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**posted on**

- Adrienne Boswell

January 13, 2014, 7:39 am

at <http://beta.aloyaltycard.com/ .

I am particularly interested in accessibility and ease of use. I would

also like testing from desktop and/or mobile. I would like to know what

browser and what device, and if you are using a mobile device, what color

the background is. Mobile devices are supposed to get a different color

and slightly different content - I want to be sure the site is behaving

as it should.

If you want to open accounts, go ahead. If you want me to remove the

account after testing, please state so in your reply.

Go ahead, be brutal. The more input I have from here, the better.

Thanks in advance.

--

Adrienne Boswell

Arbpen Web Site Design Services - http://www.cavalcade-of-coding.info/

The Good Plate - Fresh Gourmet Recipes - http://the-good-plate.com/

Please respond to the group so others can share

## Re: Site Review Request

This isn't what you're looking for, but your humanity test on the

Contact page is ambiguous. The fox is the only one which is not a

domesticated farmyard animal; the chicken is the only one which does

not have four legs. Which of them is supposed to be the right answer?

Each is equally valid.

Oh, and I don't think it's a "series", which by definition is in order

such that one can predict the next entry (2, 4, 8, 16...). It is a

group, equivalent to an unordered list.

--

Molly Mockford

Nature loves variety. Unfortunately, society hates it. (Milton Diamond Ph.D.)

(My Reply-To address *is* valid, though may not remain so for ever.)

## Re: Site Review Request

In fact all humanity tests are ambiguous in the strict sense that

there is a rule that someone can dream up that covers the given data

points, no matter what they are. Take your number series, there are

any number of continuations after 16. Where the humanity comes in is

perhaps in the fact that it is hard for humans to dream up more than

one or a very few rules that could cover the givens.

Put it this way, there is no logical deduction from 2, 4, 8, 16, to

any particular number. There is no valid argument. That is the trouble

with induction as a form of reasoning.

--

dorayme

## Re: Site Review Request

dorayme wrote:

It is indicative of a (geometric)

(multiplicative) (recursion) rule can be defined that is observed for all

items so far that allows to determine the next item from the previous one:

“a

(r = 2 here.)

It may be, but is not indicative of, a group, because it does not

(obviously) meet the requirements for a group, such as an (obvious)

operation • and closure under that operation:

“For all a, b in G, the result of the operation, a • b, is also in G.” [2]

First of all, a group operation has not been defined. Second, for example,

an arbitrarily chosen,

multiplication, with the group being abelian, too (2 × 4 = 4 × 2 = 8, 2 × 8

= 8 × 2 = 16, 4 × 8 = 8 × 4 = 32, aso.; ibid.) But there is no such

multiplication of any of these four known elements, or an element in

continuation, such that the result would be 2. Therefore, under this

assumption, this entity is not closed under such multiplication, and is not

a group. It may be that there is a non-obvious group operation to satisfy

closure, but it has to be

called a group.

I do not think so. You appear to be ignoring that the rules must be the

same for all elements.

Why is

“Each of these numbers x_i, counting i as integer from 0, satisfies the

condition x

this way, the next number must be x

not a valid argument?

[1] <http://en.wikipedia.org/wiki/Geometric_progression

[2] <http://en.wikipedia.org/wiki/Group_ (mathematics)>

F'up2 sci.math

PointedEars

--

Not with javascript. Nonsense propagates like wildfire in this field.

-- Richard Cornford, comp.lang.javascript, 2011-11-14

It is indicative of a (geometric)

***sequence***in math, because a(multiplicative) (recursion) rule can be defined that is observed for all

items so far that allows to determine the next item from the previous one:

“a

___n = r a___{n - 1} for every integer n ≥ 1.” [1](r = 2 here.)

It may be, but is not indicative of, a group, because it does not

(obviously) meet the requirements for a group, such as an (obvious)

operation • and closure under that operation:

“For all a, b in G, the result of the operation, a • b, is also in G.” [2]

First of all, a group operation has not been defined. Second, for example,

an arbitrarily chosen,

***obvious***group operation would be integer/realmultiplication, with the group being abelian, too (2 × 4 = 4 × 2 = 8, 2 × 8

= 8 × 2 = 16, 4 × 8 = 8 × 4 = 32, aso.; ibid.) But there is no such

multiplication of any of these four known elements, or an element in

continuation, such that the result would be 2. Therefore, under this

assumption, this entity is not closed under such multiplication, and is not

a group. It may be that there is a non-obvious group operation to satisfy

closure, but it has to be

***defined***before this entity can be reasonablycalled a group.

I do not think so. You appear to be ignoring that the rules must be the

same for all elements.

Why is

“Each of these numbers x_i, counting i as integer from 0, satisfies the

condition x

___i = 2 x___for i > 0. Therefore, to continue the sequence inthis way, the next number must be x

___4 = 2 x___= 2 x_3 = 2 × 16 = 32.”not a valid argument?

[1] <http://en.wikipedia.org/wiki/Geometric_progression

[2] <http://en.wikipedia.org/wiki/Group_ (mathematics)>

F'up2 sci.math

PointedEars

--

Not with javascript. Nonsense propagates like wildfire in this field.

-- Richard Cornford, comp.lang.javascript, 2011-11-14

## Re: Site Review Request

I am not so sure about that anymore. It may be a fallacy to conclude that

closure implies that the operation must be able to produce each element in a

group.

However, I think it will be hard to find an operation • and an element e in

G = {2, 4, 8, 16, …} that satisfy the following two group axioms:

- “There exists an element e in G [– the identity element –], such that for

every element a in G, the equation e • a = a • e = a holds.”

- “For each a in G, there exists an element b in G such that

a • b = b • a = e, where e is the identity element.”

None of the known elements satisfies the conditions for the identity

element, and none of the unknown elements can satisfy the condition for the

identity element under multiplication. An assumed, previously unknown

identity element 1 would satisfy the first of these axioms, but not the

second one. IOW, the required inverse element is missing.

F'up2 sci.math

PointedEars

--

Prototype.js was written by people who don't know javascript for people

who don't know javascript. People who don't know javascript are not

the best source of advice on designing systems that use javascript.

## Re: Site Review Request

Ben Bacarisse wrote:

G := {2^n, 2^(1/n); n > 0} is

it is not closed:

n := 1 ⇒ 2^1 = e ∈ G

n := 2 ⇒ a := 2^2 ∈ G

n := 3 ⇒ 2^3 ∈ G ⇒ b := 2^(1/3) ∈ G

a • b = 2^2 • 2^(1/3) = 2^(2 × 1/3) = 2^(2/3) ∉ G.

Why have you ignored the Followup-To? Set again.

PointedEars

--

Anyone who slaps a 'this page is best viewed with Browser X' label on

a Web page appears to be yearning for the bad old days, before the Web,

when you had very little chance of reading a document written on another

computer, another word processor, or another network. -- Tim Berners-Lee

G := {2^n, 2^(1/n); n > 0} is

___not___a group under 2^a • 2^b = 2^(ab) becauseit is not closed:

n := 1 ⇒ 2^1 = e ∈ G

n := 2 ⇒ a := 2^2 ∈ G

n := 3 ⇒ 2^3 ∈ G ⇒ b := 2^(1/3) ∈ G

a • b = 2^2 • 2^(1/3) = 2^(2 × 1/3) = 2^(2/3) ∉ G.

Why have you ignored the Followup-To? Set again.

PointedEars

--

Anyone who slaps a 'this page is best viewed with Browser X' label on

a Web page appears to be yearning for the bad old days, before the Web,

when you had very little chance of reading a document written on another

computer, another word processor, or another network. -- Tim Berners-Lee

## Re: Site Review Request

Good point. You need all rational powers. Thanks. I should have

stopped at e and the operation and just said "then close G" because you

never asked for the set! Anyway, we got there in the end (unless I've

make another mistake).

I wanted the people who originally saw the question to see my

suggestion. Presumably that's similar to why you ignored it when you

clarified your question.

--

Ben.

## Re: Site Review Request

In article

In simple terms has someone convinced you that there

deduction from 2, 4, 8, 16 to some particular number?

There are any number of valid deductive arguments possible if you

build into premises (directly or by assumption) the rule itself. I am

sure that is what Thomas has been doing. I would not dream of trying

to disentangle his misunderstandings.

Let me put it more strictly:

You are a logical thinker, you know maths, you know how to calculate

and you are pretty good at pattern spotting and making. You are

watching numbers (let's not quibble) come up in front of you. They

stop and you are required to say what you think the next one will be,

your only instruction being that you must base your prediction

entirely from observation of the numbers alone, not relying on any

inside knowledge about the generator. Is there some number that is

backed by a deductive argument? There cannot be, surely.

--

dorayme

In simple terms has someone convinced you that there

***is***a logicaldeduction from 2, 4, 8, 16 to some particular number?

There are any number of valid deductive arguments possible if you

build into premises (directly or by assumption) the rule itself. I am

sure that is what Thomas has been doing. I would not dream of trying

to disentangle his misunderstandings.

Let me put it more strictly:

You are a logical thinker, you know maths, you know how to calculate

and you are pretty good at pattern spotting and making. You are

watching numbers (let's not quibble) come up in front of you. They

stop and you are required to say what you think the next one will be,

your only instruction being that you must base your prediction

entirely from observation of the numbers alone, not relying on any

inside knowledge about the generator. Is there some number that is

backed by a deductive argument? There cannot be, surely.

--

dorayme

## Re: Site Review Request

Hmmm... I'd say that some are "more backed" than others. I agree 100%

that there can't be one deduced right answer, but there is something

either "hard wired" or in our culture that seems to favour simple

explanations. That makes some suggestions seem "more right" than

others, although an explanations can be deeply satisfying to some and

really annoying to others. I doubt there is anything very objective

going on[1]. I remember being posed the puzzle: a, e, f, h, i, k... at

school and the answer[2] sharply dividing option!

[1] For plain number sequences, the simplicity of the "explanation" can

be codified using algorithmic complexity theory.

[2] (rot13, in case anyone actually /likes/ puzzles) Gurfr ner gur

yrggref jubfr pncvgny sbezf ner pbairagvbanyyl jevggra hfvat bayl

fgenvtug yvarf, fb yza ner gur arkg guerr.

--

Ben.

## Re: Site Review Request

On Tue, 14 Jan 2014 11:47:53 +0000, Ben Bacarisse wrote:

Heh-heh ... in my day, the next character was an "i" again, as this was the

sequence of initial characters of the words in the then well-worn phrase

: After each failure, he is kicked in the ribs.

HTH. Cheers, -- tlvp

--

Avant de repondre, jeter la poubelle, SVP.

Heh-heh ... in my day, the next character was an "i" again, as this was the

sequence of initial characters of the words in the then well-worn phrase

: After each failure, he is kicked in the ribs.

HTH. Cheers, -- tlvp

--

Avant de repondre, jeter la poubelle, SVP.

## Re: Site Review Request

The irony of IQ tests is that the smarter you are the more likely you

are to see a pattern that was not intended, you fail not because you

are not awfully clever but because you see more possibilities than the

committee that set the question and much more than the less

intelligent who see very few possibilities and not the one intended.

--

dorayme

## Re: Site Review Request

dorayme wrote:

And there have been studies that show that IQ performace on tests

decreases with age.

I tested very high in my teens. Not so much now. And? Frankly I don't

care. Made my mark and money. What's the point? Pat myself on the

back as to how "smart" I am? Couldn't care less. I'm Popeye: I yam what

I yam.

So, real-life achievement? How do you measure it? You can be

incredibly intellgent and not achieve much at all. Or vice-versa.

What's the question?

--

Ed Mullen

http://edmullen.net/

Have you noticed since everyone has a camcorder these days no one talks

about seeing UFOs like they used to?

And there have been studies that show that IQ performace on tests

decreases with age.

I tested very high in my teens. Not so much now. And? Frankly I don't

care. Made my mark and money. What's the point? Pat myself on the

back as to how "smart" I am? Couldn't care less. I'm Popeye: I yam what

I yam.

So, real-life achievement? How do you measure it? You can be

incredibly intellgent and not achieve much at all. Or vice-versa.

What's the question?

--

Ed Mullen

http://edmullen.net/

Have you noticed since everyone has a camcorder these days no one talks

about seeing UFOs like they used to?

## Re: Site Review Request

In article

...

If we did not have the ability to stake our lives on some patterns

rather than others, we would never have evolved. We are wired to grow

to make up patterns in our brains and match them to the world outside

in predictions, guesses.

Curiously enough, evolution and the success of science in real time,

is all based on that we have

Knowledge gathering would hardly be possible if we really could

somehow keep in mind the infinite number of possible explanations

(patterns) for anything.

We know other humans cannot do this, that they are limited, that if we

can see a pattern in what they are saying, it is likely they are using

that pattern themselves (hence the confidence in predicting what

someone asking IQ type questions about series has in mind). But that

The patterns we do see, the ones we see most easily, are the simplest

ones. But simple is partly because we see them, not necessarily

because they are somehow objectively this or that. Shortness of

formulae, briefly stated theories, are often an apparent objective

measure of simplicity but there is no particular reason that I can see

why the world

We can do no other than to treat it as simple enough for us to

understand, but who are we to really know, it is just a practical

requirement, we can do no other.

--

dorayme

...

If we did not have the ability to stake our lives on some patterns

rather than others, we would never have evolved. We are wired to grow

to make up patterns in our brains and match them to the world outside

in predictions, guesses.

Curiously enough, evolution and the success of science in real time,

is all based on that we have

***limited***pattern recognition abilities.Knowledge gathering would hardly be possible if we really could

somehow keep in mind the infinite number of possible explanations

(patterns) for anything.

We know other humans cannot do this, that they are limited, that if we

can see a pattern in what they are saying, it is likely they are using

that pattern themselves (hence the confidence in predicting what

someone asking IQ type questions about series has in mind). But that

***is***having inside knowledge about the generator of the data!The patterns we do see, the ones we see most easily, are the simplest

ones. But simple is partly because we see them, not necessarily

because they are somehow objectively this or that. Shortness of

formulae, briefly stated theories, are often an apparent objective

measure of simplicity but there is no particular reason that I can see

why the world

***must***or even is***probably***simple.We can do no other than to treat it as simple enough for us to

understand, but who are we to really know, it is just a practical

requirement, we can do no other.

--

dorayme

## 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

2 4 8 16 is an abelian group, under the operation of entry-wise arithmetic

addition

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

--

Avant de repondre, jeter la poubelle, SVP.

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 beginning2 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 courseremain 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

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.

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

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

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

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 issatified 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

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