Lcp 3: the physics of the large and small
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- Fig. 1: Taken from Galileo’s Two New Sciences (Book 1) IL 1
- Fig. 2: Biology and scaling IL 3
- Fig. 3: Gulliver in the Land of Lilliput IL 4
- Fig. 4: The collapse of a giant Radio Telescope. IL 5
- Fig. 5: Scaling and small biological networks. IL 6
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1April 27 DRAFT LCP 3: THE PHYSICS OF THE LARGE AND SMALL (Old Title: GALILEO, NEWTON, AND ROBOTICS) …the mere fact that it is matter that makes the larger machine, built of the same material and in the same proportion as the smaller, correspond with exactness to the smaller in every respect except that it will not be so strong ...who does not know that a horse falling from a height of three or four cubits will break his bones, while a dog falling from the same height ... will suffer no injury? (Galileo, in the “Two New Sciences”, 1638)
… But yet it is easy to show that a hare could not be as large as a hippopotamus, or a whale as small as a herring. For every type of animal there is a most convenient size, and a large change in size inevitably carries with it a change of form. All warm blooded animals at rest lose the same amount of heat from a unit area of skin, for which purpose they need a food-supply proportional to their surface and not to their weight. Five thousand mice weigh as much as a man. Their combined surface and food or oxygen consumption are about seventeen times a man’’s. In fact a mouse eats about one quarter its own weight of food every day, which is mainly used in keeping it warm. (J.B.S. Haldane, in On Being the Right Size, 1928. See Appendix) 
Fig. 2: Biology and scaling IL 3 *** (Picture taken from IL3: An advanced discussion of scaling in biology) …consider a giant man sixty feet high——about the height of Giant Pope and Giant Pagan in the illustrated Pilgrim’’s Progress of my childhood. These monsters were not only ten times as high as Christian, but ten times as wide and ten times as thick, so that their total weight was a thousand times his, or about eighty to ninety tons. Unfortunately the cross sections of their bones were only a hundred times those of Christian, so that every square inch of giant bone had to support ten times the weight borne by a square inch of human bone. (J.B.S. Haldane, in On Being the Right Size, 1928). 
Fig. 3: Gulliver in the Land of Lilliput IL 4 **** (An excellent site for problems of scaling. Source of above picture) 1Two generalities rule the design of both living and engineered structures and devices: 1) big is weak, small is strong, and 2) horses eat like birds and birds eat like horses (1Mel Siegel, Professor, Robotics Institute – School of Computer Science Carnegie Mellon University, 2004). 
Fig. 4: The collapse of a giant Radio Telescope. IL 5 ** (Source of latter pictures above) At 9:43 p.m. EST on Tuesday the 15th of November 1988, the 300 Foot telescope in Green Bank collapsed. The collapse was due to the sudden failure of a key structural element - a large gusset plate in the box girder assembly that formed the main support for the antenna. When two biologists and a physicist, recently joined forces at the Santa Fe Institute, an interdisciplinary research center in northern New Mexico, the result was an advance in a problem that has bothered scientists for decades: the origin of biological scaling. How is one to explain the subtle ways in which various characteristics of living creatures—their life spans, their pulse rates, how fast they burn energy—change according to their body size? (George Johnson, science writer, The New York Times, 1999) 
Fig. 5: Scaling and small biological networks. IL 6 ** (A modern look at physics, biology and scaling “Of Mice and Elephants: A Matter of Scale”) Evaluation of Internet Links (IL); good, * very good, ** Excellent *** Exceptional **** THE MAIN IDEA:The elementary physics of materials and of mechanics determine the limits of structures and the motion bodies are capable of. The physical principles of strengths of materials goes back to Galileo, and the dynamics of motion we need to apply is based on an elementary understanding of Newtonian mechanics, and the mathematics of scaling required depends only on an elementary understanding of ratio and proportionality. Finally, the main ideas developed here are intimately connected to architecture, biology, bionics, and robotics. It is hard to imagine a more motivating large context to teach the foundations of statics and dynamics with a strong link to the world around us. The guiding idea for this LCP will be based on the idea that the science of materials and the physics of motion determine the limits of structures and the motion bodies are capable of. We will also discover that the energy consumption for robots as well as animals and humans is critically connected to the laws of thermodynamics. However, we will find that it is necessary to go beyond Galileo and Haldane to understand contemporary empirical evidence for new scaling laws describing metabolic rates and mass of animals. The range of the length and the mass of the smallest organism that we can see, say a small insect, about 1 mm long, and a mass of about 10-9 kg, and a whale, about 30 m long, and a mass of about 100 tons (105 kg) is 5 orders of magnitude in length and 14 orders of magnitude in mass. The scaling laws, however, we will find, are different for small things (micro systems) than large things (macrosystems). Finally, in an effort to make contact with sizes we can see with our unaided eyes (between 10-3m and 10-4m) an attempt will be made to guess the size of molecules. This will be done by calculating the thickness of a soap film and by estimating the size of a molecule, describing the method of the French mathematician an physicist Pierre Laplace who estimated the size of a molecule using measurements of surface tension and the latent heat of water.
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