XPost: sci.math.num-analysis   
   From: david.brown@hesbynett.no   
      
   On 19/02/2026 20:33, James Kuyper wrote:   
   > 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.   
      
   How likely is it that someone would guess a formula that happened to   
   generate the decimal digits of pi, without more knowledge than a part of   
   the sequence?  I don't believe it is possible to quantify such a   
   probability, but I would expect it to be very low.   
      
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