Re: Partial difference equation, primes

From: C. Bond (cbond_at_ix.netcom.com)
Date: 08/21/04 

Date: Sat, 21 Aug 2004 21:50:49 GMT

James Harris wrote:

> "C. Bond" <cbond@ix.netcom.com> wrote in message news:<412763EB.6A7A9D0A@ix.netcom.com>...
> > James Harris wrote:
> >
> > [snip]
> >
> > > Posters continually use the world "algorithm" in a derisive manner,
> > > when actually the prime counting function is just a formula.
> >
> > There is nothing derisive about the term "algorithm", the derision you sense arises from the fact that you do
> > not understand the term.
>
> Nope. Posters say I just have an algorithm for counting primes like
> any other and that the best way to evaluate an algorithm is by speed.
>
> Then they point out that the direct *algorithmic* implementation of my
> prime counting function is slow, and they say it's not worth
> discussing.

That's a complaint about *your* method -- the derisive keyword is *slow* not *algorithm*.

> It's all part of a rather steady campaign to try and dismiss my work.
>
> So yes, posters use the word "algorithm" derisively in a direct attack
> on my prime counting research to try and support arguments for
> dismissing it.

In case you didn't know it, division and square roots are implemented as algorithms on computers. You can express
the relations for a quotient formally with an equation, such as:

       q = a / b

but the computation of 'q' is done algorithmically. Don't believe it? Check it out. Many of the division algorithms
have names, and chip mfrs sometimes publish the details.

> > > The compressed explicit prime counting function exists as I've shown.
> > >
> > > Notice it too is a formula and not an algorithm.
> >
> > Here's a definition of "algorithm":
> >
> > SYLLABICATION:
> > al·go·rithm
> > PRONUNCIATION:
> > AUDIO: lg-rthm KEY
> > NOUN:
> > A step-by-step problem-solving procedure,
> > especially an established, recursive
> > computational procedure for solving a problem
> > in a finite number of steps.
> > ETYMOLOGY:
> > Variant (probably influenced by arithmetic) of
> > algorism.
> > OTHER FORMS:
> > algo·rithmic (-rthmk) ?ADJECTIVE
> > algo·rithmi·cal·ly ?ADVERB
> >
> > How does your implementation of a prime counting function differ from an algorithm?
> >
>
> By that definition ANY finite summation is an algorithm.

Well, that's the definition. So what? You have taken the time to spell out the step-by-step process used in your
method. That's what an algorithm is.

> That is, whenever you see the summation sign in mathematics for a
> finite sum then by the position of this poster it's an algorithm.

You're confused. The algorithm is the method or step-by-step process used to determine the result. The summation
sign is a mathematical symbol -- like the division sign indicating a quotient. Division can be implemented by look
up tables or by various clever algorithms. The algorithmic implementations are often robust and fast. You can't
tell anything about an implementation by looking at the divide symbol

Your prime counting method is an algorithm. That is not a derisive label, it is descriptive. You, on the other
hand, are an idiot -- that's both derisive AND descriptive.

> James "Often in error, but never in doubt!" Harris 

--
There are two things you must never attempt to prove: the unprovable -- and the obvious.
--
Democracy: The triumph of popularity over principle.
--
http://www.crbond.com

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