A Study of Primes Through Non-Resonant Sine Waves

[R.D. Silverman]

Originally Posted by S485122

I must say that the title of the paper is beautiful ! When one has such a title it is tempting to use it ;-)

Jacob

A mathematician would NOT use the term
"resonant sine waves". Such an expression in the title shouts
out that the content of the paper will be suspect.

[R.D. Silverman]

Originally Posted by fivemack

I think it's pretty pernicious to hold amateur papers to a standard lower than professional ones; the fact that you're doing it for love rather than for citations doesn't excuse incompetence in any field. If you send an incompetent piece of work to a professional venue you're wasting the time of someone generally not paid for their time, which is obviously incivil and deserves a brusque reply; if you publish it yourself you're wasting the time of your readers, which is equally incivil.

I have never reviewed a paper; I've been asked once, read through the paper which was clearly very competent work extending what I did for my thesis, decided that was no longer sufficiently au-fait with the field that I could recognise non-obvious errors or make useful comments, and refused the offer.

Something claiming to be a paper ought to be a finished piece of work and ought to be written in something close to Standard Mathematical Style; signs that a paper is not in Standard Mathematical Style include having verbatim programs in it, using the word 'basically', and almost any occurrence of 'since it exists'. (for an example, the first couple of pages of EdH's paper reduced to something like Standard Mathematical Style would be:

Let . Then an integer is prime iff is non-zero for all ; that is, if )

If a bit of work for the paper is both fundamental and incomplete, the paper is only a draft, and if you can't complete the step then the paper in that form is worthless.

That's quite strict, but remember that you've got a forum here where you can ask about the individual pieces of work; if you phrase the question as 'can you use the fact that sin(pi*A/B) is zero iff B divides A as a primality test', then you can start a discussion:

Implementations of trig functions almost always explicitly reduce the argument modulo 2*pi to get it into the right range, so the computer is just doing the underlying division; you can write an implementation of sin as a series sum that doesn't do range reduction, and it would be an interesting mathematical exercise (and one where I've no idea where to start) to find some series that converges to within 10^-12 of, say, sin(x) for x around 10^6 by summing o(x) terms each of which is, say, a rational function of x.

But even that would still be vastly slower than the division. Multiplying a number by pi and then using a convoluted method for dividing by pi to check whether the number you started with was an integer is obviously absurd.

There is a difference in holding people to a standard level of exposition,
and holding them to some standard level of mathematics.

The OP simply presented a paper as a finished work. He did not qualify the
presentation in any of a number ways: e.g. "this is a draft", "this is for my 2nd
year high school algebra class", etc. He did not ask for help in clarifying
either the exposition or the mathematics. He simply said "here it is. Critique
it". As such we should critique it as we would any paper submitted for publication.

[retina]

Originally Posted by R.D. Silverman

The OP simply presented a paper as a finished work. He did not qualify the
presentation in any of a number ways: e.g. "this is a draft", "this is for my 2nd
year high school algebra class", etc. He did not ask for help in clarifying
either the exposition or the mathematics. He simply said "here it is. Critique
it". As such we should critique it as we would any paper submitted for publication.

Hmm, I think the conclusion does not follow from the argument. A better conclusion would be "As such we should critique it however we want to".

[xilman]

Originally Posted by R.D. Silverman

A mathematician would NOT use the term
"resonant sine waves". Such an expression in the title shouts
out that the content of the paper will be suspect.

I'm co-author of a paper with the title "THE MAGIC WORDS ARE SQUEAMISH OSSIFRAGE". Gibberish written solely in upper-case letters is usually a good indication that it has been written by a crank.

To be fair, it was submitted to a cryptography conference rather than to one on mathematics, so perhaps we can be excused.

Paul

[fivemack]

Originally Posted by R.D. Silverman

A mathematician would NOT use the term
"resonant sine waves". Such an expression in the title shouts
out that the content of the paper will be suspect.

I found one paper in which a seismologist does so, using it to meaning 'sine waves at a resonant frequency of the structure being analysed' as opposed to 'recordings of real earthquakes'.

[10metreh]

Originally Posted by EdH

It is presented here for review and critique, in its unfinished form.

Originally Posted by R.D. Silverman

The OP simply presented a paper as a finished work.

Bob, with all your experience of reading carefully through lengthy papers, surely you should be able to read carefully through a post?

[EdH]

Originally Posted by R.D. Silverman

...The OP simply presented a paper as a finished work. He did not qualify the
presentation in any of a number ways: e.g. "this is a draft", "this is for my 2nd
year high school algebra class", etc. He did not ask for help in clarifying
either the exposition or the mathematics. He simply said "here it is. Critique
it". As such we should critique it as we would any paper submitted for publication.

Emphasis above added by EdH

Thank you again for your words, but I do have a minor contention with the above statement. In my original post I said:

It is presented here for review and critique, in its unfinished form. It is probably of no true worth, other than the interest I had in exploring the topic at the time.

Further, the title block clearly had:

(Draft 1 - Nov 2007)

Perhaps "draft" should have actually been within the title instead of under it.

Anyway, thank you all again for your comments. The reason I posted it was because, although I had abandoned the topic quite some time ago, it was still sitting in the back of my mind. I wondered if I should pursue it again someday. You have all helped me put it to rest. I can now continue with other studies.

Take Care,
Ed

[R.D. Silverman]

Originally Posted by EdH

Emphasis above added by EdH

Thank you again for your words, but I do have a minor contention with the above statement. In my original post I said:


Further, the title block clearly had:


Perhaps "draft" should have actually been within the title instead of under it.

Anyway, thank you all again for your comments. The reason I posted it was because, although I had abandoned the topic quite some time ago, it was still sitting in the back of my mind. I wondered if I should pursue it again someday. You have all helped me put it to rest. I can now continue with other studies.

Take Care,
Ed

If you really want to pursue the relationship between continuous
periodic functions (over R) and prime order groups it will open the doors to a
wonderfully rich field of study known as representation theory. I can help
lead you through it (at least the basics; I am not an expert in this subject),
but it will be an intense effort.

[R.D. Silverman]

Originally Posted by fivemack

I think it's pretty pernicious to hold amateur papers to a standard lower than professional ones;.

Allow me to point out that Fermat was an amateur.

I do agree that we should not hold high school students to the
same standard as professionals. But anyone who is at least at
the undergrad level should be held to strong standards of exposition.

[R.D. Silverman]

Originally Posted by fivemack

I found one paper in which a seismologist does so, using it to meaning 'sine waves at a resonant frequency of the structure being analysed' as opposed to 'recordings of real earthquakes'.

non-sequitur.

You said "seismologist". I said "mathematician"

[R.D. Silverman]

Originally Posted by xilman

I'm co-author of a paper with the title "THE MAGIC WORDS ARE SQUEAMISH OSSIFRAGE". Gibberish written solely in upper-case letters is usually a good indication that it has been written by a crank.

To be fair, it was submitted to a cryptography conference rather than to one on mathematics, so perhaps we can be excused.

Paul

It was also a QUOTE and not intended to summarize the content of
the paper.