the world we can see - a mirror of the microworld? · golden ratio in science, as random sequence...

The world we can see - a mirror of the microworld?

Eliza Rybska*1, Zbigniew Adamski 2, 3 Antoni Wójcik4 and Jerzy Błoszyk 5, 6 1The Faculty Laboratory for Teaching Biology and Natural Science. Faculty of Biology, Adam Mickiewicz University,

Poznan, Poland, 2Electron and Confocal Microscope Laboratory/3 Department of Animal Physiology and Developmental Biology, Faculty

of Biology, Adam Mickiewicz University, Poznan, Poland 4Quantum Electronics Laboratory, Faculty of Physics, Adam Mickiewicz University 5Department of General Zoology/6 Natural History Collection, Faculty of Biology, Adam Mickiewicz University, Poznan,

Poland,

Scanning electron microscopy is one of the most important techniques which enable us to examine surface of samples. Due to obvious limitations, they are not used in school practice. Also number of pictures presented in notebooks is limited. Our university cooperates with secondary schools and gives them opportunity to increase theoretical knowledge and observe microscopic work in practice. Therefore, teachers and pupils eagerly take part in events organized by our faculty. They can observe various creatures, which are practically unknown to them.

Very often we observed that our guests associate microstructures with similar structures they can observe with a naked eye. By accident or intentionally, some macrostructures made by human are more or less similar to structures made by nature. Therefore, comparison of micro- and macro pictures gives opportunity to start a discussion about the reasons for various shapes and sculptures. In our practice we find such discussions stimulating, as a good point for further discussions concerning the reasons of particular shapes and structures of various creatures in nature.

If the structures have similar function, their similarity is a direct effect of physics. The same organization of grass stems and chimneys that are empty inside gives both of them strength and flexibility. Sculpture of some parts of mites‘ exoskeleton resembles foot of an iron. Perhaps, they both are to share some similar role? Perhaps the two are meant to prevent the adhesion to the surface? Why the structure of micropylar region of moths’ egg is almost the same like rosette in church windows? Of course we do not suggest that shape of Ceratium algae impressed a designer Eiffel Tower in Paris, but this impression is almost immediate for the majority of people. Joining fun, interesting objects and creative thinking of our visitors, we are able to organize interesting lessons which show the deeper purpose of organization of nature.

Keywords electron microscopy practical; school practice; shape of biological objects.

Introduction

Interdisciplinary approach to teaching is a popular term, used in various topics and areas of science. Such an approach is difficult to accomplish, especially at schools, which suffer from permanent lack of time for realization of curricula and syllabuses. However, interdisciplinary approach can give something, what cannot be replaced by any other type of approach – it gives overall vision, proof that our world consists not only of chemical compounds, what is taught at chemistry lessons, of rocks and rivers, what is taught at geography or of words, how the linguists teach. Instead, interdisciplinary approach gives possibility to see the world as a whole. In this paper we show our proposal of the interdisciplinary activity, which joins art and sciences, especially biology, but also math and physics. The whole activity is realized on the basis of scanning electron microscopy. Sometimes the participants bring their own samples and observe them under SEM (see Rybska et al., this volume). Secrets of life and nature are one of the main interests of biologists. Symptoms of live can be observed almost everywhere on our planet. Forms of live are characterized by enormous variability. Scientists often try to describe them using mathematical equations, dependences or pictograms. One of the examples of such manifestations is a The Rule of Golden Ratio. From Phidias, through Platon, Kepler, Charles Bonnet to Roger Penrose, Golden Ratio was present in the world of science and art (Sen & Agarwal 2008, Akhtaruzzaman & Shafie 2011). Connections between nature and culture are indissoluble. Dependence between them can be proved in many cases. The fact, that we try to mimic nature is obvious and not surprising. In the space of centuries attitude to what the beauty is and where the beauty is hidden, has been evolving. Ancients claimed that the only beautiful and perfect thing on the world is nature, and the one thing we can do is to copy it - so excellence is in nature and in subject (ars simia naturae). I. Kant was first who said, that judgment of what is beautiful belongs to watcher (so basically is in one’s mind) (after Vetulani, 2009; Vetulani 2011, Gombrich 2009). However, nature always was and still is an inexhaustible source of inspiration. The fact, that nature inspires art and that art derives patterns from nature is indisputable. However, we find very interesting the fact, that many innovative patterns used in art are present in microscale.

Activity

We propose some options of lessons, depending on the age of participants.

Current Microscopy Contributions to Advances in Science and Technology (A. Méndez-Vilas, Ed.)

© 2012 FORMATEX 999

The first activity is based on the analysis of electronograms. Students are asked to assign shapes known from surroundings or art to those presented by microorganisms. In this way we create a map of associations, which reflect similarities between shapes present both in nature and in culture. Examples of such associations are shown at Fig. 1 -8. To some we give pictures that illustrate examples of associations from macroworld given by pupils. Art can be perceived as an experience of harmony. For our brain the most attractive are exactly those things, which are regular, symmetrical and proportioned. A little asymmetry can be attractive to us, but too much of it creates chaos (McManus, 2005; Vetulani 2011). The Rule of Golden Ratio (φ) was used already by ancients. They raised buildings and created sculpture on the basis of this rule. This straightforward rule says that two quantities are in the golden ratio (φ) if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one (after Akhtaruzzaman & Shafie 2011). Shape of chosen object in our world may be also described in this rule – such as for example an algal species. We ask participants to indicate, which of the shown objects fit to The Golden Ratio and use this ratio to describe chosen pictures (Fig. 5-8). Mathematics is commonly used by various branches of science. Therefore, we want the participants not only to see the original shapes of algae, but they also try to calculate their volume. This is done on the basis of methodological handbook (Hutorowicz, 2005). The pupils are asked to propose the method of calculation and then to verify their ideas with equations given by Hutorowicz (2005). Finally, we ask the students, if these shapes have any effects on functioning of algae. Whether they affect buoyancy or light absorption. Why are they not globular? By answering all that questions and those given by participants, we show, that biology, mathematics, physics are not “pure” sciences, with no transmission to other subjects and everyday life. This gives students overall vision and shows that various branches of science amalgamate and should not be isolated from each other.

Fig. 1. Asterionella sp. - algae that resambles wheelarms or a star.

Fig. 2a. Micropylar rosettae of moths (Agrotis segetum) strongly resamble rosettae from used as a pattern in windows, especially in churches (Fig. 2b) and palaces or a flower. Fig. 2b. Barcelona, Sagrada Familia, fot. R. Luciński



Fig. 3. Part of the compound eye, resembles honeycomb.

Fig. 4. Gential opening of Nenteria breviungiculata strongly resembles an iron.

a) b)

Fig. 5a. Fragilaria sp. resembles a wooden fence, an accordion or a piece of art (Fig. 5b). It may be described with The Golden Ratio rule as shown on a picture. Fig. 5b Barcelona, Sagrada Familia, fot. R. Luciński



Fig. 6. Ceratium sp., an algae belonging to the phyllum Dinoflagellata. The most often pupils describe it as “an Eifel Tower”. It may be described with The Golden Ratio rule as shown on a picture.

Fig. 7. Scale of the moth (Spodoptera exigua), presented on the micropyle. This shape is often used for this part of the workshop, where we ask pupils to show their associations to everyday-life objects. Usually pupils describe it as an oar or a wooden spoon. It may be described with The Golden Ratio rule as shown on a picture.



Fig. 8. Hydrobiological samples have often astounding shapes. This one most frequently gives association to a sandglass. It may be described with The Golden Ratio rule as shown on a picture.

Literature

[1] Akhtaruzzaman Md., Shafie A. A., 2011. Geometrical Substantiation of Phi, the Golden Ratio and the Baroque of Nature, Architecture, Design and Engineering International Journal of Arts 2011; 1(1): 1-22

[2] Gombrich E.H., 2009. Zmysł porządku. O psychologii sztuki dekoracyjnej. Universitas. Kraków [3] Hutorowicz A., 2005. Opracowanie standardowych objętości komórek do szacowania biomasy wybranych taksonów glonów

planktonowych wraz z określeniem sposobu pomiarów i szacowania. Olsztyn. Maszynopis. In Polish. [4] McManus I.C., 2005. Symmetry and asymmetry in aesthetics and the arts. European Review, Vol. 13, Supp. No. 2, 157–180 [5] Rybska E., Błoszyk J., Adamski Z. Introduction to electron microscopy – university educational programme for secondary

schools. (this volume) [6] Sen S.K., Agarwal R. P., 2008. Golden ratio in science, as random sequence source, its computation and beyond. Computers and

Mathematics with Applications 56 (2008) 469–498. [7] Vetulani J. 2009, Brain and art – lecture given on „Brain week“ at march 2009 in Cracow. [8] Vetulani J. 2011, Mózg-fascynacje, problemy, tajemnice. Homini, Kraków, pp 9-14. [9] Acknowledgement: We would like to express our thanks to dr hab. Elżbieta Szeląg-Wasielewska for SEM pictures of algae and

dr Robert Luciński for pictures taken in Sagrada Familia. Znalazłam takie:



the world we can see - a mirror of the microworld? · golden ratio in science, as random sequence...

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