"SIMILARITIES BETWEEN LENGTH AND SPEED" "How would beings and objects appear to us if we were much larger or smaller?" "How would a giant 1,000 times larger than us see the universe, or a dwarf 1,000 times smaller?" "We will attempt to answer these questions." "Bodies of differing dimensions are proportional to each other as long as their corresponding dimensions are in a constant relation," "Thus you'll notice that corresponding angles are identical in the two objects here," "whereas the surface of the larger is the square of that of the smaller, while its volume is the cube of the volume of the smaller." "Let's take a rectangle with dimensions double those of another." "Its surface is four times larger than the surface of the smaller." "A cube with dimensions twice those of another cube is eight times larger �n volume." "The glass on the left here is twice the dimensions of the smaller one." "The liquid flows from each tap at an identical rate." "The larger glass takes eight times longer to fill." "Here is a young elephant- lt has a body surface nine times smaller than its father's," "Weight being proportional to volume we'd need 27 of these small elephants to balance the weight of its father." "Let's take two hollow spheres covered by equidistant holes of equal size." "One sphere is double the diameter of the other." "If we fill them with water, we see that the smaller sphere empties twice as quickly." "The rate off low is proportional to the surface of the sphere, while the quantity of water is proportional to the volume." "Two calorimeters store heat �n quantities proportional to volume, while heat loss is proportional to surface area." "A large calorimeter is therefore better than a smaller one because it holds the heat better." "HEAT LOSS proportional TO SURFACE AREA" "HEAT conservation proportional TO VOLUME" "Similarly, toys function differently from the real machines they represent." "A model of a steam engine doesn't work as well as the real machine of a much larger size." "Heat loss is comparatively larger in a toy than in a real machine," "LENGTH 4 - 1 SURFACE 16 - 1" "The increase in weight of a man who grows ten times larger would be much greater than the increase in the size of his tibias." "WEIGHT-. 70 KG x 10 (-3) OR 70,000 KG" "TIBIA BONE 100 TIMES LARGER" "CAN SUPPORT 7,000 KG" "63,000 KG OF WEIGHT NOT SUPPORTED" "A man who grew to this size would inevitably collapse." "The rabbit has a thin and lightweight skeleton, while an elephant's skeleton is massive." "If we made an elephant larger and larger, the skeleton would have to grow so large that it would burst through the flesh." "Thus, there are definite limits to the dimensions of beings." "The same is true for human constructions." "If we made the Eiffeltower larger and larger, while keeping the same proportions, it would collapse under its weight." "Let us now imagine a being a hundred times smaller." "Here he is- He's just under an inch tall." "His molecules are compact enough that he needs no skeleton." "Any object he'd wish to ignite would be so small that the necessary reservoir of heat would immediately be dispersed through a surface excessively large for its reduced volume." "What is this enormous bubble?" "A drop of dew." "It's as firm to the touch as a rubber balloon," "Our pygmy attempts to force a pebble inside, but it bounces off the surface like off a mattress - until he cleans the pebble with alcohol." "Scientists have laid out a classic table of dimensions, from there, engineers have defined mechanical similarities" "with the added hypothesis that gravity- which is acceleration and which plays a decisive role �n mechanics - that gravity's dimensions" " LT-2 should not vary." "LT-2 should be constant." "According to this hypothesis, distance is proportional to the square of time, and therefore speed- or LT-1 is proportional to the square root of distance," "for instance here is a machine... and here is a scale model four times smaller." "Next to each is a pendulum that indicates the rhythm of each." "The smaller pendulum oscillates twice as fast as the larger, and the smaller machine turns twice as fast as the other." "Naturalists observe that according to this hypothesis, an elephant would move approximately half as quickly as its calf, which is half its size," "But this is, in fact, wrong." "A shark 33 feet long would swim approximately three times faster than a fish three feet long." "Since mechanical similarity yields results not supported by empirical data, naturalists suggest another hypothesis,- biological similarity." "Here, speed is given fundamental importance, which leads to another table of dimensions" "where speed is proportional to time and not to the square root of distance." "The rhythms of machines of different sizes are not the same under this hypothesis of biological similarity." "In actual fact, it's impossible to verify these hypotheses, since exactly similar subjects do not exist." "But the hypothesis of biological similarity often seems preferable to the other."