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Arndt–Schulz rule or Schulz' law is a claimed law concerning the effects of pharmaca or poisons in various concentrations. It states that:
For every substance, small doses stimulate, moderate doses inhibit, large doses kill.
That is to say, highly diluted pharmaca or poisons enhance life processes, while strong concentrations may inhibit these processes and even terminate them.
The rule was named after Hugo Paul Friedrich Schulz and Rudolf Arndt. The latter originally formulated it in 1888. However, the exceptions to the rule are so numerous that it can not be considered a general law. For instance, many paralysing substances have no exciting effect in weak doses, and what constitutes a weak, medium or strong stimulus is highly individual, as pointed out by Arndt himself.
The rule is no longer cited in modern pharmacology texts, having been supplanted by the theory of hormesis.
This rule has been claimed by homeopaths as supporting their theories. However, it gives no support to the dilutions typically used by homeopaths which have a high probability of containing no molecules of the diluted substance. To explain the purported therapeutic powers of homeopathic remedies Jacques Benveniste created the postulate of "water memory", but subsequent research has shown that such an effect cannot persist for as long as a nanosecond.
^Cowan ML, Bruner BD, Huse N, et al. (2005). "Ultrafast memory loss and energy redistribution in the hydrogen bond network of liquid H2O". Nature434 (7030): 199–202. doi:10.1038/nature03383. PMID15758995.