To: R.D. Silverman,

Quoting R.D. Silverman:
[QUOTE]
He did not say that it was. You need to learn to read.
He said that the [COLOR=black]polynomial[/COLOR][COLOR=red][B]s[/B][/COLOR] were [COLOR=black]well behaved[/COLOR].[/QUOTE]

Here is [B][U][I]exactly[/I][/U][/B] what CRGreathouse said...

Quoting CRGreathouse's remark [COLOR=black]about[/COLOR] [B]polygonal [COLOR=black]numbers[/COLOR] of order greater than 2:[/B]
[QUOTE]
[COLOR=black]These[/COLOR] are [COLOR=black]easy to count[/COLOR] by virtue of being well-behaved [COLOR=red][COLOR=black]polynomial[/COLOR][B]s[/B][/COLOR].
[/QUOTE]
In my paper, there is [B][U]only[/U] [U]one[/U][/B] polynomial.
There are [B][I]not[/I][/B] a multitude of polynomial[COLOR=red][B]s.[/B][/COLOR]
Now, a [B]polynomial[/B] is an [B]"[I]expression".[/I][/B]
[I][B]Nobody "counts" one expression ![/B][/I]
Therefore...
[COLOR=black][B][I]Nobody[/I][/B] [/COLOR][B][I][COLOR=black]"counts"[/COLOR][/I][/B] [B][I]one[/I][/B] [B][I][COLOR=black]polynomial ![/COLOR][/I][/B]
My paper is about counting [I][B]numbers[/B][/I],
It's [B][I]not[/I][/B] about counting one [B]polynomial[/B].

I like CRG, but clearly, he's a busy person,
didn't have time to fully digest the idea,
and "misspoke"............... as did you.

Quoting R.D. Silverman:
[QUOTE]
You need to learn to read.
[/QUOTE]
Now that's just plain rude (and absolutely uncalled for).
I never did anything to you! [B]I came here wanting to be friends![/B]

You know, there's a "phrase that fits" overly educated people
who are rude [B][I]while[/I][/B] they are wrong. That phrase is "pompous buffoon".

Quoting R.D. Silverman:
[QUOTE]
You have an approximation that works for the range(s)
for which you have computed values.
[/QUOTE]
I can't take any credit for computing those values. They were computed,
(and now verified) by a couple of exellent coders. I owe them a lot.

Quoting R.D. Silverman:
[QUOTE]
Oh? What is the underlying density function? Please specify.

Please show us the derivation of your counting function.
Or is merely an emprical result from fitting curves?
[/QUOTE]
[B]Would you answer questions posed in that manner?[/B]

I suppose that I could ask the coders to provide me with more data...
pages and pages of counts in much smaller increments that I could
then test and analyze in a thousand different ways, but what would be
the point of all that if all I would get for it is the kind of treatment that
you and others such as yourself have been giving me. It's not worth it!

The data that you see in the paper, is all the data that I have.
When I began working on this function, there was a lot less.
In fact, there was almost no data! The count was less than 1000.

The derivation involves methods that I developed over many years
and would probably fill up a book. Why should I bother explaining any of it?
So that I can be called a "crank" and a "crackpot". No thanks!

If you have no interest or curiosity when my presentation is simple,
then you will certainly have no interest or curiosity in the details.

Quoting R.D. Silverman:
[QUOTE]May we ask: Where did you get your math degree?[/QUOTE]
I am a very humble and modest person, and as such,
I prefer not to focus attention on myself, but rather,
on the problem at hand, which is, can we determine [TEX]\varpi(10^{18})[/TEX]?

C-to-the-Rank Alert...
 

Misc. Math anyone???

[quote]
The derivation involves methods that I developed over many years
and would probably fill up a book. Why should I bother explaining any of it?
So that I can be called a "crank" and a "crackpot". No thanks!

If you have no interest or curiosity when my presentation is simple,
then you will certainly have no interest or curiosity in the details.[/quote]

Let's see. We've got:

* Years of developing and implementing the "derivation", completely out of view of (and without any collaboration or review on the part of) the mathematical community. Swing and a miss, strike one.

* A theory that "fills up a book". Swing and a miss, strike two.

* Refusal to explain or expound on said theory due to supposed lack of interest or knowledge on the part of the unwashed Philistine masses. Swing and a miss, strike three.

Who wants to calculate the crank points on this one? :loco:

[QUOTE=Don Blazys;253344]To: R.D. Silverman,

Quoting R.D. Silverman:


Here is [B][U][I]exactly[/I][/U][/B] what CRGreathouse said...

Quoting CRGreathouse's remark [COLOR=black]about[/COLOR] [B]polygonal [COLOR=black]numbers[/COLOR] of order greater than 2:[/B]

In my paper, there is [B][U]only[/U] [U]one[/U][/B] polynomial.
There are [B][I]not[/I][/B] a multitude of polynomial[COLOR=red][B]s.[/B][/COLOR]
Now, a [B]polynomial[/B] is an [B]"[I]expression".[/I][/B]
[I][B]Nobody "counts" one expression ![/B][/I]
Therefore...
[COLOR=black][B][I]Nobody[/I][/B] [/COLOR][B][I][COLOR=black]"counts"[/COLOR][/I][/B] [B][I]one[/I][/B] [B][I][COLOR=black]polynomial ![/COLOR][/I][/B]
My paper is about counting [I][B]numbers[/B][/I],
It's [B][I]not[/I][/B] about counting one [B]polynomial[/B].

I like CRG, but clearly, he's a busy person,
didn't have time to fully digest the idea,
and "misspoke"............... as did you.

Quoting R.D. Silverman:

Now that's just plain rude (and absolutely uncalled for).
I never did anything to you! [B]I came here wanting to be friends![/B]

You know, there's a "phrase that fits" overly educated people
who are rude [B][I]while[/I][/B] they are wrong. That phrase is "pompous buffoon".

Quoting R.D. Silverman:

I can't take any credit for computing those values. They were computed,
(and now verified) by a couple of exellent coders. I owe them a lot.

Quoting R.D. Silverman:

[B]Would you answer questions posed in that manner?[/B]

I suppose that I could ask the coders to provide me with more data...
pages and pages of counts in much smaller increments that I could
then test and analyze in a thousand different ways, but what would be
the point of all that if all I would get for it is the kind of treatment that
you and others such as yourself have been giving me. It's not worth it!

The data that you see in the paper, is all the data that I have.
When I began working on this function, there was a lot less.
In fact, there was almost no data! The count was less than 1000.

The derivation involves methods that I developed over many years
and would probably fill up a book. Why should I bother explaining any of it?
So that I can be called a "crank" and a "crackpot". No thanks!

If you have no interest or curiosity when my presentation is simple,
then you will certainly have no interest or curiosity in the details.

Quoting R.D. Silverman:

I am a very humble and modest person, and as such,
I prefer not to focus attention on myself, but rather,
on the problem at hand, which is, can we determine [TEX]\varpi(10^{18})[/TEX]?[/QUOTE]

You are a classic crank.
Ignorant, unaware of your ignorance, and argumentative with
experts who know far more than you about the subject you
are trying to discuss.

You make handwaving claims that you can not substantiate.

Are you even aware of the relationship between the Bernoulli
numbers and the (coefficients) of the polynomials (yes, plural!)
that generate the polygonal numbers you are trying to count?

Congratulations. You have made my ignore list faster than anyone
else ever has.

A ten minute hack computed omega(10^10) in 90 seconds. Its result 6403587409 agrees with the value in your manuscript. Its run-time is roughly linear, so 10^13 should take about 24 hours. I made no effort to make the code efficient. Allowing larger values would require partitioning the sieve which would take several more minutes, which I don't think worth the time.

Quoting CRGreathouse:
[QUOTE]How do you know that you're the first?[/QUOTE]

Searched the internet, L.A. public Library, and found nothing.
Also, sufficiently large tables of [TEX]\varpi(x)[/TEX] did not exist
until the coders working with me calculated them.

Quoting CRGreathouse:
[QUOTE]
Also, you seem to have only an empirical fit.
What have you actually proved? [/QUOTE]
I'm presenting a hypothesis that I think is intriguing.
Like the R.H., it may not be provable in the mathematical sense,
but only by "a preponderance of the evidence".

A theory is only as good as it can [B]predict [/B]results, so if a determination of [TEX]\varpi(10^{23})[/TEX],
done on a supercomputer, gives us a 20 digit value of the fine structure constant
which is later corroborated by "physical experiment", then further physical experiments
would no longer be necessary and that would save a lot of time, effort and money.

Quoting CRGreathouse:
[QUOTE]
I don't suppose you'd care to back that up with a friendly bet?
[/QUOTE]

Sure!

If [TEX]B(x)[/TEX] and [TEX]\varpi(x)[/TEX] cross before and after [TEX]\varpi(10^{13})[/TEX],
then you owe me $100.00.
If not, then I owe you $100.00.

Okay?

Don.

Quoting R.D. Silverman.
[QUOTE]You are a classic crank.
Ignorant, unaware of your ignorance, and argumentative with
experts who know far more than you about the subject you
are trying to discuss.[/QUOTE]

Don't forget to stick your thumbs in your ears and sing
nyah nyah nyah nyah nyah after you write such things.

Quoting R.D. Silverman.
[QUOTE]
Are you even aware of the relationship between the Bernoulli
numbers and the (coefficients) of the polynomials (yes, plural!)
that generate the polygonal numbers you are trying to count?

[/QUOTE]

[B][U]My[/U][/B] paper has only one polynomial. [B]My[/B] paper counts [B][I]numbers[/I][/B].

You are wrong and rude. A [B][I][U]classic[/U][/I][/B] buffoon!

Don.

[QUOTE=Don Blazys;253344]Quoting CRGreathouse's remark [COLOR=black]about[/COLOR] [B]polygonal [COLOR=black]numbers[/COLOR] of order greater than 2:[/B]

In my paper, there is [B][U]only[/U] [U]one[/U][/B] polynomial.
There are [B][I]not[/I][/B] a multitude of polynomial[COLOR=red][B]s.[/B][/COLOR]
Now, a [B]polynomial[/B] is an [B]"[I]expression".[/I][/B]
[I][B]Nobody "counts" one expression ![/B][/I]
Therefore...
[COLOR=black][B][I]Nobody[/I][/B] [/COLOR][B][I][COLOR=black]"counts"[/COLOR][/I][/B] [B][I]one[/I][/B] [B][I][COLOR=black]polynomial ![/COLOR][/I][/B]
My paper is about counting [I][B]numbers[/B][/I],
It's [B][I]not[/I][/B] about counting one [B]polynomial[/B].

I like CRG, but clearly, he's a busy person,
didn't have time to fully digest the idea,
and "misspoke"............... as did you.[/QUOTE]

It's not uncommon that I'm imprecise when talking here, informally and amongst friends. But as it happens I said just what I meant there.

You have a single multivariate polynomial, but I look it as a collection of single-variable polynomials because that unlocks the ability to use inclusion-exclusion to count them. Further, I think they're susceptible to a particular form of accelerated counting in that form -- but I'd rather not say more on that subject until I do some preliminary testing of my own.

[QUOTE=Don Blazys;253366]If [TEX]B(x)[/TEX] and [TEX]\varpi(x)[/TEX] cross before and after [TEX]\varpi(10^{13})[/TEX],
then you owe me $100.00.
If not, then I owe you $100.00.[/QUOTE]

They're quite close (by construction) at the end of your calculated range, so that would be unwise. (They're likely to cross many times even if the asymptotics are wrong.) How about this: you have relative errors calculated for counts to {1, 2, ..., 11} * 10^11, and note the "very small and rapidly decreasing percentage of error."

If the geometric average of the absolute relative error is lower at {1, 2, 3, 4, 5} * 10^14 than at {1, 2, ..., 11} * 10^11 I owe you $100, otherwise you owe me $100. (Heck, we could push that number up if you'd like.)

I'll let you choose -- now, though, not when the calculations are complete -- what value to use for the constants, whether the values you used in the paper (137.035999084 and 1836.15267247), the CODATA values as of the time the calculations finish, or some other accepted standard.

Oh, and I'm talking about your more refined estimate, B(x) * (1 - alpha/(mu - 2e)). By your admission the constant in B(x) seems to be off.

[QUOTE=Don Blazys;253367]Quoting R.D. Silverman.


Don't forget to stick your thumbs in your ears and sing
nyah nyah nyah nyah nyah after you write such things.

Quoting R.D. Silverman.


[B][U]My[/U][/B] paper has only one polynomial. [B]My[/B] paper counts [B][I]numbers[/I][/B].

You are wrong and rude. A [B][I][U]classic[/U][/I][/B] buffoon!

Don.[/QUOTE]

You are an idiot studying to become an imbecile.

Your "counting function" is a function (as you gave it) of the form

C1 x + C2 sqrt(x)

You are so totally clueless that you don't even realize that this is NOT
a polynomial.