# Site Review Request - Page 2

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## Re: Site Review Request

On Tue, 14 Jan 2014 15:50:25 +1100, dorayme wrote:

Bravo, dorayme.

Here's a cute little cubic polynomial p(x) whose first four values p(1),
p(2), p(3), and p(4) coincide with the first four powers of 2, as anyone
with half a brain (or any sort of calculator) can quickly confirm: let

: p(x) = (8x)/3 - x^2 + (x^3)/3 = ((x/3 -1)x + 8/3)x .

(That p(1) = 2 = 2^1, p(2) = 4 = 2^2, p(3) = 8 = 2^3, and p(4) = 16 = 2^4
can be left as exercises. BTW, note: p(0) = 0 != 2^0, and p(5) = 30 != 2^5.
That should be no surprise, as e(n) = 2^n is not a polynomial at all :-) .

If you're willing to countenance polynomials of degree 4 (or more), one can
easily (using linear algebra) establish the existence of infinitely many
polynomials having these powers of 2 as their first four values.

And here are a few more simple (non-polynomial) rules that give functions
f(x) whose first four values are those under discussion in this thread:

1) f(n) = the lesser of 16 and 2^n = min(16, 2^n);
2) f(n) = min(2^n, the greater of n and 16) = min(2^n, max(n, 16));
3) f(n) = 2^(1 + remainder upon dividing n-1 by 4);
4) f(n) = 2^n, in case n = 1, 2, 3, or 4, but = n^th digit in the decimal
expansion of , in case n > 4;
5) f(n) = 2^n, in case n = 1, 2, 3, or 4, but = 0 in case n > 4.

Notice 1) goes 2, 4, 8, 16, 16, 16, 16, 16, 16, 16, ..., 16, ... ,
while 2) goes 2, 4, 8, 16, 17, 18, 19, 20, 21, 22, ... ,
3) goes 2, 4, 8, 16, 2, 4, 8, 16, 2, 4, ... ,
4) goes 2, 4, 8, 16, 3, 1, 4, 1, 5, 9, ... , and
5) goes 2, 4, 8, 16, 0, 0, 0, 0, 0, 0, ..., 0, ... .

There are, of course, infinitely many more such rules, some simpler than
others in the eyes of some beholders. But who am I to say which is "too
inelegant" to consider at all :-) ?

Oh: and *of course* the collection of all such infinite sequences beginning
2 4 8 16 is an abelian group, under the operation of entry-wise arithmetic
addition *after* the first four entries 2 4 8 and 16, which must of course
remain  fixed (neutral element is my function/sequence # 5 above); additive
inverse to sequence

f = { 2, 4, 8, 16, f(5), f(6), ..., f(n), ... }

is: { 2, 4, 8, 16, -(f(5)), -(f(6)), ..., -(f(n)), ... } .

:-) . Cheers, -- tlvp

PS: can we *now* get back to the proper subject matter for [ciw]ah at last?
--
Avant de repondre, jeter la poubelle, SVP.

## Re: Site Review Request

On Tue, 14 Jan 2014 11:50:30 -0500, tlvp wrote:

I see no one was awake :-{ . (mmph!) -- tlvp
--
Avant de repondre, jeter la poubelle, SVP.

## Re: Site Review Request

Well I couldn't be arsed to read all that. But looking at the above I
suppose it continues:

2, 6, 5, 3, 5, 8, 9, 7, 9, ...

--
Tim

"That excessive bail ought not to be required, nor excessive fines imposed,
nor cruel and unusual punishments inflicted"  --  Bill of Rights 1689

## Re: Site Review Request

Ben Bacarisse wrote:

You did.

Usenet is organized into groups of topics, not groups of people.

Apples and oranges.

F'up2 poster

PointedEars
--
Sometimes, what you learn is wrong. If those wrong ideas are close to the
root of the knowledge tree you build on a particular subject, pruning the
bad branches can sometimes cause the whole tree to collapse.

## Re: Site Review Request

On Mon, 13 Jan 2014 20:42:31 +1100, dorayme wrote:

To illustrate: a powers-of-two enthusiast would see: ... 32, 64, 128, ... ;
a lazy, unambitious simpleton would predict: ... 16, 16, 16, ... ;
a rinse-and-repeat expert would suggest: ... 2, 4, 8, 16, 2, 4, 8, ... ;
a conservative would think: ... 17, 18, 19, 20, ... (after an initial burst
of speed to get a running start, and now just quietly loping along :-) ).

As many more continuations possible as intellects in the universe. Cheers,

-- tlvp
--
Avant de repondre, jeter la poubelle, SVP.

## Re: Site Review Request

tlvp wrote:

JFTR: Your illustration does not prove the soundness of dorayme's argument;
for there is at least one a valid argument.  And for each of your
continuations to be valid you have to give a *mathematical* rule that is
satified not only by the continuations but also by the known elements; it
cannot be completely arbitrary.  Also, by allowing an element before 2 you
have modified the original proposition.  Therefore, I daresay your logic is
flawed, and there is a finite number of rules that pertain and satisfy the
original proposition.

F'up2 sci.math

PointedEars
--
var bugRiddenCrashPronePieceOfJunk = (
navigator.userAgent.indexOf('MSIE 5') != -1
&& navigator.userAgent.indexOf('Mac') != -1
)  // Plone, register_function.js:16

## Re: Site Review Request

dorayme wrote:

When I see those numbers, I always think 31.

/Nisse

## Re: Site Review Request

That link provides garbage results. Putting "2+4+8+16+31" (with quotes)
in the search box provided links that looked considerably more relevant.

Looks like the link should be:

Yeah, that makes a lot more sense!

## Re: Site Review Request

On Mon, 27 Jan 2014 09:33:57 -0500, David Stone wrote:

My older (but latest) Safari in Win Vista got perfectly fine results.
Evidently choice of browser may make a difference. Cheers, -- tlvp
--
Avant de repondre, jeter la poubelle, SVP.

## Re: Site Review Request

In article

Nice example:

<http://mathworld.wolfram.com/CircleDivisionbyChords.html

--
dorayme

## Re: Site Review Request

Molly Mockford wrote:

Hi Adrienne, sorry but I find these captcha schemes both very annoying
and ineffective. I looked into it when my sites stated to get hit with
comment spambots and after a bit of research I took a different tack.

I use a honeypot strategy: Put a field on your form that is irresistible
for bots like "username", "userid", etc. Then in the stylessheet set
that field to "display: none". Humans really do not disable stylesheets
so only bots will see the field. Now in your validation all you have to
do in here in pseudo-code:

If post field "userid" exists then
do nothing it is a bot
else
process "human" generated input

This is totally transparent to the user and is effective. For mine in
the "do nothing" condition I generate a log. I can confirm I have had
not one false positive and it has been 100% effective. Interesting that
the bots are coming from a few IPs (Ukraine and Russian Federation) and
they always use an ALO email address.

--
Take care,

Jonathan
-------------------
LITTLE WORKS STUDIO
http://www.LittleWorksStudio.com

## Re: Site Review Request

Jonathan, thank you so much, that is exactly what I'm going to do. I hate

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Please respond to the group so others can share

## Re: Site Review Request

So do I so much so was was very very reluctant to employ one. Other
schemes seemed too complicated, used JavaScript and other things that
was so simple and after over a year of logging I can confirm 100%
effective. The serverside can be as simple as a one liner PHP

if(array_key_exists('userid', \$_REQUEST) and \$_REQUEST['userid'] != '')
header('Location: http://' . \$_SERVER['PHP_SELF'] .  '/twilightzone.html');

I do a bit more with some logging because I want to keep tabs on the
little buggers.

--
Take care,

Jonathan
-------------------
LITTLE WORKS STUDIO
http://www.LittleWorksStudio.com

## Re: Site Review Request

Interesting. Noted.
--
Where's the Vangelis music?
Pris' tongue is sticking out in in the wide shot after Batty has kissed her.
They have put back more tits into the Zhora dressing  room scene.

## Re: Site Review Request

On Mon, 13 Jan 2014 11:19:12 -0500, "Jonathan N. Little"

Provided, of course, that your page doesn't have a polka-dot
background that makes it impossible to read with stylesheets enabled.

(Real example -- recently corrected by (I gather) a new webmaster.)

--
Joy Beeson
joy beeson at comcast dot net

## Re: Site Review Request

Joy Beeson wrote:

> (Real example -- recently corrected by (I gather) a new webmaster.)
>

Or red text on black busy background. Yes I would avoid offering a user
a "desire" to disable your stylesheet. And other methods I have found
have more chances to fail.

--
Take care,

Jonathan
-------------------
LITTLE WORKS STUDIO
http://www.LittleWorksStudio.com

## Re: Site Review Request

On Mon, 13 Jan 2014 23:20:03 -0400, Joy Beeson wrote:

Agreed. *This* human would disable not stylesheets but the offending page
-- by browsing elsewhere instead :-) . Cheers, -- tlvp
--
Avant de repondre, jeter la poubelle, SVP.

#1 Bots

## Re: Site Review Request

Hot-Text wrote:

Crawling and indexing is not the problem. Googlebot does not send forms.

--
Take care,

Jonathan
-------------------
LITTLE WORKS STUDIO
http://www.LittleWorksStudio.com

## Re: Site Review Request

Jonathan N. Little wrote:

Actually, it kind of does.  I periodically get a contact form on one of
my sites sent to me.  It looks like this:

----------------------------
To: xxxxx@guitarsnotguns.org
From: FormMail@guitarsnotguns.org

This is a test alert message
PHP version is 5.3.27
FormMail version is 8.36
Server type: non-Windows

DOCUMENT_ROOT: /home/ed_mullen/guitarsnotguns.org
SCRIPT_FILENAME: /home/ed_mullen/guitarsnotguns.org/contactform_script.php
PATH_TRANSLATED: -not set-
REAL_DOCUMENT_ROOT: /home/ed_mullen/guitarsnotguns.org

SERVER_NAME was guitarsnotguns.org

User agent was Mozilla/5.0 (compatible; Googlebot/2.1;
--------------------

I use the FormMail PHP script

<http://www.tectite.com/formmailpage.php?WWWTECTITE=eavdpic8v9p568olv6r3dm7rf4

which has a function for testing a form (see the REQUEST_URI above).
How Googlebot ever figured that out I don't know.  I posted a message on
Tectite's forum asking if anyone else is seeing this. No replies yet.

--
Ed Mullen
http://edmullen.net/
All that glitters has a high refractive index.