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brief communications Fibre-optical features of a glass Some superior technological secrets have come to light from a deep-sea organism.

odern technology cannot yet com- between the spicule and air (Fig.1d,right). shows, for example, that sodium ions are pete with some of the sophisticated These biological fibres therefore resem- present throughout the spicules,particularly Moptical systems possessed by bio- ble commercial telecommunication fibres, in the core. Although sodium ions (and logical organisms1–3. Here we show that in that they are made of the same material many other additives) are desirable fibre- the spicules of the deep-sea ‘glass’ sponge and have comparable dimensions, as well as optic dopants, they present a manufacturing have remarkable fibre-optical similar refractive indices for the high-index challenge, for example by causing devitrifi- properties, which are surprisingly similar to core and a low-index cladding. They also cation at high temperatures. those of commercial telecommunication function as efficient single-mode, few-mode Our results suggest the intriguing possi- fibres — except that the spicules themselves or multi-mode waveguides, depending on bility that the spicules of Euplectella,beyond are formed under normal ambient condi- the optical launch conditions. structural anchorage support, could also tions and have some technological advan- The principal weakness of commercial provide a highly effective fibre-optical net- tages over man-made versions. optical fibres is that they fracture as a result of work, which may be useful in distributing The of the hexactinellid class of crack growth, whereas the spicules’ lamellar light in its deep-sea environment. This illu- is constructed from amorphous, layers, connected by organic ligands at the minating sponge should also shed light on hydrated silica3–6. Euplectella builds an intri- fibre’s exterior, provide an effective crack- low-temperature, biologically inspired pro- cate cage (Fig. 1a), which typically houses a arresting mechanism and enhance fracture cesses that could give rise to better fibre- mating pair of shrimp (hence its nickname, toughness6,8,9. Another superior feature of optical materials and networks. ‘Venus flower-basket’) and is composed of a the spicules is their formation under ambi- Vikram C. Sundar*, Andrew D. Yablon†, lattice of fused spicules4 that provide extend- ent conditions, a process that is regulated John L. Grazul*, Micha Ilan‡, ed structural support. by organic molecules10,11. This ambient- Joanna Aizenberg* A network of anchorage spicules temperature process, unlike the high-tem- *Bell Laboratories/Lucent Technologies, (basalia) extend outwards in a crown-like perature manufacture of man-made fibres, Murray Hill, New Jersey 07974, USA formation. These spicules are generally 5–15 allows the structure to be doped with special- e-mail: [email protected] cm long and 40–70 m in diameter; their ized impurities that improve the refractive †OFS, Murray Hill, New Jersey 07974, USA native cross-section is homogeneous and index and therefore the wave-guiding prop- ‡Department of , Tel Aviv University, they have no structural boundaries. Under erties. Our preliminary elemental analysis Tel Aviv 69978, Israel stress or etching,the spicules reveal a charac- teristic layered morphology6 and cross-sec- a b tional variations in composition that appear as three distinct regions: a pure silica core of about 2 m in diameter that encloses an organic filament; a central cylinder that has the greatest organic content of the three; and a striated shell that has a gradually decreas- ing organic content and which is glued together by organic films (Fig.1b). We anticipated that the spicules’rich sub- structure should be reflected in their optical properties as well. Indeed, interferometric c refractive-index profiling7 revealed three regions that correspond to the three regions of structural composition (Fig. 1c): a core with high refractive index that is comparable to (or higher than) that of vitreous silica; a cylinder of lower refractive index that sur- 1.46 core rounds the core; and an oscillating pattern with progressively increasing refractive 1.45 index at the outer part of the spicule. Figure 1 Structure and fibre-optical properties of spicules in the 1.44 cladding cladding To determine whether this typical ‘core- sponge Euplectella. a, The glass sponge, showing the basket-like cladding’ refractive-index profile endows cage structure and basalia spicules (arrow). Scale bar, 5 cm. 1.43 b, Mechanically cleaved spicules show three structural regions. OF, Refractive index the spicules with wave-guiding properties, 1.42 SS CC SS we investigated their transmission charac- organic filament; SS, outer striated shell; CC, central cylinder. Inset: –30–20 –10 0 10 20 30 teristics. We found that embedded spicules smooth cross-section of a stress-free spicule. c, Interferogram Radial position (µm) act as single- or few-mode waveguides — (top) and corresponding refractive-index profile (bottom) of a that is, light waves are effectively confined spicule. Dashed line indicates the refractive index of vitreous silica. d to the core,where refractive index is highest d, Wave guiding by individual spicules upon coupling with white (Fig. 1d, left). When light was coupled into light. Spicules embedded in epoxide act as single-mode or few- free-standing spicules, they functioned as mode waveguides (left); free-standing spicules act as multi-mode multi-mode fibres, with most of the waveguides (right). Scale bar, 10 m. Further details are available light filling the entire cladding, because from the authors. of the enhanced refractive-index contrast

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1. Aizenberg, J., Tkachenko, A., Weiner, S., Addadi, L. & Hendler, should yield the same transition probability histories of countries where two languages G. Nature 412, 819–822 (2001). as a swap in the fraction of speakers and rel- coexist today generally involve split popu- 2. McPhedran, R. C. et al. Aust. J. Chem. 54, 241–244 (2001). ative status; thus Pxy(x,s) Pyx(1 x,1 s). lations that lived without significant inter- 3. Cattaneo-Vietti, R. et al. Nature 383, 397–398 (1996). We also assume that no one will adopt a action, effectively in separate, monolingual 4. Perry, C. C. & Keeling-Tucker, T. J. Biol. Inorg. Chem. 5, 537–550 (2000). language that has no speakers (Pyx(0,s) 0) societies. Only recently have these commu- 5. Simpson, T. L. The Cell Biology of Sponges (Springer, New York, or no status (Pyx(x,0) 0), and that Pyx is nities begun to mix, allowing language 1984). smooth and monotonically increasing in competition to begin. 6. Sarikaya, M. et al. J. Mater. Res. 16, 1420–1428 (2001). 7. Marcuse, D. Principles of Optical Fiber Measurements both arguments. So what can be done to prevent the rapid (Academic, New York, 1981). These mild assumptions imply that equa- disintegration of our world’s linguistic 8. Clegg,W.J.,Kendall,K.,Alford,N.M.,Button,T.W.& Birchall, tion (1) generically has three fixed points.Of heritage? The example of Quebec French J. D. Nature 347, 455–457 (1990). these, only x0 and x1 are stable. The demonstrates that language decline can be 9. Kamat, S., Su, X., Ballarini, R. & Heuer, A. H. Nature 405, 1036–1040 (2000). model therefore predicts that two languages slowed by strategies such as policy-making, 10. Cha, J. N., Stucky, G. D., Morse, D. E. & Deming, T. J. Nature cannot coexist stably — one will eventually education and advertising, in essence 403, 289–292 (2000). drive the other to extinction. increasing an endangered language’s status. 11. Kroger, N., Lorenz, S., Brunner, E. & Sumper, M. Science 298, 584–586 (2002). To test our model, we collected data on An extension to equation (1) that incor- Competing financial interests: declared none. the number of speakers of endangered lan- porates such control on s through active guages in 42 regions of Peru,Scotland,Wales, feedback does indeed show stabilization Bolivia, Ireland and Alsace-Lorraine, four of a bilingual fixed point. Linguistics instances of which are shown in Fig. 1.We fit Daniel M. Abrams, Steven H. Strogatz the model’s solutions to the data, assuming Department of Theoretical and Applied Mechanics, Modelling the dynamics transition functions of the forms Cornell University, Ithaca, New York 14853, USA P (x,s)cx as and P (x,s)c(1x)a(1s). e-mail: [email protected] of language death yx xy Unexpectedly, the exponent a was found to 1. Krauss, M. Language 68, 4–10 (1992). housands of the world’s languages are be roughly constant across cultures, with 2. Nowak, M. A., Komarova, N. L. & Niyogi, P. Nature 417, 611–617 (2002). vanishing at an alarming rate, with a 1.31 0.25 (mean standard deviation; 3. Chomsky, N. A. Syntactic Structures (Mouton, T90% of them being expected to disap- further details are available from the New York, 1957). pear with the current generation1.Here we authors). 4. Kroch, A. Lang. Variat. Change 1, 199–244 (1989). develop a simple model of language compe- Of the remaining parameters, status, s,is 5. Hawkins, J. A. & Gell-Mann, M. The Evolution of Human Languages (Addison-Wesley, Reading, Massachusetts, 1992). tition that explains historical data on the the most relevant linguistically;it could serve 6. Niyogi, P. & Berwick, R. C. Ling. Phil. 20, 697–719 (1997). decline of Welsh, Scottish Gaelic, Quechua as a useful measure of the threat to a given 7. Lightfoot, D. The Development of Language: Acquisition, (the most common surviving indigenous language. Quechua, for example, still has Changes and Evolution (Blackwell, Oxford, 1999). language in the Americas) and other endan- many speakers in Huanuco, Peru, but its low 8. Fishman, J. A. Reversing Language Shift (Multilingual Matters, Philadelphia, 1991). gered languages. A linguistic parameter that status is driving a rapid shift to Spanish, 9. Withers, C. W. J. Gaelic in Scotland 1698–1981: The Geographical quantifies the threat of language extinction which leads to an unfortunate situation in History of a Language (Donald, Edinburgh, 1984). can be derived from the model and may which a child cannot communicate with his 10.Aitchison, J. & Carter, H. A Geography of the Welsh Language (Univ. Wales Press, Cardiff, 1994). be useful in the design and evaluation of or her grandparents. 11.UK Office of Population Censuses and Surveys. 1991 Census: language-preservation programmes. Contrary to the model’s stark prediction, Report for Wales, 1 (HMSO, London, 1993). Previous models of language dynamics bilingual societies do, in fact, exist. But the Competing financial interests: declared none. have focused on the transmission and evolu- tion of syntax, grammar or other structural Figure 1 The dynamics of lan- properties of a language itself 2–7. In contrast, guage death. Symbols show the ab the model we describe here idealizes lan- proportions of speakers over time 0.9 0.7 guages as fixed, and as competing with each of: a, Scottish Gaelic in Sutherland, Scotland9; b, Quechua in Huanuco, other for speakers. For simplicity, we also s = 0.33 s = 0.26 assume a highly connected population, with Peru; c, Welsh in Monmouthshire, no spatial or social structure, in which all Wales10; d, Welsh in all of Wales, speakers are monolingual. from historical data10 (blue) and a Consider a system of two competing lan- single modern census11 (red). Fit- guages,X and Y,in which the attractiveness of ted curves show solutions of the a language increases with both its number of model in equation (1), with para- speakers and its perceived status8 (a parame- meters c, s, a and x(0) estimated 0 0 ter that reflects the social or economic by least absolute-values regres- 1880 2000 1930 2030 opportunities afforded to its speakers). Sup- sion. Where possible, data were Year pose an individual converts from Y to X with obtained from several population cd a probability, per unit of time, of Pyx(x,s), censuses collected over a long 0.14 0.5 where x is the fraction of the population timespan; otherwise, a single speaking X, and 0s1 is a measure of X’s recent census with age-structured Fraction of minority speakers relative status. A minimal model for lan- data was used (although errors are s = 0.40 s = 0.46 guage change is therefore introduced, the size of which are reflected in the differing fits in d). s = 0.43 Using the fraction of Catholic dx — yPyx(x,s) xPxy(x,s) (1) masses offered in Quechua in Peru dt as an indicator, we reconstructed an approximate history of the lan- 00 where y1x is the complementary frac- guage’s decline. 1900 2020 1900 2020 tion of the population speaking Y at time t. Year By symmetry, interchanging languages

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