XPost: sci.math.num-analysis   
   From: jameskuyper@alumni.caltech.edu   
      
   On 2026-02-19 04:01, David Brown wrote:   
   > On 18/02/2026 12:21, Tristan Wibberley wrote:   
   >> On 18/02/2026 07:47, Tim Rentsch wrote:   
   >>   
   >>> The key property of a (pseudo) random number generator is that the   
   >>> values produced exhibit no discernible pattern.   
   >>   
   >> For a PRNG, they exhibit the pattern of following the sequence of the PRNG!   
   >>   
   >   
   > As a deterministic function, a PRNG will obviously follow the pattern of   
   > its generating function.  But the aim is to have no /discernible/   
   > pattern.  The sequence 3, 4, 2, 1, 1, 7, 0, 6, 7 has no pattern that   
   > could be identified without knowledge of where they came from - and thus   
   > no way to predict the next number, 9, in the sequence.  But there is a   
   > pattern there - it's the 90th - 100th digits of the decimal expansion of pi.   
      
   I think you're being overoptimistic. I suspect that the pattern could be   
   identified, exactly, without knowing how it was generated. That's   
   because every possible pattern has infinitely many different ways in   
   which in can be produced. One of those other ways might be easier to   
   describe than the way in which the numbers were actually produced, in   
   which case that simpler way might be guessed more easily that the actual   
   one - possibly a lot easier.   
      
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