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It is pointed out that the mystery of how biological systems measure theirlengths vanishes away if one premises that they have discovered a way togenerate linear waves analogous to compressional sound. These can be used todetect length at either large or small scales using echo timing and fringecounting. It is shown that suitable linear chemical potential waves can, infact, be manufactured by tuning to criticality conventional reaction-diffusionwith a small number substances. Min oscillations in E. coli are cited asprecedent resonant length measurement using chemical potential waves analogousto laser detection. Mitotic structures in eucaryotes are identified ascandidates for such an effect at higher frequency. The engineering principle isshown to be very general and functionally the same as that used by hearingorgans.  PNAS Significance Statement: This paper invokes physical principles toaddress the question of how living things might use reaction-diffusion tomeasure out and regulate the many thousands of lengths required to make theirbody parts and internal organs. It argues that two ideas have been missing. Oneis that oscillation is necessary to achieve the necessary design stability andplasticity. The other is that the system must be tuned to criticality tostabilize the propagation velocity, thus enabling clocks to function as metersticks. The broader significance is twofold: First, a fundamental piece of themachinery of life is probably invisible to present-day biochemical methodsbecause they are too slow. Second, the simplicity of growth and form identifieda century ago by D'Arcy Thompson is probably a symptom of biologicalengineering strategies, not primitive law.

Critical Waves and the Length Problem of Biology