The Physics of Giants and Dwarves

Introduction

I often hear people argue with seemingly convincing logic that the fact that we haven’t seen something doesn’t mean that it cannot exist and that it might someday suddenly show up. They say that the world is so mysterious and relatively unknowable that pretty much anything goes. This reasoning is applied, for instance, to the weird and exotic creatures that humans throughout history have conceived in their imaginations and have claimed to have seen occasionally. The scientific method and our knowledge of the laws of nature can be used to disprove the existence and viability of these creatures.

Fig. 2: Gulliver visiting the Kingdom of Lilliput.

Fig. 1: Norse dwarves fighting cranes.

If we are to fancy strange beings it seems natural and almost by default that we would start by enlarging and shrinking our own image, creating both, gigantic and miniature versions of ourselves, endowed with our proportions and our flesh and blood. We have of course done precisely that. Perhaps the most famous of them are the ones encountered by Gulliver during his travels to the kingdom of Brobdingnag, where people were 18-m (60-ft) tall giants, followed by his visit to the kingdom of Lilliput, where people were 15-cm (6-inch) tall dwarves.¹ There are also the giants mentioned in the Bible,² the giant gorilla and movie star King Kong,³ and the giant humans from the old TV series, Land of the Giants.⁴  My favorite human-like giant is, however, Polyphemus, the wine-loving cyclops, who lost his only eye at the hands of Ulysses after having eaten several of his men.⁵

As for other miniature humans, there have been plenty of them from cultures all over the world. We have, for instance, the famous dwarves of varying size from various Norse mythologies. We also have the angels that kept medieval scholars busy with their interminable musings about how many of them could dance on the head of a pin—the same angels that pushed the planets around their orbits until Newton found in inertia and gravity a perhaps more plausible explanation.⁶  From modern times we have, for instance, the shrunk medical team in Asimov’s Fantastic Voyage, who traveled through the bloodstream in their submarine, battling antibodies and ultimately saving the patient.⁷

Fig. 3: King Kong and Ann Darrow (Naomi Watts) in the 2005 remake of the original 1933 film.

The Physics of Scale

In order to discuss the possible existence of these out-of-the-ordinary creatures we will first need to understand a little about how the dimensions of an object change as we scale it up or down, and how each change affect its physical properties.

Fig. 4:  Linear, Surface Area, and Volume comparison of a cube as it becomes enlarged. As an interesting digression, note that moving a line generates a surface area, moving a surface area generates a volume, but moving a volume... generates more volume. We seem to be stuck in three dimensions.

Let us start with a simple geometry by studying a symmetrical object like a cube. Say that we have a cube, 1 cm on the side. The surface area covered by it is 1 cm² and the volume of space occupied by it is 1 cm³. If we expand it uniformly in space by doubling its length in all directions we get a cube that is twice as long, but now covering four times as much area and occupying eight times as much volume. This new cube will, therefore, weigh eight times as much as the original cube. If we now triple the linear dimensions of our original cube, we will get an expanded one that covers nine times as much area and occupies 27 times as much volume as our original cube, as shown in the picture on the right. We can now see how if we increase the linear dimensions by only ten times, the new cube will cover a surface area 100 times larger and will weigh 1,000 times more than the original cube!

Notice how as we increase the length of an object, making it longer in every direction, its surface area and its mass and weight don’t increase in the same proportion, but rather become much larger. These two and three-dimensional changes occurring when objects are scaled up and down have all kinds of intuitively unintended consequences. The physical properties of the object, and its biological ones if we are referring to a living being, take values that are very different than the ones from the original object—and the larger the contraction or the expansion, the more drastic the changes. Examples of properties that are affected by scale are strength, weight, and energy-related processes.

The first person that wrote about scale was the 17th-century Italian Natural Philosopher, Galileo Galilei.⁸  He, along with others, noticed how the scaled-up, real-size machines with their many moving parts tended to break down much more often than their perfectly working little models.

Armed with this new dimensional understanding of scale we can now discuss how the existence and viability of human-like entities depend on the values taken by their physical and biological properties.

Fig. 5: Galileo Galilei's title page of his controversial book, "Dialogo sopra i due massimi sistemi del mondo," transl."Dialogue Concerning the Two Chief World Systems." Shown on Stefan Della Bella's frontispiece are Sagredo(the open-minded friend), Salviati(Galileo), and Simplicio(the pope, perhaps), dialoguing about how the heavens go about, or how one goes to Heaven, depending on the reader's point of view.

The Gravity of Strength

Anybody that has ever used a rope to pull a load or support a weight intuitively understands that there are limits as to what a given rope can pull or support before completely breaking up.

Fig. 6: Rope about to break.

The strength of a rope depends on two factors; namely, the material and the thickness of the rope. Ropes are made by simply twisting and braiding together many threads of a strong and flexible fibrous material. For a given material, if you want a rope that is twice as strong you can simply use two ropes together; three times as strong, three ropes, and so on. 

Fig. 7: 3-D structure of a carbon nanotube.

With ropes, as with so many other things in the history of humanity, we were initially limited by the natural resources around us, before graduating to materials derived from our scientific and technological advances. In the old days, ropes were made of natural fibers derived from plants, such as hemp and cotton, or animals such as sheep and silkworms–and spiders if we could have gotten away with it. Today, they are manufactured out of much stronger synthetic fibers, such as nylon, polyester, and other polymers. Tomorrow, they will be made out of nanofibers, such as superstrong carbon nanotubes.

Ropes are flexible, rather than rigid, so they are used exclusively for pulling and connecting.

Fig. 8: A supporting pilaster.

We use columns, beams, arches, and so on, for pushing and supporting the weight of the structures that we built, such as houses, buildings, and bridges. However, just as with ropes, the weight and push that they can bear depend on material and thickness.

For most of our history we built our structures out of trees and rocks. But practical wooden structures that fulfill our needs start to buckle as the wood piles up, finally failing under the unforgiving gravity, when the linear dimensions reach about 15 meters (50 ft). For stone structures the practical limit is about 30 meters (100 ft). It has been only within the past century, with the invention of reinforced concrete and I-shaped steel beams that we’ve been able to build structures that are much larger than a few tens of meters.

However, gravity always wins; even with today’s high-tech synthetic materials, deep mechanical understand- ing, and clever designs, there is a practical limit of just several hundreds of meters for the size of structures. Aside from flat bridges, no structure, hollow or solid, has ever made yet by humankind that is nearly close to a thousand times our own height (i.e., say about a mile, 1,609 meters).⁹  However, the current exponential growth of knowledge with its mind-boggling consequences indicates, arguably, that those limits will be a thing of the past within a few decades.¹⁰ 

So how about biological entities such as animals? What supports their weight and provides for their overall strength and mobility?  Mechanically speaking, animals can be viewed as moving structures with a supporting, light framework made out of various minerals.

Fig. 9:  Exoskeleton of an ant.

Shelled animals and insects have external skeletons that give them shape, aid them in motion, and protect their internal organs. Reptiles, birds, and mammals have, on the other hand, internal skeletons, based on a long chord with protruding extremities.

Fig. 10: Skeletons of mammals, reptiles, birds, and fish.

These internal scaffolds are made out of cavities and
jointed bones. The cavities protect vital organs such as the brain, heart and lungs. The hundreds of bones, along with the connected muscles, ligaments, tendons, and cartilage, give the animal shape, support, strength, flexibility, and ability to move. The bones move because they are attached to the muscles, whose cells twitch as they receive commands from, and send feedback to the brain, via the electrochemical wiring of the nervous system. Just as with the ropes and columns, the strength of a bone is directly proportional to its thickness. To understand this intuitively think for instance of the thigh bone or femur, the longest and thickest bone of a mammal.

Now let us see what happens when we expand our human to gigantic dimensions. If we augment the linear dimensions 10 times (i.e., our human giant’s height, fingers, nose and so on are ten times longer), the surface area of her skin will be 100 times larger and her bones 100 times thicker. Her volume will be 1,000 times larger, so that she will be supporting and moving around 1,000 times more weight than the original human.

Imagine that your neighbor Mary, who weighs 70 kg (154 lb), suddenly and magically becomes 10 times taller. Now you have 1,000 Mary's, her weight being now 70 tons!  And you thought she was overweight before. That presents us with an insoluble situation. Her weight has increased 1,000 times, but her strength has increased only 100 times, as given by the corresponding increase in bone thickness. Therefore, if she could exist, she would feel like she was carrying nine extra people on top of her! If we were actually able to construct this giant human of flesh and bone with the exact same biology as ours, she wouldn’t survive, just on the basis of strength, her bones breaking, the doomed giant crushing under her own weight.

Evolutionarily speaking, this is one, among other drastic limitations, that prevent humans as a species, from growing much larger than its present overall size–short of changing their water/carbon-based biology, its shape, or both. Furthermore, since we all have a common origin and share the same biology, we can also study other animals that are closely related to each other and see what happens as size goes up and down. All mammals, for instance, are made pretty much of the same kind of flesh and bone and share many anatomical features.

Fig. 11: Note the stocky, columnar legs of this baby elephant, and of his mother's.

Galileo was the first one to do exactly this. He compared the leg bones of a gazelle and a bison, both mammals of the deer family.¹¹  He noticed that the bison’s leg bones were disproportionally thickened, as compared to the equivalent gazelle's bones. The bison cannot grow to be so heavy and at the same time keep the graceful figure of the gazelle. A  glaring example of this needed disproportion is the stocky legs of an elephant, as shown in the figure.

Please note that it is not that human-like giants couldn’t exist, in principle, and up to a certain extent. It is simply that they would be completely different than the known human; i.e., same shape and proportions as ours, but bones of a superstrong, non-biological material; or same biology, but with a drastic change in proportions, becoming squatter and broader as the size increases.  James Trefil, a noted American physicist and author, has pointed out for the sake of argument, that if we want to design a gravitationally viable, flesh, bone, and blood human giant, five times as tall as we are, it would weigh roughly twice as much as an elephant (12 tons), and look more like a Sherman tank than a person, 9-ft tall, 8-ft from front to back, and 16-ft wide!¹²

How about if we go down in size? If we were to become Lilliputians 10 times smaller in our linear dimensions, our bone thickness would be 100 times smaller and our weight would be 1,000 times smaller. Our strength wouldn’t go down as much as our weight by a factor of 10. These miniature humans would feel very light, being able to easily piggy back nine of their friends before feeling like we do just carrying our weight. Their bones would be comparatively very strong, defying gravity to a great extent, merrily jumping around while supporting very large loads, without breaking a leg or hurting their backs.

A cat can easily jump from a second floor to the ground and survive unscathed.  But a human or a horse trying to do the same thing will easily break a leg. A roach can jump distances that are hundreds of times their body lengths and hit the ground running and an ant can carry along several times her weight.¹³

Of course we could also change gravity, instead of changing bone strength. Remember for instance how Neil Armstrong jumped around effortlessly with his terrestrially-evolved bones on the low-gravity Moon.¹⁴  We’ll see this in fiction too. I heard that Superman’s original planet, Krypton, was much more massive than Earth, so that he felt so light in his adopted planet that when he tried to walk, he jumped, and when he tried to jump, he flew.¹⁵

Fig. 12: Blue whale skeleton.

The largest animal species that has ever existed is alive right now. It is the blue whale, easily weighing 150 tons. But the only reason that it can grow so large is that its whole weight is being supported by water. Whales actually sometimes get stranded on land, closed to shore or by a coral reef, suddenly feeling part of their weight, unable to lift their ribs and breathe, eventually dying of suffocation.

Fig. 13: Some trees going nowhere.

How about trees? They are also biological entities, share a common origin with us, and just like us are made out of cells full with water. So how come that, as opposed to us, some of them can grow up to be over 100 m? Because a tree is a column in itself: solid, sturdy, and well-rooted in the ground. The big and tall trees are solid structures made out of mostly dead cells with thick walls. Furthermore, and very importantly, short of extending its roots, a tree doesn’t have to go anywhere to get its food and reproduce. Therefore, it doesn’t have to deal with the significantly larger, multiplying forces associated with motion common in animals. It is as if you were to spend your whole life, lying in bed, like a vegetable, or watching TV, like a coach…potato. (Of course let us not forget that we cannot live without plants, as explained below.)

Eating for Energy

Another property whose importance varies as we scale a biological entity is the energy associated with metabolic processes. Metabolism has to do with the chemical reactions that occur in the cells of living organisms and that are needed to maintain life. All the energy needed to drive these processes in plants and animals ultimately comes directly and indirectly from the sun. Plants get their energy from the sun. Animals get their energy from eating plants, or from eating animals that eat plants. Just as wood burns with oxygen, producing carbon dioxide, water, and heat, animals, at the cellular level, burn digested food with oxygen, producing carbon dioxide, water, and heat. This heat provides for the energy needed to drive the animal’s metabolic functions.

Animals are like furnaces that must be kept running within a given range of temperatures in order to operate. Cold-blooded animals like insects and reptiles run at temperatures close to their surroundings and obtain some of their energy simply by basking on the sun. Warm-blooded animals run in general at higher temperatures than their surroundings, need much more energy to operate, and derive practically all of it from eating plants and/or other animals. Their bodies are constantly losing heat to the environment, given that they run at higher temperatures than their surroundings and that heat always flows from the highest to the lowest temperature. Warm-blooded animals have evolved various mechanisms to regulate their temperature and keep the heat in, losing as little energy as possible, by developing on their surfaces (skins), insulating materials such as feathers, fur, and hair. In our case, we tamed fire and started covering our skins with furry skins from other animals, and much later from fibrous plants, as we moved into higher, colder latitudes. We have lost some of our hair and most of our fur.¹⁶

Now, it is easily understood that the energy stored in food is proportional to its mass; e.g., two slices of pizza have twice as much energy as one slice, and so on. It is also true that the energy lost by an animal is roughly proportional to the surface area of its skin. The amount of energy, and consequently the amount of food needed by an adult animal, is roughly proportional to the surface area of its body, given that it is mostly through its skin that the animal loses its heat.¹⁷

We are now ready to discuss what would be the food needs of our giant. If her linear dimensions grew ten times, her surface area is now 100 times larger, and her mass is now 1,000 times larger than ours. She will have to eat now 100 times as much food as before, given that her food needs are proportional to the surface area of her body (L²). Therefore, she will have to process, proportionally speaking, only 1/10 as much food as the regular-size human. As an example, if one slice of pizza fulfills the needs of the regular-size human, the giant will need only 1/10^th of the scaled-up pizza, since the new pizza mass is 1,000 times larger, but the giant energy needs are only 100 times larger. The giant will have an easy time feeding herself, having to eat ten times less often than the regular-sized human.

But look what happens to the dwarf shrunk 10 times linearly. Her energy (food) needs are 100 times lower, but her mass is now 1,000 times smaller. Therefore, proportionally speaking, she will need to eat 10 times as much food as the normal human to fulfill her energy needs. Following our pizza example, she will need 10 pizza slices, given that her pizza slice is 1,000 times smaller, but her energy needs went down only 100 times.  She must have to eat, digest, and metabolically process, proportionally speaking, ten times as much food as we do. That is of course an impossibility, under the assumption that this dwarf has the same biology as ours.

Fig. 14: Humming bird looking for nectar.

Fig. 15: Hippos cooling off at Lake Manyara National Park, Tanzania.

On the other hand, large mammals need much less food in proportion to their body masses, and actually have trouble getting rid of excess heat. A large hippo spends a great deal of time cooling off in water and an elephant has big ears to help radiate some of the excess heat, not to mention that neither of them has insulating fur, both running around naked.¹⁹ ( To be sure, of course there are other factors, so the ear, skin, cooling comparison should be made to other mammals that live in the same hot tropical temperatures.)
Cold-blooded animals, such as insects, reptiles and amphibians, live slow, lethargic lives, eating less often.
A snake gets a good meal and is done for a week or two. There are only few warm-blooded animals much smaller than a mouse or a hummingbird, but there are plenty of small cold-blooded insects and amphibians.

From the Microscopic to the Astronomical

We have seen so far that as we scale objects up or down (L¹), their surface areas (L²), and volumes (L³), don’t scale in the same proportion.  In the previous two sections we scaled living beings up and down and discussed how these unproportional dimensional changes affect properties like mechanical strength and energy needs.

As we scale an object down from everyday sizes, surface effects become very noticeable, but gravitational effects become negligible. Conversely,  as we scale an object up, surface effects tend to lose importance, whereas gravitational effects become formidable. This explains wide-range phenomena such as, for instance, why cells are so microscopic to the point that we have trillions of them; why humans in higher, colder latitudes evolve to be taller and/or bulkier; or why the earth is still geologically active, whereas the moon is full of old craters, and has been “dead” for three billion years.

As we have seen, these dimensional effects apply to all objects, including living beings, given that inert and living matter are subject to the same physical laws. Let us look for instance at energy- and strength-related changes as we scale up objects to astronomical sizes, like those of satellites and planets.

1. Energy-related effects: First let us look at how the volume-to-area ratio of an object changes with size. Take a symmetrical figure like a sphere. The volume-to-area ratio is given as follows,
This is usually expressed by saying that the ratio of volume over area is directly proportional to R. This means that, as the sphere grows in size, its volume grows faster than its surface area. As an example, for a sphere of radius 10 meters, V/A = 1/3 x 10 = 3.3, whereas for a sphere of radius 20 meters, V/A = 1/3 x 20 = 6.7.²⁰

Take astronomical bodies like the planets and satellites of our solar system. They were formed 4.5 billion years ago out of the leftover debris from the rotating cloud of gas and dust that became our star, the sun. Due to the attractive gravitational force, billions of pieces of revolving debris aggregated into ever larger chunks of matter, forming increasingly larger masses.These rotating lumps of matter in turn swept more debris in their revolution around the new sun, colliding and capturing more large chunks as they became gravitationally stronger, ultimately forming hot molten spheres that eventually solidified into the planets and satellites of our solar system.

The geological activity that shapes the planet’s surface is a direct consequence of all the heat energy coming from the interior towards the much colder outer space. As we saw above, the ratio of volume-to-surface area (V/A) becomes larger as R increases. The heat stored in the planet's interior is proportional to its volume, whereas the capacity to lose that heat is proportional to its surface area. Therefore, the bigger the planet, the more difficult it is for it to get rid of its stored heat, just in the same way that a large potato takes longer to cool off than a small one. As a matter of fact, one cools the potato off by cutting it into pieces, therefore increasing its surface area while keeping its volume the same.

Fig. 16. The moon, showing its many old craters.

The moon, having a diameter about a quarter of earth's diameter, lost all of its heat long ago, whereas the much larger earth is still hot today. That is why our planet’s surface keeps changing, through mountain formation, earthquakes, volcanoes, and so on, while the moon has been a dead rocky sphere, its surface exhibiting the same old craters formed from asteroid collisions happening mostly three to four billion years ago.²¹  We have talked about how heat energy in an elephant or a planet has relatively little surface area to get out. Conversely, if the outside is warmer and the inside is colder, there is in the same way comparatively little surface area for the heat to get in. As a suggestion, for instance, if you live in a place that snows, make a very large snow sphere and have fun seeing how many weeks it takes before it melts completely.

2. Strength (Gravitational) effects: The strength of the gravitational force, with all of its consequences, is proportional to the masses involve. The shape of everyday masses, whether we are talking about the occasional kilometer-size asteroid that hits the earth, a human, or a bacterium, is dominated by the electromagnetic force. However, as the masses become literally astronomical, the gravitational force becomes the overriding force, to the point that mostly any object larger than about 1,000 kilometers is forced into the shape of a sphere.

Fig. 17:  Phobos, Mars' potato-shape, largest satellite.

All masses comprising an object attract every other mass with a strength that depends on the value of the masses and of the distances among them. As an object grows in mass, the mutual gravitational attraction of all the masses becomes increasingly larger, eventually overcoming the strength of the materials (i.e., the electromagnetic force) from which the body is made. As the objects grows to hundreds of kilometers, the pull towards its interior becomes increasingly larger, tending to smooth out any large lumpiness on its surface. Since the gravitational force doesn’t have a preferred direction, as the object grows larger, the “wrinkles” on its surface are smoothed out in all directions at the same distance equally. The ultimate outcome of this process is the symmetrical shape of a sphere, whereas the distance from the surface to the geometrical center of the object becomes the same in all directions in space.

For the typical rocky kind of materials found in the solar system, with densities of the same order of magnitude of water (say a few g/cm³),²² that lower limit for an object's shape to become spherical is close to 1,000 kilometers. It was recently found that the smallest rocky object of the solar system, that already looks more like a sphere rather than a potato, is Ceres, our biggest asteroid, with a diameter of about 960 kilometers. That spherical threshold diameter goes down as more mass is packed per unit volume. An astronomical chunk made of osmium, the densest element, would become spherical at just a few hundred kilometers, and the incredibly dense neutron stars have not only diameters of just ten kilometers or so, but also amazingly smooth surfaces.

Fig. 18:  Diameter comparison of Ceres (950 km), Moon (3,476 km) and Earth (12,742 km).

Philosophical musings

The Universe is an eminently mysterious place, with some of its most intractable secrets perhaps destined to remain forever hidden from us. Nonetheless, the Universe lends itself to be understood; as Einstein said it, “one of the most incomprehensible things about the Universe is that it is comprehensible.” Its behavior "follows" what we called the Laws of Nature, rules that can be understood by us, and that as far as we have seen–and we have seen far, apply equally all over the Universe.

We remained for most of our history very ignorant about the workings of the Universe, down to the most basic knowledge of it. We did our best to understand ourselves and the world around us, but somehow, for a very long time, we were bogged down by superstition, unable to come up with a sound and systematic method of rational inquiry that would allow us to unravel its secrets and enable us to manipulate it.

When we heard thunder, it was the gods being angry at us. When we saw someone suddenly falling to the floor, unwillingly contorting his body and foaming at the mouth, we thought of it as perhaps a punishment for a victim’s misdeed, a curse imposed by gods or evil spirits, now taken possession of his body. Today we know better:  We understand sound, electricity, and animal physiology as explainable and interrelated natural phenomena. In short, for me—or for my cat if he could understand it, thunder comes from a brain recording the sudden motions of air made by the energy released by a huge electrical spark generated by two large charged bodies, and the unwilling contortions of an animal come from the electrochemical workings of its body going haywire due to an abnormal increase in its brain's electrical activity.²⁴

The Scientific Method has demystified the world around us, so that, gradually and inexorably, all kinds of things that at some point were the realm of the supernatural have now become part of the natural world. There is a whole lot of knowledge that we have acquired over the past few centuries, from things that we had all wrong to things that we knew nothing about. Twenty-first century humans may choose to embrace that new knowledge with due scientific skepticism, or pick and choose whatever fit their inclinations and whims, by reason, ignorance, or apathy.

There are degrees of doubt in what we have learned about the world. There are a few fundamental questions that remained so far completely unanswered, and then there is a full spectrum of questions whose answers’ reliability go from the doubtful to the indisputably certain. On the one hand, we know practically nothing about the ultimate origin of the (multi)universe, and as someone said it, for all we know, our (own) universe might be a high school project from a kid from an advanced civilization in another universe.²⁵ On the other extreme, there are things that we had all wrong, but that now we know with complete certitude. For instance, we do know that the neurological condition known as epilepsy has nothing to do with spirits possessing the body, and actually, within the next few years we are most probably going to understand everything about it, down to its ultimate details. Many thought that the earth was flat for thousands of years and nobody could disprove them completely, but now, since 1961, we have actually seen its roundness from afar, with our own eyes.²⁶

I am a learner and teacher of science and have noticed that there is a lot of misinformation about scientific knowledge in the popular media. In particular, I have heard several times in pseudo-scientific movies how when something strange happens, the answer given as perfectly reasonable is that the universe is so mysterious that the strange phenomenon must be something supernatural. This is in general a fallacy, a misconception resulting from incorrect reasoning, appealing to ignorance, rather than understanding. Our understanding of the laws of nature allow us to distinguish the plausible from the impossible, so that no matter how weird something appears to be, we can usually say a lot about it, rationally and scientifically. If one claims that some phenomenon or entity might exist, that claim has to at the very least pass an argument of physical plausibility. You might have an ontological argument (of existence) only to the extent that whatever you claim to exist does not violate the laws of nature.

If something violates the laws of nature, then we know that it cannot exist. If it does not violate the laws of nature, then it might or might not exist. You would then have to use other rational arguments common in nature and related to physical plausibility, like reproducibility, simplicity, similarity, symmetry, predictability derived from physical or mathematical models, and so on. And still it might not exist!  In the end it reduces to what Carl Sagan famously said: “Extraordinary claims require extraordinary evidence.” And the more extraordinary the claim, the most rigorous and conclusive the evidence need to be, given that it is so far from ordinary reality.

This brings us full circle back to our topic of human-like giants and dwarves. For instance, we can say conclusively and without any doubt, that King Kong, a giant gorilla, ten times larger, a thousand times heavier, and with the same biology as the normal one, does not and can not ever exist in our known universe. Period. Some people might find certain intellectual arrogance in such a statement. But it is a rational and scientific statement, for whatever rationality and science are worth to the reader. Compare and contrast that with the possible arrogance of saying that something exists, but backed only by wishful thinking, flying in the face of the natural laws. Note that we can still indulge in believing in anything supernatural and get away with it, but only provided that we start with the premise that whatever we are concocting is outside of Nature, so that its existence cannot be disproved within the confines of the physical world.

There are other related philosophical implications whose discussion is beyond the goal and scope of this knol, but which my kind reader may explore if she or he chooses to do so. My goal was to provide some food for thought as to the physics of scale, while clearing up some common misconceptions and showing some of the incredible explanatory and encompassing power of scientific inquiry. 

Video 1:  This video illustrates how an object cannot be simply scaled up or down, with its properties and overall behavior remaining unchanged: Gravity will be too much and structural failure will quickly ensue, if a normal-size plane made of known materials were to try any of the turns, twists, and graceful pirouettes that Benoit Dierickx's model airplane displays effortlessly.

Notes

1a.  The plural of dwarf, according to English usage, is dwarfs, when referring to Medicine (dwarfism) and Astronomy (brown dwarfs); and dwarves, when referring to the fictional beings, as described in the folklore of so many cultures.
1b.  From the 1726 classic of English literature, “Travels into Several Remote Nations of the World, in Four Parts. By Lemuel Gulliver, First a Surgeon, and then a Captain of several Ships,”  by Jonathan Swift. Most famous for his satirical view of life in eighteenth century England. See also the readings below for bibliographical information.

2.  Deuteronomy 3:11. See also the readings below for a link to a detailed commentary on the Giants of the Bible.

3.  King Kong’s size has varied over the years from 18 to 60 feet tall.

4.  Check www.hulu.com to see free reruns of the 1968-1970 television program Land of the Giants.

5.  In Greek mythology cyclopes were giants with a single eye in the middle of their forehead. Polyphemus was the most famous cyclops, since he had a sad encounter with Ulysses when the latter visited the former’s island. See also the readings below for an account of Polyphemus story.

6.  I actually heard that joke from the audio of one of Richard Feynman’s Lectures on Physics, the one on Gravitation.

7.  Science-fiction book by Isaac Asimov. See also the readings below for bibliographical information.

8.  As discussed on Day One of his book, "Dialogue Concerning the Two Chief World Systems," published in 1632 in Florence, Italy. See also the readings below for bibliographical information.

9.  The tallest skyscrapers have lengths between 600 and 800 m (less than half a mile): Current holder of world's tallest freestanding structure: Burj Dubai, Dubai, UAE, 818 m (2,684 ft). Some other tall/large structures: Sears Tower, Chicago, USA, 527 m (1,730 ft); Egyptian Pyramids, between 60 - 150 m (200 ft- 500 ft) ; Nuclear Supercarrier U.S Nimitz, 332.8 m (1,092 ft).

10.   Human knowledge is growing exponentially, doubling about once per year. Arguably, one consequence will be the advanced, far stronger materials of the near future derived from nanotechnology. See, for instance, the possibility of a space elevator, made of a carbon nanotubes composite ribbon, stretching vertically for about 100,000 km (62,000 miles) into space. See, for instance: http://science.howstuffworks.com/space-elevator.htm 

11.  As discussed on Day Two of his book, "Dialogue Concerning the Two Chief World Systems," published in 1632 in Florence, Italy. See also the readings below for bibliographical information.

12.   The Unexpected Vista: A Physicist’s View of Nature, by James S. Trefil, pages 161-163. Published in 1983. See also the readings below for bibliographical information.

13.  Of course there are other considerations, such as the fact that the roach would soon reach terminal velocity; i.e, a constant, relatively low speed reached by the roach when the upward dragging force matches the downward gravitational force.

14.  Neil Armstrong, U.S. Astronaut, first human to walk on another celestial body: Apollo 11, July 21,1969.

15.  For an informative and entertaining discussion, see, for instance, from "The Physics of Superheroes," Chapter 2-Deconstructing Krypton-Newton's Law of Gravity, by James Kakalios. Please see the readings below for bibliographical information.

16.   Arguably, and according to one way of looking at hair and fur, we have hair on our heads, and fur everywhere else: arms, legs, eyelashes, etc. The main difference is that hair keeps growing, whereas fur just grows to a given extent and then stops growing. Another difference is related to how long hair and fur lasts before falling off.

17.   That is a rough estimate. I would surmise that food needs are actually proportional to Lⁿ, where 2<n<3, but definitely much less than 3. If you think a little harder, you might find the argument about the amount of food needed being proportional to the surface area somewhat contradictory. After all, the food needed as we grow up has to be in some way related to our mass, since this food ultimately become our flesh and bone. No wonder kids and adolescents eat so much. On top of needing their energy to keep the furnace going, they need food to build their bodies. In general for an adult, however, all studies show that energy requirements are roughly proportional to the square of the dimensions.

18.  The smallest species of shrews digest their food very rapidly, to the point that some of it passes through, not fully digested. Some shrews actually eat their feces to assimilate the undigested nutrients. Due to their very high metabolic rates (think Lilliputian), shrews can die relatively easily, not only of starvation, but also out of fright. For more on shrews' life at the edge, see, for instance: http://science.jrank.org/pages/6130/Shrews.html

19.  Hippopotamus, from Greek hippo: horse, and potamus: river, spend a great deal of time in water, their body shape and short legs being adaptations to their semi-aquatic life, even given birth in it. Along with whales and rhinoceros, they are some of the largest mammals and animals that have ever lived. (Even the biggest dinosaurs were much smaller than a Blue Whale.) It was discovered, through DNA studies, as a very surprising finding of the past decade, that the closest (or one of the closest) relative of the hippos are the whales.

20.  Actually, of all the solids having a given volume, the sphere is the one with the smallest surface area, and conversely, of all solids having a given surface area, the sphere is the one having the greatest volume. So if you have to make a container with a given amount of material (which costs money), and want to get the maximum volume out of it, make it into a sphere, if it is practical enough.

21a.  The other very important contributor to Earth's continued geological activity is the constant liberation of energy by radioactive elements in its interior.  
21b.  Most of the craters of the Moon were actually formed during the Late Heavy Bombardment Period, approximately 3.8 to 4.1 billion years ago. The Heavy bombardment refers roughly to the first 3/4 of a billion years after the formation of the Solar System, when the young planets and satellites were constantly bombarded by the remnant debris(from less than pea-size meteors to asteroid size) orbiting around the Sun. As everybody has heard the stories of the possibility of a big asteroid hitting our planet at anytime--and watches shooting stars once in a while, the "bombardment" still continues to this day, but there is far less debris circling around. Any signs of craters on Earth have had the tendency to disappear "quickly," due to various factors, such as 3/4 of our planet being covered by deep water, the constant resurfacing due to geological activity, and plant life quickly covering them.

22.  Using orders of magnitude is the scientist way of looking at the big picture in order to gain deep insight into Nature, in an attempt to avoid reasoning from being clouded by "irrelevant" details. It corresponds to the exponent in powers of 10. Quick examples of looking at the big picture in order to gain some deeper insight out of Nature:   1. All mammals and birds live equally long: 10⁹ heartbeats. Whether it is a small bird lasting a few years with a heartbeat rate of several hundred beats/min or a large mammal living several decades with a much slower heartbeat rate, we all live equally longer. Then the scientist can ask, does that mean anything deeper, are all animals like furnaces that can burn only a given, limited amount of fuel, whether it is burnt slowly or faster?   2. Another quick example with money: say that, at this precise instant, your worth is USD$17,450.00, Bill Gates' worth is USD$47,345,363,227.05 and Warren Buffett's worth is USD$43,274,653,326.15. That means that your worth is USD$10⁴ dollars, whereas Gates and Buffett's are each worth USD$10¹⁰. They are, therefore, both immensely wealthier than you are; i.e., six orders of magnitude richer than you are, and they are both equally rich. The fact that one has 47 billion and the other 43 billion is immaterial and irrelevant for most purposes(the big picture). (the term billion is used here as in the American definition: 10⁹.)

23.   The tallest mountain on Earth, from base to peak, is Mauna Kea, one of the volcano-islands that comprise the archipelago of Hawaii, USA, in the Pacific Ocean. Mauna Kea is 10,204 meters tall (33,480 feet), rising 4,205 m (13,796 ft) above sea level. The tallest mountain above sea level is, of course, the well-know, majestic peak of Mount Everest, 8,848-m (29,029 ft) tall, in the Himalaya range. They are both young, relatively uneroded mountains, about 50-60 million years old.

24.  Epilepsy, or The Sacred Disease, as called by Hippocrates in his book, refers to a pattern of unprovoked seizures that happen when neurons (nerve cells) in the brain fire electrical impulses at a rate of up to four times higher than normal. Hippocrates was the first human to propose the hitherto strange idea that diseases actually have natural causes, unrelated to gods.

25.  As suggested jokingly by Ray Kurzweil in his Forward to James Gardner's book, "The Intelligent Universe."  His point was actually related to the evolution of intelligence in the multiverse and the speculative possibility that there could have been indeed an intelligent designer of our universe, such as an evolved intelligence from some other universe, who, as it became superintelligent, decided to create our universe: http://www.kurzweilai.net/meme/frame.html?main=/articles/art0691.html

26.  On 12^th April, 1961, Yuri Gagarin (Юрий Гагарин) became the first human to travel into space and orbit the Earth. He visually confirmed what Democritus had speculated about (c. 460 BCE – c. 370 BCE), Eratosthenes had measured indirectly (c. 276 BCE – c. 195 BCE), and Magellan had confirmed through circumnavigation (1480 CE – 1521 CE).

Further Reading

Photo Attribution

Fig. 1:  Image source: http://commons.wikimedia.org/wiki/File:Hdgs_Cranes_fighting_Dwarfes.gif, from the 1555 paint by the Swedish writer Olaus Magnus; Uploaded 20 March, 2009 - Public Domain.

Fig. 2:  Image source: http://books.google.com/books?id=2Rn4qI6GoYcC&printsec=frontcover&dq=Gulliver#PPA33,M1, image on page 33 of the Google online edition of “Gulliver's Travels into several remote nations of the world', by Jonathan Swift, Sir Henry Craik, C E Brock; Illustrated by C E Brock; Published by Macmillan, 1894; Original from Harvard University; Digitized Feb 17, 2006; 381 pages; Uploaded 18 March, 2009 - Out-Of-Copyright Book.

Fig. 3:  Image source: http://en.wikipedia.org/wiki/File:Beau-ti-ful.jpg, this image is a screenshot from a copyrighted film; Uploaded 15 March, 2009 - Fair-Use Rationale, as explained on the link above and also here.

Fig. 4:  Image source: N/A; Author's own picture. Uploaded 15 March, 2009 - Creative Commons Attribution Non-Commercial License.

Table 1:  Image source: N/A; Author's own table converted into an image. Uploaded 15 March, 2009 - Creative Commons Attribution Non-Commercial License.

Fig. 5:  Image source: http://moro.imss.fi.it/lettura/LetturaWEB.DLL?AZIONE=IMG&TESTO=E_U&PARAM=07-23-tit.jpg, Frontispiece by Stefan Della Bella, from the title page of Galileo Galilei's "Dialogue Concerning the Two Chief World Systems," published by Giovanni Battista Landini in 1632 in Florence, Italy; Uploaded 15 March, 2009 - Public Domain.

Fig. 6:  Image source: N/A; Picture licensed to the author; "Frayed Rope about to Break," Stock photo | File #: 5711173; Licensed and uploaded on 14 March, 2009 - istockphoto.com Standard License.

Fig. 7:  Image source: http://commons.wikimedia.org/wiki/File:Kohlenstoffnanoroehre_Animation.gif,  Uploaded 15 March, 2009 - GNU Free Documentation License.

Fig. 8:  Image source: http://commons.wikimedia.org/wiki/File:9983_-_Milano_-_Sant%27Ambrogio_-_Cortile_-_Pilastro_-_Foto_Giovanni_Dall%27Orto_25-Apr-2007.jpg,  Uploaded 15 March, 2009 - A pilaster in the atrium of Sant'Ambrogio Basilica in Milan, Italy. Picture by Giovanni Dall'Orto, 25 April, 2007, released with conditions; Copyright by Giovanni dall'Orto.

Fig. 9:  Image source: http://commons.wikimedia.org/wiki/File:Hym-myrmicinae.gif, The exoskeleton of an ant, as drawn by "Halvard from Norway," thank you; Uploaded 15 March, 2009 - Public Domain.

Fig. 10:  Image source: http://commons.wikimedia.org/wiki/File:Skeletons.png,  Uploaded 15 March, 2009 - Creative Commons Attribution ShareAlike 3.0.

Fig. 11:  Image source: http://nationalzoo.si.edu/Animals/PhotoGallery/AsianElephants/,  Picture showing Shanthi, a female Asian Elephant, and her calf, Kandula, born in 2001 through artificial insemination at the National Zoological Park, Smithsonian Institution, Washington, D.C., USA; Uploaded 15 March, 2009 - Fair Use License.

Fig. 12:   Image source: http://commons.wikimedia.org/wiki/File:BlueWhaleSkeleton.jpg,  Uploaded 15 March, 2009 - GNU Free Documentation License.

Fig. 13:  Image source: http://commons.wikimedia.org/wiki/File:Fenerbahce_Park_05414_tree.jpg,  Fenerbahce Park, Istanbul, HDR image, 2006 Author: Nevit Dilmen; Uploaded 15 March, 2009 - GNU Free Documentation License.

Fig. 14:  Image source: http://www.everafterimages.com,  Huzzar Texas Hummingbird; Uploaded 15 March, 2009 - Creative Commons Attribution ShareAlike 3.0.

Fig. 15:  Image source: http://commons.wikimedia.org/wiki/File:Ippopotami_Lake_Manyara_Park.jpg,  Hippopotamus - Lake Manyara National Park - Tanzania - 1996 Author: Esculapio; Uploaded 16 March, 2009 - GNU Free Documentation License.

Fig. 16:  Image source: http://commons.wikimedia.org/wiki/File:Full_Moon_Luc_Viatour.jpg,  English: Full Moon view from earth In Belgium (Hamois). Credit: http://www.lucnix.be/ ; Author: Luc Viatour; Uploaded 15 March, 2009 - Creative Commons Attribution ShareAlike 2.5.

Fig. 17:  Image source: http://photojournal.jpl.nasa.gov/catalog/PIA10369,  Author: NASA/JPL-Caltech/University of Arizona, March 23, 2008; Uploaded 15 March, 2009 - Courtesy NASA/JPL-Caltech..

Fig. 18:  Image source: http://commons.wikimedia.org/wiki/File:Ceres_Earth_Moon_Comparison.png,  This picture was composed from:Image: Mercury_Earth_Comparison.png, Image:Full Moon Luc Viatour.jpg and Image: Ceres_optimized.jpg ,by --CWitte 11:33, 26 July 2007 (UTC); Uploaded 15 March, 2009 - For the Ceres and Earth part of the composition: NASA-Public Domain; and for the lunar part of the composition: Creative Commons Attribution ShareAlike 2.5.

Video 1:  Image source: http://video.google.com/videoplay?docid=219791354625794697&ei=sgrHSaiaNaC0rQLPopzBDg&q=video+airplane+model+competition+Benoit+Dierickx&hl=en,  Indoor Acrobatics Contest in Mülheim, Germany, February, 2006 Author: Jürgen Heilig; Uploaded 15 March, 2009 - Fair Use License.

The Physics of Giants and Dwarves - http://www.wordle.net/create