To understand life and living organisms, the nature of the reality that surrounds us, mathematics plays a key role in lifting the veil to insight. It is a world of natural wonder and beauty.
Biology is the scientific study of life and living organisms. It is a broad natural science that encompasses a wide range of fields and unifying principles that explain the structure, function, growth, origin, evolution, and distribution of life.
Mathematics for exploring biology includes arithmetic and numerical computation, data handling and graphs, algebra, and understanding standard form and units to interpret biological data, model processes, and perform calculations related to phenomena like population growth or organism size. Skills like converting between units, using ratios, percentages, standard form, and drawing appropriate graphs are fundamental for biology at both the secondary and university level. More importantly, appreciation of mathematical concepts like the fibornacci sequence will assist in the esthetic and scientific appreciation of natural forms. The Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, 13...) appears in nature as an efficient growth pattern, seen in the spiral the beautiful arrangements of sunflower seeds, pinecone scales, and pineapple fruitlets, as well as the number of petals on many flowers (3, 5, 8, 13) and branching in trees.
Arithmetic and Numerical Computation
Conversions: Accurately convert between units for mass (grams, kilograms), volume (cm³, mm³), and length (meters, nanometers).
Ratios, Fractions, and Percentages: Understand and use these to express relationships, such as in inheritance or population studies.
Standard Form: Express and calculate using standard form, especially for very large or very small numbers, such as the size of cells or bacteria.
Data Handling and Graphs
Data Representation: Appropriately plot real-world biological data on graphs to draw conclusions.
Graph Interpretation: Understand how to read and interpret graphs, including those using log scales, which are increasingly used in biology.
Algebra
Equations and Models: Use algebraic expressions and equations to describe biological processes, predict outcomes, or model population dynamics.
Rates of Reaction: Apply algebra to predict and measure the rates of biological reactions.
Units and Magnification
Biological Units: Understand and apply appropriate units of measurement in a biological context.
Magnification: Use the magnification equation to calculate the real size of an organism or cell.
At a deeper level, the wondorous forms and processes of nature find their roots in mathematics which is not a static subject but an ever expanding field for formulating questions and developing mental imagery for the way things work which are so important in research and developing a nature esthetic.
Developing a natural aesthetic
The philosophy of the aesthetic is bound up with the study of nature and appreciation of its beauty. Mathematics is a mirror for that aesthetic. The conflict between the ideas of Hobbes and of Hume contine to play out in how we respect or fail to respect our natural world. These conflicting different basic aesthetics are at play in the geopolitical clashes of our time.
