New flame war idea ??

[henryzz]

#8 is the type of response that is appreciated here. #7 was harsh but shares the feelings of many on this forum.

[skan]

Originally Posted by cheesehead

Do you mean that this graph plots k on the x-axis, and Mod[272123,k] on the y-axis? I don't see how that can be.

Since 272123 = 503 * 541, Mod [272123,k] should equal k for k in the range [0,502]. The graph should be a straight line with a slope of 1 for k between 0 and 502.

My conclusion is that your first graph is not simply Mod[N, k], but something else.

I think I could guess what it actually is, given enough time, but not yet.

What is the y-coordinate for k=100, 200, 300, 400, 500, 600, 700, 800, 900 and 1000?

Hello everybody.

That was something similar I thought before doing that graphics.

I created this graphs with Mathematica but I could try to do it with other software if you want.

NN = 272123
tt = Table[Mod[NN, kk], {kk, 1, 1100}];
ListPlot[tt, Filling -> Top, GridLines -> {{503}, {}}]

You can plot it with connected points but then you get a "dangerous" continuous line.

And the "useful" graphic

NN = 272123; tt = Table[Mod[NN, kk], {kk, 1, 1200, 1}]; ListPlot[
 Differences[tt, 2], GridLines -> {{503, 541}, {}}]

I chosen N = 272123, and other similar numbers, because they are the product of two numbers with a good size to be plotted on a screen.
This is an example with small numbers and trying all divisors just to show you the pattern.

My idea is, for big numbers, NOT to try all possible divisors but only a very small part of them, just enough to "draw" the curves.
And then try to detect "hot" areas.
And that's the question, of course I don't know if this could be useful.
Maybe not just as a new method but in combination with other methods.

I'm just an amateur on "number theory" and factorization methods, and as I said English is not one of my native languages.

Regards

[xilman]

Originally Posted by R.D. Silverman

My post #10 was in response to #7. Or am I not allowed to defend myself?
I criticized an essay written out of almost total ignorance. I took the time
to dissect that essay. I extracted individual phrases and pointed out
why they were nonsense. I explained why the use of the word "curve"
was wrong. I did not respond to the "essay" with

"You're an idiot and this is complete garbage"

Of course you are allowed to defend yourself. That's not in question. The debate is entirely about the phrasing of your defen{c,s}e. IMAO anyway.

Originally Posted by R.D. Silverman

I am not well. I am still getting chemotherapy. Mantle Cell Lymphoma
never goes away. It can get better for a while, but always comes back.
I am having discussions about a possible bone marrow transplant.

Yup. happens.

To the best of us, and to the worst of us, and to everyone in between. You have my sympathy and my assurance that you are in good company.

Originally Posted by R.D. Silverman

On a more general note:

Much of the debate here should be put in a more general setting.
This isn't about math, per se. It is about basic standards of scholarship.
When one reads an essay (in any subject), one expects that the author
of the essay has performed the necessary background reading and study.
If an essay is written on (say) "Romeo and Juliet", one expects that the
author has read the play at more than just a superficial level.
Intelligent discussion of technical subjects requires "in depth" study.

I agree entirely. My only point of disagreement is whether your bedside manner is an optimal response under specific circumstances.

(For the benefit of other forum readers: Bob and I have been discussing these matters for many years, sometime by private email, sometimes in public fora and newsgroups, and once over beer in Cambridge. "These matters" include both intellectual concerns and our respective states of health)

[skan]

Hello

I wouldn't like that this thread was closed. It would be nice if some administrator could "clean" some of the posts.
And if somebody is not interested just look somewhere else.

[Batalov]

Hey, skan, from the title of your thread I gather that you yourself expected some criticism. You reiterated it now: you don't want the thread closed, you want to hear more. But there's a contradiction: at the same time, you want the thread "cleaned"? Of what parts? They are all more or less connected. Most of them have advice (some of which you may not like, but sound nevertheless).

On the bright side, you haven't received any really insightful answers yet, like

Originally Posted by davieddy

Hey, foetus boy...

Yep. That is the full message. This is the level at which we usually clean.

[skan]

Originally Posted by Batalov

Hey, skan, from the title of your thread I gather that you yourself expected some criticism. You reiterated it now: you don't want the thread closed, you want to hear more. But there's a contradiction: at the same time, you want the thread "cleaned"? Of what parts? They are all more or less connected. Most of them have advice (some of which you may not like, but sound nevertheless).

On the bright side, you haven't received any really insightful answers yet, like

Yep. That is the full message. This is the level at which we usually clean.

Hello

I meant "clean the thread from personal attacks and disqualifications", just like if nothing bad had happened.
And leave all comments related with graphics, ideas, maths, science, computers...

Regards
Cheesehead, thank you for your support.

[skan]

Hi Silverman.

I know there already exist many factorization and sieve methods.
This is not intended to replace them, just to further restrict the sieve.

I know the meaning of "Trial Division", and I even read about "quadratic sieve" and "number field sieve" some years ago. I'm not mathematician, just an engineer than loves maths. I do know what's "O(N^1/4)".

I don't like "number theory" books because they are too theoretical for me. That's why I tried to focus it from a different point of view.

Yes, There are relationship between N mod k and N mod (k+1).
I can't explain them algebraically, but I guess you mean they are the patterns in the graphics.


OK, just tell me it's evident this is not useful.
Maybe somebody else could enjoy the graphics or get new ideas from them.

[skan]

But I'm not trying to discuss about deep number number theory concepts but about heuristics and feelings.

Do you know Monte Carlo algorithms?
Sometimes they can be used to solve numerically difficult integrals quickly, even if you don't know how to solve the integral exactly. This is just another way of doing things.

[Batalov]

There already is a Monte Carlo factorization method. Since 1975.

[TheMawn]

To Skan:

It is no surprise to me that you are an Engineer. A lot of engineering is about observation. It's about observing a pattern and applying whatever knowledge is readily available to try to extend the pattern into something useful. That's exactly what you are trying to do here.

On the other hand, you are debating with a mathematician. I've dealt with a few in my first couple of years of school and I think it's adorable how much they hate us. It's hard to blame them, really.

An engineer like me takes four calculus courses (so far I have found no reason why you couldn't cut away 60% of the material and make two slightly more bearable courses rather than the four nightmares we did have) and has enough knowledge to work in several different fields. For example, I use "maths" in fluid dynamics, solid mechanics, heat transfer, thermodynamics and controls systems.

Basically, the engineer works probably 5% as hard on any given subject and gets an answer with 15% accuracy. A mathematician would pull out his teeth trying to come up with a heat transfer equation for the most basic of systems but the engineer can take the most complicated ones, just do a bunch of tests, plots the results and write up a correlation for a curve that best matches all the points.

Mathematicians hate that kind of thing but, much to their chagrin, that's the sort of thing that makes real application continue to march forward.

[TheMawn]

I was simply making the distinction between the straight-up "Math" and the "Engineering" where in engineering we can, usually, form a correlation to get "close enough" based on enough empirical evidence. To be perfectly honest, it wasn't meant to be criticism to either side. (Granted I might have been biased against mathematicians, but that wasn't the point)

I can't pretend to understand very much about what is being discussed. I saw some graphs and some-points-which-could-clearly-be-connected-by-a-relatively-simple-curve-but-do-not-of-themselves-constitute-a-curve and at a glance there is obviously a pattern. I didn't really care much about the content because I again don't understand it.

What got me was the question of could we begin this curve by learning a bit about a new number and then extend the curve and work closer to whatever values these might be. My first comment in this thread was seconding Cheesehead with respect to you being rude. Yes, you gave criticism as is your right but it just came out a bit harsh. My second comment was regarding the Engineering vs Mathematics or Approximations vs Exact Solutions.

Of course, now that I look at the graphs themselves I feel myself gravitating a bit more to the "not entirely useful" side of the fence. The "curves" in the third graph are actually just tending toward y = x, y = -x, and y = 0 which unfortunately do not tell us anything. Pretty? Sure. Useful, not so much, I'm afraid.