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From: Barb Knox on 10 Jun 2010 19:56
In article
<00537029-ea1e-4c83-a597-998c26607676(a)o30g2000yqb.googlegroups.com>,
Transfer Principle <lwalke3(a)lausd.net> wrote:
[SNIP]

> And so this gives us another generalization about the difference
> between standard theorists and "cranks" (which maight be viewed as a
> "lie"): standard theorists believe that the provability of
> counterintuitive results is a _good_ thing, since a theory that
> doesn't prove any counterintuitive results can't possibly be that
> "powerful," while "cranks" believe that the provability of
> counterintuitive results is a _bad_ thing, since they want more
> control over what can be proved in their theory.

Many authors of fiction have noted that characters often seem to take on
a life of their own and push the story in a direction different from
what the author originally planned.

This happens even more so in mathematics. Starting with intuitively
unobjectionable axioms one comes up with some unintuitive and even
counterintuitive results. This is a Good Thing; it shows where our
intuitions need adjustment.

I think your characterisation of cranks is reasonable -- they believe
that their personal intuitions should be the measure of all things,
rather than accepting the fact that their intuitions are limited to
familiar experience, and once they journey outside those borders they
will surely encounter strange and wonderful things.

[snip]

--
---------------------------
| BBB b \ Barbara at LivingHistory stop co stop uk
| B B aa rrr b |
| BBB a a r bbb | Quidquid latine dictum sit,
| B B a a r b b | altum videtur.
| BBB aa a r bbb |
-----------------------------
From: Pol Lux on 10 Jun 2010 22:16
On Jun 10, 4:56 pm, Barb Knox <s...(a)sig.below> wrote:
> In article
> <00537029-ea1e-4c83-a597-998c26607...(a)o30g2000yqb.googlegroups.com>,
>  Transfer Principle <lwal...(a)lausd.net> wrote:
> [SNIP]
>
> > And so this gives us another generalization about the difference
> > between standard theorists and "cranks" (which maight be viewed as a
> > "lie"): standard theorists believe that the provability of
> > counterintuitive results is a _good_ thing, since a theory that
> > doesn't prove any counterintuitive results can't possibly be that
> > "powerful," while "cranks" believe that the provability of
> > counterintuitive results is a _bad_ thing, since they want more
> > control over what can be proved in their theory.
>
> Many authors of fiction have noted that characters often seem to take on
> a life of their own and push the story in a direction different from
> what the author originally planned.
>
> This happens even more so in mathematics.  Starting with intuitively
> unobjectionable axioms one comes up with some unintuitive and even
> counterintuitive results.  This is a Good Thing; it shows where our
> intuitions need adjustment.
>
> I think your characterisation of cranks is reasonable -- they believe
> that their personal intuitions should be the measure of all things,
> rather than accepting the fact that their intuitions are limited to
> familiar experience, and once they journey outside those borders they
> will surely encounter strange and wonderful things.
>
> [snip]
>
> --
> ---------------------------
> |  BBB                b    \     Barbara at LivingHistory stop co stop uk
> |  B  B   aa     rrr  b     |
> |  BBB   a  a   r     bbb   |    Quidquid latine dictum sit,
> |  B  B  a  a   r     b  b  |    altum videtur.
> |  BBB    aa a  r     bbb   |  
> -----------------------------

As a side comment, it seems to me that a good part of the history of
science is about establishing on more reliable grounds than intuition.
I am very skeptical of intuition as a reliable means of acquiring
definite knowledge. But as you say, cranks usually think that if they
can intuitively see it, it's got to be right. And many a crank becomes
very assertive, instead of being interested in verification,
experiment, or contradiction.

Pollux
From: Newberry on 11 Jun 2010 00:10
On Jun 10, 4:56 pm, Barb Knox <s...(a)sig.below> wrote:
> In article
> <00537029-ea1e-4c83-a597-998c26607...(a)o30g2000yqb.googlegroups.com>,
>  Transfer Principle <lwal...(a)lausd.net> wrote:
> [SNIP]
>
> > And so this gives us another generalization about the difference
> > between standard theorists and "cranks" (which maight be viewed as a
> > "lie"): standard theorists believe that the provability of
> > counterintuitive results is a _good_ thing, since a theory that
> > doesn't prove any counterintuitive results can't possibly be that
> > "powerful," while "cranks" believe that the provability of
> > counterintuitive results is a _bad_ thing, since they want more
> > control over what can be proved in their theory.
>
> Many authors of fiction have noted that characters often seem to take on
> a life of their own and push the story in a direction different from
> what the author originally planned.
>
> This happens even more so in mathematics.  Starting with intuitively
> unobjectionable axioms one comes up with some unintuitive and even
> counterintuitive results.  This is a Good Thing; it shows where our
> intuitions need adjustment.

I am confused. These Platonic entities are counter-intuitive yet we
comprehend them by intuition?

> [snip]
>
> --
> ---------------------------
> |  BBB                b    \     Barbara at LivingHistory stop co stop uk
> |  B  B   aa     rrr  b     |
> |  BBB   a  a   r     bbb   |    Quidquid latine dictum sit,
> |  B  B  a  a   r     b  b  |    altum videtur.
> |  BBB    aa a  r     bbb   |  
> -----------------------------

From: Pol Lux on 11 Jun 2010 00:21
On Jun 10, 9:10 pm, Newberry <newberr...(a)gmail.com> wrote:
> On Jun 10, 4:56 pm, Barb Knox <s...(a)sig.below> wrote:
>
>
>
>
>
> > In article
> > <00537029-ea1e-4c83-a597-998c26607...(a)o30g2000yqb.googlegroups.com>,
> >  Transfer Principle <lwal...(a)lausd.net> wrote:
> > [SNIP]
>
> > > And so this gives us another generalization about the difference
> > > between standard theorists and "cranks" (which maight be viewed as a
> > > "lie"): standard theorists believe that the provability of
> > > counterintuitive results is a _good_ thing, since a theory that
> > > doesn't prove any counterintuitive results can't possibly be that
> > > "powerful," while "cranks" believe that the provability of
> > > counterintuitive results is a _bad_ thing, since they want more
> > > control over what can be proved in their theory.
>
> > Many authors of fiction have noted that characters often seem to take on
> > a life of their own and push the story in a direction different from
> > what the author originally planned.
>
> > This happens even more so in mathematics.  Starting with intuitively
> > unobjectionable axioms one comes up with some unintuitive and even
> > counterintuitive results.  This is a Good Thing; it shows where our
> > intuitions need adjustment.
>
> I am confused. These Platonic entities are counter-intuitive yet we
> comprehend them by intuition?
I guess you derive those results by logic, where no intuition enters.
If you then look at the results and it contradicts your intuition, you
dump intuition and you stick with the logical derivation.

Pollux
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