Braiding Designs
The Physics of Giants and Dwarves
What we know about the existence and viability of drastically scaled creatures
Not everything goes in Nature. There are some things conceived by our imaginations that we can actually prove to be impossible. In this knol I exemplify that contention by showing how we can use the scientific method through our knowledge of physics and biology to conclusively prove the impossibility of the existence of human-like creatures that are much larger or much smaller than we are. In doing so I will also discuss various aspects related to our understanding of scale, from the microscopic to the astronomical. I will end up the knol with some philosophical implications related to my main conclusion.
Introduction
I often hear people argue with seemingly convincing logic that the fact that we havent seen something doesnt 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. |
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| Fig. 1: Norse dwarves fighting cranes. |
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| 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. |
Table 1: Dimensional Scaling - Notice how the surface area and volume of an object grow ever larger as its linear dimensions are increased by factors of 2, 3, 5, and 10.
Notice how as we increase the length of an object, making it longer in every direction, its surface area and its mass and weight dont 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 objectand 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.
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| 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. |
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| Fig. 7: 3-D structure of a carbon nanotube. |
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| Fig. 8: A supporting pilaster. |
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.
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| Fig. 9: Exoskeleton of an ant. |
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| Fig. 10: Skeletons of mammals, reptiles, birds, and fish. |
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 giants 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 wouldnt 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 sizeshort 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.
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| Fig. 11: Note the stocky, columnar legs of this baby elephant, and of his mother's. |
Please note that it is not that human-like giants couldnt 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 wouldnt 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 Well see this in fiction too. I heard that Supermans 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
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| Fig. 12: Blue whale skeleton. |
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| Fig. 13: Some trees going nowhere. |
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 animals 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 1/10th 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. |
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| Fig. 15: Hippos cooling off at Lake Manyara National Park, Tanzania. |
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), dont 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,Volume of sphere / Area of sphere = V/A = 4/3 R3 / 4 R2 = 1/3 x R
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 planets 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.
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| Fig. 16. The moon, showing its many old craters. |
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| Fig. 17: Phobos, Mars' potato-shape, largest satellite. |
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| Fig. 18: Diameter comparison of Ceres (950 km), Moon (3, 476 km) and Earth (12, 742 km). |
There are actually other instances in which gravity influences shape and size. We have for example the stories of troglodytes living in large cave networks deep inside the earth; i.e., think Subway/Metro/Tube/U-Bahn, but much deeper into the earth, and with walls made of regular rock. Well, given our discussion of gravity and the strength of materials, it is now easy to understand that the existence of empty spaces or air pockets deep inside a large astronomical body is an impossibility, unless the cave "walls" were made out of some out-of-this-world superstrong material. Lastly, in the same way that a heap of sand of given volume and consistency has a distinct conical shape and limited height, the pull of gravity in a given planet puts a limit on how tall a mountain can grow on its surface. Given the rocky materials of the inner solar system, mountains on Earth can raise to a limit of about ten kilometers; e.g., the 10, 204-m tall (33, 480 ft) Mauna Kea volcano island, from the archipelago of Hawaii, in the Pacific Ocean, 23 whereas mountains on the smaller Mars can grow almost three times as tall; e.g., the 27-km tall (17-mile) Olympus Mons, the tallest known volcano and mountain in our solar system.
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 seenand 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 victims 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 meor 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.
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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 Kongs 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 formers 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 Feynmans 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 Physicists 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
Females why come some of you know how to do your hair up real pretty while some don't?
I'm a guy speaking for myself. The female that has her hair fixed nice is usually the one I will ask for a date. I notice that some females don't even know how to fix up their hair real nice. Is this something as little girls you learn or is it just a creative thing for you all. I see women with french braid designs, braids looking nice, hair done up in a bun, perms and then I see females whose hair looks like garbage it's frizzy, not combed or brushed, a pony tail with just a rubber band in the back, just straight out like those elementary girls who just go to school and don't care(that's how some adults go around with their hair looking like that) I'm talking about all races too, white, black, and hispanic. As a guy, I'm into women who have nice hair or at least hair done nice all the time. Complete turn on for me! That's the first thing I notice on her is hair! It's a shame not every female knows this secret about guys on females! How many of you all keep your hair looking nice?
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