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It scales, because the surface of the network of tubes that fills the volume also grows with the volume, unlike the external surface that encloses that volume. When the volume is scaled, the tubes (i.e. capillaries) are not scaled in size, but they grow in number per a given fraction of the volume. So the scaled devices are not geometrically similar, thus the law of variation of the area per volume with scaling does not apply. This is why a brain or a muscle can scale from a mite with a volume of one thousandth of cubic millimeter to a whale. The scaling is not ideal because the smallest capillaries must be aggregated into vessels of increasing size, so some part of the volume becomes wasted, but still the ratio of area per volume does not decrease linearly, as in the case when the external surface is used for cooling. The same technique is applied in many engineering domains. For instance, the maximum current for a power transistor depends on the perimeter of the source or emitter, not on the die area. Therefore, if one would scale a power transistor maintaining geometric similarity, the switched power per die area would drop quickly, leading to very high costs for the devices. Instead of this, a bigger power transistor does not have bigger sources or emitters, but it has more of them, with the same size as in the smallest transistors, which keeps constant the power switched per die area. |