It has been well known for a long time that the metabolisms of smaller animals are faster when compared to the metabolisms of larger animals relative to their body size. In 1883, German physiologist Max Rubner tried to define a scaling principle based on the laws of thermodynamics and geometry. The metabolism of an organism works like a perfect machine that continuously converts one form of energy into others. It also releases energy while doing so. Metabolic speed can be described as the speed at which cells convert nutrients into energy. This energy is utilized for the execution of cellular functions and the construction of new cells.

Calculations have shown that the speed of metabolism is directly proportionate to body mass. For instance, the biomass of a hamster is eight times bigger than a mouse. According to this ratio, one would expect the metabolism of a hamster to be eight times faster than that of a mouse. Similarly, the body mass of a hippopotamus is 125,000 times larger than a mouse; therefore its metabolism would be estimated to be 125,000 times faster.

The problem is that a hamster generates eight times more heat than a mouse. Furthermore, the total body surface area, which is how the heat energy leaves the hamster?s body, is four times bigger than the surface area a mouse has. Consequently, as the body of an organism grows, its surface area develops more slowly compared to its mass.

This situation is shown in Figure 1. Here a mouse, a hamster, and a hippopotamus are represented in spheres. As the spheres get larger, their volume and surface area also gets bigger. In geometry we know that the volume of a sphere is given as? ?(r is the radius of the sphere). The surface area of a sphere is also expressed as . In this case we can say that while the volume of a sphere is scaled with the cubed radius, the surface area of a sphere is scaled with the squared radius. In other terms, the volume of a sphere is directly proportionate to the cubed radius, as is the surface area of the sphere to the squared radius.

Figure 1. The scaled features of a mouse, hamster, and hippopotamus. Taken from Complexity: A Guided Tour by Melanie Mitchell, Oxford University Press.

Figure 1 displays the first model used by scientists when the relation between metabolic speed, body mass, and surface area was being investigated. According to this early model, the association between body mass, surface area, and volume was studied with spheres that encased organisms. As the volume of the sphere approximately provided the volume of the organism, the sphere?s surface area also represented the surface area of the organism (of their skin). According to this, the radius of the sphere containing the hamster is nearly twice as large as the radius of the sphere with the mouse. Therefore, it can be claimed that the volume of a hamster is approximately eight times the volume of a mouse, and its surface area is four times larger. When it comes to the hippopotamus; the radius of the sphere is 50 times larger than the one with the mouse; this shows it has a 2500 times wider surface area and a 125,000 times larger volume compared to the mouse.

As it can be seen with these examples, while the radius of the sphere increases, its surface area does, too, but at a slower ratio compared to the volume ? in other terms, it gets scaled.

Based on this model, since the surface area is scaled (enlarged) with the square of the radius, and the volume with the cube of the radius, it can be estimated that the surface area is scaled with 2/3 the power of the volume.

The interesting point that all these rough calculations take us to is that the surface-area width of the living things is adjusted in a way to permit the release of energy they generate into their surroundings in a healthy pattern. If a hamster generated more heat than the amount corresponding to four times its surface area, this would lead to the hamster overheating.

In a similar way, if you elevated the heat in a hippopotamus, which generates 125,000 times more heat than a mouse does, by eight, the hippopotamus would suffer from heat exhaustion. This is because the surface area of a hippopotamus is only 2500 times bigger than a mouse. This is called the ?surface hypothesis,? and until it was discovered that it does not correlate well with the experimental data, scientists carried out investigations based on this model for nearly 50 years.

Around 1930, Swiss animal scientist Max Kleiber performed a series of studies involving the metabolic speed of various animals. The data he collected showed that the metabolic speed is scaled to ? the power of body mass, or Metabolic speed = body mass3/4.? This is called the power law in science. Instead of the 2/3 power in the first model, the correlation of 3/4 power with the experiments demonstrated that animals, especially large ones, have higher metabolic speeds than the first model predicted.

In summary, the establishment and maintenance of this equilibrium requires knowledge beyond geometric calculations, and makes it impossible to explain via random occurrences.?

In Figure 2, the scaling of different animals in regard to their body mass is charted. The horizontal axis shows the body mass in kilograms, whereas the vertical axis marks the speed of their average basal metabolism in watts. The symbols displayed as dots are real values measured from different animals and the fact that these dots align almost on a line show the correlation of the metabolic speeds of organisms with 3/4 the power of their body masses. This points to an extraordinary order in the universe, one that has been created with perfect harmony built into it. ?

One feature of the ?power law? is that when the two axes are drawn logarithmically, the relation between the two physical magnitudes appears as a line. Here, a similar situation is present and this power law is called the ?Kleiber Law.? This law successfully provides the metabolic speeds of mammals, birds, fish, plants, and even single celled organisms.

There are also other scaling relations pertaining to these that have confounded biologists for a long time. For example, the bigger a mammal is, the longer its life span is. There are examples, like humans, who do not fit into this general principle. However this is applicable for many mammals. The life of a mouse lasts two years, typically, whereas the life of a pig is around 10 years ? and elephants live for 50 years. If you chart the average life span of many different species across their body masses, the value of the power law is seen as ?. In other terms, for mammals, the average life span is scaled to ? of the body mass (directly proportioned).

As another example of proportion and scale, if you draw a graphic displaying how the average heart beat speed changes against the body mass of different species, you will once again find the scale of the power law to be ?. This means that the larger the body mass of a mammal, the lower its heart beat is.

Biologists are trying to solve the mysteries among the relations of many power laws like this one. There is no doubt among scientists regarding the fact that these power laws manifest certain common features in living things as an important sign pointing to the presence of very significant common features for all organisms.

Figure 2. Metabolic speeds of different animals according to their body masses. Taken from Complexity: A Guided Tour by Melanie Mitchell, Oxford University Press.

The creation of living things according to a power law, which is a relation between their metabolic speeds and body sizes, is a wisdom that requires thanksgiving. To safely release their generated energy, the metabolic speeds of living things must be scaled to ? the power of their body mass. A lower value would cause a higher body heat, and a higher value would lead to very low body heat. In both situations it would not be possible for organisms to sustain their lives in the physical world. Our bodies are perfectly scaled for us to survive.

Note

Experimental values were obtained from the book of – K. Schmidt-Nielsen, Scaling: Why is animal size so important?, Cambridge University Press, 1984.

Reference

• Complexity – A Guided Tour, Melanie Mitchell, Oxford University Press, 2009.

The answer to all of these questions relies on understanding certain laws in the nature. Every existence, from stars to trees, and living to nonliving, is an example of the systems in the palace of our universe.

Closed systems never engage in any exchange of matter, energy, or information with their environments. There is not any closed system in the universe. For example, a “thermos” can be a partial example of a closed system, since the liquid contained inside it does not get cold or warm quickly.

Open systems take part in matter, energy, and information exchanges with their environments. Human bodies, plants, and animals are each open systems. For instance, chemical reactions take place under our skin: enzymes constantly move, and blood is continuously flowing; via sweating, body heat is maintained; we exhale and inhale. We feed ourselves with food and beverages for our energy needs. Unwanted materials are excreted from our body.

These are necessary exchanges, but there can be exchanges for intangible realities such as ideas and love.

As a guide for understanding systems and as an indicator of irregularities, entropy finds its true meaning in the second law of thermodynamics. The entropy of closed systems increases up to a certain value and remains constant. The higher the entropy, the higher the level of irregularity.

For example, we are born in an organized state; however, as life continues, it drives our entropy higher and we leave this world at the maximum level of entropy. In other words, we posses a lower entropy when we step into this world. We mature as our entropy gets higher and we migrate into the other world with the ticket of death at the maximum form of entropy.

When the events inside and outside ourselves are halted, death becomes inevitable. It is through the uptake of materials from the outside world (oxygen, water, food, etc) that entropy slows down, so that we can sustain an average lifespan. An open system allows us to survive.

If we close the borders and cut our relations with the outer world, open systems are observed to generate entropy quickly, causing an internal disruption that may lead to death. Hadrian’s Wall of England, the Great Wall of China, and the Berlin wall of Germany can be presented as examples of detrimental functions. Similarly, the former Soviet Union was a closed system, and the hardships it caused are further evidence that such systems are not natural when they violate the second law of thermodynamics and they are not sustainable.

It is possible to talk about the entropy of any organization by looking at the level of its irregularity. A loss of variations or tensions within an organization, or an increase in the number of units, may cause an elevation of entropy.

When a living or nonliving organization approaches the moment of death, or all units become independent or equilibrated, entropy reaches its maximum value and control starts to diminish.

Conversely, if all units have a perfect interaction with the administrator and each other, this time entropy trends towards the ideal value, which is minimal, and irregularity in the system decreases.

The flow-use of energy and information is critical in organized structures such as a factory, corporation, school, government, or living organism. Upon the degradation of this state, entropy increases and efficiency decreases. If in this system there is not a structure in which information is stored, and no effective flow of information and energy is present at all stages of the hierarchy, the information from the lowest layer cannot pass through many units on its way towards the administration, and the information/energy flow among units becomes unhealthy. Entropy inevitably increases in such a process. Therefore, to ensure the proper sustainability of all organized structures, the vertical (hierarchic) and horizontal information-energy flow channels must remain open.

If work-based conflicts are experienced in between certain units in an organization (for instance, the same task is being carried out by several units) or certain jobs are being neglected, this situation refers to a major irregularity in terms of information-energy flow.

If a great portion of the power remains at the head of the structure, it is easier to make decisions and organizational efficiency is higher. The intensity of power at the lower layers of the organization therefore reduces the effectiveness of the structure, leading to chaos and disruption in information transfers.

If all units in the organization have the same authority and are equal, they are independent for all matters, this case may be classified as maximum entropy, in other words, the end of the organization.

Entropy and infinity

To understand entropy, one must consider its relation to infinity. Infinity points to a place, a situation in which an infinite amount of information is present. We can think of a book as low-entropy, organized structure where letters of the alphabet make up the words by joining together under certain rules. These words form sentences, and sentences compose chapters. Now let’s imagine that we cut the pages with a pair of scissors, and then remove words by cutting them away one by one, finally separating the words into letters. Now we are only left with a pile of letters.

At this moment, let’s ask the following question by looking at the letters collected on the table: “What do I have now?” The first answer that comes to mind will be “a pile of very scrambled letters.” But in fact, you own more than a pile of scrambled letters, since a high level of entropy also means a large amount of information.

The collection of letters on the table possesses a very large potential of information. With these letters, not only can the original book be assembled, but many books by combining the letters into different forms; this is just like in the Book of the Universe.

When the body of each organism that experiences death decays and disintegrates under the soil, it is separated into its letters – in a physical sense. Thus, each organism is converted into a potential form of information with its death. Then each part (letter) is employed for various tasks. In other words, the remnants of deceased organisms are used for writing different words, sentences, and books in the universe. This cycle points to an infinite amount of information, and infinity.

Conversion from state to state

We are moving in a state of flow towards a maximum state of entropy, carried by the execution of natural laws. In this process, almost everything is transformed from one state into another. Instantaneous renewal and growth occurs. There are parameters that we can affect in addition to the ones we cannot. For instance, once cells reach a specific size, they divide into smaller units and growth starts again. Firms, stars, and living things are like that, too. These are systems that lose energy (dissipative systems).

These systems are constantly transformed into newer states and certain dynamically-stable statuses are built. Transformations occur by arriving at branching points and many alternative states may be possible at these divergence points. Some of these states may be beneficial for the system, and some are not. However we do know that maximum entropy and making selections, whether good or bad, at the divergence points is a result of the second law of thermodynamics. For this reason, efforts to remain constantly in the stable states, which we describe as “balanced,” will mean death in some way. Try not to change, if you like. Eventually, you will witness your break down and degradation. We now recognize that human society should act as an open system. To be able survive many years, both materially and spiritually, then the exchange of information and energy should take place in a natural fashion. The spiritual guidance of the masters of faith and thought in human history teach us to be in compliance with this nature.

Furthermore, all these incidents remind us each time that balance in its absolute meaning does not exist in this world, and that it will be established somewhere else.

Reference

• Hershey, Daniel. 2010. Entropy Theory of Aging Systems, Imperial College Press.