Mathematical methods in biology. Relationship between mathematics and biology

COURSE PROGRAM

The main prerequisites for the introduction and dissemination of mathematical methods in biological research. Mathematization as an introduction standard language; mathematical methods - a tool for research and analysis.

Stages biological research and related mathematical methods. Statement and formulation of the research problem in biological and mathematical concepts, selection adequate method analysis of expected results and planning of the experiment (observation). Analysis of the results, presentation of them in a visual form, interpretation and - adjustment of the plan further research(and analysis).

Types of biological problems. Comparison and grouping of objects; distinction and separation of groups; determining the place of an object (group) in the previously described system (identification). Relationships and dependencies; features of process analysis.

Separation of signs (variables) into independent - factors and dependent - "responses"; quality and quantitative characteristics. Influence on the nature of the analysis of the features of the representation of features. Derived "secondary" features (indices, main components, etc.).

Multiple Comparison and its features. Basics analysis of variance; its differences and advantages over pairwise comparison. Requirements for initial data for one- and multi-factor complex; influence of deviations. Data transformation; transformation of non-uniform complexes. Hierarchical model of dispersion analysis, its features. Scheme with "repeated measurements".

Evaluation and interpretation of the results of the analysis of variance. Planning multivariate analysis of variance according to the full and reduced scheme; Greek square.

Multidimensional (multi-attribute) descriptions, tasks of a / selection of features and / or compression of information for the convenience of its presentation, b / study of the structure of relationships and dependencies in the complex of features.

Correlation analysis. Various communication measures; nonlinearity and methods of linearization. Link system analysis: correlation pleiades of P.V. Terentyev. Graphical way presentation and analysis of the results: maximum correlation path (=minimum spanning tree), sections of the correlation cylinder, dendrograms and dendrites (graphs).

Comparison of correlation matrices by the level and structure of links. Levels of organization of biological systems and connections between their elements. Variability and determinism of signs; bond strength and stability.

Fundamentals of factor analysis; factors are hidden variables. The order of calculations in the centroid method. Specificity of principal component analysis. New variables - factors, their use. “Ideal structure” and rotation of factors. Interpretation and graphical presentation of the results. Limitations of factor analysis ( linear model, additivity of variables). Factor analysis as a stage of research (evaluation of a set of features, grouping of features and objects, etc.). Rotation factors. R and Q-technique of factor analysis.

Regression analysis. Planning a regression experiment; the range of values ​​of the independent variable, the number and location of intervals. General requirements in the analysis of empirical dependencies (G.G. Vinberg, 1980).

Special cases of regression analysis: study of growth and reproduction (allometry, exponent, logistic curve, etc.), analysis of dose-response curves. Probit analysis and its advantages. Multiple regression.

Dynamic series (=time series). The main components of the series of dynamics, their selection. Estimation of randomness of successive values. Time series smoothing. Autocorrelation and cross-correlation.

Multidimensional descriptions.

Grouping multidimensional descriptions. Differentiation of groups during transgression according to individual characteristics. Principles discriminant analysis. Finding and using the discriminant function. Ability to use similar methods for many groups. Canonical analysis. Classification trees.

Quantitative methods of classification. Taxonomic and environmental issues classifications, their features. Use of quantitative and alternative representation of data. The main stages of the analysis. The most commonly used measures of similarity, their specificity. Features of asymmetric and correlation measures. Classification methods for equal and unequal weights of characters: taxonomic analysis by E.S. Smirnov, "numerical taxonomy" (Sokal, Sneath); phylogenetic methods: cladistic analysis (Wagner, Hennig, Farris).

Classification and ordination, "fuzzy sets" (A.Zade). Clusters and groupings with "occurrence". Analysis of similarity matrices. The simplest grouping (clustering) algorithms: nearest neighbor method, group average method. Definition of "threshold" at grouping; the dependence of the choice of procedure and results on the objective discreteness of groups, their volume and relations between groups; compactness of groups, their remoteness and the presence of transitions (distinctness and transitivity according to S.F. Kolodyazhny). Graphical representation results.

Analysis of the form and its variability - " geometric morphometry". Basic principles (Bookstein, Zelditch). Application area.

Resampling Methods. Application for evaluation in non-standard situations and for characteristics that do not have a statistical justification. Jackknife, bootstrap, Mantel test.

MATERIALS FOR LECTURES

Review

Repeat

Analysis of variance.

Component analysis.

Regression analysis

Classification


Matrix comparison

WORKSHOPS

Editing

Lesson 1

Lesson 2

Lesson 3

Session 4-1

Session 4-2

Lesson 5

Bibliography:

Urbakh V.Yu. Statistical analysis in biological and medical research, M, 1975.
Bailey N. Mathematics in biology and medicine, M, 1970.
Efimov VM, V.Yu. Kovaleva Multidimensional analysis of biological data. 2008. St. Petersburg. (ed.2, corrected and supplemented). 86 p.

ANOVA:
Rokitsky P.F. Biological statistics (any edition except the first), ch.8
Snedecor J.W. Statistical Methods applied to research in agriculture and biology. M. 1961.
Scheffe G. Dispersion analysis. M, 1980.
Upton G. Analysis of contingency tables. M. 1982

Factor analysis:
Okun Ya. Factor analysis. M, 1974.
Liepa I.Ya. Mathematical methods in biological research. Riga, 1980.
Iberla K. Factor analysis. M, 1980

Regression analysis:
Schmidt V.M. Mathematical Methods in botany. L, 1984 ch.6, §2-3
Urbakh V.Yu. (see above) ch. 8-9.
Alimov A.F. Introduction to production hydrobiology. L, 1989.
Draper N., Smith G. Applied regression analysis. M, 1973
Vinberg G.G. Conditions for the correct application of elementary empirical formulas in biology. Quantity methods in animal ecology, L., 1980, pp. 34-36

Rows of dynamics:
Lakin G.F. Biometrics. M, 1968, ch.7.
Kendall J. Time series. M, 1981

Discriminant analysis:
Urbakh V.Yu. (see above) ch. ten

Classification:
Duran B., Odell P. Cluster analysis. M, 1977.
Andreev V.L. Classification constructions in ecology and systematics. M, 1980.
Andreev V.L. Analysis of eco-geographical data using theory fuzzy sets. L, 1987.
Pavlinov I.Ya. Methods of cladistics. M, 1989

Planning
Urbakh V.Yu. (see above), ch.1
Nalimov V.B. Theory of experiment. M, 1971.
Montgomery L.K. Experiment planning and data analysis. L, 1980.

Shape analysis
Zelditch M. et al. “Geometric morphometrics for biologists” 2003: 444 pp

Resampling Methods
Efron B., Tibshirani R.. “An introduction to the bootstrap”. 1998

Mathematics in Biology Completed by 8b grade student Marina Goncharova School 457, St. Petersburg academic year


Biologists have been using mathematics for a long time. modern biology actively uses various branches of mathematics: probability theory and statistics, the theory of differential equations, game theory, differential geometry and set theory to study the structures and principles of functioning of living objects. Ilya Ilyich Mechnikov Russian biologist, developed the theory of immunity Alexander Fleming Scottish scientist, discovered penicillin Nikolai Ivanovich Pirogov Russian scientist and surgeon. Created the theory of evolution of life on Earth. James Dewey Watson Francis Harry Compton English molecular biologists. Discovered the structures of DNA molecules




The genetic code is a way of encoding the amino acid sequence of proteins using a sequence of nucleotides, characteristic of all living organisms. Statistical methods play an important role in deciphering genetic code, as well as in the preparation of chromosome maps. Alfred Sturtevant Made the first genetic map An example of a genetic map


Biochemistry Biochemistry is the science of chemical composition living cells and organisms and chemical processes underlying their life activity. In this science, the equations of thermodynamics are widely used. Novitsky Alexey Ivanovich Created the doctrine of thermodynamics biological processes. Ilya Prigozhy Created the so-called non-classical thermodynamics Josiah Willard Gibbs Creator mathematical theory thermodynamics


Biology and analytic geometry Geometry is often used in biology. Each research biologist must match his results to static criteria, and established relationships are usually depicted using curves from analytical geometry.


Automation of biological industries In the study and study of biological phenomena, scientists must be able to manage complex equipment, as well as process its readings. This requires knowledge of mathematics. MRI machine Used to take an image internal organs Electrocardiograph Determination of heart rate and regularity Artificial heart, an example of biomedical engineering.





mathematical biology is a theory of mathematical models of biological processes and phenomena. Mathematical biology can be classified as applied mathematics and actively uses its methods. The criterion of truth in it is mathematical proof. critical role it plays mathematical modeling using computers. Unlike pure mathematical sciences, in mathematical biology, purely biological tasks and problems are studied by the methods of modern mathematics, and the results have a biological interpretation. The tasks of mathematical biology are the description of the laws of nature at the level of biology and the main task is the interpretation of the results obtained in the course of research, an example is the Hardy-Weinberg law, which is provided by means that do not exist for some reason, but it proves that the population system can be and also predicted on the basis of this law. Based on this law, we can say that a population is a group of self-sustaining alleles, in which natural selection provides the basis. Then, in itself, natural selection is, from the point of view of mathematics, as an independent variable, and the population is a dependent variable, and under the population is considered a certain number of variables that affect each other. This is the number of individuals, the number of alleles, the density of alleles, the ratio of the density of dominant alleles to the density of recessive alleles, etc., etc. Natural selection also does not stand aside, and the first thing that stands out here is strength natural selection, which refers to the impact of environmental conditions that affect the characteristics of the individuals of the population that have developed in the process of phylogenesis of the species to which the population belongs.


Literature
  • Alekseev V. V., Kryshev I. I., Sazykina T. G. Physical and mathematical modeling of ecosystems; Com. on hydrometeorology and monitoring environment M-va ecology and nature. resources Ros. Federation. - St. Petersburg: Gidrometeoizdat, 1992.
  • Bazykin A. D. Nonlinear dynamics of interacting populations.
  • Bailey N. T. J. Mathematics in biology and medicine: Per. from English. - M.: Mir, 1970. - 326 p.
  • Bratus A.S. Dynamic systems and models of biology / Bratus A. S., Novozhilov A. S., Platonov A. P. - M.: Fizmatlit, 2010. - 400 p. - ISBN 978-5-9221-1192-8.
  • Zhabotinsky A. M. Concentration self-oscillations.
  • Ivanitsky G. R., Krinsky V. I., Selkov E. E. Mathematical biophysics of the cell.
  • Malashonok G.I. Effective Mathematics: Modeling in Biology and Medicine: Proc. allowance; Ministry of Education Ros. Federation, Tamb. state un-t im. G. R. Derzhavin. - Tambov: Publishing House of TSU, 2001 - 45 p.
  • Mathematical modeling of life processes. Sat. Art., M., 1968.
  • Menshutkin V.V. Mathematical modeling of populations and communities of aquatic animals.
  • Nakhushev A. M. Equations of mathematical biology: Proc. allowance for mat and biol. specialist. Univ. - M.: Higher school, 1995. - 301 p. - ISBN 5-06-002670-1
  • Petrosyan L. A., Zakharov V. V. Mathematical models in ecology. - St. Petersburg: Publishing House of St. Petersburg University, 1997, - 256 p. - ISBN 5-288-01527-9
  • Petrosjan L.A. and Zakharov V.V. Mathematical Models in Environmental Policy Analysis. - Nova Science Publishers, 1997 - ISBN 1-56072-515-X
  • Rashevsky N. Some medical aspects mathematical biology. - M.: Medicine, 1966. - 243 p.
  • Riznichenko G. Yu. Lectures on mathematical models in biology: Proc. allowance for students of biol. university specialties. - M., Izhevsk: R&C Dynamics (PXD), 2002.
  • Riznichenko G. Yu. Mathematical models in biophysics and ecology. - M.: IKI, 2003. - 184 p. - ISBN 5-93972-245-8
  • Riznichenko G. Yu., Rubin A. B. Mathematical models of biological production processes: Proc. manual for universities in the areas of "Applied. Mathematics and Informatics", "Biology" and special. "Mat. modeling". - M.: Publishing House of Moscow State University, 1993. - 299 p. - ISBN 5-211-01755-2
  • Mathematical modeling in biophysics. Introduction to theoretical biophysics. - M.: RHD, 2004. - 472 p. - ISBN 5-93972-359-4
  • Romanovsky Yu. M., Stepanova N. V., Chernavsky D. S. Mathematical biophysics.
  • Rubin A. B., Pytyeva N. F., Riznichenko G. Yu. Kinetics of biological processes.
  • Svirezhev Yu. M. Nonlinear waves, dissipative structures and catastrophes in ecology.
  • Svirezhev Yu. M., Logofet D. O. Stability of biological communities.
  • Svirezhev Yu. M., Pasekov V. P. Fundamentals of mathematical genetics.
  • Theoretical and mathematical biology. Per. from English. - M.: Mir, 1968. - 447 p.
  • Thorntley J. G. M. Mathematical models in plant physiology.
  • Fomin S. V., Berkenblit M. B. Mathematical problems in biology.
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  • Eigen M., Shuster P. Hypercycle principles of self-organization of molecules.
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Fundamentals of mathematical modeling

In this section of the course of lectures "Mathematical models in biology" are considered basic concepts mathematical modeling. On the example of the simplest systems, the main regularities of their behavior are analyzed. The focus is not on the biological system itself, but on the approaches used to create its model.

See also:

Topic 1: Integration of data and knowledge. Objectives of modeling. Basic concepts

Models and modeling. Classification of models. Qualitative (basic) models. Simulation models of specific biological systems. Mathematical apparatus. The concept of variables and parameters. Stationary state and its stability. Computer programs. Hierarchy of scales and times in biological systems. regulatory networks.

Topic 2: Models described by an autonomous differential equation

The concept of solving an autonomous differential equation. Stationary state and its stability. Population growth models. Continuous and discrete models. exponential growth model. Logistic growth model. The model with the smallest critical number. Probabilistic models.

Topic 3: Models described by systems of two autonomous differential equations

Sustainability research stationary states. Types of dynamic behavior: monotonous change, multistationarity, fluctuations. The concept of a phase plane. Model Trays ( chemical reaction) and Volterra (interaction of species).

Topic 4: Hierarchy of times in biological systems. Fast and slow variables

Tikhonov's theorem. Derivation of the Michaelis-Menten equation. Application of the method of quasi-stationary concentrations.

Topic 5: Multistationary systems

selection models. Application of the method of quasi-stationary concentrations. Switching models in biological systems. Trigger. Model of the synthesis of two enzymes Jacob and Monod.

Topic 6: Oscillatory processes

The concept of the limit cycle and self-oscillations. Autocatalysis. Types feedback. Examples. Brusselsator. Glycolysis. Cell cycle models.

Topic 7: Quasistochastic processes. dynamic chaos

The concept of a strange attractor. Periodic influences and stochastic factors. Irregular fluctuations in glycolysis. Chaotic dynamics in species communities.

Topic 8: Living systems and active kinetic media

Nonlinear interactions and transfer processes in biological systems and their role in the formation of spatio-temporal dynamics. Equations in partial derivatives of the reaction-diffusion-convection type. Wave propagation in systems with diffusion.

Topic 9: Dissipative structures

Stability of homogeneous stationary solutions of a system of two equations of reaction-diffusion type. Turing instability. Dissipative structures near the instability threshold. Localized dissipative structures. Types of space-time regimes.

mathematical biology is an interdisciplinary branch of science in which object of study are biological systems different levels organization, and the purpose of the study is closely linked to the solution of some specific math problems, constituting subject of study. The criterion of truth in it is mathematical proof. The main mathematical apparatus of mathematical biology is the theory of differential equations and mathematical statistics.

In contrast to purely mathematical sciences, in mathematical biology the results of research are given a biological interpretation.

see also

Write a review on the article "Mathematical Biology"

Links

Literature

Source -

  • Alekseev V. V., Kryshev I. I., Sazykina T. G. Physical and mathematical modeling of ecosystems / Kom. on Hydrometeorology and Environmental Monitoring, Ministry of Ecology and Nature. resources Ros. Federation. - St. Petersburg. : Gidrometeoizdat, 1992. - ISBN 5-286-01006-7.
  • Bazykin A. D. Nonlinear dynamics of interacting populations. - M.; Izhevsk: Institute of Computer Research, 2003. - 367 p. - ISBN 5-93972-244-X.
  • Bailey N. T. J. Mathematics in biology and medicine: Per. from English. - M .: Mir, 1970. - 326 p.
  • Belintsev B. N. Physical foundations of biological shaping / Ed. M. V. Volkenshtein. - M .: Nauka, 1991. - 251 p. - ISBN 5-02-014556-4.
  • Bratus A. S., Novozhilov A. S., Platonov A. P. Dynamic systems and models of biology. - M .: Fizmatlit, 2010. - 400 p. - ISBN 978-5-9221-1192-8.
  • Deshcherevsky V.I. Mathematical models of muscle contraction / Ed. acad. G. M. Frank. - M .: Science. - T. 1977. - 160 p.
  • Dynamic Theory of Biological Populations / Ed. R. A. Poluektova. - M .: Nauka, 1974. - 455 p.
  • Zhabotinsky A. M. Concentration self-oscillations. - M .: Nauka, 1974. - 178 p.
  • Ivanitsky G. R., Krinsky V. I., Selkov E. E. Mathematical biophysics of the cell. - M .: Science. - 310 s. - (Theoretical and applied biophysics).
  • Research in Mathematical Biology: Sat. scientific tr / Nauch. ed. E. E. Shnol. - Pushchino: PNTs RAN, 1996. - 192 p. - ISBN (erroneous) .
  • Malashonok G. I., Ushakova E. V. Effective Mathematics: Modeling in Biology and Medicine: Proc. allowance. - Tambov: TGU, 2001. - 45 p.
  • Murray D. Nonlinear differential equations in biology: Lectures on models: Per. from English. / Ed. A. D. Myshkis. - M .: Mir, 1983. - 397 p. Translation of ed.: Lectures on nonlinear-differential-equation Models in biology / J.D. Murray (Oxford, 1977)
  • Mathematical modeling of life processes: Sat. articles / Editorial board: M. F. Vedenov and others - M .: Thought, 1968. - 287 p.
  • Menshutkin V.V. Mathematical modeling of populations and communities of aquatic animals. - L.: Nauka, 1971. - 196 p.
  • Nakhushev A. M. Equations of mathematical biology: Proc. allowance for mat. and biol. specialist. Univ. - M .: Higher. school, 1995. - 301 p. - ISBN 5-06-002670-1.
  • Introduction to mathematical ecology. - L. : Publishing House of Leningrad State University, 1986. - 222 p.
  • Petrosyan L. A., Zakharov V. V. Mathematical models in ecology. - St. Petersburg. : St. Petersburg State University, 1997. - 256 p. - ISBN 5-288-01527-9.
  • Rashevsky N. Some medical aspects of mathematical biology: Per. from English. / Ed. acad. V.V. Parina. - M .: Medicine, 1966. - 243 p.
  • Riznichenko G. Yu. Lectures on mathematical models in biology: Textbook. allowance for students of biol. specialist. higher textbook establishments. - M.; Izhevsk: R&C Dynamics; RHD, 2002.
  • Riznichenko G. Yu. Mathematical models in biophysics and ecology. - M.; Izhevsk: Institute of Computer. research, 2003. - 183 p. - (Mathematical biology and biophysics). - ISBN 5-93972-245-8.
  • Mathematical biophysics. - M .: Nauka, 1984. - 304 p. - (Physics of life processes).
  • Romanovsky Yu. M., Stepanova N. V., Chernavsky D. S. Mathematical Modeling in Biophysics: Introduction to Theoretical Biophysics. - M .: RHD, 2004. - 472 p. - ISBN 5-93972-359-4.
  • Rubin A. B., Pytyeva N. F., Riznichenko G. Yu. Kinetics of biological processes: Proc. allowance for universities on special. "Biology": 2nd ed., Rev. and additional - M .: Publishing House of Moscow State University, 1987. - 299 p.
  • Svirezhev Yu. M. Nonlinear waves, dissipative structures and catastrophes in ecology. - M .: Nauka, 1987. - 366 p.
  • Svirezhev Yu. M., Logofet D. O. Stability of biological communities. - M .: Nauka, 1978. - 352 p.
  • Svirezhev Yu. M., Pasekov V. P. Fundamentals of mathematical genetics. - M .: Nauka, 1982. - 511 p.
  • Smith D.M. Mathematical ideas in biology: [with tasks and answers]: Per. from English: 2nd ed., erased / Ed. Yu. I. Gilderman. - M .: KomKniga; URSS, 2005. - 179 p. - ISBN 5-484-00022-X.
  • Theoretical and mathematical biology: Per. from English. - M .: Mir, 1968. - 448 p.
  • Thornley D. G. M. Mathematical models in plant physiology: Per. from English. / Ed. B. I. Gulyaeva. - Kyiv: Naukova Dumka, 1982. - 310 p. Translated from: Mathematical models in plant physiology / J. H. M. Thornley (London etc., 1976)
  • Eigen M., Shuster P. Hypercycle: Principles of self-organization of macromolecules: Per. from English. / Ed. M. V. Volkenstein and D. S. Chernavsky. - M .: Mir, 1982. - 280 p. Translated from: The hypercycle / M. Eigen, P. Schuster (Berlin etc., 1979)
  • Haubold B., Wie T. RHD 2011. - 456 p. ISBN 978-5-4344-0014-5
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An excerpt characterizing Mathematical Biology

– Yes, yes, I know. Let's go, let's go ... - said Pierre and entered the house. tall bald an old man in a dressing gown, with a red nose, in galoshes on his bare feet, he stood in the hall; seeing Pierre, he angrily muttered something and went into the corridor.
“They were of great intelligence, but now, as you will see, they have weakened,” said Gerasim. - Do you want to go to the office? Pierre nodded his head. - The office was sealed as it was. Sofya Danilovna was ordered, if they come from you, then release the books.
Pierre entered the very gloomy office into which he had entered with such trepidation during the life of the benefactor. This office, now dusty and untouched since the death of Iosif Alekseevich, was even gloomier.
Gerasim opened one shutter and tiptoed out of the room. Pierre walked around the office, went to the cabinet in which the manuscripts lay, and took out one of the once most important shrines of the order. These were genuine Scottish acts, with notes and explanations from the benefactor. He sat down at the dusty writing table and put the manuscripts in front of him, opened them, closed them, and finally, pushing them away from him, leaning his head on his hands, thought.
Several times Gerasim carefully looked into the office and saw that Pierre was sitting in the same position. More than two hours have passed. Gerasim allowed himself to make some noise at the door in order to draw Pierre's attention to himself. Pierre did not hear him.
- Will you order the driver to let go?
“Ah, yes,” Pierre said, waking up, hastily getting up. “Listen,” he said, taking Gerasim by the button of his coat and looking down at the old man with his shining, moist, enthusiastic eyes. “Listen, do you know that tomorrow there will be a battle? ..
“They did,” answered Gerasim.
“I ask you not to tell anyone who I am. And do what I say...
- I obey, - said Gerasim. - Would you like to eat?
No, but I need something else. I need a peasant dress and a pistol,” said Pierre, suddenly blushing.
“I’m listening,” said Gerasim after thinking.
Pierre spent the rest of that day alone in the benefactor's office, pacing uneasily from one corner to another, as Gerasim heard, and talking to himself, and spent the night on the bed prepared for him right there.
Gerasim, with the habit of a servant who had seen many strange things in his lifetime, accepted Pierre's relocation without surprise and seemed to be pleased that he had someone to serve. On the same evening, without even asking himself what it was for, he got Pierre a caftan and a hat and promised to get the required pistol the next day. Makar Alekseevich that evening twice, slapping his galoshes, went up to the door and stopped, looking ingratiatingly at Pierre. But as soon as Pierre turned to him, he bashfully and angrily wrapped up his dressing gown and hurriedly left. While Pierre, in a coachman's caftan, purchased and steamed for him by Gerasim, went with him to buy a pistol at the Sukharev Tower, he met the Rostovs.

On September 1, at night, Kutuzov ordered the retreat of Russian troops through Moscow to the Ryazan road.
The first troops moved into the night. The troops marching at night were in no hurry and moved slowly and sedately; but at dawn, the moving troops, approaching the Dorogomilovsky bridge, saw in front of them, on the other side, crowding, hurrying along the bridge and on the other side rising and flooding the streets and alleys, and behind them - pushing, endless masses of troops. And causeless haste and anxiety seized the troops. Everything rushed forward to the bridge, onto the bridge, into the fords and into the boats. Kutuzov ordered that he be taken around the back streets to the other side of Moscow.
By ten o'clock in the morning on September 2, only the troops of the rear guard remained in the Dorogomilovsky suburb. The army was already on the other side of Moscow and beyond Moscow.
At the same time, at ten o'clock in the morning on September 2, Napoleon stood between his troops on Poklonnaya Hill and gazed at the sight before him. From August 26 to September 2, from the battle of Borodino to the entry of the enemy into Moscow, all the days of this anxious, this memorable week, there was that extraordinary autumn weather, always surprising people, when the low sun warms hotter than in spring, when everything glitters in rare, clean air so that it hurts the eyes when the chest grows stronger and fresher, inhaling the odorous autumn air, when the nights are even warm and when in these dark warm nights golden stars are constantly falling from the sky, frightening and delighting.
On September 2, at ten o'clock in the morning, the weather was like this. The sparkle of the morning was magical. Moscow with Poklonnaya mountain spread out spaciously with its river, its gardens and churches, and seemed to live its own life, trembling like stars, its domes in the rays of the sun.
At the sight of a strange city with unprecedented forms of extraordinary architecture, Napoleon experienced that somewhat envious and restless curiosity that people experience when they see the forms of an alien life that does not know about them. Obviously, this city lived with all the forces of its life. By those indefinable signs by which, at a long distance, a living body is unmistakably recognized from a dead one. Napoleon from Poklonnaya Gora saw the trembling of life in the city and felt, as it were, the breath of this large and beautiful body.
- Cette ville asiatique aux innombrables eglises, Moscou la sainte. La voila donc enfin, cette fameuse ville! Il etait temps, [This Asiatic city with countless churches, Moscow, their holy Moscow! Here it is, finally famous city! It's time!] - said Napoleon and, getting off his horse, ordered the plan of this Moscou to be laid out in front of him and called the translator Lelorgne d "Ideville. "Une ville occupee par l" ennemi ressemble a une fille qui a perdu son honneur, [City occupied by the enemy , is like a girl who has lost her innocence.] - he thought (as he said this to Tuchkov in Smolensk). And from this point of view, he looked at the oriental beauty lying in front of him, which he had never seen before. It was strange to him that, at last, his long-standing, which seemed to him impossible, wish had come true. In the clear morning light, he looked first at the city, then at the plan, checking the details of this city, and the certainty of possession thrilled and terrified him.
“But how could it be otherwise? he thought. - Here it is, this capital, at my feet, waiting for its fate. Where is Alexander now and what does he think? Strange, beautiful, majestic city! And strange and majestic this minute! In what light do I present myself to them! he thought of his troops. “Here it is, the reward for all these unbelievers,” he thought, looking around at those close to him and at the troops approaching and lining up. “One word of mine, one movement of my hand, and this ancient capital des Czars. Mais ma clemence est toujours prompte a descendre sur les vaincus. [kings. But my mercy is always ready to descend to the vanquished.] I must be magnanimous and truly great. But no, it's not true that I'm in Moscow, it suddenly occurred to him. “However, here she lies at my feet, playing and trembling with golden domes and crosses in the rays of the sun. But I will spare her. On the ancient monuments of barbarism and despotism, I will write great words of justice and mercy... Alexander will understand this most painfully, I know him. (It seemed to Napoleon that the main significance of what was happening was his personal struggle with Alexander.) From the heights of the Kremlin - yes, this is the Kremlin, yes - I will give them the laws of justice, I will show them the meaning of true civilization, I will force generations boyars lovingly commemorate the name of their conqueror. I will tell the deputation that I did not and do not want war; that I waged war only against the false policy of their court, that I love and respect Alexander, and that I will accept peace conditions in Moscow worthy of me and my peoples. I do not want to take advantage of the happiness of war to humiliate the respected sovereign. Boyars - I will tell them: I do not want war, but I want peace and prosperity for all my subjects. However, I know that their presence will inspire me, and I will tell them, as I always say: clear, solemn and great. But is it really true that I'm in Moscow? Yes, here she is!
- Qu "on m" amene les boyards, [Bring the boyars.] - he turned to the retinue. The general with a brilliant retinue immediately galloped after the boyars.
Two hours have passed. Napoleon had breakfast and again stood in the same place on Poklonnaya Hill, waiting for the deputation. His speech to the boyars was already clearly formed in his imagination. This speech was full of dignity and that grandeur that Napoleon understood.

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