the clearly visible holes into the toluene. SCE, standard calomel electrode; ITO, indium tin oxide. c, Diff. 25, 1153­1162 (1998). layer below in all the systems. These holes 3. Werner, J. S., Peterzell, D. H. & Scheetz, A. J. Optom. Vis. Sci. 67, CdS galvanostatically grown around a silica colloidal template 214­229 (1990). form at contact points between the spheres formed from silica spheres 1 m in diameter. The template was 4. Fletcher, R. The City University Colour Vision Test 2nd edn of the template, and their arrangement on a partly dissolved after electrodeposition by dipping the sample into (Keeler, London, 1980). triangular lattice is evidence that the hollow an aqueous 4.8% hydrogen fluoride solution for 10 min. This did voids are on a hexagonal close-packed array. not completely dissolve the template, allowing the relation between As well as determining the three-dimen- the colloidal template and the resulting three-dimensional structure corrections sional structure, the holes between the voids to be seen directly. Magnet levitation at your fingertips allow for the complete removal of A. K. Geim, M. D. Simon the template by solvent or acid, or through electronic properties, are commonly used in Nature 400, 323 (1999) burnout. Our electrodeposited materials the semiconductor industry. The potential We inadvertently omitted a second reference to the work appear to be dense, as observed in high- offered by integrating photonic band-gap of I. A. H. Boerdijk (Philips Res. Rep. 11, 45­56; 1956), magnification scanning electron micro- structures with semiconductor devices where the first demonstration, to our knowledge, of levita- graphs of other template-directed electro- could revolutionize optoelectronics and tion of a magnet using non-superconducting diamagnetic depositions11. As a result, the microporous optical computing. It will be straightfor- materials as stabilizers was reported. The more stable structures shrink by only a tiny amount ward to extend our methods to metallic two-sided configuration was first described by Ponisovskii (<2%) when the template is removed. materials, which can readily be electro- (Prib. Tekh. Eksp. 24, 7­14; 1981). We were unaware of Template-directed electrodeposition is deposited, and these three-dimensionally the earlier work until our experiments were completed. well suited to creating three-dimensional microperiodic metallic structures could microstructures: many materials of high well have unusual mechanical or thermal refractive index can be electrodeposited, properties. Tropical tree gene flow and seed dispersal including semiconductors of groups II­VI, Paul V. Braun*, Pierre Wiltzius M. B. Hamilton III­V and IV, all of which are very reluctant Bell Laboratories, Lucent Technologies, Nature 401, 129­130 (1999) to form three-dimensional microstructures 700 Mountain Avenue, Murray Hill, Two numbers were transposed in the last column of Table by traditional techniques. These materials, New Jersey 07974, USA 1: for site 7, the values for populations 41-2 and 3209 which have many desirable optical and *Present address: Department of Materials Science should have been 1.0 and 0.0, respectively. 604 © 1999 Macmillan Magazines Ltd NATURE | VOL 402 | 9 DECEMBER1999 | www.nature.com brief communications Tropical tree gene flow and seed dispersal Deforestation affects the genetic structure of the surviving forest fragments. In tropical forests, trees provide habitats and environmental conditions that sup- port thousands of species. However, deforestation creates a mosaic landscape of cleared areas and forest fragments, which become the source of future tree popula- tions. Fragmentation changes the move- ment of pollen and seed dispersal, modifying the gene flow and altering histor- ical patterns of genetic subdivision. Paterni- ty studies in tropical figs1 and trees2 have shown that pollen is dispersed over long dis- tances, maintaining gene flow among widely spaced forest fragments, but gene move- Figure 1 A 1995 LandSat image of the C. alta populations showing patterns of chloroplast (cp) DNA variation. Squares indicate continu- ment by seed dispersal has not been studied ous forest populations. Ellipses group populations with identical cpDNA haplotypes and the connecting line indicates seven haplotype dif- in tropical trees. I have estimated chloroplast ferences between groups. Two trees with unique psbB-psbF haplotypes in population 3402 are not shown. Dark green, continuous genome subdivision in the Amazonian forest; light green, second growth; pink, pasture. canopy tree Corythophora alta, and here I show that seed dispersal is limited, with Manaus, Brazil (Fig. 1). The forest frag- they had a single maternal founder. forest fragments as large as ten hectares ments were created in the early 1980s but The pattern of cpDNA subdivision is being founded by a single maternal lineage. mature trees established before forest clear- consistent with historical seed dispersal Because trees are generally long-lived, ance, as judged from growth rates for tree being limited to small areas of continuous the population-genetic effects of forest frag- species of the family Lecythidaceae4. The tropical forest. However, the seven popula- mentation are difficult to observe directly. sites are located within relatively homoge- tions are resolved into only two haplotype Studies of gene flow provide an indirect neous forest and are not separated by physi- groups, so the extent of a seed-dispersal means of gauging these effects and compar- cal or ecological barriers to seed dispersal. neighbourhood has not been estimated. ing the genetic structure in intact and frag- Chloroplast (cp) DNA is maternally Furthermore, selection can increase popu- mented forest. We can use the dispersal inherited in most angiosperms5 and dispers- lation subdivision in non-recombining distances of pollen and seeds to estimate the es only through seeds, so the spatial scale of organelle genomes10, although there are no size of a genetic `neighbourhood' or the cpDNA genetic differences among popula- obvious differences in forest composition breeding area of a population. Paternal tions is a direct estimate of previous seed over this small spatial scale that could pro- genes disperse through both pollen and dispersal that led to trees being established6. duce localized selection for cpDNA vari- seed, whereas maternal genes disperse only Insertion or deletion polymorphisms were ants. I am now collecting data from through seed. Total gene dispersal identified by sequencing five cpDNA adjacent populations and testing whether 2 ( 2 2 2 2 p /2)+ s , where p and s are the regions7,8. Individual cpDNA haplotypes for evolution in the chloroplast genome is con- variances in pollen and seed movement, seven polymorphisms were determined by sistent with a neutral model of substitution. respectively, and the factor of 1/2 is required allele-specific polymerase chain reaction My results show that restricted seed- because pollen is haploid and we should (PCR). DNA sequence from random indi- mediated gene flow has led to sharp genetic omit the contribution of maternal gametes viduals verified that those with identical PCR differentiation of adjacent populations. which do not disperse3. Seed-dispersal vari- haplotypes have identical cpDNA sequences. They indicate that small forest plots may ance therefore contributes twice as much as Haplotype frequencies among forest sites exchange seeds infrequently, limiting the pollen-dispersal variance to the size of (Table 1) indicate almost complete cpDNA size of genetic neighbourhoods. Studies of genetic neighbourhoods. subdivision (the fixation index among gene flow in tropical trees have focused Tissues were sampled from 162 mature populations, FST 0.992 0.042; calculated mostly on pollen dispersal, rather than seed trees (of at least 10 cm diameter at breast according to ref. 9) among forest sites less dispersal, which may be more limited than height) in four forest fragments and three than 10 km apart (Fig. 1). Forest fragments pollen dispersal and is as likely to be altered sites of continuous forest at the Biological of 1 and 10 hectares all contain trees with a by forest disturbance. Because gene flow Dynamics of Forest Fragments Project near single cpDNA haplotype, indicating that through seeds is responsible for two-thirds of the total genetic-neighbourhood size, it is Table 1 Frequency of chloroplast genome insertion haplotypes for C. alta essential for estimates of the size of tropical- cpDNA site tree breeding populations. Gene flow from Population Size (ha) Number 1 2 3 4 5 6 7 both seed and pollen dispersal will be 1202 10 61 1.0 1.0 0.0 1.0 0.0 0.0 1.0 required to predict fragmentation-induced 1104 1 1 1.0 1.0 0.0 1.0 0.0 0.0 1.0 genetic changes in tropical forest trees. 41-1 10 16 1.0 1.0 0.0 1.0 0.0 0.0 1.0 Matthew B. Hamilton 41-2 10 20 1.0 1.0 0.0 1.0 0.0 0.0 0.0 Georgetown University, Department of Biology, 3209 10 27 0.0 0.0 1.0 0.0 1.0 1.0 1.0 Reiss Sciences 406, Washington DC 20057, USA 3114 1 8 0.0 0.0 1.0 0.0 1.0 1.0 0.0 and Biological Dynamics of Forest Fragments Project, 3402 10 29 0.0 0.0 1.0 0.07 1.0 1.0 0.0 National Institute for Research in the Amazon, The cpDNA sites are: 1, trnL intron; 2, trnH-psbA 1; 3, trnH-psbA 2; 4, psbB-psbF; 5, rpl20-5' rps12; 6, trnS-trnG 172; and 7, trnS-trnG 520. Primers are CP 478, Manaus, AM 69011-970, Brazil described in ref. 8 for site 1 and in ref. 7 for all other sites. e-mail:hamiltmb@gusun.georgetown.edu NATURE | VOL 401 | 9 SEPTEMBER 1999 | www.nature.com © © © 1999 Macmillan Magazines Ltd 1999 Macmillan Magazines Ltd 1999 Macmillan Magazines Ltd 129 brief communications 1. Chase, M. R., Moller, C., Kesseli, R. & Bawa, K. S. Nature 383, 5. Reboud, X. & Zeyl, C. Heredity 72, 132­140 (1994). ki+1 outgoing (or incoming) links is less 398­399 (1996). 6. McCauley, D. E. Trends Ecol .Evol. 10, 198­202 (1995). than NP 2. Nason, J. D., Allen Herre, E. & Hamrick, J. L. Nature 391, 7. Hamilton, M. B. Mol. Ecol. 8, 521­522 (1999). out(ki+1) (or NPin(ki+1)). 685­687 (1998). 8. Taberlet, P. et al. Plant Mol. Biol. 17, 1105­1109 (1991). A particularly important quantity in a 3. Crawford, T. J. Heredity 52, 273­283 (1984). 9. Weir, B. S. Genetic Data Analysis II (Sinauer, Sunderland, search process is the shortest path between 4. Chambers, J. Q., Higuchi, N. & Schimel, J. P. Nature 391, Massachusetts, 1996). two documents, d, defined as the smallest 135­136 (1998). 10.Rand, D. M. Conserv. Biol. 10, 665­671 (1996). number of URL links that must be followed to navigate from one document to the other. We find that the average of d over all pairs of vertices is d 0.35+2.06log(N) Internet 100 (Fig. 1c), indicating that the web forms a a b small-world network5,7, which characterizes Diameter of the 10­2 social or biological systems. For N 8 108, dweb 18.59; that is, two randomly chosen World-Wide Web (k) 10­4 (k)P in documents on the web are on average 19 Despite its increasing role in communica- P out clicks away from each other. tion, the World-Wide Web remains uncon- 10­6 For a given N, d follows a gaussian distri- trolled: any individual or institution can bution so d can be interpreted as the diam- create a website with any number of docu- 10­8100 101 102 103 104 100 101 102 103 104 eter of the web, a measure of the shortest ments and links. This unregulated growth k+1 k+1 distance between any two points in the sys- leads to a huge and complex web, which c 11 tem. Despite its huge size, our results indi- becomes a large directed graph whose ver- cate that the web is a highly connected graph tices are documents and whose edges are 9 10­5 with an average diameter of only 19 links. links (URLs) that point from one docu- 7 10­4 (k) The logarithmic dependence of d on N is ment to another. The topology of this P out 10­6 important to the future potential of the web: graph determines the web's connectivity 5 10­8 we find that the expected 1,000% increase in and consequently how effectively we can 100 102 k+1 the size of the web over the next few years locate information on it. But its enormous 3102 103 104 105 106 will change d very little, from 19 to only 21. size (estimated to be at least 8 108 docu- N The relatively small value of d indicates ments1) and the continual changing of docu- Figure 1 Distribution of links on the World-Wide Web. a, Outgoing that an intelligent agent, who can interpret ments and links make it impossible to links (URLs found on an HTML document); b, incoming links (URLs the links and follow only the relevant one, catalogue all the vertices and edges. pointing to a certain HTML document). Data were obtained from can find the desired information quickly by The extent of the challenge in obtaining the complete map of the nd.edu domain, which contains 325,729 navigating the web. But this is not the case a complete topological map of the web is documents and 1,469,680 links. Dotted lines represent analytical for a robot that locates the information illustrated by the limitations of the com- fits used as input distributions in constructing the topological based on matching strings. We find that mercial search engines: Northern Light, the model of the web; the tail of the distributions follows P(k) k , such a robot, aiming to identify a docu- search engine with the largest coverage, is with out 2.45 and in 2.1. c, Average of the shortest path ment at distance d , needs to search estimated to index only 38% of the web1. between two documents as a function of system size, as predicted M( d ) 0.53×N0.92 documents, which, Although much work has been done to by the model. To check the validity of our predictions, we deter- with N 8 108, leads to M 8 107, or map and characterize the Internet's infra- mined d for documents in the domain nd.edu. The measured 10% of the whole web. This indicates that structure2, little is known about what really dnd.edu 11.2 agrees well with the prediction d3 105 11.6 robots cannot benefit from the highly con- matters in the search for information - obtained from our model. To show that the power-law tail of P(k) is nected nature of the web, their only success- the topology of the web. Here we take a step a universal feature of the web, the inset shows Pout(k) obtained by ful strategy being to index as much of the towards filling this gap: we have used local starting from whitehouse.gov (squares), yahoo.com (triangles) and web as possible. connectivity measurements to construct a snu.ac.kr (inverted triangles). The slope of the dashed line is The scale-free nature of the link distrib- topological model of the World-Wide Web, out 2.45, as obtained from nd.edu in a. utions indicates that collective phenomena which has enabled us to explore and char- play a previously unsuspected role in the acterize its large-scale properties. incoming links, the probability of finding development of the web8, forcing us to look To determine the local connectivity of very popular addresses, to which a large beyond the traditional random graph mod- the web, we constructed a robot that adds to number of other documents point, is non- els3­5,7. A better understanding of the web's its database all URLs found on a document negligible, an indication of the flocking topology, aided by modelling efforts, is cru- and recursively follows these to retrieve the nature of the web. Furthermore, while the cial in developing search algorithms or related documents and URLs. We used the owner of each web page has complete free- designing strategies for making information data collected to determine the probabilities dom in choosing the number of links on a widely accessible on the World-Wide Web. Pout(k) and Pin(k) that a document has k document and the addresses to which they Fortunately, the surprisingly small diameter outgoing and incoming links, respectively. point, the overall system obeys scaling laws of the web means that all that information We find that both Pout(k) and Pin(k) follow a characteristic only of highly interactive self- is just a few clicks away. power law over several orders of magnitude, organized systems and critical phenomena6. Réka Albert, Hawoong Jeong, remarkably different not only from the To investigate the connectivity and the Albert-László Barabási Poisson distribution predicted by the classi- large-scale topological properties of the Department of Physics, University of Notre Dame, cal theory of random graphs3,4, but also web, we constructed a directed random Notre Dame, Indiana 46556, USA from the bounded distribution found in graph consisting of N vertices, assigning to e-mail:alb@nd.edu models of random networks5. each vertex k outgoing (or incoming) links, 1. Lawrence, S. & Giles, C. L. Nature400,107­109 (1999). The power-law tail indicates that the such that k is drawn from the power-law 2. Claffy, K., Monk, T. E. & McRobb, D. Internet tomography. probability of finding documents with a distribution of Fig. 1a,b. To achieve this, we Nature [online] (1999). large number of links is significant, as the randomly selected a vertex i and increased 3. Erdös, P. & Rényi, A. Publ. Math. Inst. Hung. Acad. Sci.5,17­61 network connectivity is dominated by its outgoing (or incoming) connectivity to (1960). highly connected web pages. Similarly, for k 4. Bollobás, B. Random Graphs (Academic, London, 1985). i+1 if the total number of vertices with 130 © © © 1999 Macmillan Magazines Ltd 1999 Macmillan Magazines Ltd 1999 Macmillan Magazines Ltd NATURE | VOL 401 | 9 SEPTEMBER 1999 | www.nature.com scientific correspondence Colour categories in a stone-age tribe The Dani of Irian Jaya are a stone-age Melanesian people who have provided English an empirical basis for the study of cross- 5R 10R 5YR 10YR 5Y 10Y 5GY 10GY 5G 10G 5BG 10BG 5B 10B 5PB 10PB 5P 10P 5RP 10RP cultural perception and cognition1­3. Although they had only two terms for 9 Pink Yellow describing colour, the Dani memory for 8 colour seemed to be much like that of mod- * * ern English speakers. We have investigated 7 * Pink another stone-age culture, the Berinmo of Papua New Guinea, for the way in which 6 Orange they categorize colours, but the results do not support the idea that colour categories 5 * Blue Purple could be universal. According to the linguistic relativity 4 * Brown Green * hypothesis4,5, which is still influential, we Red 3 * construct our understanding of the world Red through language. Whorf4 famously argued 2 that, to an Eskimo, it would be unthinkable to use the same word for all types of snow Berinmo because of its wide range of types and dif- 5R 10R 5YR 10YR 5Y 10Y 5GY 10GY 5G 10G 5BG 10BG 5B 10B 5PB 10PB 5P 10P 5RP 10RP ferent uses. We investigated colour in a remote, pre- 9 3 2 5 Wap 2 1 1 Wap 1 5 12 6 3 2 viously unstudied, hunter-gatherer tribe, 8 the Berinmo, which lives on the upper 9 6 2 3 1 reaches of the Sepik River in Papua New 7 2 5 4 4 1 1 2 Guinea. When Berinmo subjects were asked to name the 160 colours in the stan- 6 Mehi 2 1 2 3 1 dard Munsell array, thay used five basic colour terms6. The range and boundaries of 5 6 2 Wor 1 6 7 4 Nol 2 2 Mehi 3 these terms showed good intra-subject 4 19 5 3 11 concordance, and can be seen in Fig.1 alongside the eight basic chromatic terms 3 2 Kel 1 1 1 1 in English. We replicated the Dani experiment with 2 1 1 3 4 6 12 2 1 4 3 4 4 Kel 2 the Berinmo. The accuracy with which they remembered colours bore a striking simi- FFiigguurree 11 Distribution of English and Berinmo colour names. The Munsell system provides equally spaced larity to the Dani; both groups of Melane- samples in three dimensions, but is shown here as a Mercator projection of hue (horizontal axis) against sian subjects were very poor at this (9.6 and lightness (vertical axis). The colours used to denote colour categories on these Mercator projections are for 7.7 out of 40, respectively). However, statis- illustration only. Eight colour terms for English and five for Berinmo are shown. Dots on English naming data tical analysis showed that, for both studies, represent the position of focal colours2. Numbers on the Berinmo naming data represent the number of sub- the best statistical fit (that with the lowest jects who designated that colour as best example of the category. R, red; Y, yellow; G, green; B, blue; P, pink. stress value) was between Melanesian nam- ing and Melanesian memory (Table 1a). linguistic relativity. Berinmo does not mark remember a colour over an interval of 30 This finding is consistent with the linguistic the distinction between blue and green, but seconds1,2 and then select the same colour relativity hypothesis, but not with the inter- it has a colour boundary (between `nol' from a pair of similar alternatives. Some- pretation of the original study. and `wor') in a position that does not exist times the incorrect choice was from the The differences between English and in English. We investigated categorical same colour category and sometimes from Berinmo allow a further critical test of the effects7,8 across both the blue­green and the a different one. We also added a 5-second- contrast between colour universals and nol­wor boundaries. We asked subjects to interval condition for the Berinmo as they Table 1 Statistical analysis of language data had difficulty remembering blue­green a Goodness of fit for multidimensional scaling solutions samples for 30 seconds. English subjects showed the expected Dani naming versus Dani memory 0.126 Dani memory versus US memory 0.161 advantage for cross-category blue­green Berinmo naming versus Berinmo memory 0.158 decisions but not for nol­wor decisions; Berinmo memory versus English memory 0.256 Berinmo subjects showed exactly the oppo- b Mean trials to criteria in colour-categorization tasks site pattern. The Berinmo showed no sign Blue vs green Green1 vs green 2 Nol vs wor Yellow vs green of a cross-category advantage for blue­ English speakers 3.2 5.9 3.8 1.4 Berinmo speakers 11.43 10.57 2.2 3.6 green stimuli, but maintained their cross- a, Measures of stress (departure from goodness of fit) are shown for comparison of naming and memory data. Low category advantage for nol­wor stimuli values indicate high goodness of fit. Data for comparisons between US naming and US memory are from ref. 1 and both at 30 seconds and at 5 seconds. These are compared with those from Berinmo and English subjects. In both cases, the fit between naming and memory is results indicate that categorical perception better than the fit between memory across language groups. b, Mean number of blocks to error-free performance. Categorizations are achieved more rapidly if they are consonant with distinctions made in the language of the subject. occurs, but only for speakers of the language that marks the categorical distinction, which NATURE | VOL 398 | 18 MARCH 1999 | www.nature.com © © © 1999 Macmillan Magazines Ltd 1999 Macmillan Magazines Ltd 1999 Macmillan Magazines Ltd 203 scientific correspondence is consistent with the linguistic relativity z<[(a/A)(x+y/r)]. This therefore sets the hypothesis. upper limit of cost-effective surveys for If categories always form around natural Why biodiversity reserve selection. fault lines in perceptual colour space, it surveys are good value There are few published data with which should be relatively easy to learn another to parametrize this simple model. Conserva- language's colour categories. To test this tively, we suggest that a/A (the relative saving version of the universalist position, we Article 8 of the Convention on Biological in reserve area achieved by tackling comple- asked English speakers to learn the nol­wor Diversity obliges contracting parties to mentarity) is commonly at least 5%; it will distinction and Berinmo speakers to learn establish protected areas for conservation. often be far higher1. Estimates for x and y, the blue­green and yellow­green distinc- This can be achieved in smaller networks of obtained from a diverse range of sources and tions. For comparison, subjects were also reserves if their design is based on how well expressed in 1990 US$, are summarized in asked to categorize stimuli in a manner different sites complement one another bio- Table 1. Using appropriate values for r consonant with the colour names of their logically, rather than on more commonly (from 5% to 20%), we can then estimate own language. In addition, subjects learned used criteria, such as species richness or [(a/A)(x+y/r)]. Marked variation in land a distinction not marked in either language: simple availability for acquisition1,2. How- prices6 and labour costs means that this that between two types of green (`green 1' ever, this increase in efficiency3 requires upper limit of cost-effective surveys varies and `green 2'). All tasks were made non- species lists for each candidate site, and enormously but, wherever data are available, trivial by presenting only one stimulus at a obtaining such data can be expensive; for this greatly exceeds the likely cost of high- time and by the inclusion of marginal example, a detailed survey of five taxa quality surveys. For instance, in Uganda, at examples of each category. across 15,000 km2 of forest in Uganda took r 10%, [(a/A)(x+y/r)] $800 per km2, Berinmo subjects found learning to nearly 100 person-years and cost about whereas the true value of z is less than one- divide colours into green 1 and green 2 no US$1 million4,5. Here we ask whether tenth of this, at $58 per km2. Reversing this harder than dividing them into blue and investing in such surveys makes economic calculation, detailed inventories would have green; English speakers found the sense, or whether conservation agencies to yield area savings of less than 0.4% - that blue­green task easier. Berinmo subjects would be better advised to continue follow- is, a/A0 levitating maximum, as required for stable equilib- Bi cylinder magnet rium. Diamagnets (which respond to mag- ­2R netic fields with mild repulsion) are known to flout the theorem, as their negative sus- FFiigguurree 22 Levitation at your fingertips. A strong NdFeB ceptibility results in the requirement of a magnet (1.4 tesla) levitates 2.5 metres below a pow- minimum rather than a maximum in the erful superconducting magnet. The field at the levi- field's magnitude2­4. Nevertheless, levitation tation point is about 500 Gauss. of a magnet without using superconductors is widely thought to be impossible. We find where is the density of the magnet's that the stable levitation of a magnet can be material and A 1.92. Calculation shows achieved using the feeble diamagnetism of that a magnet several millimetres in size materials that are normally perceived as with remnant magnetization of about 1 being non-magnetic, so that even human tesla (NdFeB) can be levitated with a clear- fingers can keep a magnet hovering in mid- FFiigguurree 11 A NdFeB magnet (an alloy of neodymium, ance gap, D d, of several millimetres air without touching it. iron and boron; 4 mm high and 4 mm in diameter) using a 10-cm solenoid and strongly dia- Stable levitation has been demonstrated levitating at the axis of a vertical solenoid of radius magnetic Bi or graphite, in agreement with for diamagnetic objects such as supercon- R 10 cm and length 2R in a magnetic field of 100 our experiment. ducting pellets and live creatures2,5­7. Strong gauss. The levitation is stabilized by a bismuth cylin- Equation (2) depends on the product of diamagnetism of superconductors allows der ( 1.5 10 4) with inner diameter D 8 mm. and L, which means that by increasing L the situation to be reversed, so that a magnet The photograph shows the top view of the levitating (scaling up the magnet's size) we can can be levitated above a superconductor8. magnet. The right-hand plot shows the stability func- achieve the same D as above using ordinary Paramagnetic objects can also be levitated if tions Kv and Kh calculated for a solenoid with a materials (such as plastic or wood, with placed in a stronger paramagnetic medium, height of twice its radius (solid curves). Diamagnetic 10 5). To illustrate this point, we such as ferrofluid or oxygen, which makes interaction C shifts the horizontal stability function Kh show another example of a levitating mag- them effectively diamagnetic9. to the left (dashed curve) and a small region of posi- net in Fig. 2 in which human fingers We set out to lift a magnet by applying a tive U emerges above the point where Kv 0. ( 10 5) are used as diamagnetic stabi- magnetic field and then stabilizing the lizers. Here we use an alternative geometry11 intrinsically unstable equilibrium with The presence of a diamagnetic cylinder in which L is easier to scale up because it is repulsive forces from a nearby diamagnetic results in the last term in equation (1) and, determined not only by the magnet size, but material. We found that, surprisingly, the for the geometry of Fig. 1, we find that also by its strength. The levitating magnet is forces created by almost non-magnetic C 45 0| |M2/16D5, where 0 is the per- placed below a solenoid in the region where materials (susceptibility of about 10 5) meability of free space. If there is no dia- the equilibrium is stable horizontally are sufficient to stabilize levitation over dis- magnet (C 0), the stability can never be (Kh>0) but not vertically (Kv<0) (Fig. 1). tances as large as several millimetres under reached (at no point are Kv and Kh both Vertical stability is achieved by means of Earth gravity conditions, even though they positive; Fig. 1). The diamagnetic interac- two horizontal diamagnetic plates (or by decay rapidly with distance as 1/x5 (Fig. 1). tion allows the energy U to have a mini- the fingertips). For stable levitation, an equilibrium mum (Kv>0 and Kh+C>0) which In this geometry, the positive constant requires that the magnetic force MB (z) emerges for C>MB (z)2/8B(z) just above C 6 0 M2/ D5 counters Kv and the levi- compensates the gravitational force mg, the point of a maximum field gradient tation condition is similar to equation (2), where M is the magnetic moment and B(z) (B (z) 0). It is counterintuitive that levi- except that now D denotes the separation and B (z) are the magnetic field on the axis tation is easiest in the most inhomogeneous between the plates, A 1.02 and L 4B /B and its derivative, respectively. For the equi- field region, rather than in the centre of a is approximately the distance from the cen- librium to be stable, it must be in a region solenoid where the field is almost uniform. tre of a solenoid to a levitating magnet. The where the total energy of the magnet It is instructive to introduce a character- larger the distance, the easier it is to stabilize U MB(r)+mgz+Udia has a minimum istic scale L on which the field changes: levitation by diamagnetic repulsion. L is ( U>0), where Udia is the energy of dia- B B/L. At the optimum levitation point limited by the requirement on the field gra- magnetic interaction with the cylinder. (B (z) 0), L varies between R and 1.2R dient, B (z) mg/M. To reach such a large Close to the equilibrium position at the for long and short solenoids, respectively. If L, as in Fig. 2, we used an 11-tesla supercon- field axis3,10, we approximate our levitating magnet by a ducting solenoid a metre in diameter. If U U0+[mg MB (z)]z+Kvz2+Khr2+ sphere of diameter d with a remnant field stronger diamagnets are used (such as Cr2+... (1) Br, then M ( /4 0)Brd3, and the require- graphite or bismuth), this type of levitation where Kv(z) MB (z)/2 and ment for levitation becomes can also be achieved with small permanent K 2 h(z) M[B (z)2 2B(z)B (z)]/8B(z). A( LBr d3/ 0 g)1/5>D>d (2) magnets, making miniature hand-held NATURE | VOL 400 | 22 JULY 1999 | www.nature.com © © © 1999 Macmillan Magazines Ltd 1999 Macmillan Magazines Ltd 1999 Macmillan Magazines Ltd 323 scientific correspondence devices accessible to everyone (M. D. S., unpublished data). These could replace the a b c mN mN mN existing servo levitation devices for some applications. A. K. Geim*, M. D. Simon , M. I. Boamfa*, L. O. Heflinger mN" mN" mN" *High Field Magnet Laboratory, University of Nijmegen, 6525 ED Nijmegen, The Netherlands mShore mShore mShore e-mail: geim@sci.kun.nl d e f Department of Physics and Astronomy, University of California at Los Angeles, Los Angeles, California 90095, USA 1. Earnshaw, S. Trans. Camb. Phil. Soc. 7, 97­112 (1842). 2. Brandt, E. H. Science 243, 349­355 (1989). P< 0.001 P< 0.001 3. Berry, M. V. &. Geim, A. K. Eur. J. Phys. 18, 307­313 (1997). 4. Thomson, W. (Lord Kelvin) Reprints of Papers on Electrostatics mShore mShore and Magnetism (Macmillan, London, 1872). g h 5. Braunbeck, W. Z. Phys. 112, 753­763 (1939). 6. Beaugnon, E. & Tournier, R. Nature 349, 470 (1991). 7. Geim, A. Phys. Today 51, 36­39 (September 1998). 8. Arkadiev, A. Nature 160, 330 (1947). 9. Ikezoe, Y. et al. Nature 393, 749­750 (1998). 10.Simon, M. D. et al. Am. J. Phys. 65, 286­292 (1997). P< 0.001 11.Boerdijk, A. H. Philips Tech. Rev. 18, 125­127 (1956). FFiigguurree 11 Effects of long-wavelength light and head caps on bimodal magnetic orientation in newts. a­c, Pre- dicted orientation of newts (double-headed arrow) and their perception of the direction of the magnetic field Extraocular magnetic (single-headed arrow)5,6. Training tanks have the shore towards magnetic north (mN); circular test arenas show the predicted response of the newts under either full-spectrum (beige) or long-wavelength light (yel- compass in newts low). a, Full-spectrum training and testing: newts should perceive the shore to be towards magnetic north and exhibit bimodal magnetic orientation along the shoreward axis. b, Full-spectrum training, long-wavelength testing: newts' perception of magnetic north in testing, and their orientation in the test arena, should be rotated Geomagnetic orientation is widespread 90º (mN ) from magnetic north during training. c, Long-wavelength training and testing: newts' perception of among organisms, but the mechanism(s) of the magnetic field should be rotated 90º relative to the actual field during training and testing. Their percep- magnetoreception has not been identified tion of the magnetic field in the arena would be the same as in the outdoor tank. d­h, Results. Data points convincingly in any animal1. In agreement show the magnetic bearing of a newt tested in one of four symmetrical alignments of an Earth-strength mag- with biophysical models proposing that the netic field (magnetic north is geographic north (gN), east (gE), west (gW) or south (gS)). The magnetic field geomagnetic field interacts with photo- was altered by two orthogonally orientated, double-wrapped, Ruben's coils around the test arena7. Data are receptors2­4, changes in the wavelength of plotted with respect to the magnetic direction of shore (mShore) in the training tank (shore direction, 360º). light have been shown to influence magnetic Double-headed arrows indicate mean axis of orientation with the mean axis length, r, proportional to the compass orientation in an amphibian, an strength of orientation (diameter of the circle corresponding to r 1). Dashed lines indicate 95% confidence insect and several species of birds (reviewed intervals for the mean axis. Distributions are significant at P<0.05 or less by the Rayleigh test and P-values in ref. 5). We find that light-dependent mag- between circle plots indicate significant differences between distributions (Watson U2 test). d, Newts trained netic orientation in the eastern red-spotted under natural light and tested under full-spectrum light orientated along the shoreward axis5. e, Newts trained newt, Notophthalmus viridescens, is mediated under natural light and tested under long-wavelength light orientated 90º from the shoreward direction (filled by extraocular photoreceptors, probably circles; tested under broadband long-wavelength ( 500 nm) light; filled squares, tested under a 550-nm light, located in the pineal complex or deeper in 40 nm bandwidth, 12.5 0.1 log Quanta cm 2 s 1; ref. 5). f, Newts trained and tested under long-wavelength the brain (perhaps the hypothalamus). light orientated along the shoreward axis5. g, After training under natural light, clear-capped newts tested under Experiments investigating shoreward long-wavelength light orientated ~90º from the shoreward direction. h, After training under natural light, newts magnetic compass orientation have demon- with long-wavelength-transmitting caps orientated along the shoreward axis under long-wavelength light. strated that the newt's perception of the direction of the magnetic field is rotated 90o due to a direct effect of light on the newts' tors. Small round `caps' (5 mm in diameter) under long-wavelength (greater than 500 perception of the magnetic field, we trained were attached to the dorsal surface of the nm) light5,6. We recently trained newts newts under long-wavelength light by cov- head of each newt using cyanoacrylate glue, under natural skylight to aim for the shore ering the training tank with a long-wave- and remained in place during both training by placing them for 12­16 hours in water- length-transmitting gel filter (two layers of and testing. Equal numbers of newts were filled tanks with an artificial shore at one Lee #101)5. Under long-wavelength light, capped with either a clear filter (Lee #130) end5,7. The magnetic orientation of individ- these newts orientated themselves parallel or a filter that transmitted only long-wave- ual newts was then tested in a circular, visu- to the shoreward axis, indicating that they length light (equivalent to two layers of Lee ally symmetrical indoor arena under had learned the direction of the shore with #101). The caps were positioned to alter the depolarized light. Under full-spectrum light respect to the rotated magnetic information spectral properties of light reaching the (from a xenon arc source), they exhibited under long-wavelength light (Fig. 1c,f). pineal and surrounding structures, whereas bimodal magnetic orientation parallel to As well as ocular photoreceptors, newts light reaching the eyes was unaffected. the shoreward axis in the training tank (Fig. have extraocular photoreceptors in the Clear-capped newts were tested to control 1a,d). In contrast, under long-wavelength pineal complex8 and possibly the hypothal- for any nonspecific effects of the caps on the light, they orientated themselves perpendic- amus9. To determine which photoreceptors newts' orientation behaviour. ular to the shoreward direction (Fig. 1b,e). are involved in the magnetic compass All newts were trained outdoors under To demonstrate that the 90o shift in ori- response, we manipulated the wavelength of natural skylight and tested for magnetic ori- entation under long-wavelength light was light reaching the extraocular photorecep- entation in the testing arena under long- 324 © © © 1999 Macmillan Magazines Ltd 1999 Macmillan Magazines Ltd 1999 Macmillan Magazines Ltd NATURE | VOL 400 | 22 JULY 1999 | www.nature.com