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Fw: Re: Twin primes and Pi

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  • Phil Carmody
    ... Welcome to the list, Robert, great to have a mind as sharp as yours on board! ... One might just describe them as merely expressions with higher kolmogorov
    Message 1 of 2 , Nov 28, 2012
      --- On Wed, 11/28/12, gigi_avatar27 wrote:
      > Hi folks,

      Welcome to the list, Robert, great to have a mind as sharp as yours on board!

      > I think it's important to use the best tools for the
      > job.  I'm glad to hear that RIES is useful, but I'm
      > also glad we have ISC too.
      >
      > Part of the difficulty with ISC is that if you need it, then
      > you *really* need it, but if you don't need it, it's
      > difficult to understand why anyone would. ISC is full of
      > cryptic, advanced, specialized mathematics.

      One might just describe them as merely expressions with higher
      kolmogorov complexity than what RIES considers.

      > So while I did create RIES partly out of frustration with
      > ISC and Simon Plouffe's Inverter, I was far more motivated
      > by having fun with maths and helping show people how easy it
      > is to match any real number with equations of high-school
      > simplicity.

      Because your alphabet is deliberately small. The same principles
      work equally well on a bigger alphabet.

      And as you open source RIES, there's nothing stopping people from
      adding more constants and functions, for which I'm most grateful,
      even if I've not actually got around to doing that yet - I certainly
      plan to! (However, I'd probably drop phi as a leaf-node too!)

      > In a sense, RIES is too frivolous for the problem at hand,
      > namely the infinite product PI[t/(t-1)] for all twin primes t.
      > My "Stupid Math Tricks" examples (http://goo.gl/v541k) are
      > more in line with the true spirit of RIES.

      Well, even the ISC can't tell you the answer to the actual problem
      at hand. However, once you've got a sufficiently accurate
      approximation both ISC and RIES can tell you what the expression
      might be equal to, *neither* being able to give any justification
      stronger than coincidence. In David's and Werner's proven expressions,
      *both* ISC and RIES give the same correct answer.

      Phil
    • gigi_avatar27
      Thanks, glad to be here. ... You can already drop phi, if that s all you want to do, by excluding the phi symbol from the search with the option -Nf. Adding
      Message 2 of 2 , Nov 28, 2012
        Thanks, glad to be here.

        --- In primenumbers@yahoogroups.com, Phil Carmody <thefatphil@...> wrote:
        > And as you open source RIES, there's nothing stopping people from
        > adding more constants and functions, for which I'm most grateful,
        > even if I've not actually got around to doing that yet - I certainly
        > plan to! (However, I'd probably drop phi as a leaf-node too!)

        You can already drop phi, if that's all you want to do, by excluding the phi symbol from the search with the option -Nf.

        Adding constants and functions was and is a conscious motivation from the very start, and I consider it in any refactoring and enhancements. In the source code you can see that I've already specified the syntax for custom constants and functions through the existing -include mechanism. For example:

        --define : EulerGamma # seft-a (constant)
        ( -- The Euler-Mascheroni constant, 0.57721... )
        # 50 digits for when RIES goes to higher precision
        0.57721566490153286060651209008240243104215933593992
        ;

        This isn't implemented yet but at least I thought of it.
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