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Re: And they say C is obscure

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  Re: And they say C is obscure "J. Clarke" <j.clarke.873638@gmail.com> - 2017-05-28 16:03 -0400
    Re: And they say C is obscure Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2017-05-30 02:21 -0700
      Re: And they say C is obscure "J. Clarke" <j.clarke.873638@gmail.com> - 2017-06-04 20:55 -0400
        Re: And they say C is obscure Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2017-06-05 01:44 -0700
          Re: And they say C is obscure raltbos@xs4all.nl (Richard Bos) - 2017-06-05 09:47 +0000
            Re: And they say C is obscure Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2017-06-05 03:51 -0700
              Re: And they say C is obscure Gareth Owen <gwowen@gmail.com> - 2017-06-05 15:43 +0100
                Re: And they say C is obscure Tim Rentsch <txr@alumni.caltech.edu> - 2017-06-05 13:51 -0700
                Re: And they say C is obscure raltbos@xs4all.nl (Richard Bos) - 2017-06-06 17:26 +0000
        Re: And they say C is obscure Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-06-05 11:59 +0100
          Re: And they say C is obscure Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2017-06-05 04:12 -0700
            Re: And they say C is obscure asetofsymbols@gmail.com - 2017-06-05 05:54 -0700
            Re: And they say C is obscure Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-06-05 15:03 +0100
              Re: And they say C is obscure Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2017-06-05 07:22 -0700
                Re: And they say C is obscure GOTHIER Nathan <nathan.gothier@gmail.com> - 2017-06-05 16:22 +0200
                  Re: And they say C is obscure Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2017-06-05 07:40 -0700
                    Re: And they say C is obscure GOTHIER Nathan <nathan.gothier@gmail.com> - 2017-06-05 16:41 +0200
                Re: And they say C is obscure Gareth Owen <gwowen@gmail.com> - 2017-06-05 15:44 +0100
                Re: And they say C is obscure Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-06-05 16:12 +0100
                  Re: And they say C is obscure Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2017-06-05 09:08 -0700
                    Re: And they say C is obscure David Kleinecke <dkleinecke@gmail.com> - 2017-06-05 12:08 -0700
                    Re: And they say C is obscure asetofsymbols@gmail.com - 2017-06-05 13:10 -0700
                    Re: And they say C is obscure Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-06-05 23:54 +0100
                      Re: And they say C is obscure Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2017-06-06 01:15 -0700
                        Re: And they say C is obscure David Brown <david.brown@hesbynett.no> - 2017-06-06 11:10 +0200
                          Re: And they say C is obscure Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2017-06-06 02:39 -0700
                            Re: And they say C is obscure David Brown <david.brown@hesbynett.no> - 2017-06-06 12:15 +0200
                              Re: And they say C is obscure Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2017-06-06 03:47 -0700
                                Re: And they say C is obscure David Brown <david.brown@hesbynett.no> - 2017-06-06 13:09 +0200
                                  Re: And they say C is obscure Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2017-06-06 05:26 -0700
                                    Re: And they say C is obscure GOTHIER Nathan <nathan.gothier@gmail.com> - 2017-06-06 14:25 +0200
                                      Re: And they say C is obscure Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2017-06-06 05:34 -0700
                                        Re: And they say C is obscure GOTHIER Nathan <nathan.gothier@gmail.com> - 2017-06-06 15:41 +0200
                                    Re: And they say C is obscure David Brown <david.brown@hesbynett.no> - 2017-06-06 15:04 +0200
                                    Re: And they say C is obscure raltbos@xs4all.nl (Richard Bos) - 2017-06-06 17:37 +0000
                                      Re: And they say C is obscure David Brown <david.brown@hesbynett.no> - 2017-06-07 10:17 +0200
                                Re: And they say C is obscure Keith Thompson <kst-u@mib.org> - 2017-06-06 08:49 -0700
                                  Re: And they say C is obscure Gareth Owen <gwowen@gmail.com> - 2017-06-06 19:17 +0100
                              Re: And they say C is obscure Gareth Owen <gwowen@gmail.com> - 2017-06-06 19:16 +0100
                            Re: And they say C is obscure Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-06-06 12:44 +0100
                            Re: And they say C is obscure raltbos@xs4all.nl (Richard Bos) - 2017-06-06 17:34 +0000
                              Re: And they say C is obscure David Brown <david.brown@hesbynett.no> - 2017-06-06 21:14 +0200
                            Re: And they say C is obscure Tim Rentsch <txr@alumni.caltech.edu> - 2017-06-06 13:10 -0700
                              Re: And they say C is obscure Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2017-06-06 14:34 -0700
                                Re: And they say C is obscure Keith Thompson <kst-u@mib.org> - 2017-06-06 15:27 -0700
                                Re: And they say C is obscure Tim Rentsch <txr@alumni.caltech.edu> - 2017-06-11 16:06 -0700
                        Re: And they say C is obscure Ben Bacarisse <ben.usenet@bsb.me.uk> - 2017-06-06 12:10 +0100
                          Re: And they say C is obscure Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2017-06-06 04:36 -0700
                        Re: And they say C is obscure raltbos@xs4all.nl (Richard Bos) - 2017-06-06 17:32 +0000
                Re: And they say C is obscure David Brown <david.brown@hesbynett.no> - 2017-06-05 17:58 +0200

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#111570

On Monday, June 5, 2017 at 9:08:39 AM UTC-7, Malcolm McLean wrote:
> On Monday, June 5, 2017 at 4:12:17 PM UTC+1, Ben Bacarisse wrote:
> > 
> > Why must you leap to saying that nesting and indexing are
> > interchangeable just because you've concluded there is /some/ relation
> > between two 3s appearing in ones observation's (or, in this case, in
> > ones assumptions)?  To make that leap you'd have to know the nature of
> > the relationship and you'd have to make another case about general
> > indexing (where this is not topology) and 3D geometry (where there is).
> > 
> An array of arrays of arrays is nesting.

I think the evidence from linguistics is that tolerance for
embedding (of clauses within clauses in English) varies from
person to person and is more like six or seven than three.

I know that I can count the number of items in a set (for
example pills) in a glance if the number is no greater than
six but I make mistakes at seven. A very practical problem
if one fills a weekly pill box.

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#111580

If array of array is nesting are nesting recursive functions too...

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#111594

Malcolm McLean <malcolm.arthur.mclean@gmail.com> writes:

> On Monday, June 5, 2017 at 4:12:17 PM UTC+1, Ben Bacarisse wrote:
>> 
>> Why must you leap to saying that nesting and indexing are
>> interchangeable just because you've concluded there is /some/ relation
>> between two 3s appearing in ones observation's (or, in this case, in
>> ones assumptions)?  To make that leap you'd have to know the nature of
>> the relationship and you'd have to make another case about general
>> indexing (where this is not topology) and 3D geometry (where there is).
>> 
> An array of arrays of arrays is nesting.

"X is a kind of Y" does not mean that "X and Y are interchangeable".  I
don't think there's much point in going on is there?

-- 
Ben.

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#111611

On Monday, June 5, 2017 at 11:55:00 PM UTC+1, Ben Bacarisse wrote:
> Malcolm McLean <malcolm.arthur.mclean@gmail.com> writes:
> 
> > On Monday, June 5, 2017 at 4:12:17 PM UTC+1, Ben Bacarisse wrote:
> >> 
> >> Why must you leap to saying that nesting and indexing are
> >> interchangeable just because you've concluded there is /some/ relation
> >> between two 3s appearing in ones observation's (or, in this case, in
> >> ones assumptions)?  To make that leap you'd have to know the nature of
> >> the relationship and you'd have to make another case about general
> >> indexing (where this is not topology) and 3D geometry (where there is).
> >> 
> > An array of arrays of arrays is nesting.
> 
> "X is a kind of Y" does not mean that "X and Y are interchangeable".  I
> don't think there's much point in going on is there?
> 
You're thinking too much like a mathematician.

But the rule of three is a psychological claim, not a mathematical one.

If X is a kind of Y then we expect so in X, as in Y, just as we know 
as in Y, so in X.

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#111612

On 06/06/17 10:15, Malcolm McLean wrote:
> On Monday, June 5, 2017 at 11:55:00 PM UTC+1, Ben Bacarisse wrote:
>> Malcolm McLean <malcolm.arthur.mclean@gmail.com> writes:
>>
>>> On Monday, June 5, 2017 at 4:12:17 PM UTC+1, Ben Bacarisse wrote:
>>>>
>>>> Why must you leap to saying that nesting and indexing are
>>>> interchangeable just because you've concluded there is /some/ relation
>>>> between two 3s appearing in ones observation's (or, in this case, in
>>>> ones assumptions)?  To make that leap you'd have to know the nature of
>>>> the relationship and you'd have to make another case about general
>>>> indexing (where this is not topology) and 3D geometry (where there is).
>>>>
>>> An array of arrays of arrays is nesting.
>>
>> "X is a kind of Y" does not mean that "X and Y are interchangeable".  I
>> don't think there's much point in going on is there?
>>
> You're thinking too much like a mathematician.
> 
> But the rule of three is a psychological claim, not a mathematical one.
> 
> If X is a kind of Y then we expect so in X, as in Y, just as we know 
> as in Y, so in X.
> 

It does not matter if you are thinking mathematically, or
psychologically - if X is a kind of Y, then X has the features of Y.
But that does not mean X and Y are interchangeable!

<https://www.youtube.com/watch?v=yp_l5ntikaU>

As Ben says, there is probably not much point in continuing.  Watching
your frantic back-peddling and attempts to re-write the twaddle you
posted is entertaining for a bit, but not very constructive.

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#111613

On Tuesday, June 6, 2017 at 10:11:02 AM UTC+1, David Brown wrote:
> On 06/06/17 10:15, Malcolm McLean wrote:
> 
> It does not matter if you are thinking mathematically, or
> psychologically - if X is a kind of Y, then X has the features of Y.
> But that does not mean X and Y are interchangeable!
> 
But we can toggle between a nesting and a multi-dimensional view of
an array. It's either an array of arrays of arrays ... (how many "arrays" 
are allowed before you resort to counting them?) or it's a cube 
with each sub-cube representing a data item (how many dimensions
can you visualise before this becomes difficult?).
>
> As Ben says, there is probably not much point in continuing.  Watching
> your frantic back-peddling and attempts to re-write the twaddle you
> posted is entertaining for a bit, but not very constructive.
>
Pure arrogance. Ben's an academic thus notorious for being catty,
but you don't even have that excuse.

In mathematics, if we know A is in B, that tells us nothing about B other 
than the A subset. In science, "as in E. coli, so in elephant".

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#111615

On 06/06/17 11:39, Malcolm McLean wrote:
> On Tuesday, June 6, 2017 at 10:11:02 AM UTC+1, David Brown wrote:
>> On 06/06/17 10:15, Malcolm McLean wrote:
>>
>> It does not matter if you are thinking mathematically, or
>> psychologically - if X is a kind of Y, then X has the features of Y.
>> But that does not mean X and Y are interchangeable!
>>
> But we can toggle between a nesting and a multi-dimensional view of
> an array. It's either an array of arrays of arrays ... (how many "arrays" 
> are allowed before you resort to counting them?) or it's a cube 
> with each sub-cube representing a data item (how many dimensions
> can you visualise before this becomes difficult?).
>>
>> As Ben says, there is probably not much point in continuing.  Watching
>> your frantic back-peddling and attempts to re-write the twaddle you
>> posted is entertaining for a bit, but not very constructive.
>>
> Pure arrogance. Ben's an academic thus notorious for being catty,
> but you don't even have that excuse.
> 

Don't you even /realise/ how often you have changed your point of view?
 You make absurd concrete, precise statements that you claim are obvious
and irrefutable rules, then gradually reduce them to being vague ideas
that might be related to other ideas, or might not.

> In mathematics, if we know A is in B, that tells us nothing about B other 
> than the A subset. In science, "as in E. coli, so in elephant".
> 

It is exactly the same - if you say animal A is a type of B, that tells
us nothing more about them.  Equally, in mathematics, saying the set of
integers is a subset of the set of rationals conveys more information.

Oh, and E. coli are not types of elephants, nor are elephants a type of
E. coli.  And for the sake of anyone with food poisoning, I am glad they
are not interchangeable.

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#111616

On Tuesday, June 6, 2017 at 11:15:49 AM UTC+1, David Brown wrote:
> On 06/06/17 11:39, Malcolm McLean wrote:
> > On Tuesday, June 6, 2017 at 10:11:02 AM UTC+1, David Brown wrote:
> >> On 06/06/17 10:15, Malcolm McLean wrote:
> >>
> >> It does not matter if you are thinking mathematically, or
> >> psychologically - if X is a kind of Y, then X has the features of Y.
> >> But that does not mean X and Y are interchangeable!
> >>
> > But we can toggle between a nesting and a multi-dimensional view of
> > an array. It's either an array of arrays of arrays ... (how many "arrays" 
> > are allowed before you resort to counting them?) or it's a cube 
> > with each sub-cube representing a data item (how many dimensions
> > can you visualise before this becomes difficult?).
> >>
> >> As Ben says, there is probably not much point in continuing.  Watching
> >> your frantic back-peddling and attempts to re-write the twaddle you
> >> posted is entertaining for a bit, but not very constructive.
> >>
> > Pure arrogance. Ben's an academic thus notorious for being catty,
> > but you don't even have that excuse.
> > 
> 
> Don't you even /realise/ how often you have changed your point of view?
>  You make absurd concrete, precise statements that you claim are obvious
> and irrefutable rules, then gradually reduce them to being vague ideas
> that might be related to other ideas, or might not.
> 
> > In mathematics, if we know A is in B, that tells us nothing about B other 
> > than the A subset. In science, "as in E. coli, so in elephant".
> > 
> 
> It is exactly the same - if you say animal A is a type of B, that tells
> us nothing more about them.  Equally, in mathematics, saying the set of
> integers is a subset of the set of rationals conveys more information.
> 
> Oh, and E. coli are not types of elephants, nor are elephants a type of
> E. coli.  And for the sake of anyone with food poisoning, I am glad they
> are not interchangeable.
>
"As in E. coli, so in elephant" is a famous aphorism in biochemistry.
They're both organisms. What we see in one tells us quite a bit about the 
other, and therefore about all organisms, or maybe all organisms except
a narrow subset. But it's not a mathematical rule, it doesn't even always
hold.

We can't prove mathematically that humans can't parse more than 3 levels 
of nested parentheses. Yes, it is in a sense a statement about mathematics,
but it's also a statement about psychology. We can show, indeed you showed
yourself, that three seems to be the limit. We can then speculate why that might
be.

Since nested arrays and cubes are two ways of visualising the same thing, it
seems reasonable that they are related. But we can't prove that in a mathematical
way. It's a poverty of thinking to insist you must. The naive idea is that statements 
must either be provably, irrefutably correct, or they are to be dismissed. That applies 
to computer programs, it's either correct or it is bugged, it doesn't apply to other areas of
life, including even laying out programs so that they are humanly understandable.

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#111618

On 06/06/17 12:47, Malcolm McLean wrote:
> On Tuesday, June 6, 2017 at 11:15:49 AM UTC+1, David Brown wrote:
>> On 06/06/17 11:39, Malcolm McLean wrote:
>>> On Tuesday, June 6, 2017 at 10:11:02 AM UTC+1, David Brown wrote:
>>>> On 06/06/17 10:15, Malcolm McLean wrote:
>>>>
>>>> It does not matter if you are thinking mathematically, or
>>>> psychologically - if X is a kind of Y, then X has the features of Y.
>>>> But that does not mean X and Y are interchangeable!
>>>>
>>> But we can toggle between a nesting and a multi-dimensional view of
>>> an array. It's either an array of arrays of arrays ... (how many "arrays" 
>>> are allowed before you resort to counting them?) or it's a cube 
>>> with each sub-cube representing a data item (how many dimensions
>>> can you visualise before this becomes difficult?).
>>>>
>>>> As Ben says, there is probably not much point in continuing.  Watching
>>>> your frantic back-peddling and attempts to re-write the twaddle you
>>>> posted is entertaining for a bit, but not very constructive.
>>>>
>>> Pure arrogance. Ben's an academic thus notorious for being catty,
>>> but you don't even have that excuse.
>>>
>>
>> Don't you even /realise/ how often you have changed your point of view?
>>  You make absurd concrete, precise statements that you claim are obvious
>> and irrefutable rules, then gradually reduce them to being vague ideas
>> that might be related to other ideas, or might not.
>>
>>> In mathematics, if we know A is in B, that tells us nothing about B other 
>>> than the A subset. In science, "as in E. coli, so in elephant".
>>>
>>
>> It is exactly the same - if you say animal A is a type of B, that tells
>> us nothing more about them.  Equally, in mathematics, saying the set of
>> integers is a subset of the set of rationals conveys more information.
>>
>> Oh, and E. coli are not types of elephants, nor are elephants a type of
>> E. coli.  And for the sake of anyone with food poisoning, I am glad they
>> are not interchangeable.
>>
> "As in E. coli, so in elephant" is a famous aphorism in biochemistry.
> They're both organisms. What we see in one tells us quite a bit about the 
> other, and therefore about all organisms, or maybe all organisms except
> a narrow subset. But it's not a mathematical rule, it doesn't even always
> hold.

It is not science either - because in science, to be a rule it should
always hold as far as we know.  It's just a saying that can be a useful
guideline - like in mathematics you might say "this looks like a pattern".

You are making a distinction between mathematics and other sciences that
does not exist - pretending that this lets you off the hook for writing
something that is at best a vague idea of yours, formulated as though it
were a clearly defined absolute rule.

> 
> We can't prove mathematically that humans can't parse more than 3 levels 
> of nested parentheses. Yes, it is in a sense a statement about mathematics,
> but it's also a statement about psychology. We can show, indeed you showed
> yourself, that three seems to be the limit. We can then speculate why that might
> be.

You have been shown countless examples of when humans /can/ parse more
than 3 levels of nested parentheses.  You have been shown countless
examples (including my own) of when /2/ levels is enough to give a high
chance of error.  Everyone is happy with the idea that increased nesting
usually means complex expressions, and that complex expressions are
harder to parse correctly than simple ones.  /Why/ are you so obsessed
with the idea that 3 is a magic number in all this?

It is pointless to speculate why "three seems to be the limit" when it
has been so clearly demonstrated that there is no particular limit at all.

> 
> Since nested arrays and cubes are two ways of visualising the same thing, 

No, they are not.  Depending on what you are dealing with, a set of
three nested arrays /might/ be visualised as a cube - but it might not
make any sense at all.

> it
> seems reasonable that they are related.

No, that does not follow - even if your premise about what we can parse
and the dimensions of a cube was correct.  At best, it might seem
reasonable to consider if they are related.

> But we can't prove that in a mathematical
> way. 

On the other hand, we have had no problem /disproving/ it in a
scientific way.

> It's a poverty of thinking to insist you must.

If you are going to make a claim as an absolute rule, as you have been
doing, then it is perfectly reasonable to insist that you give a
reasonable level of proof.  I agree that it could not be proven
mathematically - but if it were true then you should certainly be able
to show statistical evidence for it along with a reasonable scientific
argument for why it might be so.

As it stands, your claim has all the authority of a claim that the earth
is flat.

> The naive idea is that statements 
> must either be provably, irrefutably correct, or they are to be dismissed. 

Maybe that is the way /you/ like to think, but it is not how I or others
here think.  What we do think, however, is that an extraordinary claim
that runs contrary to the evidence presented, needs some backing up.

> That applies 
> to computer programs, it's either correct or it is bugged, it doesn't apply to other areas of
> life, including even laying out programs so that they are humanly understandable.
> 

There is only one area of life in which people regularly make wild and
dramatic claims that run contrary to the evidence around them and the
opinions of others.  We have seen that sort of thing too much in c.l.c.
for most people's tastes.

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#111625

On Tuesday, June 6, 2017 at 12:09:37 PM UTC+1, David Brown wrote:
> On 06/06/17 12:47, Malcolm McLean wrote:
> 
> > "As in E. coli, so in elephant" is a famous aphorism in biochemistry.
> > They're both organisms. What we see in one tells us quite a bit about the 
> > other, and therefore about all organisms, or maybe all organisms except
> > a narrow subset. But it's not a mathematical rule, it doesn't even always
> > hold.
> 
> It is not science either - because in science, to be a rule it should
> always hold as far as we know.  It's just a saying that can be a useful
> guideline - like in mathematics you might say "this looks like a pattern".
> 
> You are making a distinction between mathematics and other sciences that
> does not exist - pretending that this lets you off the hook for writing
> something that is at best a vague idea of yours, formulated as though it
> were a clearly defined absolute rule.
> 
It depends on your science.

A lot of science, like psychology, is mainly descriptive. Skinner tried to turn
psychology into a hard science like physics by ruthlessly stripping behaviour
down to its bare essentials. The "Skinner box" was closed box in which a rat 
lived, with only levers to interact with. He did succeed in making his results
reproducible. But the conclusion on his work was that it wasn't applicable,
it didn't tell us much about anything except rats in boxes.

A psychological observation - that three is the limit on parentheses that can
be easily parsed (it should go without saying that we mean similar symbols in
short expressions, and without devices to increase symmetry) - leads to a
theory - since we can express array dimensions as nesting, and we know why
three is the limit for visualising arrays, doesn't the same limit apply for the same
underlying reason to nesting.

But that remains just a theory. It's hard to test. The first test is to make sure that
the observations are correct, that three is in fact a limit. That seems to be pretty
solid, the exceptions that have been given are either cheats or failure to understand
the self similarity requirement.

>
>  /Why/ are you so obsessed with the idea that 3 is a magic number in all this?
> 
> It is pointless to speculate why "three seems to be the limit" when it
> has been so clearly demonstrated that there is no particular limit at all.
> 
Because it's potentially a useful result. The observation that the more complex
the expression the harder it is to read doesn't tell us anything. If we can put
a number on it then we can being to understand. That's how science works, you
start with description (these caves are full of bats), then try to assign numbers
(2,300 bats live in this cave), then to formulae (we have 50 bats per metre squared,
will that apply to other caves, are populations limited by roosting space or by
other factors?). If there's "no particular limit" you're just giving up. Bats live in
the cave, something must limit their numbers, even if it is only cave volume
divided by bat volume. Humans can parse expressions, something must limit the
complexity of those expressions, even if it's just the size of the visual field.
>
> If you are going to make a claim as an absolute rule, as you have been
> doing, then it is perfectly reasonable to insist that you give a
> reasonable level of proof.  
>
You yourself provided a reasonable level of proof. Three is your limit.
As In David Brown, so in Malcolm McLean.

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#111626

On Tue, 6 Jun 2017 05:26:44 -0700 (PDT)
Malcolm McLean <malcolm.arthur.mclean@gmail.com> wrote:
 
> A lot of science, like psychology, is mainly descriptive. Skinner tried to turn

If your consider psychology as a science... :o)

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#111627

On Tuesday, June 6, 2017 at 1:28:25 PM UTC+1, GOTHIER Nathan wrote:
> On Tue, 6 Jun 2017 05:26:44 -0700 (PDT)
> Malcolm McLean <malcolm.arthur.mclean@gmail.com> wrote:
>  
> > A lot of science, like psychology, is mainly descriptive. Skinner tried to turn
> 
> If your consider psychology as a science... :o)
>
We fundamentally don't understand what psychology is. We don't know what
it means to be aware of something, or to take a decision. That doesn't mean 
the results aren't often replicable. But psychological experiments on humans
are notoriously hard to devise and control properly.

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#111630

On Tue, 6 Jun 2017 05:34:37 -0700 (PDT)
Malcolm McLean <malcolm.arthur.mclean@gmail.com> wrote:

> We fundamentally don't understand what psychology is. We don't know what
> it means to be aware of something, or to take a decision. That doesn't mean 
> the results aren't often replicable. But psychological experiments on humans
> are notoriously hard to devise and control properly.

There's no logic in the human behavior. There's only recurrence with
approximately 7 billions of individuals on Earth. Some people do good things
others do bad things and even some think psychology is a science... :o)

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#111628

On 06/06/17 14:26, Malcolm McLean wrote:
> On Tuesday, June 6, 2017 at 12:09:37 PM UTC+1, David Brown wrote:
>> On 06/06/17 12:47, Malcolm McLean wrote:
>>
>>> "As in E. coli, so in elephant" is a famous aphorism in biochemistry.
>>> They're both organisms. What we see in one tells us quite a bit about the 
>>> other, and therefore about all organisms, or maybe all organisms except
>>> a narrow subset. But it's not a mathematical rule, it doesn't even always
>>> hold.
>>
>> It is not science either - because in science, to be a rule it should
>> always hold as far as we know.  It's just a saying that can be a useful
>> guideline - like in mathematics you might say "this looks like a pattern".
>>
>> You are making a distinction between mathematics and other sciences that
>> does not exist - pretending that this lets you off the hook for writing
>> something that is at best a vague idea of yours, formulated as though it
>> were a clearly defined absolute rule.
>>
> It depends on your science.
> 
> A lot of science, like psychology, is mainly descriptive.

Sorry, I was talking about /science/.  You know, theories, evidence,
data, experiments, predictions, repeatable results - that sort of thing?

Psychology is not a science.  It is a "craft" - there is a certain basis
in logical and scientific theory, but much of it is about how the
practitioner prefers to do things.  The "descriptive" bits are not
science - they are a collection of ideas and experiences.  (This is not
a condemnation of psychology.)

> Skinner tried to turn
> psychology into a hard science like physics by ruthlessly stripping behaviour
> down to its bare essentials. The "Skinner box" was closed box in which a rat 
> lived, with only levers to interact with. He did succeed in making his results
> reproducible. But the conclusion on his work was that it wasn't applicable,
> it didn't tell us much about anything except rats in boxes.
> 
> A psychological observation - that three is the limit on parentheses that can
> be easily parsed

/Your/ personal observation, unrelated to anyone else or other people's
experience.

> (it should go without saying that we mean similar symbols in
> short expressions, and without devices to increase symmetry)

Why should that "go without saying"?  Do you just mean some extra
conditions that you forgot to mention when first declaring your absolute
fixed rule, and that you have added in afterwards?

> - leads to a
> theory - since we can express array dimensions as nesting, and we know why
> three is the limit for visualising arrays, doesn't the same limit apply for the same
> underlying reason to nesting.

That is not a "theory" - certainly not in the scientific sense.  I would
not even count it as a "theory" in a pseudo-scientific sense.  It is a
vague idea, with no evidence or basis.  That is all.

> 
> But that remains just a theory. It's hard to test. The first test is to make sure that
> the observations are correct, that three is in fact a limit. That seems to be pretty
> solid, the exceptions that have been given are either cheats or failure to understand
> the self similarity requirement.

How often are you going to deny reality?  Even when you change the rules
as you go along, such as now introducing a "self similarity
requirement", it is still nonsense.

> 
>>
>>  /Why/ are you so obsessed with the idea that 3 is a magic number in all this?
>>
>> It is pointless to speculate why "three seems to be the limit" when it
>> has been so clearly demonstrated that there is no particular limit at all.
>>
> Because it's potentially a useful result.

No, it is not.

Even if your "rule of three" were approximately correct, and even if
your explanation for it were approximately correct, it still would not
be useful.  We already know that we should write code that is clear and
easy to understand - what benefit could it possibly be to anyone to know
that the reason we can't understand more than 3 levels of nesting is
that we live in a 3D world?

Now, if you had said "because it would be an /interesting/ result", I
would agree.  It is still nonsense, of course, but if it had been true,
it would have been interesting.

> The observation that the more complex
> the expression the harder it is to read doesn't tell us anything. 

It tells us that we should keep our expressions simple.  And that is
about as concrete a rule as we can get here - the details all vary
according to circumstance.

> If we can put
> a number on it then we can being to understand. That's how science works, you
> start with description (these caves are full of bats), then try to assign numbers
> (2,300 bats live in this cave), then to formulae (we have 50 bats per metre squared,
> will that apply to other caves, are populations limited by roosting space or by
> other factors?). If there's "no particular limit" you're just giving up. 

It is not "giving up" - it is accepting that programming is not a
science (it is better described as a craft), and that some things do not
have a single number answer.  Your idea is to count the 2300 bats living
in one cave, and declare that all caves contain 2300 bats, perhaps
because there are 2300 trees in the woods near your house.

> Bats live in
> the cave, something must limit their numbers, even if it is only cave volume
> divided by bat volume. Humans can parse expressions, something must limit the
> complexity of those expressions, even if it's just the size of the visual field.

Great.  With something about 100 million retina cells, and say a 6x8
minimal readable font, that leaves us room for about 1,000,000 pairs of
brackets.  If you want to claim that humans cannot parse more a million
sets of nested brackets at a glance, I will not argue with you (unless
it is because you think that is the average total length of a person's
hair, in cm).

>>
>> If you are going to make a claim as an absolute rule, as you have been
>> doing, then it is perfectly reasonable to insist that you give a
>> reasonable level of proof.  
>>
> You yourself provided a reasonable level of proof. Three is your limit.
> As In David Brown, so in Malcolm McLean.
> 

Look it up - I made a mistake with /three/ levels of nesting.  If it is
proof of anything, it is that /two/ levels is the limit.

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#111647

Malcolm McLean <malcolm.arthur.mclean@gmail.com> wrote:

> On Tuesday, June 6, 2017 at 12:09:37 PM UTC+1, David Brown wrote:

> > If you are going to make a claim as an absolute rule, as you have been
> > doing, then it is perfectly reasonable to insist that you give a
> > reasonable level of proof.  
> >
> You yourself provided a reasonable level of proof. Three is your limit.

McLean, stop slandering David. That's my job, not yours.

Richard

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#111684

On 06/06/17 19:37, Richard Bos wrote:
> Malcolm McLean <malcolm.arthur.mclean@gmail.com> wrote:
> 
>> On Tuesday, June 6, 2017 at 12:09:37 PM UTC+1, David Brown wrote:
> 
>>> If you are going to make a claim as an absolute rule, as you have been
>>> doing, then it is perfectly reasonable to insist that you give a
>>> reasonable level of proof.  
>>>
>> You yourself provided a reasonable level of proof. Three is your limit.
> 
> McLean, stop slandering David. That's my job, not yours.
> 

:-)

(Actually, your criticisms usually have at least some validity - and are
thus not slander.)

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#111634

Malcolm McLean <malcolm.arthur.mclean@gmail.com> writes:
[...]
> We can't prove mathematically that humans can't parse more than 3
> levels of nested parentheses. Yes, it is in a sense a statement about
> mathematics, but it's also a statement about psychology. We can show,
> indeed you showed yourself, that three seems to be the limit. We can
> then speculate why that might be.
[...]

If I may summarize the discussion:

Malcolm claims that his "rule of three" is obvious and universally true.

Malcolm is demonstrably wrong.

Malcolm will never acknowledge the possibility that he is wrong.

I think that pretty much covers it.

-- 
Keith Thompson (The_Other_Keith) kst-u@mib.org  <http://www.ghoti.net/~kst>
Working, but not speaking, for JetHead Development, Inc.
"We must do something.  This is something.  Therefore, we must do this."
    -- Antony Jay and Jonathan Lynn, "Yes Minister"

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#111650

Keith Thompson <kst-u@mib.org> writes:

> If I may summarize the discussion:
>
> Malcolm claims that his "rule of three" is obvious and universally true.
> Malcolm is demonstrably wrong.
> Malcolm will never acknowledge the possibility that he is wrong.
>
> I think that pretty much covers it.

Gee, I wish I'd pointed that out weeks ago.

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#111649

David Brown <david.brown@hesbynett.no> writes:

> Don't you even /realise/ how often you have changed your point of view?
>  You make absurd concrete, precise statements that you claim are obvious
> and irrefutable rules, then gradually reduce them to being vague ideas
> that might be related to other ideas, or might not.

Hanlon's Razor applies

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#111623

Malcolm McLean <malcolm.arthur.mclean@gmail.com> writes:

> On Tuesday, June 6, 2017 at 10:11:02 AM UTC+1, David Brown wrote:
>> On 06/06/17 10:15, Malcolm McLean wrote:
>> 
>> It does not matter if you are thinking mathematically, or
>> psychologically - if X is a kind of Y, then X has the features of Y.
>> But that does not mean X and Y are interchangeable!
>> 
> But we can toggle between a nesting and a multi-dimensional view of
> an array. It's either an array of arrays of arrays ... (how many "arrays" 
> are allowed before you resort to counting them?) or it's a cube 
> with each sub-cube representing a data item (how many dimensions
> can you visualise before this becomes difficult?).

But you are hoping to make the leap to nesting like this:

 (()()(()())(())()(()))(())())

Your evidence (or reasoning) must link 3-dimensional space, indexing of
arrays and nesting of parentheses.

It's not helped by multiple claims (some thing are impossible, some at a
glance, which is it today?) nor by failing to track all exceptions
you've acknowledged.  The result is that no one but you even knows
what's being claimed at any one time.

>> As Ben says, there is probably not much point in continuing.  Watching
>> your frantic back-peddling and attempts to re-write the twaddle you
>> posted is entertaining for a bit, but not very constructive.
>>
> Pure arrogance. Ben's an academic thus notorious for being catty,
> but you don't even have that excuse.

I am fine with you calling me catty, but to make sweeping claims about a
whole profession is petty and patently absurd.

> In mathematics, if we know A is in B, that tells us nothing about B other 
> than the A subset. In science, "as in E. coli, so in elephant".

What do you hope to convey by this vague wording?  If you want to say
that the perception of nesting and the perception of 3D space share the
same sort of relationship as E. coli and elephants?  I'm happy to accept
that as a starting point.

-- 
Ben.

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