Read here pertinent facts about someone whose work is critical to a proper comprehension of scale.


John Tyler Bonner is a biologist and Nobel laureate. His last book, "Why Size Matters", was an in-depth analysis of allometry, his research on the relationships between scale and biology.


"Size Rules Life" - Bonner, Why Size Matters, Introduction p.3

In fact, everything seems to be rushing around at amazing speed, both galaxies and elementary particles. It is the nexus of life and molecules where things are the slowest. The three phase states solid, liquid, gas, are defined by movement of molecules, and this movement carries the diffusion and entropy pumping essential to life. The smaller the molecule, the faster it moves. The largest molecules form the smallest living creatures. In this region of minimal speed of the material world we are in the realm of Brownian motion... In terms of size and speed, large molecules are more or less in the league of living bacteria, but keep in mind life took millions of years of evolution. - Bonner, Why Size Matters

Why Size Matters

In this book, Bonner gives his five rules of scale:
RULE 1 Strength varies with size.
RULE 2 Surfaces that permit diffusion of oxygen, of food, and of heat in and out of the body, vary with size.
RULE 3 The division of labor (complexity) varies with size.
RULE 4 The rate of various living processes varies with size, such as metabolism, generation time, longevity, and the speed of locomotion.
RULE 5 The abundance of organisms in nature varies with their size.

For a detailed discussion and charts, see Allometry.

Introduction by Bonner

John Tyler Bonner: Why Size Matters is published by Princeton University Press and copyrighted, © 2006, by Princeton University Press. All rights reserved.

In the seventeenth century it was held by some that inside a human sperm there was a minute human being—a homunculus—that was planted inside the womb. Development consisted of the miniature homunculus enlarging and passing through birth and on to maturity—just like infl ating a balloon. There were others, going back to the early ideas of Aristotle and the many who followed him, who took the view that vast changes in shape occurred between egg and adult, for it could be plainly seen that the early stages of development of any animal bore no resemblance to what came later.These two views frame the point I want to make in this book. In the case of the homunculus, shape is totally unconnected to size; as size increases shape remains unaltered. In the other case—now totally accepted—as size increases from egg to adult, the shape must change; there is no alternative.

Let me put the matter in another way. If an engineer is commissioned to build two bridges, one across the Hudson River and the other across a brook no more than 30 feet wide, it is quite obvious that the two bridges will be very different in their appearance. Even more importantly, they will differ in their construction and materials. These differences will have nothing to do with the artistic whims of the engineer, at least for the larger bridge: they are absolute requirements. Any attempt to build the Hudson River bridge with wooden planks would collapse into the water long before it was finished.The elaborate steel trusses and the carefully designed architecture of the huge bridge are demanded by the width of the Hudson—it is dictated by its large size. As we shall see, this perfectly mirrors what happens in living organisms; they too cannot escape the conditions set by size; they have no choice.

With these thoughts in mind, let me state the main argument of this book. Changes in size are not a consequence of changes in shape, but the reverse: changes in size often require changes in shape. To put it another way, size is a supreme regulator of all matters biological. No living entity can evolve or develop without taking size into consideration. Much more than that, size is a prime mover in evolution.There is abundant evidence for the natural selection of size, for both increases and decreases.Those size changes have the remarkable effect that they guide and encourage novelties in the structure of all organisms. Size is not just a by-product of evolution, but a major player. Size increase requires changes in structure, in function, and, as we will see, in other familiar evolutionary innovations. It requires them because they are needed for the individual to exist. Life would be impossible without the appropriate size-related modifications.

The subject of size has not been ignored in the past. Quite to the contrary, and as will be clear in the pages to come, there is a great literature on matters of size, beginning with the Greeks and bursting into flower with Galileo.This is true for the West, and no doubt there are similar traditions in other cultures.

However, the subject is always to some degree fragmented because it is generally introduced as an adjunct to some other biological phenomenon or property. For instance, the topic might be running speed, or rate of metabolism, or one of many other possibilities, and in the discussion of each of these phenomena the crucial role of size would be included. Many of the themes treated in this book can be found elsewhere. Here I wish to look at them from a different point of view—from the other end of the telescope—and show that the biological world revolves around size.

The mindset that size is not a central issue is quite understandable.To say an elephant is big says nothing about all the things that make an elephant: its anatomy, its physiology, and even its behavior.These are the aspects that draw our attention and the matters we want to study.Yet size is an overarching issue. Its effect is something that no organism, from the smallest bacteria to the largest whale, can escape. It governs their shape and all their activities in a way that is of fundamental significance. Size dictates the characteristics of all living forms. It is the supreme and universal determinant of what any organism can be and can do.Therefore, why is it a subject that always resides in the wings rather than center stage?

The main reason is that organisms are material objects while size is a bloodless geometric construct. Any object, whether animate or inanimate, will have a size. Airplanes, boats, or musical string instruments vary in size just like animals and plants, and in all cases their size and their material construction are totally different matters even though they affect one another.

That the role of size has been to some degree neglected in biology may lie in its simplicity. Size may be a property that affects all of life, but it seems pallid compared to the matter which makes up life. Yet size is an aspect of the living that plays a remarkable, overreaching role that affects life’s matter in all its aspects. It is a universal frame from which nothing escapes.

There are many things one wants to know about size, in particular those that concern its evolution. For instance, what is the evidence for my contention that size differences are a prime object of natural selection and are followed by changes in construction? What is the relation between size and internal complexity—that is, the division of labor—and, again, what is the evidence for which came first? What is the relation between size and the timing of all living activities such as the speed of movement of animals, or life span; and does size impose the timing, or the reverse? As we shall see, it is generally true that size is the prime mover: if size changes occur through the agency of natural selection, all those other matters must follow.

Outline Of Bonner's Book

Below are tags, notes, or headlines of the different parts of Bonner's book, in order of appearance. The list is included here to facilitate future, more in depth analysis
  • Telescope vs microscope, Galileo and Leeuwenhoek
  • Size of living things
  • Size and shape are inextricably connected
  • Weight-strength, rule 1: Strength <varies as> Weight ^ 2/3
  • Size and diffusion, rule 2: Surface <varies as> Weight ^ 2/3
  • Diffusion of oxygen into the blood. “the only way an organism larger than a millimeter can survive is to bring its interior near the surface everywhere so that no part is farther away than one millimeter.” P. 36
  • Gravity and cohesion
  • The effect of gravity becomes progressively insignificant the smaller an organism, while molecular forces come to the fore and play an increasingly important role. Even though these forces decline and rise smoothly as the size changes, one can artificially designate a critical point where one jumps from one world into the other. P.40
  • The force of attraction between molecules and the distance between the molecules on the two surfaces.
  • Reynolds number <varies as> (inertial forces) / (viscous forces)
  • Microscopic organisms live in a world of low Reynolds numbers.
  • To imagine it: imagine swimming in thick molasses in which one was not allowed to move one’s arms or legs faster than the hands of a clock.
  • Bacteria only appear to move quickly, a distortion of the magnification: they move exceedingly slowly. Since speed is distance divided by time.
  • Diameter <varies as> height
  • Size increases over geologic time
  • Size increased by becoming multicellular
  • Animals have a division of physiological labor (Henri Milne-Edwards). Durkheim applied it to society.
  • Size complexity is best investigated in slime molds and quorum sensing.
  • Enumerating cell types.
  • Size decrease in larger organisms: sometimes animals get smaller and decrease their number of cell types.
  • Number of cell types <varies as> size
  • Given a particular species such as animals, the change in size has the same number of cell types, but is accounted fro by lower metabolic rates. Animals have more cell types than plants: plants have a much lower metabolic rate.
  • Society: the larter a nation or community, the greater the division of labor.
  • Societies compete to improve their efficiency. They signal by memes and not genes.
  • Abundance: the greater the size of the organism, the fewer individuals there are in a geographic area.
  • Chart of visualizing animal abundance: by dividing the distance between organisms (B) and their diameter (D) it can be seen that over a size span of 7 orders of magnitude the ratio is moderately constant.
  • Size and time: a single bacterium may have its entire life cycle in half an hour, but a generation for an elephant takes 12 years and a giant sequoia take 60 years.
  • A huge elephant has about 25 heartbeats per minute, while the tiny shrew has 600 beats/minute. A shrew lives a year or two, an elephant 40 to 50 years; but the total number of heartbeats they have in their whole lifetime is approximately the same.
  • The total budget for their actions is the same.
  • Size and metabolism.
  • Mouse to elephant curve.
  • Size and song. Sound range of animals.
  • Size and generation time.
  • Longevity and size.
  • Size and speed.
  • The fastest animals are in the general neighborhood of one meter in length, and this is true for swimmers, runners, flyers.
  • Size and speed in the cosmos.
  • Size dictates locomotion.
  • Envoi, or code

Bonner 2006: Why Size Matters, by John Tyler Bonner, Princeton University Press, 2006

Links and References

A full treatment of Bonner's work appears in the article, Allometry.

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