Scale Invariance
TL;DR
Scale invariance means the relationship has the same form at all scales.
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Scale invariance means the relationship has the same form at all scales. In metabolic scaling, doubling body mass increases metabolic rate by factor of 2^0.75 ≈ 1.68, regardless of whether doubling from 1 gram to 2 grams (bacteria to protozoa) or from 1000 kg to 2000 kg (cow to elephant). There is no characteristic scale - the same mathematical rule applies across the entire range.
Business Application of Scale Invariance
Scale invariance in power laws means the same distributional pattern holds whether examining the top 1% or top 20%, creating predictable relationships that, once recognized, allow strategic optimization despite extreme ranges in size.